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3E LEARNING

Maths By Amiya 500 CAT 2016 QUANT 500 By :- Amiya

2016

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3E LEARNING - MATHS BY AMIYA 500 CAT 2016

Maths By Amiya 500 (2017 (2017-19) 1. Mohit calculated sum of first N natural number and he found sum is 337 and he knows he counted one number twice or missed one number. then find his minimum possible % error made by him. a. 3% b. 3.99% c. 3.69% d. 3.23% 2. The integers 1,2,….. 30 are written on a board. A person came and erased any two numbers say "a" & "b" and wrote a new number "a+b+2" this process is done by total 29 persons (including first one) then . What is the number left on the board at the end? = (3,5) , T3 = (7,9,11) , T(4) = (13,15,17,19) ..... Then what is the sum of all 3. If T1=(1) , T2= terms of T(10) 4. phi (n) is defined as number of co co-prime prime less than n. If ‘P’ is product of two different prime numbers, whose sum is 1200 then what is the max phi(M) {1,2,3,………..10000}, How many APs can be formed from the elements of S that 5. Consider the set S = {1,2,3,………..1000 start with 1 and end with 100000 and have minimum 3 terms?

6. Total number of integral solutions of 13x - 3y = 1000 for 100< x < 200 7. For how many integral "n" is

is an integer

8. If HCF , LCM and sum of two numbers are 6 , 15 and 23 then find their difference. 9. If 1 7 6 3 , then find the value of f(x - 1). 10. Find the area of the enclosed fig by | x- 5 | FGM and if the area ratio of ∎DEGF to that of ∎BCED is 1:8 then what is ∎DEGF to that of ∎BCED is 1:8 then what is the ratio of AF:FD:DB a. 7: 3:2 b. 2:3:7 c. 2:1:4 d. 1:2:3 e. NoT 197. If in ∆ ABC , points D, F & H are on side AB ; and points E, G & I are on side AC such that ∆ ABC , points D, F & H are on side AB ; and points E, G & I are on side AC such that BC || DE || FG || HI and AH :HF:FD:DB 2:3:5:7 then what is the ratio of BC : DE : FG : HI BC || DE || FG || HI and AH :HF:FD:DB 2:3:5:7 then what is the ratio of BC : DE : FG : HI 198.

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199. A number on being divided by ing divided by 6, 8 and 10 successively leaves the remainders successively leaves the remainders 5, 7 and 9 respectively. Find the remainder when the same number is divided by respectively. Find the remainder when the same number is divided by 120. 200. A number on being divided by 7 , 9 and 11 successively leaves the remainders 5, 7 and 9 respectively. Find the remainder when the same number is divided by 693 the remainder when the same number is divided by 693 the remainder when the same number is divided by 693 201.

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202. If

³ q7 3 ∗ Z7 3 ∗ r7 3 ∗ √7 ⋯&µ q7 3 ∗ Z7 3 ∗ r7 3 ∗ √7 … and X-

YR 0 then R ???

203. If P is the set of all possible products of numerical values of f P is the set of all possible products of numerical values of three consecutive dates three consecutive dates e.g.11*12*13 in calendar then , how many elements of P are not divisible by 6. 11*12*13 in calendar then , how many elements of P are not divisible by 6. 11*12*13 in calendar then , how many elements of P are not divisible by 6.

204. If 0 . U 30.U 0 . U ; a 1889 , b1888 then what is c if c is a what is c if c is a positive number. a. 1889 b. 1888 c. a or b d. NoT 205. 1333 1334 1333 3999 ∗ 1333 ∗ 1334 ? ? ?

206. If x-3 , x-4 & fx are factors of 4 & fx are factors of 0 ∗ 68 . the what is the the what is then value of f1 207. What will be the last three digits of the product 5 * 25 * 125 * 625 * 3125 * ………* 5^30

208. AC is the chord of a circle as shown in the fig, BD is perpendicular to AC. Find the length of chord AC if BD 4cm , CD 2cm & radius of circle cm & radius of circle 10 cm.

209. There are many less than 10000 which are perfect square an There are many less than 10000 which are perfect square and tenth place digit is odd. d tenth place digit is odd.

210. What is the probability of choosing a number is Natural number set so that number is a perfect square with same last two digits. perfect square with same last two digits. 211. What is the probability of choosing a number What is the probability of choosing a number whose last two digits are same and it whose last two digits are same and it becomes a prefect square. becomes a prefect square.

212. In a triangle ABC the length of altitude AD is 20 cm and BD:DC 1 : 5 D is point in ABC the length of altitude AD is 20 cm and BD:DC 1 : 5 D is point in between B & C . Find the length of a line segment EF parallel to AD if ratio of area o ∆EFC to that of ∆ABC is 8:15 ∆EFC to that of ∆ABC is 8:15. www.facebook.com/groups/MBAMathsByAmiya 3E Learning Maths By Amiya Ranchi | 19

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213. If ABCD a trapezium , in which CD=15 cm , AB = 3 cm & area of ∆DOC = 25 sq. cm then find the area of trapezium ABCD.

214. If ABCD a trapezium , in which CD=6 cm , AB = 2 cm & area of ∆ ∆ADC = 24 sq. cm then find the area of trapezium ABCD.

215. In a triangle ABC the length of an altitude AD is 8 cm, D is on side BC and this altitude divides the opposite side internally in the ratio 1 : 8. A line segment EF parallel to the altitude which bisects the area of the given triangle ABC (as shown in fig) then what is the ratio of AO:OF.

¸ ? ? ? 216. ∑3¹ 3¹K ·- 1 ∗ - 2¸ a. 2212 b. 2480 c. 2722

d. 2590

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217.

218.

219.

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3E LEARNING - MATHS BY AMIYA 500 CAT 2016

220.

221.

222. 223. Which one is smallest a. √101 √96 b.√111 111 √106

c.√11 √6

d.√®ª d. ®ª √ªº

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224. Which one is smallest b.√123 123 √73 a. √101 √99 225. Which one is largest a. √101 √99 b.√123 123 √73

c.√150 √50

d. 1 √199

c.√150 √50 d.√199 1 1

226. How many statements are How many statements are always correct always correctwhere a, m & n non zero real numbers always correctwhere a, m & n non zero real numbers I. 0» 3 0»∗3 II.0» ∗ 03 0»∗3 III.0» 3 03 » a.

Only one

b. only two b. only two

c. all three

d. None d. None

227. A car and a bus start from opposite end of a national highway. Car starts at 11:00AM A car and a bus start from opposite end of a national highway. Car and reaches opposite end at 2:OOPM same day and bus starts at 10:00AM and reaches opposite at 4:00PM same day same day . then at what time they meet each other. . then at what time they meet each other. 2 such that numerically ³ - & µ - 2 2 228. If X_B Y_B-2 such that numerically then n,B ??? a. 8,10 b. 10,10 b. 10,10 c. 10,8 d. NoT d. NoT

229. If X_B Y_B-2 such that numerically 2 such that numerically ³ - & µ - 2 2 then n,B ??? b. 10,10 b. 10,10 c. 10,8 d. NoT d. NoT a. 8,10 If 50!_10 N_50 then number of trailing 0's in N is ____ 230. If 50!_10 N_50 then number of trailing 0's in N is ____

231. If length of a rectangle is increased by 5.88% then what should be change in area to a rectangle is increased by 5.88% then what should be change in area to keep area constant. b. 5.43% decrease b. 5.43% decrease c. 5.56% decrease d. 6.66%decrease d. 6.66%decrease a. 5.55% decrease

Number of positive integral solutions ordered triplets of 9 bxyzb 20 232. Number of positive integral solutions ordered triplets of 9 bxyzb 20 a. 775 b. 657 c. 885 d. NoT

233. A shopkeeper uses a double pan balance to purchase and to sell his goods. To balance both the pans one has to put 20% more weight on left pan than right pan. If shopkeepers claims that he sells his goods on cost price then find maximum profit claims that he sells his goods on cost price then find maximum profit earned by him if he sold all his items what he purchased. sold all his items what he purchased.

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234.

235.

236.

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237.

238.

239.

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240.

241.

242.

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243.

244. A deck of card has 16 cards which include 4 Aces, 4 Kings, 4 Queens & 245. A deck of card has 16 cards which include 4 Aces, 4 Kings, 4 Queens & 4 Jacks. In How many ways we can arrange these 16 cards such that All Kings should be above All Queens. assume all are of different assume all are of different

246. A shopkeeper claims that he gives 10% discount on his cost price but uses X gm of weight instead of 1000 gm during weight instead of 1000 gm during sell of his goods and earn 12.5% profit, Then X ? sell of his goods and earn 12.5% profit, Then X ?

247. Container A has 10 lit of 30% acid, B has 10 lit of 40% acid & C has 10lit of 60% acid. If 5 lit of A is poured in to B then 5 lit from B to C then finally 5 lit of C is poured in to A. then what would be ratio of be ratio of acid is to water in final solution of A . 248. If 4A ? o 0 then x y ?

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If a car is traveling with the speed of 60 km/hr and after applying break it 0 km/hr and after applying break it 249. If a car is traveling with the speed of stops after 4 m, if the same care is moving with m, if the same care is moving with 120 km/hr then after applying km/hr then after applying break it stops after Xm. Then find X break it stops after Xm. Then find X

250. How many 9 digits numbers are possible by in which all digits are different and number is divisible by 9 a. 18*9! - 1 b. 2*9! b. 2*9! c. 17*8! D. NoT 2? 251. ( – 2 7 , *+,- ? ¿

252. ( 3 3 0 , *+,,- 1= À ?

253. ( 9 24 0 , *+ +,- 4 ? ? =

254. In ∆ ABC, AB4cm, BC6cm & AC5cm. Side AB and AC produced till E & F ∆ ABC, AB4cm, BC6cm & AC5cm. Side AB and AC produced till E & F respectively such that BECF1cm. AD median of respectively such that BECF1cm. AD median of ∆ ABC cuts line EF at G then what is ∆ ABC cuts line EF at G then what is the length of DG.

255. A, B & C start working on a project of BOOK MAKING, in which they have to type pages. They completed this project in 12 days. After completion of the project A , B & C received Rs 1200, Rs 2400 &Rs 3600 as their wages Rs 1200, Rs 2400 &Rs 3600 as their wages respectively, which is proportio , which is proportional to to number of pages they typed Lassuming they worked for equal numbers of hours per dayM. Then in how many days does A alone completes the working same hours a day. dayM. Then in how many days does A alone completes the working same hours a day. 256. If N is a 100 digits largest number and a perfect square of a natural number then which If N is a 100 digits largest number and a perfect square of a natural number then wh digit is 50th digit from left? digit is 50th digit from left? A. 0 B. 8 C. 9 d. 1

257. If A & B are points on circles as shown in fig, and line AB passes through centre of circles O & P. QO & RO are perpendicular on line AB, and AQ & BR meet at C then what is the area of ∆ABC if AO 5 cm & BP 4 cm AO 5 cm & BP 4 cm

258. ( 0. @ 3

· ¸

?

@ 0 **+,- choose best option b. 3 3 b b 2 c. 2 2

d.1 1 b b 0

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259. If two circles cut each other orthogonally then find length of common chord if radii of circles are 3 cm & 4 cm. radii of circles are 3 cm & 4 cm.

solved a quadratic equation and find roots as 3 & 4 & Sood finds roots of same Sood finds roots of same 260. Amiya solved a quadratic equation and find roots as 3 & quadratic equation as 1 & 6 then among options which could be a correct option if it is known that none of them did make mistake in writing coefficient of x^2 did make mistake in writing coefficient of x^2 but made mistake in either coefficient of x or constant term then among options which statement n either coefficient of x or constant term then among options which statement is correct a. Amiya makes mistake in coefficient of x and Sood makes mistake in constant term a. Amiya makes mistake in coefficient of x and Sood makes mistake in constant term b. Amiya makes mistake in constant term and Sood makes mistake in coefficient of x b. Amiya makes mistake in constant term and Sood makes mistake in coefficient of x c. Both of them made mistakes in constant term c. Both of them made mistakes in constant term d. NoT 261. Find the total number of terms in the expansion of Find the total number of terms in the expansion of 1 1 1 ? 1 … 1 262. If P 1 and [ 1 are the factors of are the factors of 1 ? . . . for distinct a and b find maximum value of ab and b find maximum value of ab

263. To complete a piece of work A alone takes 12 days more than A & B together & B alone takes 3 days more than A & B together if C alone takes 3 more days then A & C together then in how many days A, B & C can complete the same work if they work together then in how many days A, B & C can complete the same work if they work together. 264. If Á & Â are roots of equation are roots of equation 2 4 6 0 then what would be equation whose then what would be equation whose Ã Ä roots are & Ä

Ã

265. If EN is defined as euler of a number, which is number of co If EN is defined as euler of a number, which is number of co-primes less than equal primes less than equal to N and DN as positive divisor of a natural number N. to N and DN as positive divisor of a natural number N. Then what would be sum of all Then what would be sum of all possible values or E D1200 ??? possible values or E D1200 ??? 266. For how many integral “x” ,

is also an integer

267. If ratio of time taken to complete a piece of work by A, B, C & D alone is 1:2:3:4 and when they all work together take hen they all work together take12 days to complete the same work. If on every ODD to complete the same work. If on every ODD DATE only day only A&C work together and on every EVEN DATE only B & D wor DATE only day only A&C work together and on every EVEN DATE only B & D work together and they started on 01 together and they started on 01-FEB-2016 then on which date total work would be 2016 then on which date total work would be completed. 268. For how many natural “n” less than 100, 5- 6- 3 is divisible by 7

269. In ∆ABC , point D & E lie on BC & F lies on AC. If BD:BE:BC 1:2:3 & AF : FC1:1 then ∆ABC , point D & E lie on BC & F lies on AC. If BD:BE:BC 1:2:3 & AF : FC1:1 then what is the ratio of BO:OP:PF , if O & P are point of intersection of line AD & BF and AE & BF www.facebook.com/groups/MBAMathsByAmiya 3E Learning Maths By Amiya Ranchi | 29

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270.

how many different values of x , 1/x has only 4 reoccurring digits after decimal.i.e. 271. For how many different values of x , 1/x has only 4 reoccurring digits after decimal.i.e. 1/x 0.abcdabcdabcd.... Lfew could be same but not allM 1/x 0.abcdabcdabcd.... Lfew could be same but not allM

272. There are three boys Amar, Akbar & Anthony and three girls, Sita, Gita &Sheela. They Amar &Sita started a grou Amar &Sita started a group on 1st of Feb, Akabr joins them on 2ndfeb , Anthony on 4th Feb Gita joins them on 3rd Feb &Sheela on 5th Feb. On 1st , 3rd& 5th Feb total age of boys Feb total age of boys nd th were half of that of girls& on 2 & 4 Feb total age of boys were doub Feb total age of boys were double of that of girls. If age of Sheela is 120 yrs then who is youngest boy and what is his the age??? e of Sheela is 120 yrs then who is youngest boy and what is his the age??? e of Sheela is 120 yrs then who is youngest boy and what is his the age???

273. If red is painted on three sides of a cuboid of dimension 6cm*7cm*8cm and other three sides are painted white and then then by different cuts cuboid is divided in to 336 smaller cubes of volume 1 cubic cm. . If same coloured sides are adjacent to each other, cubes of volume 1 cubic cm. . If same coloured sides are adjacent to each other, then there are how many smaller cubes having minimum one red coloured side. then there are how many smaller cubes having minimum one red coloured side. 274. Ram wrote first 1000 numbers on a word sheet, and then he replaced all 2’s & 7 by 3 and saved the file. Then find the total number of 3’s in saved file. file. Then find the total number of 3’s in saved file.

275. Ram wrote first 1000 numbers on a word sheet, and then he replaced all 2’s & 7 by 3 and saved the file. Then find how many numbers have digit 3. and saved the file. Then find how many numbers have digit 3. 276. Ram wrote first 1000 numbers on a word sheet, and then Ram wrote first 1000 numbers on a word sheet, and then he replaced all 2’s & 7’s by 3 he replaced all 2’s & 7’s by 3 and saved the file. Then find how many numbers have only one 3. and saved the file. Then find how many numbers have only one 3.

277. Ram wrote all first 444 natural numbers side by side , from left hand side and created a big number N 123456..... 444 four hundred forty four big number N 123456..... 444 four hundred forty four. If Mohan del If Mohan deleted all 7's from N then find there are how many digits in N N then find there are how many digits in N 278. If Mark has Rs 5000 in his easy If Mark has Rs 5000 in his easy-recharge wallet, an online mobile recharge portal. Find recharge wallet, an online mobile recharge portal. Find the maximum amount of recharge, which can be possible with his current balance and cash backs, under cash back scheme of 20% cash back on recharge of any amount h back scheme of 20% cash back on recharge of any amount more than or equal to Rs 100 Lassume he is not adding extra amount from any other source except cash backs & he can recharge any integral amountM source except cash backs & he can recharge any integral amountM 279. For how positive integral X For how positive integral X less than 100, X^3 - X^2 is a perfect square. X^2 is a perfect square.

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280. If there are 3 black balls, 6 white balls and 5 green balls. Find the minimum number of picks required to get at number of picks required to get at-least one ball of each colour always. LAssume always. LAssume one can pick only one ball at a timeM one can pick only one ball at a timeM

281. How many obtuse angled integra How many obtuse angled integral sided isosceles triangles are possible if unequal side es are possible if unequal side is 8 cm 282. How many obtuse angled integral sided isosceles triangl How many obtuse angled integral sided isosceles triangles are possible if one side is 5 es are possible if one side is 5 cm Find minimum value of expression 8x 16x 1 283. Find minimum value of expression 284. Find minimum value of expression Find minimum value of expression 4 sec θ sec θ 1

Find the total number of solution pairs of real x,y for below given equation 285. Find the total number of solution pairs of real x,y for below given equation 2 8 15A 10A A 4 6 286. Find the total number of solution pairs of real x,y for below given equation Find the total number of solution pairs of real x,y for below given equation 3 6 72A 4A A 3 4

287. If 3x È 12 then x x ? x = ?

School. 10%,15%, 20%, ,25% & 30% of branch seats Direction: There are only 5 branches in a B Direction: There are only 5 branches in a B-School. 10%,15%, 20%, ,25% & 30% of branch seats are vacant and it is known that each branch has minimum 1/7th of total PGP seats , are vacant and it is known that each branch has minimum 1/7th of total PGP seats , If total vacant seats are x % of total PGP seats then vacant seats are x % of total PGP seats then 288. Find minimum value of x Find minimum value of x Find maximum value of x 289. Find maximum value of x 290. For how many natural numbers less than equal to 100, such that last two digits of its 8th power and 9th power are same. power are same. 291. For how many natural numbers less than equal to 100, such that last three digits of its 5th power and 8th power are same. r are same. 292. 123123123 ...... a 38 digits number mod 13 ???? 123123123 ...... a 38 digits number mod 13 ???? 293. There are how many two digits numbers are possible such that their last two digits of 23rd& 25th powers are same. powers are same. 294. Raman is an intelligent mathematician. He has Rs Raman is an intelligent mathematician. He has Rs830 in his Paytm account. in his Paytm account. Find the maximum amount of transaction transaction which can be possible with his current balance and which can be possible with his current balance and cash backs, under cash back scheme of cash backs, under cash back scheme of 14.28% cash back on recharge of any amount % cash back on recharge of any amount more than or equal to Rs14 14 Lassume he is not adding extra amount from any other Lassume he is not adding extra amount from any other source except cash backs & he can urce except cash backs & he can do transaction in paisa too M www.facebook.com/groups/MBAMathsByAmiya 3E Learning Maths By Amiya Ranchi | 31

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Patna, Patiala&Pathankotis7:3:2 & Ratio of number of Pathankotis7:3:2 & Ratio of number of 295. If population ratio of Patna males in Patna, Patiala&Pathankotis 6:2:1 Pathankotis 6:2:1 then which city has maximum female which city has maximum female population and which city has minimum population population and which city has minimum population ? 296. Among the options which one is Among the options which one is largest? a. 13= 18 b. 16 16 19 c. 16 18

d.13 13= 19

297. Arrange A, B & C in ascending order , if A 123^45678 , B 12345^678 & C1234^5678

298. Arrange A, B , C & D in ascending order , if A 1234^5 , B 123^45, C12^345 & D1^2345

Direction :Nakistan is a small country, which has 4 states. Name of states are A,B,C&D and Direction :Nakistan is a small country, which has 4 states. Name of states are A,B,C&D and population of each states is minimum 1/7th of total population of Nakistan. If sex ratio of states of total population of Nakistan. If sex ratio of states A,B,C & D are 600 , 700, 800 & 900 then A,B,C & D are 600 , 700, 800 & 900 then 299. Find minimum possible sex ratio of Nakistan Find minimum possible sex ratio of Nakistan a. 600.17 b. 678 678.61 c. 516.79 d. NoT 300. Find maximum possible sex ratio of Nakistan Find maximum possible sex ratio of Nakistan a. 818.18 b. 828.87 b. 828.87 c. 806.89 d. NoT If John distributed his entire pension into his wife Mona, son William, d 301. If John distributed his entire pension into his wife Mona, son William, daughter Kate, girl-friend Sona and her daughter Sara. If it is known that Mona gets minimum 1/6 friend Sona and her daughter Sara. If it is known that Mona gets minimum 1/6th . William gets minimum 1/8th , Kate gets minimum 1/10th , Sona gets mi , Sona gets minimum 1/6th& Sara gets minimum 1/4th of Ram’s pension. Saving % of their individual sharing of Mona, of Ram’s pension. Saving % of their individual sharing of Mona, William, Kate, Sona& Sara is 30%, 40%, 40% , 50% & 60% .If total saving of all five is X% of total pension of Ram, then among option which could not be val of total pension of Ram, then among option which could not be value of X. ue of X. a. 44.15 % b. 45.83% b. 45.83% c. 48.32% d. 48.89% d. 48.89% 302. There are many natural numbers are possible which is less than 400000 and divisible by 3 but not have any of digits from m 6, 7,8 , 9 < by 3 but not have any of digits from m 6, 7,8 , 9 < 303. How many four digits can be made from the digits m1,2,3,4< How many four digits can be made from the digits m1,2,3,4< that are perfectly divisible that are perfectly divisible by 3? repetition allowed by 3? repetition allowed 304. If Speed of Ram is 20 kmph then he reaches office from home 20 min before his usual time, and if his speed is 10 kmph then he reaches office from home 40 min after his usual time then find distan usual time then find distance between home to office. 305. Raman bought a combined total of 25 bought a combined total of 25 mobiles and tabs. He marked up the . He marked up the mobiles by 20% on their cost price while each while each tabs was marked up by Rs. 2000. He was able to sell was marked up by Rs. 2000. He was able to sell 75% of the mobiles and 2 and 2 tabs and make a profit of Rs. 49,000. The remaining and make a profit of Rs. 49,000. The remaining mobiles and 3 tabs could not be sold by him. Find his overall profit or loss if he gets no return on could not be sold by him. Find his overall profit or loss if he gets no return on unsold items and it is known that a unsold items and it is known that a tabs costs 50% of a monitor. www.facebook.com/groups/MBAMathsByAmiya 3E Learning Maths By Amiya Ranchi | 32

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Find the distance in km, for which if we increase our speed by 20 km/hr we if we increase our speed by 20 km/hr we 306. Find the distance in km, for which reach the destination 2 hours earlier but when we reduce our speed by 10 km/hr we take 3 hours more to reach the same destination. we take 3 hours more to reach the same destination.

307. Find the actual time in hour actual time in hour, to cover a distance for which if we increase our spe for which if we increase our speed by "a a" km/hr we reach the destination b" hours earlier but when we reduce our speed by km/hr we reach the destination "b hours earlier but when we reduce our speed by "cc" km/hr we take "d km/hr d" hours hours more to reach the same destination. [4^P[^ [4^P[^ [4^P[^ [4^P[^ a. P^[4 b. P^[4 c. P^[4 d. P^[4 e. NoT 308. When a man covers 2/3rd of distance by car and rest by bus then he takes 12 hours to cover the distance, but if he takes 3/4th of distance by cover the distance, but if he takes 3/4th of distance by car and rest by car then takes 10 and rest by car then takes 10 hours, then find total time to cover same distance, when he hours, then find total time to cover same distance, when he covers half of the distance by covers half of the distance by car and rest by bus.

