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CLASS 12
Contents ªª 4th IMO 2010 ªª 5th IMO 2011 ªª 6th IMO 2012 - SET A ªª 6th IMO 2012 - SET B ªª 7th IMO 2013 - SET A ªª 7th IMO 2013 - SET B ªª 8th IMO 2014 - SET A ªª 8th IMO 2014 - SET B
MTG Work-Books / olympiad books CLASS 1
International Mathematics Olympiad
National Science Olympiad
International English Olympiad
MTG CSS Series
CLASS 2
International Mathematics Olympiad
National Science Olympiad
National Cyber Olympiad
International English Olympiad
MTG CSS Series
International English Olympiad
MTG CSS Series
CLASS 3
International Mathematics Olympiad
National Science Olympiad
National Cyber Olympiad
MTG Work-Books / olympiad books CLASS 4
International Mathematics Olympiad
National Science Olympiad
National Cyber Olympiad
International English Olympiad
MTG CSS Series
International English Olympiad
MTG CSS Series
International English Olympiad
MTG CSS Series
CLASS 5
International Mathematics Olympiad
National Science Olympiad
National Cyber Olympiad
CLASS 6
International Mathematics Olympiad
National Science Olympiad
National Cyber Olympiad
MTG Work-Books / olympiad books CLASS 7
National Science Olympiad
International Mathematics Olympiad
National Cyber Olympiad
Science IQ Challenge
Math IQ Challenge
International English Olympiad
MTG CSS Series
Master Mental Ability in 30 Days
CLASS 8
International Mathematics Olympiad
National Science Olympiad
National Cyber Olympiad
International English Olympiad
MTG CSS Series
Math IQ Challenge
Science IQ Challenge
Psychology of Success
The Secrets of SUCCESS
Master Mental Ability in 30 Days
MTG Work-Books / olympiad books CLASS 9
International Mathematics Olympiad
Math IQ Challenge
National Science Olympiad
Science IQ Challenge
National Cyber Olympiad
Psychology of Success
The Secrets of SUCCESS
International English Olympiad
Master Mental Ability in 30 Days
CLASS 10
International Mathematics Olympiad
Math IQ Challenge
National Science Olympiad
Science IQ Challenge
National Cyber Olympiad
Psychology of Success
The Secrets of SUCCESS
International English Olympiad
Master Mental Ability in 30 Days
MTG Work-Books / olympiad books CLASS 11
International Mathematics Olympiad
Math IQ Challenge
Science IQ Challenge
National Science Olympiad
Psychology of Success
National Cyber Olympiad
The Secrets of SUCCESS
Master Mental Ability in 30 Days
CLASS 12
International Mathematics Olympiad
Math IQ Challenge
Science IQ Challenge
National Science Olympiad
Psychology of Success
National Cyber Olympiad
The Secrets of SUCCESS
Master Mental Ability in 30 Days
Class
1 to 10
JEE (Main & Advanced) | AIPMT | BOARDS | OLYMPIAD | NTSE
FOUNDATION COURSE For Classes 7, 8, 9 & 10 Class 7
Class 8
Class 9
Class 10
Class 10 4th
Year 2010
Copyright©2015. Science Olympiad Foundation (SOF)
4th IMO - 2010
SECTION I : LOGICAL REASONING 1.
If the positions of the fifth and twelfth letters of the word GLORIFICATIONS are interchanged, and likewise the positions of the fourth and fourteenth letters, the third and tenth letters, the second and eleventh letters and the first and the thirteenth letters are interchanged, which of the following will be the twelfth letter from the right end? (A) I
2.
(B) O
(C) R
(D) T
In a row of boys, Samrat is seventh from the left and Rohit is twelfth from the right. If they interchange their positions, Samrat becomes twentysecond from the left. How many boys are there in the row? (A) 19
3.
(B) 31
(D) 38
If L stands for +, M stands for –, N stands for ×, P stands for ¸, then 14 N 10 L 42 P 2 M 8 = ? (A) 153
4.
(C) 33
(B) 216
(C) 248
(D) 251
Deepa moved a distance of 75 metres towards the north. She then turned to the left and walked 25 metres, again turned to the left and walk 80 metres and finally turned to the right at an angle of 45°. In which direction was she moving finally? (A) Northeast
5.