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If a thief flew with constant speed of "60 km/hr" in a straight road, Direction :If a thief flew with constant speed of "60 km/hr" in a straight road, Direction : and after 2 hours a police and his dog started to chase the thief with speed of "80 km/hr" and "100 km/hr" respectively km/hr" and "100 km/hr" respectively. In this complete journey, Dog touches the Thief . In this complete journey, Dog touches the Thief and comes and touches the Police and move towards Thief and continues the proces and comes and touches the Police and move towards Thief and continues the process, until The Thief is caught. 309. Find total distance travelled by Dog in this process Find total distance travelled by Dog in this process

310. Find total distance travelled by Dog in Find total distance travelled by Dog in this process towards police. this process towards police. 311. Find total distance travelled by Dog in this process towards thief. Find total distance travelled by Dog in this process towards thief.

1 *0-3 … 1 *0-431 *0-44 ;ÌV 7 ? ? ? 312. 1 *0-11 *0-21

313. A boat takes total 4 hours to cover 22 km upstream and 28 km downstream and takes total 6 hours to cover 33 km upstream and 42 km downstream then find speed of hours to cover 33 km upstream and 42 km downstream then find speed of stream.

314. In a 1000 m race A beats B by 250 m and in 1500 m race A beats C by 250 m , then in B Vs C , who win the race and by how much meter if length of track is 2520 m. Vs C , who win the race and by how much meter if length of track is 2520 m. 315. For how many integral values of X integral values of X , |X-1||X2||X-3||X4| b 70 3||X4| b 70

316. Which one is true

¿Ê

? Ë A. W?X ¿Ê

? Ë B. W?X

¿Í

? ¿Ê > WKX ¿Í

? ¿Ê b WKX

317. If Josephus leaves his home for office at a fix time every day , but he reaches his office at different time due to different speeds. different speeds. If his average speed is 60 kmph he reaches If his average speed is 60 kmph he reaches office at 10:45AM , but when his average speed is 40 kmph he reaches at 10:50 AM, what should be his average speed to reach office at 10:47 AM. should be his average speed to reach office at 10:47 AM. 318. If ratio of incomes of A, B & C I'd 5:4:3 & savin If ratio of incomes of A, B & C I'd 5:4:3 & savings ratio of A, B & C is 2:3:4. gs ratio of A, B & C is 2:3:4. If ratio of A's income to C's saving is 10:9 then find the ratio of total expenditure to total savings of all three 319. What would be last 4 digits of What would be last 4 digits of 38 in base 2

320. There are three most active groups on facebook, e three most active groups on facebook, CAT PREPRATION PREPRATION CP, GHANTA CAT GC & MBA. Mentors organised four events named . Mentors organised four events named Chotu Quant Chotu Quant, Motu Quant, Patlu Quant & All Quant. In Chotu Quant, all members of CP & GC participated and average weight of all members of this event is 42 kg In Motu Quant, all members of CP & MBA participated and average weight of all members of CP & MBA participated and average weight of all members of this event is 30 kg is 30 kg In Patlu Quant, all members of MBA & GC participated and average weight of all members of this event is 60 kg is 60 kg www.facebook.com/groups/MBAMathsByAmiya 3E Learning Maths By Amiya Ranchi | 34

3E LEARNING - MATHS BY AMIYA 500 CAT 2016

& if In ALL Quant, all members of CP, GC & MBA participated and average weight ted and average weight & if In ALL Quant, all members of CP of all members of this event event is X kg

Then what is the range of X. Then what is the range of X. Lassume Facebook has "one member one group" policyM Lassume Facebook has "one member one group" policyM

321. If Raman left his room at X AM and reaches office at Y PM of the same date and Mohan left his room at X AM and reaches office at Y AM of same date. If both stay together and and reaches office at Y AM of same date. If both stay together and work together and time taken by Mohan to reach office is square of that by Raman then what is the ratio of Average Speed of Raman from home to office to that of Mohan. what is the ratio of Average Speed of Raman from home to office to that of Mohan.

322. Raman left his room at 7:00 7:00 AM and reaches office at 12 PM of the same date and PM of the same date and Shobhit left his room at 8:00 8:00 AM and reaches office at 11 AM of same date. If both stay AM of same date. If both stay together and work together together and work together at same place then at what time Shobhit overtakes Raman then at what time Shobhit overtakes Raman.

323. Shobhit & Bitan planned an infinite round race on a circular track of length 100 km. planned an infinite round race on a circular track of length 100 km. Both started race at same point of track, but Bitan cheated Shobhit and started half an hour before the actual race timing and choose Swift , whose speed is 40 km/hr. Shobhit who is a good guy started race at actual time but choose Benz whose speed if 140 km/hr d guy started race at actual time but choose Benz whose speed if 140 km/hr but by mistakes he moves in anticlockwise direction. If at 9:30 AM Bitan reaches starting point for the first time then at what time their 4th meeting would happen if they maintained constant speed throughout the race. ed constant speed throughout the race.

324. Sandeep Patra is a very handsome but a shy guy. Whenever he sees a girl he doubles his speed but start moving in the opposite direction of direction just before seeing girl. If on a day he starts moving with speed If on a day he starts moving with speed of 1 m/s from his home and he sees a girl after of 1 m/s from his home and he sees a girl after every 1sec, then find how far he is from his house just after 11sec when he started. every 1sec, then find how far he is from his house just after 11sec when he started. 325. There is a regular nonagon, whose vertices are alphabets of words DANGEROUS in nonagon, whose vertices are alphabets of words DANGEROUS in same order then what is the value of same order then what is the value of ∠ NGO in degree ???? If ABCDEFGH is a regular octagon then find angle ∠ CDG in degree 326. If ABCDEFGH is a regular octagon then find angle If ABCDEFGHIJ is a regular decagon then find ∠ EAI in degree 327. If ABCDEFGHIJ is a regular decagon then find

328. Find the sum of all internal angles at red dots of all four figures Find the sum of all internal angles at red dots of all four figures

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^...^1 then what is the least value of N natural number what is the least value of N natural number 329. If M 17^16^15^...^1 then for which M mod N is neither o nor 1. Lmod is remainder functionM for which M mod N is neither o nor 1. Lmod is remainder functionM

age of 11 members committee on 31st Dec 2014 was 2014 was 30.27. On 330. If the approx average age of 1st Jan 2017 Ram who is Ram who is one of the member quits the committee and then approx quits the committee and then approx average becomes 29.5. If it is known that . If it is known that , to find average only integral age if 11 years to find average only integral age if 11 years 11 months or 11 years 1 months then in both cases considers as 11 years only is considered then find in which year Ram was bor considered then find in which year Ram was born.

331. Two cities X and Y lie on a straight line. Two men P and Q left simultaneously from same city X towards Y at same time. Both reaches Y and immediately turn around and move towards X. On reaching X, again they turn around and move towards Y. This movement continues indefinitely. nt continues indefinitely. If the distance between X and Y is 60 km and speed of If the distance between X and Y is 60 km and speed of P and Q are 20 Km/hr & 10 Km/hr respectively P and Q are 20 Km/hr & 10 Km/hr respectively . Find the total number of OVERTAKES Find the total number of OVERTAKES in 120 hour after start. 332. Two cities X and Y lie on a straight line. Two men P and Q left s Two cities X and Y lie on a straight line. Two men P and Q left simultaneously from imultaneously from same city X towards Y at same time. Both reaches Y and immediately turn around and move towards X. On reaching X, again they turn around and move towards Y. This movement continues indefinitely. movement continues indefinitely. If the distance between X and Y is 60 km a If the distance between X and Y is 60 km and speed of P and Q are 20 Km/hr & 10 Km/hr respectively P and Q are 20 Km/hr & 10 Km/hr respectively Whenever they meet or overtake they Whenever they meet or overtake they shake hands. Find the total number of handshakes in 60 hour after start shake hands. Find the total number of handshakes in 60 hour after start 333. In a right angled triangle with integral sides, smallest side is four times of difference of In a right angled triangle with integral sides, smallest side is four times of differenc other two sides and sum of all sides is 120 then find area of this triangle other two sides and sum of all sides is 120 then find area of this triangle

334. Two cities Rampur and Sitapur lie on a straight line. Two men A and B left simultaneously from Rampur and Sitapur towards each other. A reaches Sitapur and immediately turns around and move towards Rampur. On reaching Rampur, again he around and move towards Rampur. On reaching Rampur, again he turns around and move towards Sitapur. This movement continues indefinitely. B also travels in a similar manner. travels in a similar manner. The distance between Rampur and Sitapur is 120 km and The distance between Rampur and Sitapur is 120 km and speed of A and B are 40 km/h speed of A and B are 40 km/hr & 10 km/hr respectively. If both started together then in If both started together then in 24 hours find the total number of interactions between them. 24 hours find the total number of interactions between them. 335. Two cities Rampur and Sitapur lie on a straight line. Two men A and B left simultaneously from Rampur and Sitapur towards each other. simultaneously from Rampur and Sitapur towards each other. A reaches Sitapur and A reaches Sitapur and immediately turns around and move towards Rampur. On reaching Rampur, again he turns around and move towards Sitapur. This movement continues indefinitely. B also travels in a similar manner. travels in a similar manner. The distance between Rampur and Sitapur is The distance between Rampur and Sitapur is 60 km and speed of A and B are 20 km/hr & 10 km/hr respectively speed of A and B are 20 km/hr & 10 km/hr respectively. If both started together then in If both started together then in 12 hours find the total number of interactions between them. 12 hours find the total number of interactions between them.

336. Two cities X and Y lie on a straight line. Two men P and Q left simultaneously from X and Y towards each other. P reaches Y and immediately turns around and move towards ards each other. P reaches Y and immediately turns around and move towards X. On reaching X, again he turns around and move towards Y. This movement continues indefinitely. Q also travels in a similar manner. indefinitely. Q also travels in a similar manner. The distance between X and Y is 1000m The distance between X and Y is 1000m and speed of P and Q are 200m/s & 800 m/s respectively are 200m/s & 800 m/s respectively. Whenever they meet or Whenever they meet or overtake they shake hands. overtake they shake hands. www.facebook.com/groups/MBAMathsByAmiya 3E Learning Maths By Amiya Ranchi | 36

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337. If in a test there are 5 objective question, each having 4 options with only one option as correct answer. If 1 is awarded for correct answer and no penalty option as correct answer. If 1 is awarded for correct answer and no penalty for wrong or non-attempt. If it is known that 3 is passing marks of this test then , In how If it is known that 3 is passing marks of this test then , In how many ways one can attempt this test so that he passes the test. many ways one can attempt this test so that he passes the test.

338. When I started my today's journey from Hazaribagh to Ranchi. I checked first mile stone it showed Ranchi 100 km , after 40 min I checked another mile stone and found anchi 100 km , after 40 min I checked another mile stone and found Ranchi XY km and after another 20 min when I checked mile stone I realised Ranchi YX km. If I managed a constant speed through my journey, please help me to know speed of my car , since speedometer is not working edometer is not working 339. Mango bite offer - Return 3 empty rappers and get 1 mango bite free Return 3 empty rappers and get 1 mango bite free. If cost of one Return 3 empty rappers and get 1 mango bite free mango bite is Rs 1 and i have Rs 100 then maximum how many mango bite i can eat. mango bite is Rs 1 and i have Rs 100 then maximum how many mango bite i can eat. 340. If P & P2 both are prime numbers P>3 then how many different values of R be If P & P2 both are prime numbers P>3 then how many different val possible if R LP*P2M mod 9 R LP*P2M mod 9 341. ÐÑ Ò Ó Ô , then find PDR , if P,Q & R are distinct prime numbers , then find PDR , if P,Q & R are distinct prime numbers , then find PDR , if P,Q & R are distinct prime numbers

Direction Direction 344 344 - 345 345 :Number of Hair fall is directly proportional to TQ Tension Quotient and TQ is directly proportional to square of pe TQ is directly proportional to square of person integral age ignoring months and days. If at rson integral age ignoring months and days. If at the time of birth a person is considered as tension free 0 TQ and person has 100,000 hairs. the time of birth a person is considered as tension free 0 TQ and person has 100,000 hairs. If at the age of 4 number of hairs a person has is 77,500 then at the age of 4 number of hairs a person has is 77,500 then Total number if hairs at the age of 8 is ____ 342. Total number if hairs at the age of 8 is ____ What is the minimum age of complete baldness 343. What is the minimum age of complete baldness Find ab if a & b are positive integer and a³ - 1 b² 1. 344. Find ab if a & b are positive integer and Find the least value of n for which n output of below given sum is an integer 345. Find the least value of n for which n output of below given sum is an integer n/1*2*3 n/2*3*4 n/3*4*5 ... n/7*8*9 n/1*2*3 n/2*3*4 n/3*4*5 ... n/7*8*9 346. 1³2³3³4³...10³ 1357....n 1357....m, Then find integral 1³2³3³4³...10³ 1357....n 1357....m m & n 347. 1² 4² 7² 10² ..... 40² ??? 1² 4² 7² 10² ..... 40² ??? 348. If average of 11different numbers x1 , x2, x3. .... , x11 is X then what would be average in terms of X if all 11 numbers are multi in terms of X if all 11 numbers are multiplied by 2 then decreased by X. plied by 2 then decreased by X. 349. For different positive integral a, b & c For different positive integral a, b & c ; a² b² c³ then find minimum value of c a² b² c³ then find minimum value of c 350. If N m² , where m is a natural number more than 99 but less than 1000, then for how values of m , N & m are having same last two digits values of m , N & m are having same last two digits 351. Ram and Shyamali each has a fair coin. Ram tossed his coin 5 times and got 4 heads and one tail , Shyamali also tossed her coin 5 times and got 3 heads and 2 tails one tail , Shyamali also tossed her coin 5 times and got 3 heads and 2 tails. One day both meet and both tossed their coins once. What is the probability of getting dif meet and both tossed their coins once. What is the probability of getting different outcomes on each coins ??? outcomes on each coins ??? www.facebook.com/groups/MBAMathsByAmiya 3E Learning Maths By Amiya Ranchi | 37

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HCF of sum of all sides of an integral sided right angled triangle is ________ ??? 352. HCF of sum of all sides of an integral sided right angled triangle is ________ ???

HCF of product of all sides of an integral sided right angled triangle is ________ ??? 353. HCF of product of all sides of an integral sided right angled triangle is ________ ???

354. If a ball is dropped from a height of 2000 m and If a ball is dropped from a height of 2000 m and it bounces back but looses 1/9 of it bounces back but looses 1/9 of height after every bounce then find total distance covered by ball till it comes to rest or near to rest 355. Find area of graph in side x² y² 16 but outside |x||y|4 in items of pi Find area of graph in side x² y² 16 but outside |x||y|4 in items of pi

356. Find maximum value of n if n & m are Find maximum value of n if n & m are natural numbers and 90! 20!^n * m 90! 20!^n * m

357. There are how many natural numbers less than equal to 100 , whose product of all factors are square of the number factors are square of the number 358. Number of trailing zeros in C512, 32 Number of trailing zeros in C512, 32 ; Cn,r n!/r!*n-r!

359. There are how many natural There are how many natural numbers less than 1000 , has only odd number of factors numbers less than 1000 , has only odd number of factors total number of factors are odd total number of factors are odd

360. John and Shaw started running from same point , at same time in same direction. John John and Shaw started running from same point , at same time in same direction. maintained a constant speed of 40 km/hr maintained a constant speed of 40 km/hr. But Shaw started with 5km/hr and in ev But Shaw started with 5km/hr and in every next hour he increase his speed by 10 km/hr. next hour he increase his speed by 10 km/hr. Then find after how time from start Shaw Then find after how time from start Shaw will catch John

361. If average of 10 consecutive increasing multiple of 8 is 324 then find 4th smallest term among these 10 terms

362. If N is a two digit largest number whi If N is a two digit largest number which is a factor of 35^10 - 17^10 then N mod 7 ??? 17^10 then N mod 7 ???

Find the sum of all terms of 10th row of below given series 363. Find the sum of all terms of 10th row

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 ....................................... .............................................

364.

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365.

internal angles at vertex of given figure 366. Sum of all internal angles at vertex of given figure

367. If in a row Jhon is 23rd from right and Tina is 32nd from left end and there are 5 persons between then , what is the difference between maximum and minimum possible persons in the row 368. If X² YX , XX² AYBX, , XXX² AAYBBX, XXXX² AAAYBBX. Then AB Then AB - Y ??? Where X, XX, XXX are 1, 2, 3 digit numbers so rest are Where X, XX, XXX are 1, 2, 3 digit numbers so rest are

369. If ab bc ca 27 then total number of unordered positive integral solution is ____ then total number of unordered positive integral solution is ____ then total number of unordered positive integral solution is ____ 370. For how many natural N , For how many natural N , N 32^2 is divisible by N4 371. 3 ∗ 9Ê ∗ 27Í ∗ 81 81× … … . ?

372. If ABC & BCA are two three digits perfect squares where A, B & C are different digits then ABC ??? 373. There how many numbers less than 1,00,000 whose sum of digits is 3 There how many numbers less than 1,00,000 whose sum of digits is 3

374. If Sita and Gita daily jog from their home to If Sita and Gita daily jog from their home to park and park to home and then park and park and park to home and then park and so on for two hours, park is 10 km from their home. If they live together and both stats www.facebook.com/groups/MBAMathsByAmiya 3E Learning Maths By Amiya Ranchi | 39

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at 7:00 AM, and speed of Sita is 20 km/hr and that of Gita is 30 at 7:00 AM, and speed of Sita is 20 km/hr and that of Gita is 30 km/hr then when km/hr then when Gita overtakes Sita for the first time after ita for the first time after start.

Among the options select correct statements 375. Among the options select correct statements 1. Sum of three different primes can't be divisible by 6 1. Sum of three different primes can't be divisible by 6 2. Product of three different primes can't be divisible by 6 2. Product of three different primes can't be divisible by 6 3. Last two digits of all primes less than 100 is 50 3. Last two digits of all primes less than 100 is 50 4. In an integral sided right angled triangle all sides can't prime. ght angled triangle all sides can't prime.

376. There are how many different integral sided right angled triangles are possible whose There are how many different integral sided right angled triangles ar one side is 25 unit ¿ ¿ ¿ 377. s8 q8 Z8 r8 √8 … ?? ¿

¿

378. If √

√

√3 then Í ?

379. In how many ways we can rearrange the word In how many ways we can rearrange the word NAGIN such that no vowels be together. NAGIN such that no vowels be together. 380. Find the length of line segment between axes line of a line whose equation is 4x-3y Find the length of line segment between axes line of a line whose equation is 4x 12 381. If A*B*C*D*E*F 60 , where A,B,C,D & E are different integers then what is the maximum value of ABCDEF maximum value of ABCDEF

382. Total number of integral ordered pair solutions for of integral ordered pair solutions for A b 64 64 is a. 175 b. 163 c. 150 d. NoT

383. What if the value of c to get maximum value of What if the value of c to get maximum value of 0 ∗ . ∗ U ? under condition abc under condition abc 108 and all a,b&c are positive numbers. 108 and all a,b&c are positive numbers. 384. If in a ∆ABC, D is midpoint of BC , E is ∆ABC, D is midpoint of BC , E is midpoint of BD , F is midpoint of BE and G is midpoint of BD , F is midpoint of BE and G is midpoint of AF then what is the ratio of area of midpoint of AF then what is the ratio of area of ∆BGF to that of ∆ABC ∆BGF to that of ∆ABC

385. What could be minimum value of N , which COULD satisfy What could be minimum value of N , which COULD satisfy Y 0 . U V where a,b,c & d are distinct distinct natural numbers

386. If few students of section A of PGP transfer to section B then ration of number of nts of section A of PGP transfer to section B then ration of number of students of A to that of B 3:7 but if few students of section B of PGP transfer to section A then ration of number of students of A to that of B 5:2 A then ration of number of students of A to that of B 5:2, then find minimum number , then find minimum number of total students of section A & B. al students of section A & B. 387. If 10 lit of pure alcohol is replaced by 50% of 2 lit alcohol and this process is repeated one more time then find the % of alcohol in final solution. one more time then find the % of alcohol in final solution.

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Total number of terms after expansion of 1 388. Total number of terms after expansion of 389. Total number of terms after expansion of Total number of terms after expansion of A Q

390. How many perfect squares less than 1000 would give remainder 3 when divided by 7 How many perfect squares less than 1000 would give remainder 3 when divided by 7 How many perfect squares less than 1000 would give remainder 7 when divided by 9 391. How many perfect squares less than 1000 would give remainder 7 when divided by 9

392. If C is circum-centre & G is centroid of a G is centroid of a triangle whose sides are 7 , 24 and 25 cm then e 7 , 24 and 25 cm then what is the length of line segment what is the length of line segment CG 393. There are how many days in between next palindromic date DDMMYYYY and last palindromic dateDDMMYYYY if today is 14062016 palindromic dateDDMMYYYY if today is 14062016 394. Find the least value of n more than 4 for which 234567.... n is which 234567.... n is a perfect square a. 15 b. 24 c. 25 d. 26

395. Ram and Mohan started their journey from two opposite extreme end of a tunnel. If Ram started his journey at 8 :00 AM with speed 60 km/hr and Mohan at 7:00 with Ram started his journey at 8 :00 AM with speed 60 km/hr and Mohan at 7:00 with speed 40 km/hr. When both met to each other it is found that one of them covers double distance of other then find the different between maximum or minimum possible length of tunnel. 396. Total number of positive ordered solution of abcd Total number of positive ordered solution of abcd 10 Í ÍÍ Í Í

7

397. Unit digit of

7 is _____ is _____

6666. . . . 398. What is the value of 1.6666 a. 2.66666..... b. 2.565656....... b. 2.565656.......

399. Zx rx √x ⋯ 3xx then x ?

c. 2.77777.....

d. NoT d. NoT

400. What is the minimum value of value of |x1| |x2||x3|

401. What is the minimum value of value of |x| - |x1| |x2|-|x3||x4|

402. If LCM of first N natural numbers is "L" and that of first "N2" natural number is "2*L" then less than 100 how many different N are possible then less than 100 how many different N are possible 403. If 130 20. U V 120. 8.U 40V , 0 ∗ . ∗ U _ 0 then then 4^ ? P[

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24 23A 6A 11Q 2Q 4 42 then 404. If for real x, y & z ; 9 A Q ? 405. What would be remainder What would be remainder when 19

ÊÊ

is divided by 1200

2K Ë ? 406. If 3 9 then

407. Maximum how many vertices could be common in a regular dodecagon 12-sided Maximum how many vertices could be common in a regular dodecagon polygon and regular nonagon 9 nonagon 9-sided polygon

408. Find the maximum value of a2*b3*c4 if 2a3b4c 7 and a , b & c are value of a2*b3*c4 if 2a3b4c 7 and a , b & c are positive numbers 409. Find the Maximum value of a1*b2*c3 if a b c 3 and a , b & c are positive numbers

410. For natural number m, n, x & y if For natural number m, n, x & y if m*x n*y 100 then what would be last digit of m*x n*y 100 then what would be last digit of maximum value of » ∗ A 3 ? ? ?

411. If in a race A beats B by 100 m , B beats C by 100 m and in the same race if A can beats C by "X" m then what is the range of "X" by "X" m then what is the range of "X" a. 100 ³ 200 b. 100 b ³ 200 c. 100 ³ b 200 d. 100 b ³ b 200 e. NoT 412. If abcabc is a 6 digit number and has If abcabc is a 6 digit number and has 20 positive divisors then abc ? positive divisors then abc ?

413. Above image is actual time zone clocks Above image is actual time zone clocks and all are showing their local time all are showing their local time of a same time. If a flight departs from Central at If a flight departs from Central at 02:00 local time at central to city X and arrives at 10:00 and arrives at 10:00 local time at city X and then depart from city X at 11:00 local time at city X to Central and arrives at 09:00 local time at central on same day. Then CITY X is _______ arrives at 09:00 local time at central on same day. Then CITY X is _______ 414. If given figure is a 12 sided regular dodecagon then find angle X in degree is a 12 sided regular dodecagon then find angle X in degree is a 12 sided regular dodecagon then find angle X in degree

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In given fig if AB2unit, BC3unit, CDCA4unit and DA5 unit then find BD 415. In given fig if AB2unit, BC3unit, CDCA4unit and DA5 unit then find BD

If HCF of three natural numbers is same as their LCM then sum of all three numbers are 416. If HCF of three natural numbers is same as their LCM then sum of all three numbers are a. 2*LCM 3*HCF b. 5*HCF - 2*LCM c. HCFLCM c. HCFLCM d. NoT 417. If average of 5 different positive numbers are A and X is average of average of all possible pairs of these 5 numbers then possible pairs of these 5 numbers then a. AX b. g @ ³ c. A b X d. g ³ e. NoT e. NoT

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hour clock as shown in fig, in which outer dial 418. There is a 24 - hour clock as shown in fig, in which outer dial is representing hours and inner dial is minutes and seconds, then find the angle between hands X if time is 20:10. then find the angle between hands X if time is 20:10. 419. If A sold an article to B at 20% profit and B to C at 10% profit t If A sold an article to B at 20% profit and B to C at 10% profit then C sold to A at 20% hen C sold to A at 20% loss then find over all monetary % profit or loss of A. LAssume all transactions happen in $M 420. For natural numbers x, y if For natural numbers x, y if 6 ∗ 44 A then x y ??? then x y ??? 421. Ù1

Ú Ú Ú⋯

Û ? ? ?

422. Find least palindromic natural number which Find least palindromic natural number which has odd number of digits , divisible by 11 has odd number of digits , divisible by 11 and has 9 as a middle digit. and has 9 as a middle digit. 423. If a palindromic number which has odd number of digits is divisible by 11 then middle digit of this number can not be digit of this number can not be a. 3 b. 2 c. 4 d. 6 e. All possible as a middle digit e. All possible as a middle digit

424. If A increases 10% then 20% then 30% then 40% then it becomes B, But if A increases , A increases 10% then 20% then 30% then 40% then it becomes B, But if A increases , 12% then 22% then 32% then 34% then it becomes C, Then 12% then 22% then 32% then 34% then it becomes C, Then a. BC b. B>C c. BbC d. NoT 425. Find maximum power if 20! Factorial 20 which perfectly divides 202! Factorial 202 Find maximum power if 20! Factorial 20 which perfectly divides 202! Factorial 202 426. Total number of real solutions of x³ sin x Total number of real solutions of x³ sin x 427. s6 2q6 2Z6 2r6 2√6 ⋯ ? a. √2 1

b. √3 3 1

c. 1

d. √3 1

428. Find the sum of common terms/elements of m3,7,11,15,....,103< & m1,7,13,19,....,103< Find the sum of common terms/elements of m3,7,11,15,....,103< & m1,7,13,19,....,103< www.facebook.com/groups/MBAMathsByAmiya 3E Learning Maths By Amiya Ranchi | 44

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show nth term of two different APs whose sum of first n terms are 429. If ÜÝ and ÞÝ show nth term of two different APs whose sum of first n terms are denoted by ßÝ and àÝ respectively. If respectively. If ßªª : à Þ¬ . : ªâ 17:11 then find Ü 17:11 º : Þ 430. For natural number x, y and z , For natural number x, y and z , 2 3o 5p 114 then x y - z ? z ?

431. If %profit is same as cost price of article and selling price is 131.25 then find its profit in rupees.

432. Find the concentration % of acid in final solution if 80 lit of 80% acid solution is first replaced by 20 lit water then 40 lit water. replaced by 20 lit water then 40 lit water.

433. If 1000th prime is a four digit number and it is rime is a four digit number and it is equal to 7909 X then X ?? 7909 X then X ?? a. 20 b. 6 c. 8 d. 10 434. Data Sufficiency : What is the cost Data Sufficiency : What is the cost price of the article I. If loss % is same as cost price of the article and selling price is Rs. 24. I. If loss % is same as cost price of the article and selling price is Rs. 24. II. If cost price is 20% of selling price. II. If cost price is 20% of selling price.

2 , 3 , 4 , 5 0-V 6 6

435. Which one is largest among largest among ã

ã

¿ã

Ëã

Àã

436. There are how many four digit number ABCD are possible such that AB, BC, & CD are perfect squares repetition of digits are allowed perfect squares repetition of digits are allowed

437. There are how many three digit numbers are possible say XYZ, if we interchange digits of unit place and hundredth place ZYX then digits of unit place and hundredth place ZYX then resultant number is also a three digit number is also a three digit number and | XYZ - ZYX| is divisible by 7 ZYX| is divisible by 7, such that _ Q 438. What is the last two digits of product of all positive divisors of 1024 digits of product of all positive divisors of 1024 digits of product of all positive divisors of 1024

439. A cone of height X is cut by a plane parallel to the base and at a distance is cut by a plane parallel to the base and at a distance Y from the is cut by a plane parallel to the base and at a distance base, then what is the ratio of what is the ratio of volume of the resulting cone and that of resulting that of resulting the ª « frustum ? where X & Y are pos X & Y are positive integral solution of ä ª â ; where Z is also a positive integer

å

æ

440. If ∆ABC is an equilateral triangle , and point D & E are on sides AB & AC such that , ∆ABC is an equilateral triangle , and point D & E are on sides AB & AC such that , DE||BC, and perimeter of DE||BC, and perimeter of ∆ADE is same as perimeter of quadrilateral BCED then find ∆ADE is same as perimeter of quadrilateral BCED then find ratio of DE:BC.

441. If speed of the group is 1 m/s and that of the joker is 3m/s. Joker starts from back of the last person and moves towards the front one, touches him and turns back, and goes, back to last person. If in this process The Joker covers 16 back to last person. If in this process The Joker covers 16 m when he is going forward m when he is going forward right hand side then find distance traveled by him when he turned back and moves towards left. assume speed of all remains same in entire process and no time loss by The Joker when he was turning back The Joker when he was turning back www.facebook.com/groups/MBAMathsByAmiya 3E Learning Maths By Amiya Ranchi | 45

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How many pairs of natural numbers m, n satisfy , where where 20>m 442. How many pairs of natura » 3 K

?

443. A quadratic function fx attains a A quadratic function fx attains a minimum of -5 at x -1. The value of the function at 1. The value of the function at x 0 is -3 . What is the value of f x at x What is the value of f x at x 5?

Direction for 446 to 448 : If the total intake in IIM A , B & C together is 900, and below chart is Direction for 446 to 448 : If the total intake in IIM A , B & C together is 900, and below chart is giving % of Male Mand that of Work giving % of Male Mand that of Work-ExEx in B-Schools. It is also known that 40% of whom Schools. It is also known that 40% of whom are in IIM-C are rest are equally divided between IIM A & IIM C. C are rest are equally divided between IIM A & IIM C. Male (M)

IIM A IIM B IIM C Total

444. What is the % of Male in IIM A What is the % of Male in IIM A

37.037% 33.333% 34.444%

Work Ex (Ex) 55.556% 66.667% 56.667%

445. What is the % of Fresher Fresher Non work Ex in IIM C

446. If in IIM -B , 50% work ex are male then what is the ratio of Male Fresher to Female B , 50% work ex are male then what is the ratio of Male Fresher to Female Work ex in IIM - B

447. One day Bagga with his dog planed to go to Park from their home which is 1200 m from home. Speed of Bagga was 30 m/s and that of his dog was 60 m/s. Both started from same time. His dog reached Park much earlier than Bagga, but dog returned back without wasting any time and came near to Bagga and again run towards Parks and asting any time and came near to Bagga and again run towards Parks and after reaching park came back to Bagga and continue the same process until Bagga reached the Park. If both maintained a constant speed in entire journey and there was no time loss in this process then find is process then find how much meter more did dog move towards park than towards Bagga. 448. If 2 is a root of a quadratic function fx0 and 7*f3f6 then find another roots of fx0

449. If WEIGHT of number a, ab , abc & of number a, ab , abc & abcd a single , double, triple and four digit number abcd a single , double, triple and four digit number respectively is defined by ; respectively is defined by ; WEIGHT a a ; WEIGHT ab ab ; WEIGHTabc bc - a and a and WEIGHTabcd cd-ab ; ab ; then for how many natural number less than 8995, then for how many natural number less than 8995, WIGHT WIGHT WIGHT of that number is 7. of that number is 7.

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450. ABCD is rectangle such that AB12cm and BC5cm, another Rectangle AEFC is such that point D lies on side EF then find the area of rectangle AEFC

451. If log log · 2√ 9¸ 0 then find x

452. If mileage of a car is 17 km per lit If mileage of a car is 17 km per lit with extra 3 lit per hour as wastage as wastage . What should be minimum speed of the car to cover 34 km in 3 lit. minimum speed of the car to cover 34 km in 3 lit. 453. W1 X W1 X W1 X W1 X … … … ? =K=

454.

K

K

K = K

?

K

K

⋯ … … … . ?

455. If 9th term of an AP is 20 20 then sum of first 17 terms of this AP is _____ sum of first 17 terms of this AP is _____

456. If the pendulum of a clock the pendulum of a clock takes 3 seconds to strike 3 o’clock. then h then how much time will it take to strike 9 o’clock? o’clock? 457. W

∗∗K

∗K∗

K∗ ∗

⋯

X ? ? ?

∗∗K

What would be remainder if 1 1 1 ? 1 is divided by is divided by 458. What would be remainder if

3 2

459. If mileage of a car is 15 km per lit with extra km per lit with extra 2 lit per hour as wastage . What should be lit per hour as wastage . What should be minimum speed of the car to cover minimum speed of the car to cover 45 km in 4 lit. 460. If an article was selling at 20% profit , to earn Rs 1320 more profit shopkeeper purchased article at 10% lesser than his cost price and sold it at 10% higher pri purchased article at 10% lesser than his cost price and sold it at 10% higher price than his selling price, then find oldoriginal selling price of his selling price, then find oldoriginal selling price of

461. Find the maximum value of Find the maximum value of a b, if following set of equations has infinite many roots has infinite many roots a-1*x 5*y 140 & 7 & 7*x a1*y b

462. What would be area of triangle formed by axes lines and a line which is perpendicular to a line 3x-2y6 and passing through 2,2 2y6 and passing through 2,2

463. If A is X% of B and B is Y% of A and X is A% of Y and Y is B% of X then what is X% of 20 If A is X% of B and B is Y% of A and X is A% of Y and Y is B% of X then what is X% of 20 464. If aaabcccd is a 8 digit perfect If aaabcccd is a 8 digit perfect square then abcd ???

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465. If ratio of income of X &Y is 3:4 and their expenditure ratio is 4:7 then then whose % saving on income is more whose % saving on income is more a. X b. Y c. can't say d. NoT

466. L√1ML√2ML√3ML√4M.....L√24M ??? ;Where LxM is defined as nearest integer, L √1ML√2ML√3ML√4M.....L√24M ??? ;Where LxM is defined as nearest integer, L3M3, √1ML√2ML√3ML√4M.....L√24M ??? ;Where LxM is defined as nearest integer, L L4.3M4 & L4.51M 5 467. How many integral solutions are possible for L√ M 25 ;Where LxM is defined as ;Where LxM is defined as nearest integer, L3M3, L4.3M4 & L4.51M 5 nearest integer, L3M3, L4.3M4 & L4.51M 5

;Where LxM is defined 468. What is the sum of all integral solutions possible for L√ M 25 ;Where LxM is defined as nearest integer, L3M3, L4.3M4 & L4.51M 5 as nearest integer, L3M3, L4.3M4 & L4.51M 5 469. 4 4 4 . . . . 4 = ;ÌV 17 ? ? ? 470. 4 ∗ 4 ∗ 4 ∗ . . . .∗ 4 = ;ÌV 17 ? ? ?

471. 2= 2 2 . . . . 2 ;ÌV 13 ? ? ?

472. If A,B,C,D,E, & F are points on a circle such that ratio of le If A,B,C,D,E, & F are points on a circle such that ratio of lengths of arc ngths of arc AB , arc BC, arc CD, arc DE, arc EF, arc FA is 1:2:3:4:6:6 then what is the value of angle CDF FA is 1:2:3:4:6:6 then what is the value of angle CDF FA is 1:2:3:4:6:6 then what is the value of angle CDF 473. 1234512345.... 300 digits mod 41 ??? 1234512345.... 300 digits mod 41 ???

474. If A,B,C,D,E, & F are points on a circle such that ratio of lengths of arc AB , arc BC, arc If A,B,C,D,E, & F are points on a circle such that ratio of lengths of arc AB , CD, arc DE, arc EF, arc FA is 1: arc EF, arc FA is 1:1:2:2:3:3 then what is the value of angle then what is the value of angle ACE 475. If fxx-1x5x-9...x61 , then for how many integral "x" fxb0. 9...x61 , then for how many integral "x" fxb0. 9...x61 , then for how many integral "x" fxb0.

476. Ram wrote first "N" natural numbers on a black board then removed one number and found that new average becomes found that new average becomes 21.1 then find which number was removed ? 21.1 then find which number was removed ? 477. If A,B C & D are points on circle and E,F,G & H are mid points of side DA, AB, BC & CD. Find the area of quadrilateral EFGH if AB12cm, BC6 cm, CD8cm & DA 10 cm. AB12cm, BC6 cm, CD8cm & DA 10 cm.

478. What is the area of a right angled triangl What is the area of a right angled triangle whose inradius and circum radius are 10 and e whose inradius and circum radius are 10 and 12 cm respectively 479. What is the area of a right angled triangle whose inradius and circum radius are 4 and 12 cm respectively

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3E LEARNING - MATHS BY AMIYA 500 CAT 2016

480. Inside an equilateral triangle there is a point from which the length of perpendicular on all the three sides are 2 lar on all the three sides are 2cm, 3cm, & 4cm then. what would be area cm then. what would be area of equilateral triangle.

481. If fresh grapes has 90% water content and dry grapes kishmish has 30% water content. In the procedure of making kismish one just need to dry grap content. In the procedure of making kismish one just need to dry grapes, then if a shopkeeper purchased 210kg of grapes at 30 Rs per kg then at what price per kg he should sell kismish to earn 33.33% profit. should sell kismish to earn 33.33% profit.

13x19...x115; Then for how many integral x , fxb 0 Then for how many integral x , fxb 0. 482. If fx x-1x7x-13x19...x115 483. If in the given fig , AD3cm , DF 1cm, FC 2cm & , AD3cm , DF 1cm, FC 2cm & EF || BC then

PçèP 5é ∆deê

find

PçèP 5é ∆ëêì

484. If in the given fig , AD3cm , DF 1cm, FC 2cm & EF || BC then

PçèP 5é ∆deê

find

PçèP 5é ∆def

485. If in the given fig , AD3cm , DF If in the given fig , AD3cm , DF 1cm, FC 2cm & EF || BC

PçèP 5é êìfe êìfe

then find

PçèP 5é ∆def def

486. In the given fig if then find the area of ∆íîï then find the area of íîï

BD:DCCE:EA1:2 and area of ∆AFO is 144 sq. cm, BD:DCCE:EA1:2 and area of ∆AFO is 144 sq. cm,

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3E LEARNING - MATHS BY AMIYA 500 CAT 2016

487. If in the given fig ABCD is parallelogram, O is a point inside the parallelogram. If areas of three triangles are given check fig then find the fourth triangle.

area of

488. In the given triangle D, E & F are mid points of respective sides then find the area ratio of quad find the area ratio of quad BGOF to that of ABC

489. If in the given fig ABCD is quadrilateral and E,F,G H are mid points of respective sides as shown in fig. Areas of three quadrilaterals are given check fig then find the area of fourth quadrilateral.

&

490. If angle ratio of a triangle is 1:2:9 then what is the side ratio of this triangle If angle ratio of a triangle is 1:2:9 then what is the side ratio of this triangle a. 1:2:9 b. 18:9:2 c.√3 ∶ √2 ∶ 2 d. √3 1 ∶ √2 ∶ 2 e. NoT

491. If N the least natural number which is subtracted from 10000*10001*10002*10003 to make it a perfect square then N mod 9 ??? square then N mod 9 ??? 492. Sum of all coefficients of expansion of x1x2x3....x15 is S then S mod 17 of expansion of x1x2x3....x15 is S then S mod 17 ?

493. If an alloy is having Zn, Cd and Fe in the ratio of 3:4:9 and another alloy has the same elements in the ratio of 2:3:4 then find the elements in the ratio of 2:3:4 then find the ratio of these elements in the same order of ratio of these elements in the same order of first alloy and second alloy is mixed in the ratio of 2:3 first alloy and second alloy is mixed in the ratio of 2:3 www.facebook.com/groups/MBAMathsByAmiya 3E Learning Maths By Amiya Ranchi | 50

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Total number of positive integral solution of 10x 7y 7z 100 is ______ 494. Total number of positive integral solution of 10x 7y 7z 100 is ______

495. If añ b ñ c ñ dñ is always divisible by abcd , where a,b,c,&d are natura is always divisible by abcd , where a,b,c,&d are natural is always divisible by abcd , where a,b,c,&d are natura numbers and p is a prime more than 101 then numbers and p is a prime more than 101 then a. a, b , c& d are odd numbers a. a, b , c& d are odd numbers b. c, d , a & b are in AP c. a, b, c & d are in HP d. a, b, c & d are in GP e. NoT

496. If 32A65B is divisible by 72 then what would be remainder if AAABBB is divided by 7, where A & B are two digits both could be same. ere A & B are two digits both could be same. 497. Shopkeeper A : Gives 25% extra and charges 20% less than market price Gives 25% extra and charges 20% less than market price Gives 25% extra and charges 20% less than market price Shopkeeper B: Gives 20% extra and charges 25% less than market price Gives 20% extra and charges 25% less than market price Gives 20% extra and charges 25% less than market price

If both shopkeepers sell same product of same market price then for a customer which shopkeeper is better... ???? shopkeeper is better... ????

498. There is a tilted glass in perfect cylindrical shape with base in perfect cylindrical shape with base radius 7cm and height 10 cm. Glass radius 7cm and height 10 cm. Glass is partially filled with water, in such a way that, that, water level is just touching bottom end and top end of the glass as shown in bottom end and top end of the glass as shown in the figure. Then find the amount of water figure. Then find the amount of water in litter inside the glass.

499. Find the total number of positive integral solution of o p 1 1

500. Amiya and Raman is playing a game Toss laying a game Toss-Toss. Raman wins when tails comes and Toss. Raman wins when tails comes and losses when heads come. Raman gains Rs 10 for tail and loses Rs 10 for head. If Raman wins in first toss then he quits but tries only once more if he losses on the first toss. Then in this game how much could be expected win of Raman. uch could be expected win of Raman.

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SOLUTION :Maths Maths By Amiya 500 (2017(2017 19) 1. Mohit calculated sum of first N natural number and he found sum is 337 and he knows he counted one number twice or missed one number. then find his minimum possible % error made by him. a. 3% b. 3.99% c. 3.69% d. 3.23% Sol: [c] Actual sum should be near to 338 for minimum error, so it should be either 325 or 351 % error on 325 = 12/325*100 = 3.69% % error on 351 = 14/351*100 = 3.99 2. The integers 1,2,….. 30 are written on a board. A person came and erased any two numbers say "a" & "b" and wrote a new number "a+b+2" this pro process cess is done by total 29 persons (including first one) then . What is the number left on the board at the end? Sol: Every time sum would increase by 2 , so total increase = 2*29 = 58 So last number = ∑ « ò¯ = 465+58 = 523 3. If T1=(1) , T2= (3,5) , T3 = (7,9,11) , T(4) = (13,15,17,19) ..... Then what is the sum of all terms of T(10) Answer : 1000 4. phi (n) is defined as number of co co-prime prime less than n. If ‘P’ is product of two different prime numbers, whose sum is 1200 then what is the max phi(M) Sol: phi (n) = n *(1 -1/p)*(1-1/q) 1/q) and so on ... where p and q are primes in prime factors of n. since we need this max so by gó @ ôó ôó ,, value should be close means both prime should be closer to 60 for max phi , so 59 & 61 ; P = 59*61 & phi(P) = 58*60 = =3480. 5. Consider the set S = {1,2,3,………..10000}, How many APs can be formed from the elements of S that start with 1 and end with 10000 and have minimum 3 terms?

Ans: 11 ; a=1 ,Tn=10000 , so 1 + (n (n-1)d = 10000; ; (n-1)d 1)d = 9999 = 3^2*11*101 so 12 factors. n-1 cannot be 1. so 11 6. Total number of integral solutions of 13x - 3y = 1000 for 100< x < 200 Sol: 33 , all numbers which gives remainder 1 when divided by 3 7. For how many integral "n" is

is an integer

Sol: [12] 7 21 7 9 mod (x--3) = 12 , so x-3 3 should be a factor of 12 means 12 values are possible including negative.

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3E LEARNING - MATHS BY AMIYA 500 CAT 2016 8. If HCF , LCM and sum of two numbers are 6 , 15 and 23 then find their difference. Sol: Not a possible case 9. If 1 7 6 3 , then find the value of f(x - 1). Sol: put x = x -2 ,âõ® ®®õ ª¬ 10. Find the area of the enclosed fig by | x- 5 | öõ ö âú öõ – ºú « ®

ª

ª

ª

So 343 216 so 560 integral solution.

13. When a number divided by 6 and 35 remainders are 5 and 7 then what would be remainder when 11 times of the number is divided by 15 a. 8 b. 13 c. 7 d. Data inadequate e. NoT Sol: By CRT 77 is least number for 210 and we want 11*77 mod 15 = 7 14. In a circle AB is diameter of length 34 unit and BC is chord of length 16 unit. If CD is perpendicular on AB such that D lies on AB then what is the length AD. Ans: 450/17 , can do by similarity Ans: ª¯√® ; Area = ÷® ∗ àøÝù

15. What is the area of a rhombus whose one side is 6 unit and one internal angle is 135 degree. 16. If major (longest diagonal) of a rhombus is 6√3 cm and one internal angle of rhombus is 120° then what is the area of rhombus.

Ans :ª¯√

17. 113 100 is divisible by 209 (True / False) ANS: TRUE 18. 113 100 is divisible by 247 (True / False) ANS: TRUE 19. 113 100 is divisible by 143 (True / False) ANS: TRUE 20. 113 100 is divisible by 71 (True / False) ANS: TRUE

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3E LEARNING - MATHS BY AMIYA 500 CAT 2016 21. 113 100 is divisible by 781 (True / False) ANS: TRUE 22. What is the rate per annum if compound interest after 2 years is same as simple interest after 3 years. Ans: 100% Ans: ∶

ò°«

∶ °ª

â

23. At what time between 3&44 both the hands are equi equidistant from figure 6 but not together ª

ª

24. What is the least natural number N for 101^N mod 280 = 1 Ans: N =6 ,cyclicity 280 = 2^3*5*7 ; no need to check for 5 , since 101^n mod 5 = 0 , for all n ; also not for 2^3 since 101^(2m) mod 8 = 1, for all m ; now just check 7 , cyclicityoteuler of 7 is 6 which satisfy all conditions 25. If A takes "a" hours more than time taken to complete a work when A & B work together and B takes "b" hours more than time taken to complete a work when A & B work together. Then what is efficiency ratio of A and B 1. a : b 2. b:a 3. √.: 0 4. √0: . 5. b^2 : a^2 Ans: [3] 26. If X + (1/Y)=1 , Y + (1/Z) = 1 then what is the value of X*Y*Z , if none of X, Y & Z are 0 Ans: -1 ; solve by putting values 27. What is the minimum value of of2123 2451

Ans: ®

ªW

ª X √®

at x = 225

√1! √2! √3! ⋯ … . √1000! ? Ans : 1*7+2*19+3*37+4*61+5*91+6*127+7*169+8*217+9*271+10=6985 28. If [ N ] is greatest integer less than equal to N then

29. What is the coefficient of x^5 in the expansion of (1+x)(2+x)(3+x)(4+x)(5+x)(6+x) Ans: 21 , -(sum (sum of all roots)

30. If P = { x /x : x 15 , $% -0*890: -8;.,9 < ; then how many subset of P would have at least one prime number Ans : ®ªò ®¬

31. 1 2 3 4 … . . 101 ? Ans :5151

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3E LEARNING - MATHS BY AMIYA 500 CAT 2016 32. ( 2 ; *+,- = … … ?