(B) Northwest
(D) Southwest
What number should replace the question mark in the given figures ? 9
6
7
13
36
?
2
(A) 41 6.
(C) South
9
5
8
18
(B) 32
15
(C) 45
(D) 48
There is a set of five figures marked P, Q, R, S and T called as problem figures. Select a figure among the four options, which will continue the series established by the five problem figures. Problem Figures ? P
(A)
7.
Q
R
(B)
S
T
(C)
(D)
How many triangles are contained in the given figure?
(A) 18 4 th IMO | LevelI | Class 10
(B) 12
(C) 16 2
Copyright©2015. Science Olympiad Foundation (SOF)
(D) None of these
4th IMO - 2010
8.
Complete the given series : 23, 48, 99, 203, 413, ___ ?__ (A) 927
9.
(B) 837
(C) 937
(D) 437
Choose from the given options, the box that will be formed when figure X is folded.
+
Fig. (X)
(A)
(B)
(C)
(D)
10. Sasha was facing east. She walked 20 metres. Turning left she moved 15 metres and then turning right moved 25 metres. Finally, she turned right and moved 15 metres more. How far is she from her starting point? (A) 25 metres
(B) 35 metres
(C) 50 metres
(D) 45 metres
11. Which one of the following Venn diagrams correctly illustrates the relationship among the classes: Elephants, Wolves, Animals?
(A)
(B)
(C)
(D)
12. Find the missing number in the given set of numbers.
(A) 13
25 17
38 18
89 16
6
8
?
(B) 15
(C) 17
(D) 19
13. If the first and second letters in the word DEPRESSION were interchanged, also the third and the fourth letters, the fifth and sixth letters and so on, which of the following would be the seventh letter from the right? (A) R
(B) O
(C) S
(D) P
14. If eye is called hand, hand is called mouth, mouth is called ear, ear is called nose and nose is called tongue, with which of the following would a person hear? (A) Eye
(B) Mouth
(C) Nose
(D) Ear
15. If P denotes ¸, Q denotes ×, R denotes + and S denotes –, then the value of 18 Q 12 P 4 R 5 S 6 is _____ . (A) 36
(B) 53
(C) 59
3
Copyright©2015. Science Olympiad Foundation (SOF)
(D) 65 4 th IMO | LevelI | Class 10
4th IMO - 2010
16. There is a set of four figures marked P, Q, R and S called as Problem figures. Select a figure from the four alternatives which will continue the series established by the four problem figures. Problem F igures
P
(A)
Q
R
(B)
S
(C)
(D)
17. Between two ends of a bookshelf in your study, five of your favourite puzzle books are displaced. If you decide to arrange these five books in every possible combination and move just one book every minute, how long would it take you to do so? (A) One hour
(B) Two hours
(C) Three hours
(D) Four hours
DIRECTION (18 19) : Read the information carefully given below and answer the following questions: In a group of five boys P, Q, R, S and T, P and R are good in English and Maths, Q and R are good in English and General Knowledge, T and S are good in Science and Drawing, Q and S are good in Drawing and General Knowledge, while T is good in Drawing, Maths and Science. 18. Who is good in English, Drawing and General Knowledge ? (A) P
(B) Q
(C) T
(D) R
19. Who is good in English and Maths but weak in General Knowledge ? (A) T
(B) Q
(C) P
(D) S
20. If you count 21 letters in the English alphabet from the end and 20 letters from the beginning, which letter will exactly appear in the middle of the sequence thus formed? (A) N
(B) L
(C) K
(D) M
SECTION II : MATHEMATICAL REASONING 21. Two alarm clocks ring their alarms at regular intervals of 50 seconds and 48 seconds respectively. If they first beep together at 12 noon, at what time will they beep together again ? (A) 12:20 p.m.
(B) 12:12 p.m.
(C) 12:11 p.m.