Ans : 0 33. Find the cubic equation whose roots are one more than roots of 1 0 Ans: x^3-2x^2+2x= 0 ;Put x = x--1 34. What is the minimum value of sinx + cosecx + tanx + cotx Ans :infinity 35. What is the sum of first 1000 terms of series - 1,2,1,2,2,1,2,2,2,1,2,2,2,2,1,.... Ans : 1956 ; 2*1000-44= 44= 1956 ; just check how many one's by checking positions of 1's. 1,3,6,10...990 so 44 36. DS - What is the ratio of Cost Price to Selling Price A. Markup % is 26% more than Profit % and 10% more than Discount % B. Markup is Rs 26 more than Profit (RS) and Rs 10 more than Discount (in RS) Ans: A alone. 37. What would be remainder er if 98! Is divided by 101 ? Ans: 50 38. What is the sum of all internal angles of this star Ans :(11-5×2)×180=180

)...(1+x^99) 39. Coefficient of x⁴ in the expansion of (1+x)(1+x²)(1+x³)(1+x⁴)...(1+x^99) Ans: 2 40. Max number umber of segments we can create on a plane (open or closed ) by the help of a circle , a trianglee and a line is ______ Ans: 12 41. If magnitude of speed in Km/hr of a man is same as rest time in minute in an hour of that man. Find maximum distance covered by man in 5 hours. Ans :x(5-x/12), 5x-x^2/12,5=x/6,x=30, x^2/12,5=x/6,x=30, so 30*(5 30*(5-30/12),150-25*3=75 42. If N is smallest est prime number which is equal to sum of three consecutive prime numbers then what is the sum of digits of N Ans: 4 ; 23 = 5+7+11 www.facebook.com/groups/MBAMathsByAmiya 3E Learning Maths By Amiya Ranchi | 56

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73% are passed in Phy , 89% in Che, 69% 69 in Bio & 43. If in an examination of PCMB , 73 71% in Maths, then minimum how many % people have passed in all four papers. Ans : 2% Work on students who failed in each sub - 27, 11, 31 & 29 , means max 98% fail in at least one so minimum 2% pass in all 44. Total number of positive integral solution of 3x + 2y = 100 such that @ A Ans : 7

45. If in an examination of PCM , 75 75% are passed in Phy , 65% in Che, & 70% 70 in Maths, then minimum how many % people have passed in all three papers. Ans: 10% 46. If in an examination mination of PCM , 60 60% are passed in Phy , 65% in Che, & 70% 70 in Maths, then max how many % people have passed in all three papers. Ans : 47.5% 47. For a natural "n" 2^(12n) - 6^(4n) is div by a. 10 b. 20 c. 50 d. 100 Ans: All

e.All

48. Mohan sells out a toy at 25% profit. Had he purchased at 25% less and sold it for Rs 25 less, then he would have still gained 25%. Find the cost price of toy Ans: 80 49. If sin ∅ cos ∅ then for 0 ∅

Ans :8/3

H

; tan ∅ cot ∅ ? ?

50. Product of first 24 prime number is not divis divisible by a. 391 b. 371 c. 247 d. 279 Ans: [d] 279

e.NoT

51. If product of two sides of an integral sided triangle is 6 then triangle is always I. Acute Angled II. Obtuse Angled III.Right Angled IV. Isosceles V. Equilateral VI. Scalene VII. None of the above is always correct Ans : VII Not ; sides are 2,3,3 & 2,3,4 & 2,3,2 52. How many integral sided isosceles triangle is possible , if sum of two sides is 20 Ans: 31 Sol: If 20 is sum of equal sides, then sides are 10,10,x so total 19 triangles are possible If unequal sides sum id 20 the www.facebook.com/groups/MBAMathsByAmiya 3E Learning Maths By Amiya Ranchi | 57

3E LEARNING - MATHS BY AMIYA 500 CAT 2016 Smallest side , 1,2,3,4,5,6, only one iso triangle is possible so 6 possibility 7,8,9 - two iso triangles are possible so again 6 possibilities Total isosceles triangles are = 19 + 6 + 6 = 31 53. What is the maximum area of a triangle - if it is known that sum of any two sides of this triangle is less than equal to 20 unit. Ans: It should be (1/2) *a*bsinC , for max sinC should be 1 , so max area is (1/2)*a*b = 1/2*10*10 = 50 max

54. Fig is a regular octagon then what is the measurement of angle ADH Ans: 22.5 degree

55. Find the max value of n for which 124K 1 is divisible by 53 Ans: 5; 125*50 = 5^5 * k 56. What would be remainder if 344^49 - 1 is divided by 7^5 Ans: 0 57. What is the minimum value of x^2 - 4x +3 Ans: -1 , at x=2 58. What is the minimum value of sin^2 x - 4sin x +3 Ans: 0 , at 90 59. If a , b & c are sides of a right angled triangle and natural numbers then what would be remainder if a*b*c is divisible by 15 Ans: 0 60. (1 - cot1)(1 - cot2)(1 - cot3).....(1 - cot42)(1 - cot43)(1 - cot44) is a. A perfect Square b. A perfect cube c. A perfect square as well as a perfect cube d. Irrational Number e. NoT Ans: [a]; 2^22 , a perfect square 61. If N = (tan46-1)(tan47 -1)(tan48 1)(tan48 -1).....(tan87 -1 )(tan88 -1)(tan89 -1) 1) , then N mod 7 = ? Ans: 2 , 2^22 mod 7 www.facebook.com/groups/MBAMathsByAmiya 3E Learning Maths By Amiya Ranchi | 58

3E LEARNING - MATHS BY AMIYA 500 CAT 2016 62. If x + y + z =1 , x^2 + y^2 + z^2 =2 & x^3 + y^3 + z^3 =3 , xyz = ? Ans: 1/6 (x + y + z)^2 = x^2 + y^2 + z^2 +2 (xy + yz + zx) 1 = 2 +2 (xy + yz + zx) =>xy + yz + zx = -1/2 x^3 + y^3 + z^3 - 3xyz = (x + y + z) ( x^2 + y^2 + z^2 - (xy + yz + zx)) 3 - 3xyz = 1(2 + 1/2) = 5/2 3xyz = 1/2 ; xyz = 1/6 63. DS If f(f(x)) = f(f(f(x))) then f(x) = ? A. It is not a constant function B. [f(x)]^2 = f(x^2) Ans: Only A ;If If f(f(x)) = f(f(f(x))) ; It means f(x) = k or f(x) = x A. It is not a constant function so f(x) = x [sufficient] B. [f(x)]^2 = f(x^2) does hold for f(x)=k so f(x) = x , f(x) = 0 and f(x) = 1 , not sufficient only A is sufficient si of rectangle 64. If ratio of perimeter of a rectangle and that of a square is 5:1 and ratio of one side to one side of square is 3:2 then what is the ratio of area of square to that of rectangle. Ans: 4:51 (l+b) : a = 10 : 1 = 20:2 & b / a = 3:2 so a:l:b = 2 :17 :3 ; a^2 : l*b = 4 : 51 65. If ABCDEFGHIJ are a regular polygon then what is meas measurement urement of angle EHA Ans: 72 degree 66. A husband alone can do a piece of work in 60 hours & wife alone in 40 hours, but due to a baby who always destroy their work they together take 16 more hours to complete their work Then in how many days baby alone can destroy all the work. Ans: 60 67. If a + b +c = 5 then what is the maximum value a^2 + 4*b^2 + 9*c^2 Ans: Infinity 68. In a section of PGP18 of IIM IIM-X X the average weight of 30 students is 60 kg. If x new students join the section and average wt of these new students are "70 - X" kgs, then find the maximum possible average weight (approx) of the section after joining new students. a. 60.66 b. 60.73 c. 60.71 d. 60.56 e. NoT Ans: [c] , for x = 5 69. Arrange A, B & C in ascending order If A = pi^(1/pi) , B = e^(1/e) & C = 1 , where pi is 3.14 , e = 2.71 Ans : C,A, Bhttps://youtu.be/4MWD5C5qt84 https://youtu.be/4MWD5C5qt84 70. If log P . log P . log P . 60 then log P . ? ?

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3E LEARNING - MATHS BY AMIYA 500 CAT 2016 Ans: 40

71. If ? 1 is one factor of f(x) = 0 ∗ K . ∗ ? U ∗ V ∗ , ∗ then what is the real roots of f(x)=0 a. 1 b. -1 c. -f/a d. a*b*c*d*e*f e. NoT Ans:[c] ÷ ∗ õò û ∗ õ° ü ∗ õ ý ∗ õ® þ ∗ õ = a(õ° õ õ® õ ª ∗ õ R is real root then by equating constant term R = - f/a 72. There are 6 identical toys and three boys. In how many ways all toys would be distributed among three boys. Ans: 28 ways. (0, 0, 6), (1, 1, 4), (3, 3, 0), (2, 2, 2), (1, 2, 3), (1, 5, 0) and (2, 4, 0) 73. In JhumriTillaiya a Paamwala priced his beedi at 85 paise per beedi, but after budget, he reduced the price of beedi and andand soldbeediof beediof Rs.77.28 in a day. Then what is the total number of beedies he sold in a day day? a.37 b. 47 c. 84 d. 92 Ans: [d] check by options 74. In AB and BC are two chords of a circle, then find length of chord AC C if AB=BC=6cm and radius of circle is 5cm Ans: 9.6 cm 75. If third term of a GP is 4096 andits common ratio is positive.The Product of first 7 terms is less than that of first 6 terms and Product of first 6 terms is greater than that of first 5 terms. then which option is best describing range of common ratio. a. [ 1/32 , 1/16] b. ] 1/32 , 1/16[ c. [ 1/16 , 1/8] d. ] 1/16 , 1/8 [ e. Not Ans: [d] P7 < P6 => P6*T7 < P6 so T7 < 1 P6 < P5 =>P5*T6 > P5 so T6 > 1 T7 = 4096*r^4 < 1 so , r < 1/8 T6 = 4096*r^3 > 1, so , r > 1/6

76. Ans: 23 degree angle by same chord

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3E LEARNING - MATHS BY AMIYA 500 CAT 2016 77. All words having three different vowels and three different consonant are written in dictionary then what would be rank of word BAEI BAEICD Ans: 137 Keeping A fixed in the first place, we have 120 words. Keeping BAC fixed, we have 6 words Keeping BAD fixed, we have 6 words Now comes BAE (CDI, CID, DCI, DIC) after which BAEICD will come. Hence rank = 120+6+6+4+1 = 137 78. In group of 12 people, 4 speak on only Hindi, 5 speak only Tamil and the rest speak both Hindi and Tamil.. In how many ways can the 112 people be arranged in a row such that so are all those who speak only Hindi are together and so are all those who speak only Tamil. Further her all people should be able to converse with both their neighbours. Ans :_HBT_ or _TBH_ 79. If a three hree digit number xyz has only 5 factors then what is the last digit of sum of all factors of six digit number "xyzxyz" . Ans:4 , xyz = 625 then n whose expenditure 80. If Income ratio of A, B & C are 3:7:9 & their saving ratios are 3:1:4 the is maximum ? Ans: CBD 81. If Income ratio of A, B & C are 3:7:9 & their saving ratios are 3:1:4 the then n whose expenditure is minimum? Ans: A Direction for Q 82 & 83 - DOVAFONE has two monthly tariff plans for calling - details are given below Name of Plan P300

Fixed Monthly Charge ` 300

P100

` 100

Benefit 600 min free , after that `1 per min , fractional charge is applied 30 paisa per min, fractional charge is applied

Fractional Charge - If you talk in fraction of min charge would be in fraction of that tariff .eg if extra 1.5 min pay extra ``1.5 in P300 and 45 paisa or 1.66 min then `1.66 1.66 in P300 and 50 paisa in P100 82. If one person talks 500 min per month then which plan is better. Ans: P100 83. If one person talks N min per month and for him both plans cost the same. Then N = ? Ans: Not Possible

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3E LEARNING - MATHS BY AMIYA 500 CAT 2016 84. If ∗ W X W X and f(3) = 82 then what is f(5) = ?

Ans : f(x) = 1 + x^n ; f(3) = 1 + 3^4 = 82 , f(x) = 1 + x^4 f(5) = 1 + 5^4 = 626

85. If angles of a triangle are 30 30° , 60° and 90° then what is the ratio of it's in-radius in to circum radius Ans: r/R = cos 30 + cos 60 + cos 90 - 1=

√ ®

ª ª ®

√ª ®

86. which one is largest among all option options K a. 12 14 b. 13 15? c. 12K 14 d. 15 13? Ans: (a) 87. What is the sum of all external angles of a 8 sided concave polygon. Ans: 1800 ; 180(n+2) 88. If ABCD is a prallelogram. Point E and F are mid points of side BC & CD respectively then what is the area ratioo of Quard AGFD to that of parallelogram ABCD.

Ans :11:20 Solve it by assuming ing a square or rectangle coordinate

on

89. How many numbers are the in the set of first 1000 natural numbers which can be written as sum of two or more consecutive natural numbers. Ans: 990 , all except 2^n terms 90. Total number of integral solution of w^4 + x^4 + y^4 + z^4 = 1797 Ans: 0 , check divisibility by 7 91. If Y √123 ∗ 124 ∗ 125 ∗ 126 1 then what is the digital sum of N (N mod 9) Ans: 1 92. Total number of integral solution ofa³ + b³ + c³ = 43655 Ans : 0

93. If diagonals of a parallelogram are 30cm and 10 cm then among the options which could be sides of parallelogram a. 22 cm & 4 cm b. 20cm & 10 cm c. a & b both possible d. NoT

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3E LEARNING - MATHS BY AMIYA 500 CAT 2016 Ans: [b] - "a" cant be since we can not make 4cm with diagonals (as part of triangle) 94. If A,B& C three cities are in a highway. Distance between two cities A & B is 200 km and city C is 100 km from B & A both. From city "A" a man starts towards "B" with speed of 30 km/hr and on the same time another man start startss from B towards "A" with speed of 20 km/hr. After how much time they exchange their speeds (new speed of man from A and man from B becomes 20 kmph and 30 kmph respectively ) so that they meet at C Sol: After 2 hours 95. If a , b & c are in GP then roots of 0 . U 0 has a. Real b. Equal c. Imaginary d. (b) or (c) Ans: [c]

e. Not

96. If O is centre of the circle, angle DOC = 42° then what is the measurement of angle BFC Ans: 69

97. Sum of two positive integers A &B and its LCM is 455. Then how many unordered pairs of A & B are possible. Sol: Let number be h*x & h*y , h being HCF of numbers. then hx + hy + hxy = 455 Ans: 14; h(x+y+xy)=455 = 5*7*13 So , h = 1, 5, 7, 13 , 5*13 , 7*13 , 5*7 & 5*7*13 if h = 1 , x+y+xy = 455 ; (x+1)(y+1)= 456 sso 5 cases if h = 5 , x+y+xy = 91 ; (x+1)(y+1)= 92 so 2 cases if h = 7 , x+y+xy = 65 ; (x+1)(y+1)= 66 so 2 cases if h = 13 , x+y+xy = 35 ; (x+1)(y+1)= 36 so 3 cases if h = 65 , x+y+xy = 7 ; (x+1)(y+1)= 8 so 2 cases 98. If O is a point inside a parallelogram AB ABCD such that areas of ∆ABO ,∆ ∆BCO & ∆CDO are 12cm^2 , 15 cm^2 and 10 cm^2 then what is the area of ∆ AOD. Ans: 7 cm^2

99. If in ∆ABC ABC , AB = 6 cm , BC = 7 cm and CA = 8 cm , AD is an internal angle bisector of angle A such that point D lies on side BC then le length of AD = ? Ans :AD = 6 cm www.facebook.com/groups/MBAMathsByAmiya 3E Learning Maths By Amiya Ranchi | 63

3E LEARNING - MATHS BY AMIYA 500 CAT 2016 where AB = c, BC= a & CA=b í Zû ∗ ü ö ª ûü® úwhere ÷®

100. A34 56B is a 6 digit number in base 12 and when we write this in base 10 then it is divisible by 143 then A * B = ? Ans: 3 , (1,3) 101. If a , b, c, & d are sides of given quadrilateral ABCD then area of ABCD 1. a*b*c*d 2. √0 0∗.∗U∗V 3. 3√0 ∗ . ∗ U ∗ V

Ans: (2)

4. Z

P P4

∗

[^

102. For how many different (0 0 _ . _ U non zero digit ordered combinations (a,b,c) 0[ b 0[ 4 a

Sol:

Case 1 : b =1 , 8*7 = 56

103. In a trapezium ABCD , E & F are mid points of its diagonals and AB || CD . Find length of side CD if AB = 12 cm & EF = 4 cm. Ans: 20 cm. ( a-b/2=EF) 104. In a trapezium PQRS , S & T are mid points of its diagonals and PQ || RS . Find length of side RS if PQ = 12 cm &ST ST = 3 cm. Ans: 6cm or 18 cm 105. If [ x ] denotes greatest integer less than equal to x then 1 1 1 1 1 1 1 1 1 1 \ ]\ ]\ ]\ ] ⋯ ? 3 3 9 3 9 27 3 9 27 81 Ans: 0 106. Three students have each brought his father and mother for admission to a school. The admission head wishes tointerview the nine people one by one, taking care that no child is interviewed before its mother and no husband is interviewed before his wife. wife In howmany different ways can be interviews be arranged? Ans :8*9!/216 [in 2^3 ways father and child can be arranged] 107. In how many ways can we select two squares on a chessboard such that they share either a common side or a common vertex? Ans: 210

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3E LEARNING - MATHS BY AMIYA 500 CAT 2016 108. A person invests Rs.3000 in 3 months fixed deposit scheme of a bank at the rate of 13%. Due to some changes in policies, the rate of interest changed in every three months, after the first period, to 12%, 11% and 10% respectively. Assuming that the person withdraws the interest after every 3 months but continues deposit, how much more interest would that person have earned in oone ne year, if there was no change in the interest rate? a. 50 b. 45 c. 0 d. 180 Ans: [b] 12% , 11% and 10% means reduction of 1% , 2% & 3% =6 % cumulative change (quarterly) Change = 3000*6*1/100*4 = 45 admission ission in health course. The instructor 109. Three wives have each brought his husband for adm wishes to interview all six people one by one, taking care that no wife is interviewed before its husband. In how many different ways can be interviews be arranged? (1) 120 (2) 100 (3) 72 (4) 90 Ans: [4] 90 Total tal ways = Total Ways / ways in which pairs can attached = 6! / (2!*2!*2!) = 90 110. A passenger is planning a trip that involves three connecting buses that leave from Ambikapur, Bokaro and Chandanpur respectively. The first bus leaves Ambikapur every hour, beginning at 8:00 am, and arrives at Bokaro 2.5 hours later. The second bus leaves Bokaro every 20 minutes, beginning at 8:00 am, and arrives at Chandanpur 7/6 hours later. The third bus leaves Chandanpur every hour, beginning at 8:45 am. What is the least total amount of time the passenger must spend between buses if all buses keep to their schedules? a. 25 minutes b. 1 hour 5 minutes c. 1 hour 15 minutes d. 2 hours 20 minutes Ans: 65 min =1 hour 5 minutes Regardless of the time of departure from Ambikapur, arrival at Bokaro will be at 30 minutes past the hour. Buses leave Bokaro on the hour, and at either 20 or 40minutes past the hour. Therefore, the earliest a passenger from Ambikapur could leave Bokaro would be 40 minutes past the hour with a 10 minute wait betweenbuses.. The bus from Bokaro to Chandanpur takes 7/6 hours or 1 hour 10 minutes. A bus taken at 40 minutes past the hour, causing the passenger to have missedthe bus from Chandanpur by 5 minutes.. The passenger therefore has a 55minuteswait, and the least total amount of time the passenger must spend between buses is10 + 55 = 65 minutes or 1 hour 5 minutes. 111. The lengths of the sides CB and CA of a triangle ABC are 4cm and 6cm respectively and the angle C is 120°.. If the line CD bisects the angle C and meets AB at D, then the length of CD is b. 3cm c. 2.4cm d. None of these a. 4 cm

Ans: [c] In Triangle ABC üà ª®« ª®« x = √76 So AD= (2/5)*√76 UÌ% 60

Ë

? o W ∗√ =X

∗?∗o

°® º® õ® ®∗°∗º

; õ íî

, A kl , y = 2.4

Direct Formula = a*b/(a+b) = 4*6/(4+6) if we bisect 120 120° www.facebook.com/groups/MBAMathsByAmiya 3E Learning Maths By Amiya Ranchi | 65

3E LEARNING - MATHS BY AMIYA 500 CAT 2016

112. An alloy X consists of 10% Cadmium and 6% zinc and alloy Y consists of 5% Cadmium and 10% zinc. If he needs at least 14 kg of Cadmium and 14 kg of zinc for his h experiment. If alloy X costs 60 paisa per kg and alloy X costs 40 paisa per kg, What is the minimum cost he would occur to fulfil his requirement a. Rs.72 b. Rs.82 c. Rs.92 d. None of these Ans: [c] ; Let a & b are wt of alloy X & Y respectively 0.1a + 0.05b = 14 ....(1) 0.06a + 0.1b = 14 ....(2) a= 100 & b = 80 , so minimum cost = 92 113. What is the unit digit of 1 2 3 ⋯ . 9 a. 0 b. 1 c. 5 d. 9 Ans: [c] 1 9 is divisible by 10 so 2 8 and so on, only 5 left so unit digit = 5 = 5

114. If in a hotel Ram checked in between 1 and 2 o’clock and cheeked out in between 4 and 5 o’clock , if positions of minute hand and hour exchange and maintained same position then at what time did Ram check-out out from hotel? a. 4: 11: 15 b. 4: 11: 45 c 4: 12: 15 d. None of these Ans: [b] no need to solve check time it should be between 4:5 :.. to 4:10:00 115. If numerators of three fractions are in A.P. and their denominators are in G.P and common difference of the numerators is equal to the common ratio of the ddenominators enominators . The product of the first fraction and reciprocal of the second fraction is 6/5 and the product of the second fraction and reciprocal of third fraction is 15/8. If the, then the denominator of the third fraction is a. 9 b. 18 c. 27 d. cannot be determined Ans: [d] , 2/a ; 5/3a; 8/9a Assume numerators be a -d d , a &a+d and denominators be b/d . b& b*d in same order, from question we can get a= 5 , d=3 but cant get b , so cant be determined. 116. Two quadratic equations with positive roots have on onee common root. The sum of the product of all four roots taken two at a time is 143. The equation whose roots are the two different roots is – 14 45 0. The sum of all different roots is a. 20 b. 21 c. 22 d. 24 Ans: [b] , roots are 5,7,9 From – 14 45 0,, we can say two different roots are 9 & 5 , and sum of product of all four roots taken two at a time is 143 so 9*5 + 9*a + 5*a = 143, so a = 7 117. There are 10 pipes that are connected to a tank. Some of them are inlet pipes and the others are outlet pipes. Each of the fill pipes can fill the tank in 6 hours and each of the outlet can www.facebook.com/groups/MBAMathsByAmiya 3E Learning Maths By Amiya Ranchi | 66

3E LEARNING - MATHS BY AMIYA 500 CAT 2016 empty the tank completely in 4 hours. If all the fill pipes and outlet pipes are kept open, an filled tank gets emptied in 10 hours. How many of the 10 pipes are inlets pipes? c. 2 d. None of these a. 8 b. 4 Ans: [d] Not a possible case 118. In how many ways can we select two squares on a chessboard such that they share a common vertex and of same colour? Ans 98 = [4*1 + 24*2 + 36*4]/2 possible value of d e f ⋯ j

119. If A, B , C ,... Z are 26 positive numbers such that A+B+C+....+Z = 13, then find minimum Ans: 26^2/13 = 52

120. If A, B , C & D are sets of few natural numbers then how many ordered set (A,B,C,D) are possible such that g ∪ i ∪ k ∪ l m1,2,3, . . . ,10

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Maths By Amiya 500 CAT 2016 QUANT 500 By :- Amiya

2016

3E LEARNING RANCHI

WWW.3ELEARNING.COM

3E LEARNING - MATHS BY AMIYA 500 CAT 2016

Maths By Amiya 500 (2017 (2017-19) 1. Mohit calculated sum of first N natural number and he found sum is 337 and he knows he counted one number twice or missed one number. then find his minimum possible % error made by him. a. 3% b. 3.99% c. 3.69% d. 3.23% 2. The integers 1,2,….. 30 are written on a board. A person came and erased any two numbers say "a" & "b" and wrote a new number "a+b+2" this process is done by total 29 persons (including first one) then . What is the number left on the board at the end? = (3,5) , T3 = (7,9,11) , T(4) = (13,15,17,19) ..... Then what is the sum of all 3. If T1=(1) , T2= terms of T(10) 4. phi (n) is defined as number of co co-prime prime less than n. If ‘P’ is product of two different prime numbers, whose sum is 1200 then what is the max phi(M) {1,2,3,………..10000}, How many APs can be formed from the elements of S that 5. Consider the set S = {1,2,3,………..1000 start with 1 and end with 100000 and have minimum 3 terms?

6. Total number of integral solutions of 13x - 3y = 1000 for 100< x < 200 7. For how many integral "n" is

is an integer

8. If HCF , LCM and sum of two numbers are 6 , 15 and 23 then find their difference. 9. If 1 7 6 3 , then find the value of f(x - 1). 10. Find the area of the enclosed fig by | x- 5 | FGM and if the area ratio of ∎DEGF to that of ∎BCED is 1:8 then what is ∎DEGF to that of ∎BCED is 1:8 then what is the ratio of AF:FD:DB a. 7: 3:2 b. 2:3:7 c. 2:1:4 d. 1:2:3 e. NoT 197. If in ∆ ABC , points D, F & H are on side AB ; and points E, G & I are on side AC such that ∆ ABC , points D, F & H are on side AB ; and points E, G & I are on side AC such that BC || DE || FG || HI and AH :HF:FD:DB 2:3:5:7 then what is the ratio of BC : DE : FG : HI BC || DE || FG || HI and AH :HF:FD:DB 2:3:5:7 then what is the ratio of BC : DE : FG : HI 198.

qªª«Zªª«rªª«√ªª«⋯ q¬«Z¬«r¬«√¬«⋯

?

199. A number on being divided by ing divided by 6, 8 and 10 successively leaves the remainders successively leaves the remainders 5, 7 and 9 respectively. Find the remainder when the same number is divided by respectively. Find the remainder when the same number is divided by 120. 200. A number on being divided by 7 , 9 and 11 successively leaves the remainders 5, 7 and 9 respectively. Find the remainder when the same number is divided by 693 the remainder when the same number is divided by 693 the remainder when the same number is divided by 693 201.

∗q®¯∗Z®¯∗r®¯∗√®¯ ⋯ °∗q®°Z®°r®°√®⋯ ⋯

?

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3E LEARNING - MATHS BY AMIYA 500 CAT 2016

202. If

³ q7 3 ∗ Z7 3 ∗ r7 3 ∗ √7 ⋯&µ q7 3 ∗ Z7 3 ∗ r7 3 ∗ √7 … and X-

YR 0 then R ???

203. If P is the set of all possible products of numerical values of f P is the set of all possible products of numerical values of three consecutive dates three consecutive dates e.g.11*12*13 in calendar then , how many elements of P are not divisible by 6. 11*12*13 in calendar then , how many elements of P are not divisible by 6. 11*12*13 in calendar then , how many elements of P are not divisible by 6.

204. If 0 . U 30.U 0 . U ; a 1889 , b1888 then what is c if c is a what is c if c is a positive number. a. 1889 b. 1888 c. a or b d. NoT 205. 1333 1334 1333 3999 ∗ 1333 ∗ 1334 ? ? ?

206. If x-3 , x-4 & fx are factors of 4 & fx are factors of 0 ∗ 68 . the what is the the what is then value of f1 207. What will be the last three digits of the product 5 * 25 * 125 * 625 * 3125 * ………* 5^30

208. AC is the chord of a circle as shown in the fig, BD is perpendicular to AC. Find the length of chord AC if BD 4cm , CD 2cm & radius of circle cm & radius of circle 10 cm.

209. There are many less than 10000 which are perfect square an There are many less than 10000 which are perfect square and tenth place digit is odd. d tenth place digit is odd.

210. What is the probability of choosing a number is Natural number set so that number is a perfect square with same last two digits. perfect square with same last two digits. 211. What is the probability of choosing a number What is the probability of choosing a number whose last two digits are same and it whose last two digits are same and it becomes a prefect square. becomes a prefect square.

212. In a triangle ABC the length of altitude AD is 20 cm and BD:DC 1 : 5 D is point in ABC the length of altitude AD is 20 cm and BD:DC 1 : 5 D is point in between B & C . Find the length of a line segment EF parallel to AD if ratio of area o ∆EFC to that of ∆ABC is 8:15 ∆EFC to that of ∆ABC is 8:15. www.facebook.com/groups/MBAMathsByAmiya 3E Learning Maths By Amiya Ranchi | 19

3E LEARNING - MATHS BY AMIYA 500 CAT 2016

213. If ABCD a trapezium , in which CD=15 cm , AB = 3 cm & area of ∆DOC = 25 sq. cm then find the area of trapezium ABCD.

214. If ABCD a trapezium , in which CD=6 cm , AB = 2 cm & area of ∆ ∆ADC = 24 sq. cm then find the area of trapezium ABCD.

215. In a triangle ABC the length of an altitude AD is 8 cm, D is on side BC and this altitude divides the opposite side internally in the ratio 1 : 8. A line segment EF parallel to the altitude which bisects the area of the given triangle ABC (as shown in fig) then what is the ratio of AO:OF.

¸ ? ? ? 216. ∑3¹ 3¹K ·- 1 ∗ - 2¸ a. 2212 b. 2480 c. 2722

d. 2590

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3E LEARNING - MATHS BY AMIYA 500 CAT 2016

217.

218.

219.

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3E LEARNING - MATHS BY AMIYA 500 CAT 2016

220.

221.

222. 223. Which one is smallest a. √101 √96 b.√111 111 √106

c.√11 √6

d.√®ª d. ®ª √ªº

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3E LEARNING - MATHS BY AMIYA 500 CAT 2016

224. Which one is smallest b.√123 123 √73 a. √101 √99 225. Which one is largest a. √101 √99 b.√123 123 √73

c.√150 √50

d. 1 √199

c.√150 √50 d.√199 1 1

226. How many statements are How many statements are always correct always correctwhere a, m & n non zero real numbers always correctwhere a, m & n non zero real numbers I. 0» 3 0»∗3 II.0» ∗ 03 0»∗3 III.0» 3 03 » a.

Only one

b. only two b. only two

c. all three

d. None d. None

227. A car and a bus start from opposite end of a national highway. Car starts at 11:00AM A car and a bus start from opposite end of a national highway. Car and reaches opposite end at 2:OOPM same day and bus starts at 10:00AM and reaches opposite at 4:00PM same day same day . then at what time they meet each other. . then at what time they meet each other. 2 such that numerically ³ - & µ - 2 2 228. If X_B Y_B-2 such that numerically then n,B ??? a. 8,10 b. 10,10 b. 10,10 c. 10,8 d. NoT d. NoT

229. If X_B Y_B-2 such that numerically 2 such that numerically ³ - & µ - 2 2 then n,B ??? b. 10,10 b. 10,10 c. 10,8 d. NoT d. NoT a. 8,10 If 50!_10 N_50 then number of trailing 0's in N is ____ 230. If 50!_10 N_50 then number of trailing 0's in N is ____

231. If length of a rectangle is increased by 5.88% then what should be change in area to a rectangle is increased by 5.88% then what should be change in area to keep area constant. b. 5.43% decrease b. 5.43% decrease c. 5.56% decrease d. 6.66%decrease d. 6.66%decrease a. 5.55% decrease

Number of positive integral solutions ordered triplets of 9 bxyzb 20 232. Number of positive integral solutions ordered triplets of 9 bxyzb 20 a. 775 b. 657 c. 885 d. NoT

233. A shopkeeper uses a double pan balance to purchase and to sell his goods. To balance both the pans one has to put 20% more weight on left pan than right pan. If shopkeepers claims that he sells his goods on cost price then find maximum profit claims that he sells his goods on cost price then find maximum profit earned by him if he sold all his items what he purchased. sold all his items what he purchased.

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3E LEARNING - MATHS BY AMIYA 500 CAT 2016

234.

235.

236.

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3E LEARNING - MATHS BY AMIYA 500 CAT 2016

237.

238.

239.

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240.

241.

242.

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243.

244. A deck of card has 16 cards which include 4 Aces, 4 Kings, 4 Queens & 245. A deck of card has 16 cards which include 4 Aces, 4 Kings, 4 Queens & 4 Jacks. In How many ways we can arrange these 16 cards such that All Kings should be above All Queens. assume all are of different assume all are of different

246. A shopkeeper claims that he gives 10% discount on his cost price but uses X gm of weight instead of 1000 gm during weight instead of 1000 gm during sell of his goods and earn 12.5% profit, Then X ? sell of his goods and earn 12.5% profit, Then X ?

247. Container A has 10 lit of 30% acid, B has 10 lit of 40% acid & C has 10lit of 60% acid. If 5 lit of A is poured in to B then 5 lit from B to C then finally 5 lit of C is poured in to A. then what would be ratio of be ratio of acid is to water in final solution of A . 248. If 4A ? o 0 then x y ?

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If a car is traveling with the speed of 60 km/hr and after applying break it 0 km/hr and after applying break it 249. If a car is traveling with the speed of stops after 4 m, if the same care is moving with m, if the same care is moving with 120 km/hr then after applying km/hr then after applying break it stops after Xm. Then find X break it stops after Xm. Then find X

250. How many 9 digits numbers are possible by in which all digits are different and number is divisible by 9 a. 18*9! - 1 b. 2*9! b. 2*9! c. 17*8! D. NoT 2? 251. ( – 2 7 , *+,- ? ¿

252. ( 3 3 0 , *+,,- 1= À ?

253. ( 9 24 0 , *+ +,- 4 ? ? =

254. In ∆ ABC, AB4cm, BC6cm & AC5cm. Side AB and AC produced till E & F ∆ ABC, AB4cm, BC6cm & AC5cm. Side AB and AC produced till E & F respectively such that BECF1cm. AD median of respectively such that BECF1cm. AD median of ∆ ABC cuts line EF at G then what is ∆ ABC cuts line EF at G then what is the length of DG.

255. A, B & C start working on a project of BOOK MAKING, in which they have to type pages. They completed this project in 12 days. After completion of the project A , B & C received Rs 1200, Rs 2400 &Rs 3600 as their wages Rs 1200, Rs 2400 &Rs 3600 as their wages respectively, which is proportio , which is proportional to to number of pages they typed Lassuming they worked for equal numbers of hours per dayM. Then in how many days does A alone completes the working same hours a day. dayM. Then in how many days does A alone completes the working same hours a day. 256. If N is a 100 digits largest number and a perfect square of a natural number then which If N is a 100 digits largest number and a perfect square of a natural number then wh digit is 50th digit from left? digit is 50th digit from left? A. 0 B. 8 C. 9 d. 1

257. If A & B are points on circles as shown in fig, and line AB passes through centre of circles O & P. QO & RO are perpendicular on line AB, and AQ & BR meet at C then what is the area of ∆ABC if AO 5 cm & BP 4 cm AO 5 cm & BP 4 cm

258. ( 0. @ 3

· ¸

?

@ 0 **+,- choose best option b. 3 3 b b 2 c. 2 2

d.1 1 b b 0

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259. If two circles cut each other orthogonally then find length of common chord if radii of circles are 3 cm & 4 cm. radii of circles are 3 cm & 4 cm.

solved a quadratic equation and find roots as 3 & 4 & Sood finds roots of same Sood finds roots of same 260. Amiya solved a quadratic equation and find roots as 3 & quadratic equation as 1 & 6 then among options which could be a correct option if it is known that none of them did make mistake in writing coefficient of x^2 did make mistake in writing coefficient of x^2 but made mistake in either coefficient of x or constant term then among options which statement n either coefficient of x or constant term then among options which statement is correct a. Amiya makes mistake in coefficient of x and Sood makes mistake in constant term a. Amiya makes mistake in coefficient of x and Sood makes mistake in constant term b. Amiya makes mistake in constant term and Sood makes mistake in coefficient of x b. Amiya makes mistake in constant term and Sood makes mistake in coefficient of x c. Both of them made mistakes in constant term c. Both of them made mistakes in constant term d. NoT 261. Find the total number of terms in the expansion of Find the total number of terms in the expansion of 1 1 1 ? 1 … 1 262. If P 1 and [ 1 are the factors of are the factors of 1 ? . . . for distinct a and b find maximum value of ab and b find maximum value of ab

263. To complete a piece of work A alone takes 12 days more than A & B together & B alone takes 3 days more than A & B together if C alone takes 3 more days then A & C together then in how many days A, B & C can complete the same work if they work together then in how many days A, B & C can complete the same work if they work together. 264. If Á & Â are roots of equation are roots of equation 2 4 6 0 then what would be equation whose then what would be equation whose Ã Ä roots are & Ä

Ã

265. If EN is defined as euler of a number, which is number of co If EN is defined as euler of a number, which is number of co-primes less than equal primes less than equal to N and DN as positive divisor of a natural number N. to N and DN as positive divisor of a natural number N. Then what would be sum of all Then what would be sum of all possible values or E D1200 ??? possible values or E D1200 ??? 266. For how many integral “x” ,

is also an integer

267. If ratio of time taken to complete a piece of work by A, B, C & D alone is 1:2:3:4 and when they all work together take hen they all work together take12 days to complete the same work. If on every ODD to complete the same work. If on every ODD DATE only day only A&C work together and on every EVEN DATE only B & D wor DATE only day only A&C work together and on every EVEN DATE only B & D work together and they started on 01 together and they started on 01-FEB-2016 then on which date total work would be 2016 then on which date total work would be completed. 268. For how many natural “n” less than 100, 5- 6- 3 is divisible by 7

269. In ∆ABC , point D & E lie on BC & F lies on AC. If BD:BE:BC 1:2:3 & AF : FC1:1 then ∆ABC , point D & E lie on BC & F lies on AC. If BD:BE:BC 1:2:3 & AF : FC1:1 then what is the ratio of BO:OP:PF , if O & P are point of intersection of line AD & BF and AE & BF www.facebook.com/groups/MBAMathsByAmiya 3E Learning Maths By Amiya Ranchi | 29

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270.

how many different values of x , 1/x has only 4 reoccurring digits after decimal.i.e. 271. For how many different values of x , 1/x has only 4 reoccurring digits after decimal.i.e. 1/x 0.abcdabcdabcd.... Lfew could be same but not allM 1/x 0.abcdabcdabcd.... Lfew could be same but not allM

272. There are three boys Amar, Akbar & Anthony and three girls, Sita, Gita &Sheela. They Amar &Sita started a grou Amar &Sita started a group on 1st of Feb, Akabr joins them on 2ndfeb , Anthony on 4th Feb Gita joins them on 3rd Feb &Sheela on 5th Feb. On 1st , 3rd& 5th Feb total age of boys Feb total age of boys nd th were half of that of girls& on 2 & 4 Feb total age of boys were doub Feb total age of boys were double of that of girls. If age of Sheela is 120 yrs then who is youngest boy and what is his the age??? e of Sheela is 120 yrs then who is youngest boy and what is his the age??? e of Sheela is 120 yrs then who is youngest boy and what is his the age???

273. If red is painted on three sides of a cuboid of dimension 6cm*7cm*8cm and other three sides are painted white and then then by different cuts cuboid is divided in to 336 smaller cubes of volume 1 cubic cm. . If same coloured sides are adjacent to each other, cubes of volume 1 cubic cm. . If same coloured sides are adjacent to each other, then there are how many smaller cubes having minimum one red coloured side. then there are how many smaller cubes having minimum one red coloured side. 274. Ram wrote first 1000 numbers on a word sheet, and then he replaced all 2’s & 7 by 3 and saved the file. Then find the total number of 3’s in saved file. file. Then find the total number of 3’s in saved file.

275. Ram wrote first 1000 numbers on a word sheet, and then he replaced all 2’s & 7 by 3 and saved the file. Then find how many numbers have digit 3. and saved the file. Then find how many numbers have digit 3. 276. Ram wrote first 1000 numbers on a word sheet, and then Ram wrote first 1000 numbers on a word sheet, and then he replaced all 2’s & 7’s by 3 he replaced all 2’s & 7’s by 3 and saved the file. Then find how many numbers have only one 3. and saved the file. Then find how many numbers have only one 3.

277. Ram wrote all first 444 natural numbers side by side , from left hand side and created a big number N 123456..... 444 four hundred forty four big number N 123456..... 444 four hundred forty four. If Mohan del If Mohan deleted all 7's from N then find there are how many digits in N N then find there are how many digits in N 278. If Mark has Rs 5000 in his easy If Mark has Rs 5000 in his easy-recharge wallet, an online mobile recharge portal. Find recharge wallet, an online mobile recharge portal. Find the maximum amount of recharge, which can be possible with his current balance and cash backs, under cash back scheme of 20% cash back on recharge of any amount h back scheme of 20% cash back on recharge of any amount more than or equal to Rs 100 Lassume he is not adding extra amount from any other source except cash backs & he can recharge any integral amountM source except cash backs & he can recharge any integral amountM 279. For how positive integral X For how positive integral X less than 100, X^3 - X^2 is a perfect square. X^2 is a perfect square.

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280. If there are 3 black balls, 6 white balls and 5 green balls. Find the minimum number of picks required to get at number of picks required to get at-least one ball of each colour always. LAssume always. LAssume one can pick only one ball at a timeM one can pick only one ball at a timeM

281. How many obtuse angled integra How many obtuse angled integral sided isosceles triangles are possible if unequal side es are possible if unequal side is 8 cm 282. How many obtuse angled integral sided isosceles triangl How many obtuse angled integral sided isosceles triangles are possible if one side is 5 es are possible if one side is 5 cm Find minimum value of expression 8x 16x 1 283. Find minimum value of expression 284. Find minimum value of expression Find minimum value of expression 4 sec θ sec θ 1

Find the total number of solution pairs of real x,y for below given equation 285. Find the total number of solution pairs of real x,y for below given equation 2 8 15A 10A A 4 6 286. Find the total number of solution pairs of real x,y for below given equation Find the total number of solution pairs of real x,y for below given equation 3 6 72A 4A A 3 4

287. If 3x È 12 then x x ? x = ?

School. 10%,15%, 20%, ,25% & 30% of branch seats Direction: There are only 5 branches in a B Direction: There are only 5 branches in a B-School. 10%,15%, 20%, ,25% & 30% of branch seats are vacant and it is known that each branch has minimum 1/7th of total PGP seats , are vacant and it is known that each branch has minimum 1/7th of total PGP seats , If total vacant seats are x % of total PGP seats then vacant seats are x % of total PGP seats then 288. Find minimum value of x Find minimum value of x Find maximum value of x 289. Find maximum value of x 290. For how many natural numbers less than equal to 100, such that last two digits of its 8th power and 9th power are same. power are same. 291. For how many natural numbers less than equal to 100, such that last three digits of its 5th power and 8th power are same. r are same. 292. 123123123 ...... a 38 digits number mod 13 ???? 123123123 ...... a 38 digits number mod 13 ???? 293. There are how many two digits numbers are possible such that their last two digits of 23rd& 25th powers are same. powers are same. 294. Raman is an intelligent mathematician. He has Rs Raman is an intelligent mathematician. He has Rs830 in his Paytm account. in his Paytm account. Find the maximum amount of transaction transaction which can be possible with his current balance and which can be possible with his current balance and cash backs, under cash back scheme of cash backs, under cash back scheme of 14.28% cash back on recharge of any amount % cash back on recharge of any amount more than or equal to Rs14 14 Lassume he is not adding extra amount from any other Lassume he is not adding extra amount from any other source except cash backs & he can urce except cash backs & he can do transaction in paisa too M www.facebook.com/groups/MBAMathsByAmiya 3E Learning Maths By Amiya Ranchi | 31

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Patna, Patiala&Pathankotis7:3:2 & Ratio of number of Pathankotis7:3:2 & Ratio of number of 295. If population ratio of Patna males in Patna, Patiala&Pathankotis 6:2:1 Pathankotis 6:2:1 then which city has maximum female which city has maximum female population and which city has minimum population population and which city has minimum population ? 296. Among the options which one is Among the options which one is largest? a. 13= 18 b. 16 16 19 c. 16 18

d.13 13= 19

297. Arrange A, B & C in ascending order , if A 123^45678 , B 12345^678 & C1234^5678

298. Arrange A, B , C & D in ascending order , if A 1234^5 , B 123^45, C12^345 & D1^2345

Direction :Nakistan is a small country, which has 4 states. Name of states are A,B,C&D and Direction :Nakistan is a small country, which has 4 states. Name of states are A,B,C&D and population of each states is minimum 1/7th of total population of Nakistan. If sex ratio of states of total population of Nakistan. If sex ratio of states A,B,C & D are 600 , 700, 800 & 900 then A,B,C & D are 600 , 700, 800 & 900 then 299. Find minimum possible sex ratio of Nakistan Find minimum possible sex ratio of Nakistan a. 600.17 b. 678 678.61 c. 516.79 d. NoT 300. Find maximum possible sex ratio of Nakistan Find maximum possible sex ratio of Nakistan a. 818.18 b. 828.87 b. 828.87 c. 806.89 d. NoT If John distributed his entire pension into his wife Mona, son William, d 301. If John distributed his entire pension into his wife Mona, son William, daughter Kate, girl-friend Sona and her daughter Sara. If it is known that Mona gets minimum 1/6 friend Sona and her daughter Sara. If it is known that Mona gets minimum 1/6th . William gets minimum 1/8th , Kate gets minimum 1/10th , Sona gets mi , Sona gets minimum 1/6th& Sara gets minimum 1/4th of Ram’s pension. Saving % of their individual sharing of Mona, of Ram’s pension. Saving % of their individual sharing of Mona, William, Kate, Sona& Sara is 30%, 40%, 40% , 50% & 60% .If total saving of all five is X% of total pension of Ram, then among option which could not be val of total pension of Ram, then among option which could not be value of X. ue of X. a. 44.15 % b. 45.83% b. 45.83% c. 48.32% d. 48.89% d. 48.89% 302. There are many natural numbers are possible which is less than 400000 and divisible by 3 but not have any of digits from m 6, 7,8 , 9 < by 3 but not have any of digits from m 6, 7,8 , 9 < 303. How many four digits can be made from the digits m1,2,3,4< How many four digits can be made from the digits m1,2,3,4< that are perfectly divisible that are perfectly divisible by 3? repetition allowed by 3? repetition allowed 304. If Speed of Ram is 20 kmph then he reaches office from home 20 min before his usual time, and if his speed is 10 kmph then he reaches office from home 40 min after his usual time then find distan usual time then find distance between home to office. 305. Raman bought a combined total of 25 bought a combined total of 25 mobiles and tabs. He marked up the . He marked up the mobiles by 20% on their cost price while each while each tabs was marked up by Rs. 2000. He was able to sell was marked up by Rs. 2000. He was able to sell 75% of the mobiles and 2 and 2 tabs and make a profit of Rs. 49,000. The remaining and make a profit of Rs. 49,000. The remaining mobiles and 3 tabs could not be sold by him. Find his overall profit or loss if he gets no return on could not be sold by him. Find his overall profit or loss if he gets no return on unsold items and it is known that a unsold items and it is known that a tabs costs 50% of a monitor. www.facebook.com/groups/MBAMathsByAmiya 3E Learning Maths By Amiya Ranchi | 32

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Find the distance in km, for which if we increase our speed by 20 km/hr we if we increase our speed by 20 km/hr we 306. Find the distance in km, for which reach the destination 2 hours earlier but when we reduce our speed by 10 km/hr we take 3 hours more to reach the same destination. we take 3 hours more to reach the same destination.

307. Find the actual time in hour actual time in hour, to cover a distance for which if we increase our spe for which if we increase our speed by "a a" km/hr we reach the destination b" hours earlier but when we reduce our speed by km/hr we reach the destination "b hours earlier but when we reduce our speed by "cc" km/hr we take "d km/hr d" hours hours more to reach the same destination. [4^P[^ [4^P[^ [4^P[^ [4^P[^ a. P^[4 b. P^[4 c. P^[4 d. P^[4 e. NoT 308. When a man covers 2/3rd of distance by car and rest by bus then he takes 12 hours to cover the distance, but if he takes 3/4th of distance by cover the distance, but if he takes 3/4th of distance by car and rest by car then takes 10 and rest by car then takes 10 hours, then find total time to cover same distance, when he hours, then find total time to cover same distance, when he covers half of the distance by covers half of the distance by car and rest by bus.