(D) None of these
22. Solve for x and y : 2 3 17 + = ; 3 x + 2y 3 x – 2y 5
(A) x = 1, y = 3
(B) x = –2, y = 1
5 1 + = 2 3 x + 2y 3 x – 2 y
(C) x = 1, y = 1
(D) x =
1 1 , y = 5 5
23. If tan A + cot A = 4, then tan 4 A + cot 4 A is equal to ______ . (A) 196
(B) 194
(C) 192
(D) 190
24. For x 2 + 2x + 5 to be a factor of x 4 + px 2 + q, the value of p and q respectively must be ____. (A) –2, 5 4 th IMO | LevelI | Class 10
(B) 5, 25
(C) 10, 20 4
Copyright©2015. Science Olympiad Foundation (SOF)
(D) 6, 25
4th IMO - 2010
25. Match the column: 1. In DABC and DPQR ,
(a) AA similarity criterion
AB AC = , Ð A = Ð P PQ PR
2. In DABC and DPQR,
(b) SAS similarity criterion
ÐA = ÐP, ÐB = ÐQ Þ
DABC ~ DPQR
3. In DABC and DPQR, AB AC BC = = PQ PR QR Þ DABC ~ DPQR
(c) SSS similarity criterion
4. In DABC, DE || BC
(d) BPT
Þ
AD AE = BD CE
(A) 1 ® a, 2 ® b, 3 ® c, 4 ® d
(B) 1 ® d, 2 ® a, 3 ® c, 4 ® b
(C) 1 ® b, 2 ® a, 3 ® c, 4 ® d
(D) 1 ® c, 2 ® b, 3 ® d, 4 ® a
26. The mean and median of 100 items are 50 and 52 respectively. The value of the largest item is 100. It was later found that it is 110 not 100. The true mean and median are _____. (A) 50.10, 52
(B) 50, 52
(C) 50.20, 52
(D) None of these
27. If sec A + tan A = x, then tan A = (A)
2 x
(B)
1 2x
(C)
x 2 - 1 2 x
(D)
2 x x 2 - 1
28. Two friends were discussing their marks in an examination. While doing so they realized that both the numbers had the same prime factors, although one got a score which had two more factors than the other. If their marks are represented by one of the options given below, which of the following options would correctly represent the number of marks they got? (A) 30, 60
(B) 20, 80
(C) 40, 80
(D) 20, 60
29. If sinq and cosq are the roots of the equation ax 2 – bx + c = 0, then a, b, c satisfy the relation ____. (A) b 2 – a 2 = 2ac
(B) a 2 – b 2 = 2ac
(C) a 2 + b 2 = c 2
(D) a 2 + b 2 = 2ac
30. Find the mode of the given data : Classes
Frequencies
10 - 15
30
15 - 20
45
20 - 25
75
25 - 30
35
30 - 35
25
35 - 40
15
Total
(A) 22.89
225
(B) 15.68
(C) 20.35 5
Copyright©2015. Science Olympiad Foundation (SOF)
(D) 22.14 4 th IMO | LevelI | Class 10
4th IMO - 2010
A
31. In the given figure, AD = 3 cm, AE = 5 cm, BD = 4 cm, CE = 4 cm, CF = 2 cm, BF = 2.5 cm, then D
(A) DE || BC
E
(B) DF || AC (C) EF || AB B
(D) None of these
C
F
32. The median of a given frequency distribution is found graphically with the help of ____. (A) Histogram
(B) Ogive
(C) Bar Graph
(D) None of these
33. The value of q will be _____ , if sin 2q = 1 – cos 2q. (A) 45°
(B) 30°
(C) 60°
(1) 2x + 3y = 40 6x + 5y = 10
(a) Coincident lines
(2) 2x + 3y = 40 6x + 9y = 50
(b) Intersecting lines
(3) 2x + 3y = 10 4x + 6y = 20
(c) Parallel lines
(D) All of these
34. Match the column :
(A) 1 ® a, 2 ® b, 3 ® c (B) 1 ® b, 2 ® a, 3 ® c
(C) 1 ® b, 2 ® c, 3 ® a (D) 1 ® c, 2 ® a, 3 ® b
35. The HCF and LCM of two numbers are 33 and 264 respectively. When the first number is divided by 2 the quotient is 33. The other number is _____. (A) 66
(B) 130
(C) 132
(D) 196
36. Find the missing frequencies in the given frequency distribution if it is given that the mean is 1.46. Variables 0 1 2 3 4 5 Total Frequency 46 ? ? 25 10 5 200 (A) 76, 36
(B) 37, 38
(C) 76, 38
(D) 70, 38