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If a thief flew with constant speed of "60 km/hr" in a straight road, Direction :If a thief flew with constant speed of "60 km/hr" in a straight road, Direction : and after 2 hours a police and his dog started to chase the thief with speed of "80 km/hr" and "100 km/hr" respectively km/hr" and "100 km/hr" respectively. In this complete journey, Dog touches the Thief . In this complete journey, Dog touches the Thief and comes and touches the Police and move towards Thief and continues the proces and comes and touches the Police and move towards Thief and continues the process, until The Thief is caught. 309. Find total distance travelled by Dog in this process Find total distance travelled by Dog in this process

310. Find total distance travelled by Dog in Find total distance travelled by Dog in this process towards police. this process towards police. 311. Find total distance travelled by Dog in this process towards thief. Find total distance travelled by Dog in this process towards thief.

1 *0-3 … 1 *0-431 *0-44 ;ÌV 7 ? ? ? 312. 1 *0-11 *0-21

313. A boat takes total 4 hours to cover 22 km upstream and 28 km downstream and takes total 6 hours to cover 33 km upstream and 42 km downstream then find speed of hours to cover 33 km upstream and 42 km downstream then find speed of stream.

314. In a 1000 m race A beats B by 250 m and in 1500 m race A beats C by 250 m , then in B Vs C , who win the race and by how much meter if length of track is 2520 m. Vs C , who win the race and by how much meter if length of track is 2520 m. 315. For how many integral values of X integral values of X , |X-1||X2||X-3||X4| b 70 3||X4| b 70

316. Which one is true

¿Ê

? Ë A. W?X ¿Ê

? Ë B. W?X

¿Í

? ¿Ê > WKX ¿Í

? ¿Ê b WKX

317. If Josephus leaves his home for office at a fix time every day , but he reaches his office at different time due to different speeds. different speeds. If his average speed is 60 kmph he reaches If his average speed is 60 kmph he reaches office at 10:45AM , but when his average speed is 40 kmph he reaches at 10:50 AM, what should be his average speed to reach office at 10:47 AM. should be his average speed to reach office at 10:47 AM. 318. If ratio of incomes of A, B & C I'd 5:4:3 & savin If ratio of incomes of A, B & C I'd 5:4:3 & savings ratio of A, B & C is 2:3:4. gs ratio of A, B & C is 2:3:4. If ratio of A's income to C's saving is 10:9 then find the ratio of total expenditure to total savings of all three 319. What would be last 4 digits of What would be last 4 digits of 38 in base 2

320. There are three most active groups on facebook, e three most active groups on facebook, CAT PREPRATION PREPRATION CP, GHANTA CAT GC & MBA. Mentors organised four events named . Mentors organised four events named Chotu Quant Chotu Quant, Motu Quant, Patlu Quant & All Quant. In Chotu Quant, all members of CP & GC participated and average weight of all members of this event is 42 kg In Motu Quant, all members of CP & MBA participated and average weight of all members of CP & MBA participated and average weight of all members of this event is 30 kg is 30 kg In Patlu Quant, all members of MBA & GC participated and average weight of all members of this event is 60 kg is 60 kg www.facebook.com/groups/MBAMathsByAmiya 3E Learning Maths By Amiya Ranchi | 34

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& if In ALL Quant, all members of CP, GC & MBA participated and average weight ted and average weight & if In ALL Quant, all members of CP of all members of this event event is X kg

Then what is the range of X. Then what is the range of X. Lassume Facebook has "one member one group" policyM Lassume Facebook has "one member one group" policyM

321. If Raman left his room at X AM and reaches office at Y PM of the same date and Mohan left his room at X AM and reaches office at Y AM of same date. If both stay together and and reaches office at Y AM of same date. If both stay together and work together and time taken by Mohan to reach office is square of that by Raman then what is the ratio of Average Speed of Raman from home to office to that of Mohan. what is the ratio of Average Speed of Raman from home to office to that of Mohan.

322. Raman left his room at 7:00 7:00 AM and reaches office at 12 PM of the same date and PM of the same date and Shobhit left his room at 8:00 8:00 AM and reaches office at 11 AM of same date. If both stay AM of same date. If both stay together and work together together and work together at same place then at what time Shobhit overtakes Raman then at what time Shobhit overtakes Raman.

323. Shobhit & Bitan planned an infinite round race on a circular track of length 100 km. planned an infinite round race on a circular track of length 100 km. Both started race at same point of track, but Bitan cheated Shobhit and started half an hour before the actual race timing and choose Swift , whose speed is 40 km/hr. Shobhit who is a good guy started race at actual time but choose Benz whose speed if 140 km/hr d guy started race at actual time but choose Benz whose speed if 140 km/hr but by mistakes he moves in anticlockwise direction. If at 9:30 AM Bitan reaches starting point for the first time then at what time their 4th meeting would happen if they maintained constant speed throughout the race. ed constant speed throughout the race.

324. Sandeep Patra is a very handsome but a shy guy. Whenever he sees a girl he doubles his speed but start moving in the opposite direction of direction just before seeing girl. If on a day he starts moving with speed If on a day he starts moving with speed of 1 m/s from his home and he sees a girl after of 1 m/s from his home and he sees a girl after every 1sec, then find how far he is from his house just after 11sec when he started. every 1sec, then find how far he is from his house just after 11sec when he started. 325. There is a regular nonagon, whose vertices are alphabets of words DANGEROUS in nonagon, whose vertices are alphabets of words DANGEROUS in same order then what is the value of same order then what is the value of ∠ NGO in degree ???? If ABCDEFGH is a regular octagon then find angle ∠ CDG in degree 326. If ABCDEFGH is a regular octagon then find angle If ABCDEFGHIJ is a regular decagon then find ∠ EAI in degree 327. If ABCDEFGHIJ is a regular decagon then find

328. Find the sum of all internal angles at red dots of all four figures Find the sum of all internal angles at red dots of all four figures

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^...^1 then what is the least value of N natural number what is the least value of N natural number 329. If M 17^16^15^...^1 then for which M mod N is neither o nor 1. Lmod is remainder functionM for which M mod N is neither o nor 1. Lmod is remainder functionM

age of 11 members committee on 31st Dec 2014 was 2014 was 30.27. On 330. If the approx average age of 1st Jan 2017 Ram who is Ram who is one of the member quits the committee and then approx quits the committee and then approx average becomes 29.5. If it is known that . If it is known that , to find average only integral age if 11 years to find average only integral age if 11 years 11 months or 11 years 1 months then in both cases considers as 11 years only is considered then find in which year Ram was bor considered then find in which year Ram was born.

331. Two cities X and Y lie on a straight line. Two men P and Q left simultaneously from same city X towards Y at same time. Both reaches Y and immediately turn around and move towards X. On reaching X, again they turn around and move towards Y. This movement continues indefinitely. nt continues indefinitely. If the distance between X and Y is 60 km and speed of If the distance between X and Y is 60 km and speed of P and Q are 20 Km/hr & 10 Km/hr respectively P and Q are 20 Km/hr & 10 Km/hr respectively . Find the total number of OVERTAKES Find the total number of OVERTAKES in 120 hour after start. 332. Two cities X and Y lie on a straight line. Two men P and Q left s Two cities X and Y lie on a straight line. Two men P and Q left simultaneously from imultaneously from same city X towards Y at same time. Both reaches Y and immediately turn around and move towards X. On reaching X, again they turn around and move towards Y. This movement continues indefinitely. movement continues indefinitely. If the distance between X and Y is 60 km a If the distance between X and Y is 60 km and speed of P and Q are 20 Km/hr & 10 Km/hr respectively P and Q are 20 Km/hr & 10 Km/hr respectively Whenever they meet or overtake they Whenever they meet or overtake they shake hands. Find the total number of handshakes in 60 hour after start shake hands. Find the total number of handshakes in 60 hour after start 333. In a right angled triangle with integral sides, smallest side is four times of difference of In a right angled triangle with integral sides, smallest side is four times of differenc other two sides and sum of all sides is 120 then find area of this triangle other two sides and sum of all sides is 120 then find area of this triangle

334. Two cities Rampur and Sitapur lie on a straight line. Two men A and B left simultaneously from Rampur and Sitapur towards each other. A reaches Sitapur and immediately turns around and move towards Rampur. On reaching Rampur, again he around and move towards Rampur. On reaching Rampur, again he turns around and move towards Sitapur. This movement continues indefinitely. B also travels in a similar manner. travels in a similar manner. The distance between Rampur and Sitapur is 120 km and The distance between Rampur and Sitapur is 120 km and speed of A and B are 40 km/h speed of A and B are 40 km/hr & 10 km/hr respectively. If both started together then in If both started together then in 24 hours find the total number of interactions between them. 24 hours find the total number of interactions between them. 335. Two cities Rampur and Sitapur lie on a straight line. Two men A and B left simultaneously from Rampur and Sitapur towards each other. simultaneously from Rampur and Sitapur towards each other. A reaches Sitapur and A reaches Sitapur and immediately turns around and move towards Rampur. On reaching Rampur, again he turns around and move towards Sitapur. This movement continues indefinitely. B also travels in a similar manner. travels in a similar manner. The distance between Rampur and Sitapur is The distance between Rampur and Sitapur is 60 km and speed of A and B are 20 km/hr & 10 km/hr respectively speed of A and B are 20 km/hr & 10 km/hr respectively. If both started together then in If both started together then in 12 hours find the total number of interactions between them. 12 hours find the total number of interactions between them.

336. Two cities X and Y lie on a straight line. Two men P and Q left simultaneously from X and Y towards each other. P reaches Y and immediately turns around and move towards ards each other. P reaches Y and immediately turns around and move towards X. On reaching X, again he turns around and move towards Y. This movement continues indefinitely. Q also travels in a similar manner. indefinitely. Q also travels in a similar manner. The distance between X and Y is 1000m The distance between X and Y is 1000m and speed of P and Q are 200m/s & 800 m/s respectively are 200m/s & 800 m/s respectively. Whenever they meet or Whenever they meet or overtake they shake hands. overtake they shake hands. www.facebook.com/groups/MBAMathsByAmiya 3E Learning Maths By Amiya Ranchi | 36

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337. If in a test there are 5 objective question, each having 4 options with only one option as correct answer. If 1 is awarded for correct answer and no penalty option as correct answer. If 1 is awarded for correct answer and no penalty for wrong or non-attempt. If it is known that 3 is passing marks of this test then , In how If it is known that 3 is passing marks of this test then , In how many ways one can attempt this test so that he passes the test. many ways one can attempt this test so that he passes the test.

338. When I started my today's journey from Hazaribagh to Ranchi. I checked first mile stone it showed Ranchi 100 km , after 40 min I checked another mile stone and found anchi 100 km , after 40 min I checked another mile stone and found Ranchi XY km and after another 20 min when I checked mile stone I realised Ranchi YX km. If I managed a constant speed through my journey, please help me to know speed of my car , since speedometer is not working edometer is not working 339. Mango bite offer - Return 3 empty rappers and get 1 mango bite free Return 3 empty rappers and get 1 mango bite free. If cost of one Return 3 empty rappers and get 1 mango bite free mango bite is Rs 1 and i have Rs 100 then maximum how many mango bite i can eat. mango bite is Rs 1 and i have Rs 100 then maximum how many mango bite i can eat. 340. If P & P2 both are prime numbers P>3 then how many different values of R be If P & P2 both are prime numbers P>3 then how many different val possible if R LP*P2M mod 9 R LP*P2M mod 9 341. ÐÑ Ò Ó Ô , then find PDR , if P,Q & R are distinct prime numbers , then find PDR , if P,Q & R are distinct prime numbers , then find PDR , if P,Q & R are distinct prime numbers

Direction Direction 344 344 - 345 345 :Number of Hair fall is directly proportional to TQ Tension Quotient and TQ is directly proportional to square of pe TQ is directly proportional to square of person integral age ignoring months and days. If at rson integral age ignoring months and days. If at the time of birth a person is considered as tension free 0 TQ and person has 100,000 hairs. the time of birth a person is considered as tension free 0 TQ and person has 100,000 hairs. If at the age of 4 number of hairs a person has is 77,500 then at the age of 4 number of hairs a person has is 77,500 then Total number if hairs at the age of 8 is ____ 342. Total number if hairs at the age of 8 is ____ What is the minimum age of complete baldness 343. What is the minimum age of complete baldness Find ab if a & b are positive integer and a³ - 1 b² 1. 344. Find ab if a & b are positive integer and Find the least value of n for which n output of below given sum is an integer 345. Find the least value of n for which n output of below given sum is an integer n/1*2*3 n/2*3*4 n/3*4*5 ... n/7*8*9 n/1*2*3 n/2*3*4 n/3*4*5 ... n/7*8*9 346. 1³2³3³4³...10³ 1357....n 1357....m, Then find integral 1³2³3³4³...10³ 1357....n 1357....m m & n 347. 1² 4² 7² 10² ..... 40² ??? 1² 4² 7² 10² ..... 40² ??? 348. If average of 11different numbers x1 , x2, x3. .... , x11 is X then what would be average in terms of X if all 11 numbers are multi in terms of X if all 11 numbers are multiplied by 2 then decreased by X. plied by 2 then decreased by X. 349. For different positive integral a, b & c For different positive integral a, b & c ; a² b² c³ then find minimum value of c a² b² c³ then find minimum value of c 350. If N m² , where m is a natural number more than 99 but less than 1000, then for how values of m , N & m are having same last two digits values of m , N & m are having same last two digits 351. Ram and Shyamali each has a fair coin. Ram tossed his coin 5 times and got 4 heads and one tail , Shyamali also tossed her coin 5 times and got 3 heads and 2 tails one tail , Shyamali also tossed her coin 5 times and got 3 heads and 2 tails. One day both meet and both tossed their coins once. What is the probability of getting dif meet and both tossed their coins once. What is the probability of getting different outcomes on each coins ??? outcomes on each coins ??? www.facebook.com/groups/MBAMathsByAmiya 3E Learning Maths By Amiya Ranchi | 37

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HCF of sum of all sides of an integral sided right angled triangle is ________ ??? 352. HCF of sum of all sides of an integral sided right angled triangle is ________ ???

HCF of product of all sides of an integral sided right angled triangle is ________ ??? 353. HCF of product of all sides of an integral sided right angled triangle is ________ ???

354. If a ball is dropped from a height of 2000 m and If a ball is dropped from a height of 2000 m and it bounces back but looses 1/9 of it bounces back but looses 1/9 of height after every bounce then find total distance covered by ball till it comes to rest or near to rest 355. Find area of graph in side x² y² 16 but outside |x||y|4 in items of pi Find area of graph in side x² y² 16 but outside |x||y|4 in items of pi

356. Find maximum value of n if n & m are Find maximum value of n if n & m are natural numbers and 90! 20!^n * m 90! 20!^n * m

357. There are how many natural numbers less than equal to 100 , whose product of all factors are square of the number factors are square of the number 358. Number of trailing zeros in C512, 32 Number of trailing zeros in C512, 32 ; Cn,r n!/r!*n-r!

359. There are how many natural There are how many natural numbers less than 1000 , has only odd number of factors numbers less than 1000 , has only odd number of factors total number of factors are odd total number of factors are odd

360. John and Shaw started running from same point , at same time in same direction. John John and Shaw started running from same point , at same time in same direction. maintained a constant speed of 40 km/hr maintained a constant speed of 40 km/hr. But Shaw started with 5km/hr and in ev But Shaw started with 5km/hr and in every next hour he increase his speed by 10 km/hr. next hour he increase his speed by 10 km/hr. Then find after how time from start Shaw Then find after how time from start Shaw will catch John

361. If average of 10 consecutive increasing multiple of 8 is 324 then find 4th smallest term among these 10 terms

362. If N is a two digit largest number whi If N is a two digit largest number which is a factor of 35^10 - 17^10 then N mod 7 ??? 17^10 then N mod 7 ???

Find the sum of all terms of 10th row of below given series 363. Find the sum of all terms of 10th row

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 ....................................... .............................................

364.

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365.

internal angles at vertex of given figure 366. Sum of all internal angles at vertex of given figure

367. If in a row Jhon is 23rd from right and Tina is 32nd from left end and there are 5 persons between then , what is the difference between maximum and minimum possible persons in the row 368. If X² YX , XX² AYBX, , XXX² AAYBBX, XXXX² AAAYBBX. Then AB Then AB - Y ??? Where X, XX, XXX are 1, 2, 3 digit numbers so rest are Where X, XX, XXX are 1, 2, 3 digit numbers so rest are

369. If ab bc ca 27 then total number of unordered positive integral solution is ____ then total number of unordered positive integral solution is ____ then total number of unordered positive integral solution is ____ 370. For how many natural N , For how many natural N , N 32^2 is divisible by N4 371. 3 ∗ 9Ê ∗ 27Í ∗ 81 81× … … . ?

372. If ABC & BCA are two three digits perfect squares where A, B & C are different digits then ABC ??? 373. There how many numbers less than 1,00,000 whose sum of digits is 3 There how many numbers less than 1,00,000 whose sum of digits is 3

374. If Sita and Gita daily jog from their home to If Sita and Gita daily jog from their home to park and park to home and then park and park and park to home and then park and so on for two hours, park is 10 km from their home. If they live together and both stats www.facebook.com/groups/MBAMathsByAmiya 3E Learning Maths By Amiya Ranchi | 39

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at 7:00 AM, and speed of Sita is 20 km/hr and that of Gita is 30 at 7:00 AM, and speed of Sita is 20 km/hr and that of Gita is 30 km/hr then when km/hr then when Gita overtakes Sita for the first time after ita for the first time after start.

Among the options select correct statements 375. Among the options select correct statements 1. Sum of three different primes can't be divisible by 6 1. Sum of three different primes can't be divisible by 6 2. Product of three different primes can't be divisible by 6 2. Product of three different primes can't be divisible by 6 3. Last two digits of all primes less than 100 is 50 3. Last two digits of all primes less than 100 is 50 4. In an integral sided right angled triangle all sides can't prime. ght angled triangle all sides can't prime.

376. There are how many different integral sided right angled triangles are possible whose There are how many different integral sided right angled triangles ar one side is 25 unit ¿ ¿ ¿ 377. s8 q8 Z8 r8 √8 … ?? ¿

¿

378. If √

√

√3 then Í ?

379. In how many ways we can rearrange the word In how many ways we can rearrange the word NAGIN such that no vowels be together. NAGIN such that no vowels be together. 380. Find the length of line segment between axes line of a line whose equation is 4x-3y Find the length of line segment between axes line of a line whose equation is 4x 12 381. If A*B*C*D*E*F 60 , where A,B,C,D & E are different integers then what is the maximum value of ABCDEF maximum value of ABCDEF

382. Total number of integral ordered pair solutions for of integral ordered pair solutions for A b 64 64 is a. 175 b. 163 c. 150 d. NoT

383. What if the value of c to get maximum value of What if the value of c to get maximum value of 0 ∗ . ∗ U ? under condition abc under condition abc 108 and all a,b&c are positive numbers. 108 and all a,b&c are positive numbers. 384. If in a ∆ABC, D is midpoint of BC , E is ∆ABC, D is midpoint of BC , E is midpoint of BD , F is midpoint of BE and G is midpoint of BD , F is midpoint of BE and G is midpoint of AF then what is the ratio of area of midpoint of AF then what is the ratio of area of ∆BGF to that of ∆ABC ∆BGF to that of ∆ABC

385. What could be minimum value of N , which COULD satisfy What could be minimum value of N , which COULD satisfy Y 0 . U V where a,b,c & d are distinct distinct natural numbers

386. If few students of section A of PGP transfer to section B then ration of number of nts of section A of PGP transfer to section B then ration of number of students of A to that of B 3:7 but if few students of section B of PGP transfer to section A then ration of number of students of A to that of B 5:2 A then ration of number of students of A to that of B 5:2, then find minimum number , then find minimum number of total students of section A & B. al students of section A & B. 387. If 10 lit of pure alcohol is replaced by 50% of 2 lit alcohol and this process is repeated one more time then find the % of alcohol in final solution. one more time then find the % of alcohol in final solution.

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Total number of terms after expansion of 1 388. Total number of terms after expansion of 389. Total number of terms after expansion of Total number of terms after expansion of A Q

390. How many perfect squares less than 1000 would give remainder 3 when divided by 7 How many perfect squares less than 1000 would give remainder 3 when divided by 7 How many perfect squares less than 1000 would give remainder 7 when divided by 9 391. How many perfect squares less than 1000 would give remainder 7 when divided by 9

392. If C is circum-centre & G is centroid of a G is centroid of a triangle whose sides are 7 , 24 and 25 cm then e 7 , 24 and 25 cm then what is the length of line segment what is the length of line segment CG 393. There are how many days in between next palindromic date DDMMYYYY and last palindromic dateDDMMYYYY if today is 14062016 palindromic dateDDMMYYYY if today is 14062016 394. Find the least value of n more than 4 for which 234567.... n is which 234567.... n is a perfect square a. 15 b. 24 c. 25 d. 26

395. Ram and Mohan started their journey from two opposite extreme end of a tunnel. If Ram started his journey at 8 :00 AM with speed 60 km/hr and Mohan at 7:00 with Ram started his journey at 8 :00 AM with speed 60 km/hr and Mohan at 7:00 with speed 40 km/hr. When both met to each other it is found that one of them covers double distance of other then find the different between maximum or minimum possible length of tunnel. 396. Total number of positive ordered solution of abcd Total number of positive ordered solution of abcd 10 Í ÍÍ Í Í

7

397. Unit digit of

7 is _____ is _____

6666. . . . 398. What is the value of 1.6666 a. 2.66666..... b. 2.565656....... b. 2.565656.......

399. Zx rx √x ⋯ 3xx then x ?

c. 2.77777.....

d. NoT d. NoT

400. What is the minimum value of value of |x1| |x2||x3|

401. What is the minimum value of value of |x| - |x1| |x2|-|x3||x4|

402. If LCM of first N natural numbers is "L" and that of first "N2" natural number is "2*L" then less than 100 how many different N are possible then less than 100 how many different N are possible 403. If 130 20. U V 120. 8.U 40V , 0 ∗ . ∗ U _ 0 then then 4^ ? P[

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24 23A 6A 11Q 2Q 4 42 then 404. If for real x, y & z ; 9 A Q ? 405. What would be remainder What would be remainder when 19

ÊÊ

is divided by 1200

2K Ë ? 406. If 3 9 then

407. Maximum how many vertices could be common in a regular dodecagon 12-sided Maximum how many vertices could be common in a regular dodecagon polygon and regular nonagon 9 nonagon 9-sided polygon

408. Find the maximum value of a2*b3*c4 if 2a3b4c 7 and a , b & c are value of a2*b3*c4 if 2a3b4c 7 and a , b & c are positive numbers 409. Find the Maximum value of a1*b2*c3 if a b c 3 and a , b & c are positive numbers

410. For natural number m, n, x & y if For natural number m, n, x & y if m*x n*y 100 then what would be last digit of m*x n*y 100 then what would be last digit of maximum value of » ∗ A 3 ? ? ?

411. If in a race A beats B by 100 m , B beats C by 100 m and in the same race if A can beats C by "X" m then what is the range of "X" by "X" m then what is the range of "X" a. 100 ³ 200 b. 100 b ³ 200 c. 100 ³ b 200 d. 100 b ³ b 200 e. NoT 412. If abcabc is a 6 digit number and has If abcabc is a 6 digit number and has 20 positive divisors then abc ? positive divisors then abc ?

413. Above image is actual time zone clocks Above image is actual time zone clocks and all are showing their local time all are showing their local time of a same time. If a flight departs from Central at If a flight departs from Central at 02:00 local time at central to city X and arrives at 10:00 and arrives at 10:00 local time at city X and then depart from city X at 11:00 local time at city X to Central and arrives at 09:00 local time at central on same day. Then CITY X is _______ arrives at 09:00 local time at central on same day. Then CITY X is _______ 414. If given figure is a 12 sided regular dodecagon then find angle X in degree is a 12 sided regular dodecagon then find angle X in degree is a 12 sided regular dodecagon then find angle X in degree

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In given fig if AB2unit, BC3unit, CDCA4unit and DA5 unit then find BD 415. In given fig if AB2unit, BC3unit, CDCA4unit and DA5 unit then find BD

If HCF of three natural numbers is same as their LCM then sum of all three numbers are 416. If HCF of three natural numbers is same as their LCM then sum of all three numbers are a. 2*LCM 3*HCF b. 5*HCF - 2*LCM c. HCFLCM c. HCFLCM d. NoT 417. If average of 5 different positive numbers are A and X is average of average of all possible pairs of these 5 numbers then possible pairs of these 5 numbers then a. AX b. g @ ³ c. A b X d. g ³ e. NoT e. NoT

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hour clock as shown in fig, in which outer dial 418. There is a 24 - hour clock as shown in fig, in which outer dial is representing hours and inner dial is minutes and seconds, then find the angle between hands X if time is 20:10. then find the angle between hands X if time is 20:10. 419. If A sold an article to B at 20% profit and B to C at 10% profit t If A sold an article to B at 20% profit and B to C at 10% profit then C sold to A at 20% hen C sold to A at 20% loss then find over all monetary % profit or loss of A. LAssume all transactions happen in $M 420. For natural numbers x, y if For natural numbers x, y if 6 ∗ 44 A then x y ??? then x y ??? 421. Ù1

Ú Ú Ú⋯

Û ? ? ?

422. Find least palindromic natural number which Find least palindromic natural number which has odd number of digits , divisible by 11 has odd number of digits , divisible by 11 and has 9 as a middle digit. and has 9 as a middle digit. 423. If a palindromic number which has odd number of digits is divisible by 11 then middle digit of this number can not be digit of this number can not be a. 3 b. 2 c. 4 d. 6 e. All possible as a middle digit e. All possible as a middle digit

424. If A increases 10% then 20% then 30% then 40% then it becomes B, But if A increases , A increases 10% then 20% then 30% then 40% then it becomes B, But if A increases , 12% then 22% then 32% then 34% then it becomes C, Then 12% then 22% then 32% then 34% then it becomes C, Then a. BC b. B>C c. BbC d. NoT 425. Find maximum power if 20! Factorial 20 which perfectly divides 202! Factorial 202 Find maximum power if 20! Factorial 20 which perfectly divides 202! Factorial 202 426. Total number of real solutions of x³ sin x Total number of real solutions of x³ sin x 427. s6 2q6 2Z6 2r6 2√6 ⋯ ? a. √2 1

b. √3 3 1

c. 1

d. √3 1

428. Find the sum of common terms/elements of m3,7,11,15,....,103< & m1,7,13,19,....,103< Find the sum of common terms/elements of m3,7,11,15,....,103< & m1,7,13,19,....,103< www.facebook.com/groups/MBAMathsByAmiya 3E Learning Maths By Amiya Ranchi | 44

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show nth term of two different APs whose sum of first n terms are 429. If ÜÝ and ÞÝ show nth term of two different APs whose sum of first n terms are denoted by ßÝ and àÝ respectively. If respectively. If ßªª : à Þ¬ . : ªâ 17:11 then find Ü 17:11 º : Þ 430. For natural number x, y and z , For natural number x, y and z , 2 3o 5p 114 then x y - z ? z ?

431. If %profit is same as cost price of article and selling price is 131.25 then find its profit in rupees.

432. Find the concentration % of acid in final solution if 80 lit of 80% acid solution is first replaced by 20 lit water then 40 lit water. replaced by 20 lit water then 40 lit water.

433. If 1000th prime is a four digit number and it is rime is a four digit number and it is equal to 7909 X then X ?? 7909 X then X ?? a. 20 b. 6 c. 8 d. 10 434. Data Sufficiency : What is the cost Data Sufficiency : What is the cost price of the article I. If loss % is same as cost price of the article and selling price is Rs. 24. I. If loss % is same as cost price of the article and selling price is Rs. 24. II. If cost price is 20% of selling price. II. If cost price is 20% of selling price.

2 , 3 , 4 , 5 0-V 6 6

435. Which one is largest among largest among ã

ã

¿ã

Ëã

Àã

436. There are how many four digit number ABCD are possible such that AB, BC, & CD are perfect squares repetition of digits are allowed perfect squares repetition of digits are allowed

437. There are how many three digit numbers are possible say XYZ, if we interchange digits of unit place and hundredth place ZYX then digits of unit place and hundredth place ZYX then resultant number is also a three digit number is also a three digit number and | XYZ - ZYX| is divisible by 7 ZYX| is divisible by 7, such that _ Q 438. What is the last two digits of product of all positive divisors of 1024 digits of product of all positive divisors of 1024 digits of product of all positive divisors of 1024

439. A cone of height X is cut by a plane parallel to the base and at a distance is cut by a plane parallel to the base and at a distance Y from the is cut by a plane parallel to the base and at a distance base, then what is the ratio of what is the ratio of volume of the resulting cone and that of resulting that of resulting the ª « frustum ? where X & Y are pos X & Y are positive integral solution of ä ª â ; where Z is also a positive integer

å

æ

440. If ∆ABC is an equilateral triangle , and point D & E are on sides AB & AC such that , ∆ABC is an equilateral triangle , and point D & E are on sides AB & AC such that , DE||BC, and perimeter of DE||BC, and perimeter of ∆ADE is same as perimeter of quadrilateral BCED then find ∆ADE is same as perimeter of quadrilateral BCED then find ratio of DE:BC.

441. If speed of the group is 1 m/s and that of the joker is 3m/s. Joker starts from back of the last person and moves towards the front one, touches him and turns back, and goes, back to last person. If in this process The Joker covers 16 back to last person. If in this process The Joker covers 16 m when he is going forward m when he is going forward right hand side then find distance traveled by him when he turned back and moves towards left. assume speed of all remains same in entire process and no time loss by The Joker when he was turning back The Joker when he was turning back www.facebook.com/groups/MBAMathsByAmiya 3E Learning Maths By Amiya Ranchi | 45

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How many pairs of natural numbers m, n satisfy , where where 20>m 442. How many pairs of natura » 3 K

?

443. A quadratic function fx attains a A quadratic function fx attains a minimum of -5 at x -1. The value of the function at 1. The value of the function at x 0 is -3 . What is the value of f x at x What is the value of f x at x 5?

Direction for 446 to 448 : If the total intake in IIM A , B & C together is 900, and below chart is Direction for 446 to 448 : If the total intake in IIM A , B & C together is 900, and below chart is giving % of Male Mand that of Work giving % of Male Mand that of Work-ExEx in B-Schools. It is also known that 40% of whom Schools. It is also known that 40% of whom are in IIM-C are rest are equally divided between IIM A & IIM C. C are rest are equally divided between IIM A & IIM C. Male (M)

IIM A IIM B IIM C Total

444. What is the % of Male in IIM A What is the % of Male in IIM A

37.037% 33.333% 34.444%

Work Ex (Ex) 55.556% 66.667% 56.667%

445. What is the % of Fresher Fresher Non work Ex in IIM C

446. If in IIM -B , 50% work ex are male then what is the ratio of Male Fresher to Female B , 50% work ex are male then what is the ratio of Male Fresher to Female Work ex in IIM - B

447. One day Bagga with his dog planed to go to Park from their home which is 1200 m from home. Speed of Bagga was 30 m/s and that of his dog was 60 m/s. Both started from same time. His dog reached Park much earlier than Bagga, but dog returned back without wasting any time and came near to Bagga and again run towards Parks and asting any time and came near to Bagga and again run towards Parks and after reaching park came back to Bagga and continue the same process until Bagga reached the Park. If both maintained a constant speed in entire journey and there was no time loss in this process then find is process then find how much meter more did dog move towards park than towards Bagga. 448. If 2 is a root of a quadratic function fx0 and 7*f3f6 then find another roots of fx0

449. If WEIGHT of number a, ab , abc & of number a, ab , abc & abcd a single , double, triple and four digit number abcd a single , double, triple and four digit number respectively is defined by ; respectively is defined by ; WEIGHT a a ; WEIGHT ab ab ; WEIGHTabc bc - a and a and WEIGHTabcd cd-ab ; ab ; then for how many natural number less than 8995, then for how many natural number less than 8995, WIGHT WIGHT WIGHT of that number is 7. of that number is 7.

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450. ABCD is rectangle such that AB12cm and BC5cm, another Rectangle AEFC is such that point D lies on side EF then find the area of rectangle AEFC

451. If log log · 2√ 9¸ 0 then find x

452. If mileage of a car is 17 km per lit If mileage of a car is 17 km per lit with extra 3 lit per hour as wastage as wastage . What should be minimum speed of the car to cover 34 km in 3 lit. minimum speed of the car to cover 34 km in 3 lit. 453. W1 X W1 X W1 X W1 X … … … ? =K=

454.

K

K

K = K

?

K

K

⋯ … … … . ?

455. If 9th term of an AP is 20 20 then sum of first 17 terms of this AP is _____ sum of first 17 terms of this AP is _____

456. If the pendulum of a clock the pendulum of a clock takes 3 seconds to strike 3 o’clock. then h then how much time will it take to strike 9 o’clock? o’clock? 457. W

∗∗K

∗K∗

K∗ ∗

⋯

X ? ? ?

∗∗K

What would be remainder if 1 1 1 ? 1 is divided by is divided by 458. What would be remainder if

3 2

459. If mileage of a car is 15 km per lit with extra km per lit with extra 2 lit per hour as wastage . What should be lit per hour as wastage . What should be minimum speed of the car to cover minimum speed of the car to cover 45 km in 4 lit. 460. If an article was selling at 20% profit , to earn Rs 1320 more profit shopkeeper purchased article at 10% lesser than his cost price and sold it at 10% higher pri purchased article at 10% lesser than his cost price and sold it at 10% higher price than his selling price, then find oldoriginal selling price of his selling price, then find oldoriginal selling price of

461. Find the maximum value of Find the maximum value of a b, if following set of equations has infinite many roots has infinite many roots a-1*x 5*y 140 & 7 & 7*x a1*y b

462. What would be area of triangle formed by axes lines and a line which is perpendicular to a line 3x-2y6 and passing through 2,2 2y6 and passing through 2,2

463. If A is X% of B and B is Y% of A and X is A% of Y and Y is B% of X then what is X% of 20 If A is X% of B and B is Y% of A and X is A% of Y and Y is B% of X then what is X% of 20 464. If aaabcccd is a 8 digit perfect If aaabcccd is a 8 digit perfect square then abcd ???

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3E LEARNING - MATHS BY AMIYA 500 CAT 2016

465. If ratio of income of X &Y is 3:4 and their expenditure ratio is 4:7 then then whose % saving on income is more whose % saving on income is more a. X b. Y c. can't say d. NoT

466. L√1ML√2ML√3ML√4M.....L√24M ??? ;Where LxM is defined as nearest integer, L √1ML√2ML√3ML√4M.....L√24M ??? ;Where LxM is defined as nearest integer, L3M3, √1ML√2ML√3ML√4M.....L√24M ??? ;Where LxM is defined as nearest integer, L L4.3M4 & L4.51M 5 467. How many integral solutions are possible for L√ M 25 ;Where LxM is defined as ;Where LxM is defined as nearest integer, L3M3, L4.3M4 & L4.51M 5 nearest integer, L3M3, L4.3M4 & L4.51M 5

;Where LxM is defined 468. What is the sum of all integral solutions possible for L√ M 25 ;Where LxM is defined as nearest integer, L3M3, L4.3M4 & L4.51M 5 as nearest integer, L3M3, L4.3M4 & L4.51M 5 469. 4 4 4 . . . . 4 = ;ÌV 17 ? ? ? 470. 4 ∗ 4 ∗ 4 ∗ . . . .∗ 4 = ;ÌV 17 ? ? ?

471. 2= 2 2 . . . . 2 ;ÌV 13 ? ? ?

472. If A,B,C,D,E, & F are points on a circle such that ratio of le If A,B,C,D,E, & F are points on a circle such that ratio of lengths of arc ngths of arc AB , arc BC, arc CD, arc DE, arc EF, arc FA is 1:2:3:4:6:6 then what is the value of angle CDF FA is 1:2:3:4:6:6 then what is the value of angle CDF FA is 1:2:3:4:6:6 then what is the value of angle CDF 473. 1234512345.... 300 digits mod 41 ??? 1234512345.... 300 digits mod 41 ???

474. If A,B,C,D,E, & F are points on a circle such that ratio of lengths of arc AB , arc BC, arc If A,B,C,D,E, & F are points on a circle such that ratio of lengths of arc AB , CD, arc DE, arc EF, arc FA is 1: arc EF, arc FA is 1:1:2:2:3:3 then what is the value of angle then what is the value of angle ACE 475. If fxx-1x5x-9...x61 , then for how many integral "x" fxb0. 9...x61 , then for how many integral "x" fxb0. 9...x61 , then for how many integral "x" fxb0.

476. Ram wrote first "N" natural numbers on a black board then removed one number and found that new average becomes found that new average becomes 21.1 then find which number was removed ? 21.1 then find which number was removed ? 477. If A,B C & D are points on circle and E,F,G & H are mid points of side DA, AB, BC & CD. Find the area of quadrilateral EFGH if AB12cm, BC6 cm, CD8cm & DA 10 cm. AB12cm, BC6 cm, CD8cm & DA 10 cm.

478. What is the area of a right angled triangl What is the area of a right angled triangle whose inradius and circum radius are 10 and e whose inradius and circum radius are 10 and 12 cm respectively 479. What is the area of a right angled triangle whose inradius and circum radius are 4 and 12 cm respectively

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3E LEARNING - MATHS BY AMIYA 500 CAT 2016

480. Inside an equilateral triangle there is a point from which the length of perpendicular on all the three sides are 2 lar on all the three sides are 2cm, 3cm, & 4cm then. what would be area cm then. what would be area of equilateral triangle.

481. If fresh grapes has 90% water content and dry grapes kishmish has 30% water content. In the procedure of making kismish one just need to dry grap content. In the procedure of making kismish one just need to dry grapes, then if a shopkeeper purchased 210kg of grapes at 30 Rs per kg then at what price per kg he should sell kismish to earn 33.33% profit. should sell kismish to earn 33.33% profit.

13x19...x115; Then for how many integral x , fxb 0 Then for how many integral x , fxb 0. 482. If fx x-1x7x-13x19...x115 483. If in the given fig , AD3cm , DF 1cm, FC 2cm & , AD3cm , DF 1cm, FC 2cm & EF || BC then

PçèP 5é ∆deê

find

PçèP 5é ∆ëêì

484. If in the given fig , AD3cm , DF 1cm, FC 2cm & EF || BC then

PçèP 5é ∆deê

find

PçèP 5é ∆def

485. If in the given fig , AD3cm , DF If in the given fig , AD3cm , DF 1cm, FC 2cm & EF || BC

PçèP 5é êìfe êìfe

then find

PçèP 5é ∆def def

486. In the given fig if then find the area of ∆íîï then find the area of íîï

BD:DCCE:EA1:2 and area of ∆AFO is 144 sq. cm, BD:DCCE:EA1:2 and area of ∆AFO is 144 sq. cm,

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3E LEARNING - MATHS BY AMIYA 500 CAT 2016

487. If in the given fig ABCD is parallelogram, O is a point inside the parallelogram. If areas of three triangles are given check fig then find the fourth triangle.

area of

488. In the given triangle D, E & F are mid points of respective sides then find the area ratio of quad find the area ratio of quad BGOF to that of ABC

489. If in the given fig ABCD is quadrilateral and E,F,G H are mid points of respective sides as shown in fig. Areas of three quadrilaterals are given check fig then find the area of fourth quadrilateral.

&

490. If angle ratio of a triangle is 1:2:9 then what is the side ratio of this triangle If angle ratio of a triangle is 1:2:9 then what is the side ratio of this triangle a. 1:2:9 b. 18:9:2 c.√3 ∶ √2 ∶ 2 d. √3 1 ∶ √2 ∶ 2 e. NoT

491. If N the least natural number which is subtracted from 10000*10001*10002*10003 to make it a perfect square then N mod 9 ??? square then N mod 9 ??? 492. Sum of all coefficients of expansion of x1x2x3....x15 is S then S mod 17 of expansion of x1x2x3....x15 is S then S mod 17 ?

493. If an alloy is having Zn, Cd and Fe in the ratio of 3:4:9 and another alloy has the same elements in the ratio of 2:3:4 then find the elements in the ratio of 2:3:4 then find the ratio of these elements in the same order of ratio of these elements in the same order of first alloy and second alloy is mixed in the ratio of 2:3 first alloy and second alloy is mixed in the ratio of 2:3 www.facebook.com/groups/MBAMathsByAmiya 3E Learning Maths By Amiya Ranchi | 50

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Total number of positive integral solution of 10x 7y 7z 100 is ______ 494. Total number of positive integral solution of 10x 7y 7z 100 is ______

495. If añ b ñ c ñ dñ is always divisible by abcd , where a,b,c,&d are natura is always divisible by abcd , where a,b,c,&d are natural is always divisible by abcd , where a,b,c,&d are natura numbers and p is a prime more than 101 then numbers and p is a prime more than 101 then a. a, b , c& d are odd numbers a. a, b , c& d are odd numbers b. c, d , a & b are in AP c. a, b, c & d are in HP d. a, b, c & d are in GP e. NoT

496. If 32A65B is divisible by 72 then what would be remainder if AAABBB is divided by 7, where A & B are two digits both could be same. ere A & B are two digits both could be same. 497. Shopkeeper A : Gives 25% extra and charges 20% less than market price Gives 25% extra and charges 20% less than market price Gives 25% extra and charges 20% less than market price Shopkeeper B: Gives 20% extra and charges 25% less than market price Gives 20% extra and charges 25% less than market price Gives 20% extra and charges 25% less than market price

If both shopkeepers sell same product of same market price then for a customer which shopkeeper is better... ???? shopkeeper is better... ????

498. There is a tilted glass in perfect cylindrical shape with base in perfect cylindrical shape with base radius 7cm and height 10 cm. Glass radius 7cm and height 10 cm. Glass is partially filled with water, in such a way that, that, water level is just touching bottom end and top end of the glass as shown in bottom end and top end of the glass as shown in the figure. Then find the amount of water figure. Then find the amount of water in litter inside the glass.

499. Find the total number of positive integral solution of o p 1 1

500. Amiya and Raman is playing a game Toss laying a game Toss-Toss. Raman wins when tails comes and Toss. Raman wins when tails comes and losses when heads come. Raman gains Rs 10 for tail and loses Rs 10 for head. If Raman wins in first toss then he quits but tries only once more if he losses on the first toss. Then in this game how much could be expected win of Raman. uch could be expected win of Raman.

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3E LEARNING - MATHS BY AMIYA 500 CAT 2016

SOLUTION :Maths Maths By Amiya 500 (2017(2017 19) 1. Mohit calculated sum of first N natural number and he found sum is 337 and he knows he counted one number twice or missed one number. then find his minimum possible % error made by him. a. 3% b. 3.99% c. 3.69% d. 3.23% Sol: [c] Actual sum should be near to 338 for minimum error, so it should be either 325 or 351 % error on 325 = 12/325*100 = 3.69% % error on 351 = 14/351*100 = 3.99 2. The integers 1,2,….. 30 are written on a board. A person came and erased any two numbers say "a" & "b" and wrote a new number "a+b+2" this pro process cess is done by total 29 persons (including first one) then . What is the number left on the board at the end? Sol: Every time sum would increase by 2 , so total increase = 2*29 = 58 So last number = ∑ « ò¯ = 465+58 = 523 3. If T1=(1) , T2= (3,5) , T3 = (7,9,11) , T(4) = (13,15,17,19) ..... Then what is the sum of all terms of T(10) Answer : 1000 4. phi (n) is defined as number of co co-prime prime less than n. If ‘P’ is product of two different prime numbers, whose sum is 1200 then what is the max phi(M) Sol: phi (n) = n *(1 -1/p)*(1-1/q) 1/q) and so on ... where p and q are primes in prime factors of n. since we need this max so by gó @ ôó ôó ,, value should be close means both prime should be closer to 60 for max phi , so 59 & 61 ; P = 59*61 & phi(P) = 58*60 = =3480. 5. Consider the set S = {1,2,3,………..10000}, How many APs can be formed from the elements of S that start with 1 and end with 10000 and have minimum 3 terms?

Ans: 11 ; a=1 ,Tn=10000 , so 1 + (n (n-1)d = 10000; ; (n-1)d 1)d = 9999 = 3^2*11*101 so 12 factors. n-1 cannot be 1. so 11 6. Total number of integral solutions of 13x - 3y = 1000 for 100< x < 200 Sol: 33 , all numbers which gives remainder 1 when divided by 3 7. For how many integral "n" is

is an integer

Sol: [12] 7 21 7 9 mod (x--3) = 12 , so x-3 3 should be a factor of 12 means 12 values are possible including negative.

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3E LEARNING - MATHS BY AMIYA 500 CAT 2016 8. If HCF , LCM and sum of two numbers are 6 , 15 and 23 then find their difference. Sol: Not a possible case 9. If 1 7 6 3 , then find the value of f(x - 1). Sol: put x = x -2 ,âõ® ®®õ ª¬ 10. Find the area of the enclosed fig by | x- 5 | öõ ö âú öõ – ºú « ®

ª

ª

ª

So 343 216 so 560 integral solution.

13. When a number divided by 6 and 35 remainders are 5 and 7 then what would be remainder when 11 times of the number is divided by 15 a. 8 b. 13 c. 7 d. Data inadequate e. NoT Sol: By CRT 77 is least number for 210 and we want 11*77 mod 15 = 7 14. In a circle AB is diameter of length 34 unit and BC is chord of length 16 unit. If CD is perpendicular on AB such that D lies on AB then what is the length AD. Ans: 450/17 , can do by similarity Ans: ª¯√® ; Area = ÷® ∗ àøÝù

15. What is the area of a rhombus whose one side is 6 unit and one internal angle is 135 degree. 16. If major (longest diagonal) of a rhombus is 6√3 cm and one internal angle of rhombus is 120° then what is the area of rhombus.

Ans :ª¯√

17. 113 100 is divisible by 209 (True / False) ANS: TRUE 18. 113 100 is divisible by 247 (True / False) ANS: TRUE 19. 113 100 is divisible by 143 (True / False) ANS: TRUE 20. 113 100 is divisible by 71 (True / False) ANS: TRUE

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3E LEARNING - MATHS BY AMIYA 500 CAT 2016 21. 113 100 is divisible by 781 (True / False) ANS: TRUE 22. What is the rate per annum if compound interest after 2 years is same as simple interest after 3 years. Ans: 100% Ans: ∶

ò°«

∶ °ª

â

23. At what time between 3&44 both the hands are equi equidistant from figure 6 but not together ª

ª

24. What is the least natural number N for 101^N mod 280 = 1 Ans: N =6 ,cyclicity 280 = 2^3*5*7 ; no need to check for 5 , since 101^n mod 5 = 0 , for all n ; also not for 2^3 since 101^(2m) mod 8 = 1, for all m ; now just check 7 , cyclicityoteuler of 7 is 6 which satisfy all conditions 25. If A takes "a" hours more than time taken to complete a work when A & B work together and B takes "b" hours more than time taken to complete a work when A & B work together. Then what is efficiency ratio of A and B 1. a : b 2. b:a 3. √.: 0 4. √0: . 5. b^2 : a^2 Ans: [3] 26. If X + (1/Y)=1 , Y + (1/Z) = 1 then what is the value of X*Y*Z , if none of X, Y & Z are 0 Ans: -1 ; solve by putting values 27. What is the minimum value of of2123 2451

Ans: ®

ªW

ª X √®

at x = 225

√1! √2! √3! ⋯ … . √1000! ? Ans : 1*7+2*19+3*37+4*61+5*91+6*127+7*169+8*217+9*271+10=6985 28. If [ N ] is greatest integer less than equal to N then

29. What is the coefficient of x^5 in the expansion of (1+x)(2+x)(3+x)(4+x)(5+x)(6+x) Ans: 21 , -(sum (sum of all roots)

30. If P = { x /x : x 15 , $% -0*890: -8;.,9 < ; then how many subset of P would have at least one prime number Ans : ®ªò ®¬

31. 1 2 3 4 … . . 101 ? Ans :5151

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3E LEARNING - MATHS BY AMIYA 500 CAT 2016 32. ( 2 ; *+,- = … … ?