37. If one zero of the polynomial 5z 2 + 13z – p is reciprocal of the other, then p is ____ (A) 4
(B) –5
(C) 1
(D) –8
38. In the given figure, ABC is a triangle and GHED is a rectangle. BC = 12 cm, HE = 6 cm, FC = BF and altitude AF is 24 cm. The area of the rectangle is _____. A
2
(A) 56 cm
(B) 54 cm 2 E
D 2
(C) 60 cm
B
(D) 72 cm 2
G
39. Evaluate : cos 2 20° + cos 2 70° + sin 48° sec 42° + cos 40° cosec 50°. (A) 1 4 th IMO | LevelI | Class 10
(B) 3
(C) 2 6
Copyright©2015. Science Olympiad Foundation (SOF)
(D) 0
F
H
C
4th IMO - 2010
40. There are two positive numbers such that sum of twice the first and thrice the second is 39, while the sum of thrice the first and twice the second is 36. The larger of the two is _____. (A) 6
(B) 8
(C) 9
(D) 10
SECTION III : EVERYDAY MATHEMATICS 41. P can do a piece of work in 10 days. Q can do it in 24 days. If R also works with them then it takes only 6 days to complete the whole work. In how many days R alone can complete the whole work? (A) 25
(B) 40
(C) 50
(D) 75
42. 1854 seats in a theatre form a perfect square except for five seats at the back. The number of seats in each row is _____. (A) 42
(B) 43
(C) 47
(D) 48
43. The average weight of Meenu, Binu and Dia is 45 kg. If the average weight of Meenu and Binu is 40 kg and the average weight of Binu and Dia is 43 kg, then the weight of Binu is _____. (A) 17 kg
(B) 20 kg
(C) 26 kg
(D) 31 kg
44. A boat goes 40 km upstream in 8 hours and 36 km downstream in 6 hours. The speed of the boat in standing water is _____. (A) 6.5 km/hr
(B) 6 km/hr
(C) 5.5 km/hr
(D) 5 km/hr
45. If 20 typists can type 480 pages in 6 hours, how many pages will be typed by 25 typists in 4 hours? (A) 256
(B) 576
(C) 900
(D) 400
46. A dealer buys 200 quintals of wheat at ` 1200 per quintal. He spends ` 10,000 on transportation and storage. Then he sells the wheat at ` 13 per kg. His profit percentage is _____. (A) 4%
(B) 5%
(C) 6%
(D) 7%
47. A student who secures 20% marks in an examination fails by 30 marks. Another student who secures 32% marks gets 42 marks more than those required to pass. The percentage of marks required to pass is ______. (A) 20%
(B) 25%
(C) 28%
(D) 30%
48. A sum is being lent at 20% p.a. compound interest. What is the ratio of increase in amount of 4 th year to 5 th year? (A) 4 : 5
(B) 5 : 4
(C) 5 : 6
(D) Can't be determined
49. Pipes A and B can fill a cistern in 10 hours and 15 hours respectively. When a third pipe C which works as an outlet pipe is also open then the cistern can be filled in 18 hours. The outlet pipe can empty a full cistern in _____. (A) 12 hours
(B) 8 hours
(C) 9 hours
(D) 14 hours
50. By selling 8 bananas, a fruit seller gains the selling price of 1 banana. His gain per cent is ____. (A) 12%
(B) 14
2 % 7
(C) 14
1 % 7
7
Copyright©2015. Science Olympiad Foundation (SOF)
(D) 16
2 % 7
4 th IMO | LevelI | Class 10
Class 10 5th
Year 2011
Copyright©2015. Science Olympiad Foundation (SOF)
2
5th IMO - 2011
Section I : Logical Reasoning 1.
Using first, third, sixth and seventh digits of the number 9 3 4 2 6 1 8 5, one time each, how many numbers of two digits are possible which are perfect squares of a number. What is that number? If two such numbers are possible then answer 11, if no such number is possible then answer zero. (A) 0 (B) 7 (C) 9 (D) 11
2.
If 323 × 41 = 14323; 137 × 72 = 27731 and 48 × 87 = 7884, then 34 × 75 = ? (C) 2550 (D) 4357 (A) 5743 (B) 7534
3.
There is a matrix followed by four answer figures. In the matrix there are eight designs and one space is left blank as shown by a question mark. Find which answer figures will replace the question mark.
(A)
(B)
(C)
(D)
4.
If the expressions ‘E < J ≤ H > Z’, ‘H ≤ Y’ and ‘E > F’ are true, which of the following conclusions
will be definitely false ? (A) F < Y (B) Y > E
5.
Six people A, B, C, D, E and F are sitting on the ground in a hexagonal shape. All the sides of
?
(C) F < H
(D) All are true
the hexagon so formed are of same length. A is not adjacent to B or C; D is not adjacent to C or E; B and C are adjacent; F is in the middle of D and C.
Which of the following is not a correct neighbour pair? (B) D and F (C) B and E (A) A and F
6.
In a shop, there were 4 dolls of different heights A, B, C and D. D is neither as tall as A nor as
(D) C and F
short as C. B is shorter than D but taller than C. If Mani wants to purchase the tallest doll, which 7.
one should she purchase ? (A) Only A (B) Only D
(C) Either A or D
(D) Either B or D
Find the missing number in the adjoining figure. S T W 3 15 D J
10 ? P T G
(A) 5
(B) 9
(C) 11
(D) 13
8.
Select a figure from amongst the four alternatives, which when placed in the blank space of the given figure would complete the pattern.
? ?
(A)
(B)
(C)
Copyright©2015. Science Olympiad Foundation (SOF)
(D)
3
5th IMO - 2011 9.
In a row of 40 boys, Satish was shifted 10 places to the right of Rohan and Kewal was shifted 10 places to the left of Vilas. If Vilas was twenty-sixth from the left and there were three boys between
Kewal and Satish after shifting, what was the position of Rohan in the row ? (B) 10th from the left end (A) 10th from the right end th (D) Data inadequate (C) 39 from the right end
10. ‘+’ stands for division, ‘÷’ stands for multiplication, ‘×’ stands for subtraction and ‘–’ stands for
addition. Which one of the following equations is correct ? (A) 18 ÷ 6 – 7 + 5 × 2 = 20 (B) 18 + 6 ÷ 7 × 5 – 2 = 18 (C) 18 × 6 + 7 ÷ 5 – 2 = 16 (D) 18 ÷ 6 × 7 + 5 – 2 = 22
11. At a farm, there are hens, cows, bullocks and keepers to look after them. There are 69 heads less than legs. The number of cows is double than that of the bullocks but the number of cows and hens is the same. There is one keeper per 10 birds and cattle. The total number of hens plus cows
and bullocks and their keepers does not exceed 50. How many cows are there ? (A) 10 (B) 14 (C) 16 (D) 12
12. All the faces of a cube are painted with blue colour. Then it is cut into 125 small equal cubes.
How many small cubes will be formed having no face coloured ? (A) 27 (B) 8 (C) 16
(D) 24
13. In a certain code language, ‘123’ means ‘bright little boy’, ‘145’ means ‘tall big boy’ and ‘637’ means
‘beautiful little flower’. Which digit in that language means ‘bright’ ? (A) 1 (B) 2 (C) 3
(D) 4
14. Which letter will be sixth to the left of the nineteenth letter from the right end of the English
alphabet series ? (A) M
(B) N
(C) X
(D) None of these
15. If animals that live on land and the animals that live in water are represented by two big circles and animals that live both in water and on land are represented by a small circle, the combination of these three can be best represented as _____.
(A)
(B)
(C)
(D)
16. Find the figure from the options which will continue the series established by the problem figures.
(A)
(B)
(C)
(D) None of these
17. Rohit walked 25 m towards south. Then he turned to his left and walked 20 m. He then turned to his left and walked 25 m. He again turned right and walked 15 m. At what distance is he from the starting point and in which direction ?