Ans : 0 33. Find the cubic equation whose roots are one more than roots of 1 0 Ans: x^3-2x^2+2x= 0 ;Put x = x--1 34. What is the minimum value of sinx + cosecx + tanx + cotx Ans :infinity 35. What is the sum of first 1000 terms of series - 1,2,1,2,2,1,2,2,2,1,2,2,2,2,1,.... Ans : 1956 ; 2*1000-44= 44= 1956 ; just check how many one's by checking positions of 1's. 1,3,6,10...990 so 44 36. DS - What is the ratio of Cost Price to Selling Price A. Markup % is 26% more than Profit % and 10% more than Discount % B. Markup is Rs 26 more than Profit (RS) and Rs 10 more than Discount (in RS) Ans: A alone. 37. What would be remainder er if 98! Is divided by 101 ? Ans: 50 38. What is the sum of all internal angles of this star Ans :(11-5×2)×180=180

)...(1+x^99) 39. Coefficient of x⁴ in the expansion of (1+x)(1+x²)(1+x³)(1+x⁴)...(1+x^99) Ans: 2 40. Max number umber of segments we can create on a plane (open or closed ) by the help of a circle , a trianglee and a line is ______ Ans: 12 41. If magnitude of speed in Km/hr of a man is same as rest time in minute in an hour of that man. Find maximum distance covered by man in 5 hours. Ans :x(5-x/12), 5x-x^2/12,5=x/6,x=30, x^2/12,5=x/6,x=30, so 30*(5 30*(5-30/12),150-25*3=75 42. If N is smallest est prime number which is equal to sum of three consecutive prime numbers then what is the sum of digits of N Ans: 4 ; 23 = 5+7+11 www.facebook.com/groups/MBAMathsByAmiya 3E Learning Maths By Amiya Ranchi | 56

3E LEARNING - MATHS BY AMIYA 500 CAT 2016

73% are passed in Phy , 89% in Che, 69% 69 in Bio & 43. If in an examination of PCMB , 73 71% in Maths, then minimum how many % people have passed in all four papers. Ans : 2% Work on students who failed in each sub - 27, 11, 31 & 29 , means max 98% fail in at least one so minimum 2% pass in all 44. Total number of positive integral solution of 3x + 2y = 100 such that @ A Ans : 7

45. If in an examination of PCM , 75 75% are passed in Phy , 65% in Che, & 70% 70 in Maths, then minimum how many % people have passed in all three papers. Ans: 10% 46. If in an examination mination of PCM , 60 60% are passed in Phy , 65% in Che, & 70% 70 in Maths, then max how many % people have passed in all three papers. Ans : 47.5% 47. For a natural "n" 2^(12n) - 6^(4n) is div by a. 10 b. 20 c. 50 d. 100 Ans: All

e.All

48. Mohan sells out a toy at 25% profit. Had he purchased at 25% less and sold it for Rs 25 less, then he would have still gained 25%. Find the cost price of toy Ans: 80 49. If sin ∅ cos ∅ then for 0 ∅

Ans :8/3

H

; tan ∅ cot ∅ ? ?

50. Product of first 24 prime number is not divis divisible by a. 391 b. 371 c. 247 d. 279 Ans: [d] 279

e.NoT

51. If product of two sides of an integral sided triangle is 6 then triangle is always I. Acute Angled II. Obtuse Angled III.Right Angled IV. Isosceles V. Equilateral VI. Scalene VII. None of the above is always correct Ans : VII Not ; sides are 2,3,3 & 2,3,4 & 2,3,2 52. How many integral sided isosceles triangle is possible , if sum of two sides is 20 Ans: 31 Sol: If 20 is sum of equal sides, then sides are 10,10,x so total 19 triangles are possible If unequal sides sum id 20 the www.facebook.com/groups/MBAMathsByAmiya 3E Learning Maths By Amiya Ranchi | 57

3E LEARNING - MATHS BY AMIYA 500 CAT 2016 Smallest side , 1,2,3,4,5,6, only one iso triangle is possible so 6 possibility 7,8,9 - two iso triangles are possible so again 6 possibilities Total isosceles triangles are = 19 + 6 + 6 = 31 53. What is the maximum area of a triangle - if it is known that sum of any two sides of this triangle is less than equal to 20 unit. Ans: It should be (1/2) *a*bsinC , for max sinC should be 1 , so max area is (1/2)*a*b = 1/2*10*10 = 50 max

54. Fig is a regular octagon then what is the measurement of angle ADH Ans: 22.5 degree

55. Find the max value of n for which 124K 1 is divisible by 53 Ans: 5; 125*50 = 5^5 * k 56. What would be remainder if 344^49 - 1 is divided by 7^5 Ans: 0 57. What is the minimum value of x^2 - 4x +3 Ans: -1 , at x=2 58. What is the minimum value of sin^2 x - 4sin x +3 Ans: 0 , at 90 59. If a , b & c are sides of a right angled triangle and natural numbers then what would be remainder if a*b*c is divisible by 15 Ans: 0 60. (1 - cot1)(1 - cot2)(1 - cot3).....(1 - cot42)(1 - cot43)(1 - cot44) is a. A perfect Square b. A perfect cube c. A perfect square as well as a perfect cube d. Irrational Number e. NoT Ans: [a]; 2^22 , a perfect square 61. If N = (tan46-1)(tan47 -1)(tan48 1)(tan48 -1).....(tan87 -1 )(tan88 -1)(tan89 -1) 1) , then N mod 7 = ? Ans: 2 , 2^22 mod 7 www.facebook.com/groups/MBAMathsByAmiya 3E Learning Maths By Amiya Ranchi | 58

3E LEARNING - MATHS BY AMIYA 500 CAT 2016 62. If x + y + z =1 , x^2 + y^2 + z^2 =2 & x^3 + y^3 + z^3 =3 , xyz = ? Ans: 1/6 (x + y + z)^2 = x^2 + y^2 + z^2 +2 (xy + yz + zx) 1 = 2 +2 (xy + yz + zx) =>xy + yz + zx = -1/2 x^3 + y^3 + z^3 - 3xyz = (x + y + z) ( x^2 + y^2 + z^2 - (xy + yz + zx)) 3 - 3xyz = 1(2 + 1/2) = 5/2 3xyz = 1/2 ; xyz = 1/6 63. DS If f(f(x)) = f(f(f(x))) then f(x) = ? A. It is not a constant function B. [f(x)]^2 = f(x^2) Ans: Only A ;If If f(f(x)) = f(f(f(x))) ; It means f(x) = k or f(x) = x A. It is not a constant function so f(x) = x [sufficient] B. [f(x)]^2 = f(x^2) does hold for f(x)=k so f(x) = x , f(x) = 0 and f(x) = 1 , not sufficient only A is sufficient si of rectangle 64. If ratio of perimeter of a rectangle and that of a square is 5:1 and ratio of one side to one side of square is 3:2 then what is the ratio of area of square to that of rectangle. Ans: 4:51 (l+b) : a = 10 : 1 = 20:2 & b / a = 3:2 so a:l:b = 2 :17 :3 ; a^2 : l*b = 4 : 51 65. If ABCDEFGHIJ are a regular polygon then what is meas measurement urement of angle EHA Ans: 72 degree 66. A husband alone can do a piece of work in 60 hours & wife alone in 40 hours, but due to a baby who always destroy their work they together take 16 more hours to complete their work Then in how many days baby alone can destroy all the work. Ans: 60 67. If a + b +c = 5 then what is the maximum value a^2 + 4*b^2 + 9*c^2 Ans: Infinity 68. In a section of PGP18 of IIM IIM-X X the average weight of 30 students is 60 kg. If x new students join the section and average wt of these new students are "70 - X" kgs, then find the maximum possible average weight (approx) of the section after joining new students. a. 60.66 b. 60.73 c. 60.71 d. 60.56 e. NoT Ans: [c] , for x = 5 69. Arrange A, B & C in ascending order If A = pi^(1/pi) , B = e^(1/e) & C = 1 , where pi is 3.14 , e = 2.71 Ans : C,A, Bhttps://youtu.be/4MWD5C5qt84 https://youtu.be/4MWD5C5qt84 70. If log P . log P . log P . 60 then log P . ? ?

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3E LEARNING - MATHS BY AMIYA 500 CAT 2016 Ans: 40

71. If ? 1 is one factor of f(x) = 0 ∗ K . ∗ ? U ∗ V ∗ , ∗ then what is the real roots of f(x)=0 a. 1 b. -1 c. -f/a d. a*b*c*d*e*f e. NoT Ans:[c] ÷ ∗ õò û ∗ õ° ü ∗ õ ý ∗ õ® þ ∗ õ = a(õ° õ õ® õ ª ∗ õ R is real root then by equating constant term R = - f/a 72. There are 6 identical toys and three boys. In how many ways all toys would be distributed among three boys. Ans: 28 ways. (0, 0, 6), (1, 1, 4), (3, 3, 0), (2, 2, 2), (1, 2, 3), (1, 5, 0) and (2, 4, 0) 73. In JhumriTillaiya a Paamwala priced his beedi at 85 paise per beedi, but after budget, he reduced the price of beedi and andand soldbeediof beediof Rs.77.28 in a day. Then what is the total number of beedies he sold in a day day? a.37 b. 47 c. 84 d. 92 Ans: [d] check by options 74. In AB and BC are two chords of a circle, then find length of chord AC C if AB=BC=6cm and radius of circle is 5cm Ans: 9.6 cm 75. If third term of a GP is 4096 andits common ratio is positive.The Product of first 7 terms is less than that of first 6 terms and Product of first 6 terms is greater than that of first 5 terms. then which option is best describing range of common ratio. a. [ 1/32 , 1/16] b. ] 1/32 , 1/16[ c. [ 1/16 , 1/8] d. ] 1/16 , 1/8 [ e. Not Ans: [d] P7 < P6 => P6*T7 < P6 so T7 < 1 P6 < P5 =>P5*T6 > P5 so T6 > 1 T7 = 4096*r^4 < 1 so , r < 1/8 T6 = 4096*r^3 > 1, so , r > 1/6

76. Ans: 23 degree angle by same chord

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3E LEARNING - MATHS BY AMIYA 500 CAT 2016 77. All words having three different vowels and three different consonant are written in dictionary then what would be rank of word BAEI BAEICD Ans: 137 Keeping A fixed in the first place, we have 120 words. Keeping BAC fixed, we have 6 words Keeping BAD fixed, we have 6 words Now comes BAE (CDI, CID, DCI, DIC) after which BAEICD will come. Hence rank = 120+6+6+4+1 = 137 78. In group of 12 people, 4 speak on only Hindi, 5 speak only Tamil and the rest speak both Hindi and Tamil.. In how many ways can the 112 people be arranged in a row such that so are all those who speak only Hindi are together and so are all those who speak only Tamil. Further her all people should be able to converse with both their neighbours. Ans :_HBT_ or _TBH_ 79. If a three hree digit number xyz has only 5 factors then what is the last digit of sum of all factors of six digit number "xyzxyz" . Ans:4 , xyz = 625 then n whose expenditure 80. If Income ratio of A, B & C are 3:7:9 & their saving ratios are 3:1:4 the is maximum ? Ans: CBD 81. If Income ratio of A, B & C are 3:7:9 & their saving ratios are 3:1:4 the then n whose expenditure is minimum? Ans: A Direction for Q 82 & 83 - DOVAFONE has two monthly tariff plans for calling - details are given below Name of Plan P300

Fixed Monthly Charge ` 300

P100

` 100

Benefit 600 min free , after that `1 per min , fractional charge is applied 30 paisa per min, fractional charge is applied

Fractional Charge - If you talk in fraction of min charge would be in fraction of that tariff .eg if extra 1.5 min pay extra ``1.5 in P300 and 45 paisa or 1.66 min then `1.66 1.66 in P300 and 50 paisa in P100 82. If one person talks 500 min per month then which plan is better. Ans: P100 83. If one person talks N min per month and for him both plans cost the same. Then N = ? Ans: Not Possible

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3E LEARNING - MATHS BY AMIYA 500 CAT 2016 84. If ∗ W X W X and f(3) = 82 then what is f(5) = ?

Ans : f(x) = 1 + x^n ; f(3) = 1 + 3^4 = 82 , f(x) = 1 + x^4 f(5) = 1 + 5^4 = 626

85. If angles of a triangle are 30 30° , 60° and 90° then what is the ratio of it's in-radius in to circum radius Ans: r/R = cos 30 + cos 60 + cos 90 - 1=

√ ®

ª ª ®

√ª ®

86. which one is largest among all option options K a. 12 14 b. 13 15? c. 12K 14 d. 15 13? Ans: (a) 87. What is the sum of all external angles of a 8 sided concave polygon. Ans: 1800 ; 180(n+2) 88. If ABCD is a prallelogram. Point E and F are mid points of side BC & CD respectively then what is the area ratioo of Quard AGFD to that of parallelogram ABCD.

Ans :11:20 Solve it by assuming ing a square or rectangle coordinate

on

89. How many numbers are the in the set of first 1000 natural numbers which can be written as sum of two or more consecutive natural numbers. Ans: 990 , all except 2^n terms 90. Total number of integral solution of w^4 + x^4 + y^4 + z^4 = 1797 Ans: 0 , check divisibility by 7 91. If Y √123 ∗ 124 ∗ 125 ∗ 126 1 then what is the digital sum of N (N mod 9) Ans: 1 92. Total number of integral solution ofa³ + b³ + c³ = 43655 Ans : 0

93. If diagonals of a parallelogram are 30cm and 10 cm then among the options which could be sides of parallelogram a. 22 cm & 4 cm b. 20cm & 10 cm c. a & b both possible d. NoT

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3E LEARNING - MATHS BY AMIYA 500 CAT 2016 Ans: [b] - "a" cant be since we can not make 4cm with diagonals (as part of triangle) 94. If A,B& C three cities are in a highway. Distance between two cities A & B is 200 km and city C is 100 km from B & A both. From city "A" a man starts towards "B" with speed of 30 km/hr and on the same time another man start startss from B towards "A" with speed of 20 km/hr. After how much time they exchange their speeds (new speed of man from A and man from B becomes 20 kmph and 30 kmph respectively ) so that they meet at C Sol: After 2 hours 95. If a , b & c are in GP then roots of 0 . U 0 has a. Real b. Equal c. Imaginary d. (b) or (c) Ans: [c]

e. Not

96. If O is centre of the circle, angle DOC = 42° then what is the measurement of angle BFC Ans: 69

97. Sum of two positive integers A &B and its LCM is 455. Then how many unordered pairs of A & B are possible. Sol: Let number be h*x & h*y , h being HCF of numbers. then hx + hy + hxy = 455 Ans: 14; h(x+y+xy)=455 = 5*7*13 So , h = 1, 5, 7, 13 , 5*13 , 7*13 , 5*7 & 5*7*13 if h = 1 , x+y+xy = 455 ; (x+1)(y+1)= 456 sso 5 cases if h = 5 , x+y+xy = 91 ; (x+1)(y+1)= 92 so 2 cases if h = 7 , x+y+xy = 65 ; (x+1)(y+1)= 66 so 2 cases if h = 13 , x+y+xy = 35 ; (x+1)(y+1)= 36 so 3 cases if h = 65 , x+y+xy = 7 ; (x+1)(y+1)= 8 so 2 cases 98. If O is a point inside a parallelogram AB ABCD such that areas of ∆ABO ,∆ ∆BCO & ∆CDO are 12cm^2 , 15 cm^2 and 10 cm^2 then what is the area of ∆ AOD. Ans: 7 cm^2

99. If in ∆ABC ABC , AB = 6 cm , BC = 7 cm and CA = 8 cm , AD is an internal angle bisector of angle A such that point D lies on side BC then le length of AD = ? Ans :AD = 6 cm www.facebook.com/groups/MBAMathsByAmiya 3E Learning Maths By Amiya Ranchi | 63

3E LEARNING - MATHS BY AMIYA 500 CAT 2016 where AB = c, BC= a & CA=b í Zû ∗ ü ö ª ûü® úwhere ÷®

100. A34 56B is a 6 digit number in base 12 and when we write this in base 10 then it is divisible by 143 then A * B = ? Ans: 3 , (1,3) 101. If a , b, c, & d are sides of given quadrilateral ABCD then area of ABCD 1. a*b*c*d 2. √0 0∗.∗U∗V 3. 3√0 ∗ . ∗ U ∗ V

Ans: (2)

4. Z

P P4

∗

[^

102. For how many different (0 0 _ . _ U non zero digit ordered combinations (a,b,c) 0[ b 0[ 4 a

Sol:

Case 1 : b =1 , 8*7 = 56

103. In a trapezium ABCD , E & F are mid points of its diagonals and AB || CD . Find length of side CD if AB = 12 cm & EF = 4 cm. Ans: 20 cm. ( a-b/2=EF) 104. In a trapezium PQRS , S & T are mid points of its diagonals and PQ || RS . Find length of side RS if PQ = 12 cm &ST ST = 3 cm. Ans: 6cm or 18 cm 105. If [ x ] denotes greatest integer less than equal to x then 1 1 1 1 1 1 1 1 1 1 \ ]\ ]\ ]\ ] ⋯ ? 3 3 9 3 9 27 3 9 27 81 Ans: 0 106. Three students have each brought his father and mother for admission to a school. The admission head wishes tointerview the nine people one by one, taking care that no child is interviewed before its mother and no husband is interviewed before his wife. wife In howmany different ways can be interviews be arranged? Ans :8*9!/216 [in 2^3 ways father and child can be arranged] 107. In how many ways can we select two squares on a chessboard such that they share either a common side or a common vertex? Ans: 210

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3E LEARNING - MATHS BY AMIYA 500 CAT 2016 108. A person invests Rs.3000 in 3 months fixed deposit scheme of a bank at the rate of 13%. Due to some changes in policies, the rate of interest changed in every three months, after the first period, to 12%, 11% and 10% respectively. Assuming that the person withdraws the interest after every 3 months but continues deposit, how much more interest would that person have earned in oone ne year, if there was no change in the interest rate? a. 50 b. 45 c. 0 d. 180 Ans: [b] 12% , 11% and 10% means reduction of 1% , 2% & 3% =6 % cumulative change (quarterly) Change = 3000*6*1/100*4 = 45 admission ission in health course. The instructor 109. Three wives have each brought his husband for adm wishes to interview all six people one by one, taking care that no wife is interviewed before its husband. In how many different ways can be interviews be arranged? (1) 120 (2) 100 (3) 72 (4) 90 Ans: [4] 90 Total tal ways = Total Ways / ways in which pairs can attached = 6! / (2!*2!*2!) = 90 110. A passenger is planning a trip that involves three connecting buses that leave from Ambikapur, Bokaro and Chandanpur respectively. The first bus leaves Ambikapur every hour, beginning at 8:00 am, and arrives at Bokaro 2.5 hours later. The second bus leaves Bokaro every 20 minutes, beginning at 8:00 am, and arrives at Chandanpur 7/6 hours later. The third bus leaves Chandanpur every hour, beginning at 8:45 am. What is the least total amount of time the passenger must spend between buses if all buses keep to their schedules? a. 25 minutes b. 1 hour 5 minutes c. 1 hour 15 minutes d. 2 hours 20 minutes Ans: 65 min =1 hour 5 minutes Regardless of the time of departure from Ambikapur, arrival at Bokaro will be at 30 minutes past the hour. Buses leave Bokaro on the hour, and at either 20 or 40minutes past the hour. Therefore, the earliest a passenger from Ambikapur could leave Bokaro would be 40 minutes past the hour with a 10 minute wait betweenbuses.. The bus from Bokaro to Chandanpur takes 7/6 hours or 1 hour 10 minutes. A bus taken at 40 minutes past the hour, causing the passenger to have missedthe bus from Chandanpur by 5 minutes.. The passenger therefore has a 55minuteswait, and the least total amount of time the passenger must spend between buses is10 + 55 = 65 minutes or 1 hour 5 minutes. 111. The lengths of the sides CB and CA of a triangle ABC are 4cm and 6cm respectively and the angle C is 120°.. If the line CD bisects the angle C and meets AB at D, then the length of CD is b. 3cm c. 2.4cm d. None of these a. 4 cm

Ans: [c] In Triangle ABC üà ª®« ª®« x = √76 So AD= (2/5)*√76 UÌ% 60

Ë

? o W ∗√ =X

∗?∗o

°® º® õ® ®∗°∗º

; õ íî

, A kl , y = 2.4

Direct Formula = a*b/(a+b) = 4*6/(4+6) if we bisect 120 120° www.facebook.com/groups/MBAMathsByAmiya 3E Learning Maths By Amiya Ranchi | 65

3E LEARNING - MATHS BY AMIYA 500 CAT 2016

112. An alloy X consists of 10% Cadmium and 6% zinc and alloy Y consists of 5% Cadmium and 10% zinc. If he needs at least 14 kg of Cadmium and 14 kg of zinc for his h experiment. If alloy X costs 60 paisa per kg and alloy X costs 40 paisa per kg, What is the minimum cost he would occur to fulfil his requirement a. Rs.72 b. Rs.82 c. Rs.92 d. None of these Ans: [c] ; Let a & b are wt of alloy X & Y respectively 0.1a + 0.05b = 14 ....(1) 0.06a + 0.1b = 14 ....(2) a= 100 & b = 80 , so minimum cost = 92 113. What is the unit digit of 1 2 3 ⋯ . 9 a. 0 b. 1 c. 5 d. 9 Ans: [c] 1 9 is divisible by 10 so 2 8 and so on, only 5 left so unit digit = 5 = 5

114. If in a hotel Ram checked in between 1 and 2 o’clock and cheeked out in between 4 and 5 o’clock , if positions of minute hand and hour exchange and maintained same position then at what time did Ram check-out out from hotel? a. 4: 11: 15 b. 4: 11: 45 c 4: 12: 15 d. None of these Ans: [b] no need to solve check time it should be between 4:5 :.. to 4:10:00 115. If numerators of three fractions are in A.P. and their denominators are in G.P and common difference of the numerators is equal to the common ratio of the ddenominators enominators . The product of the first fraction and reciprocal of the second fraction is 6/5 and the product of the second fraction and reciprocal of third fraction is 15/8. If the, then the denominator of the third fraction is a. 9 b. 18 c. 27 d. cannot be determined Ans: [d] , 2/a ; 5/3a; 8/9a Assume numerators be a -d d , a &a+d and denominators be b/d . b& b*d in same order, from question we can get a= 5 , d=3 but cant get b , so cant be determined. 116. Two quadratic equations with positive roots have on onee common root. The sum of the product of all four roots taken two at a time is 143. The equation whose roots are the two different roots is – 14 45 0. The sum of all different roots is a. 20 b. 21 c. 22 d. 24 Ans: [b] , roots are 5,7,9 From – 14 45 0,, we can say two different roots are 9 & 5 , and sum of product of all four roots taken two at a time is 143 so 9*5 + 9*a + 5*a = 143, so a = 7 117. There are 10 pipes that are connected to a tank. Some of them are inlet pipes and the others are outlet pipes. Each of the fill pipes can fill the tank in 6 hours and each of the outlet can www.facebook.com/groups/MBAMathsByAmiya 3E Learning Maths By Amiya Ranchi | 66

3E LEARNING - MATHS BY AMIYA 500 CAT 2016 empty the tank completely in 4 hours. If all the fill pipes and outlet pipes are kept open, an filled tank gets emptied in 10 hours. How many of the 10 pipes are inlets pipes? c. 2 d. None of these a. 8 b. 4 Ans: [d] Not a possible case 118. In how many ways can we select two squares on a chessboard such that they share a common vertex and of same colour? Ans 98 = [4*1 + 24*2 + 36*4]/2 possible value of d e f ⋯ j

119. If A, B , C ,... Z are 26 positive numbers such that A+B+C+....+Z = 13, then find minimum Ans: 26^2/13 = 52

120. If A, B , C & D are sets of few natural numbers then how many ordered set (A,B,C,D) are possible such that g ∪ i ∪ k ∪ l m1,2,3, . . . ,10

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