(A) 35 m East
(B) 35 m North
(C) 40 m East
Copyright©2015. Science Olympiad Foundation (SOF)
(D) 60 m East
4
5th IMO - 2011
18. The adjoining diagram represents those students who play cricket, football and kabaddi. Study the diagram and identify the students who play all the three games. Kabaddi A
B
C
D
E
F
Football G
Cricket
(A) A + B + C
(B) G + E
(C) D + E + G
(D) D
19. In the adjoining figure, find out how the figure will look like after rotation.
(A)
(B)
(C)
(D)
20. In the adjoining figure, count the number of triangles and squares.
(A) 23 triangles, 7 squares
(B) 18 triangles, 8 squares
(C) 20 triangles, 8 squares
(D) None of these
Section II : Mathematical reasoning 21. A set of numbers consists of four 5’s, six 7’s, ten 9’s, eleven 12’s, three 13’s, two 14’s. The approximate difference between mean and median of this set of numbers is _____.
(A) 1
(B) 2
(C) 5
(D) 4
22. In the given figure, ABCD and AEFG are squares. Then in DAGE and DADC which of the following holds ? E
A G
D
(A)
GF AC = AG AD
(B) CF = AF AG DG
B F
C
(C) AF = AC AD AG
Copyright©2015. Science Olympiad Foundation (SOF)
(D) None of these
5
5th IMO - 2011
23. An equilateral triangle is inscribed in a circle of circumference equal to perimeter of a square with side 22 cm. Find its side.
(A) 7 3 cm
(B) 14 cm
(C) 14 3 cm
(D) 17 cm
24. L.C.M. of two prime numbers x and y (x > y) is 161. The value of 3y – x is _____. (A) – 2 (B) – 1 (C) 1 (D) 2 25. If a quadratic polynomial of the form x2 + ax + b has no linear term and the constant term is
negative, then _____. (A) One of the zeroes is reciprocal of the other. (C) One of the zeroes is twice of the other.
(B) One of the zeroes is negative of the other. (D) One of the zeroes is half of the other.
(A) 6, 1
(B) 3, 2
(C) 4, 1
(D) 13, 7
3x + y
26. Find the values of x and y in the given rectangle if its length is cube root of 2197 and width is x + 3y one less than the fourth multiple of first prime number.
27. If l is the last term, d is the common difference and ‘s’ is the sum of n terms of an A.P. be connected by the equation 8ds = (d + 2l)2, then d = _____.
(A) a
(B) 2a
(C) 3a
(D) –a
28. A bridge across a river makes an angle of 30° with the river bank (Fig. given). If the length of the bridge across the river is sum of the arithmetic progression 5, 10, 15, ....., 55, what is the width of the river ?
(A) 160 m
(B) 150 m
(C) 165 m
(D) 155 m
29. If (2, –2), (–2, 1) and (5, 2) are vertices of a right angled triangle, then the area of the triangle is _____.
(A) 12.5 sq. units
(B) 22.5 sq. units
(C) 12 sq. units
(D) 20 sq. units
30. A number is chosen at random among the first 120 natural numbers. The probability of the number
chosen being a multiple of 5 is _____. (A) 1/5 (B) 1/6
(C) 1/7
(D) 1/9
31. If area of a parallelogram with sides ‘l’ and ‘b’ is ‘A’ and that of a rectangle with sides ‘l’ and ‘b’
is ‘B’, then _____. (A) A < B
(B) A = B
(C) A > B
(D) None of these
p q 32. If the roots of a quadratic equation are , − , then the equation is _____. q p (B) pqx2 – (p 2 – q2)x – pq = 0 (A) qx2 – (q2 + p 2)x – pq = 0
(C) px2 – (p 2 + 1)x + p = 0
(D) p 2x2 – (p 2 – q2)x – pq = 0
Copyright©2015. Science Olympiad Foundation (SOF)
6
5th IMO - 2011
33. If x = 7 − 5 , y = 5 − 3 , z = 3 − 7 , then find the value of x3 + y3 + z3 – 2xyz.
(A) − 4 5 − 12 3 + 7 (B) − 4 5 + 2 3 + 2 7
(C) 4 5 + 12 3 + 2 7
(D) 4 5 − 12 3 + 7
34. A hemispherical container with radius 6 cm contains 325 ml of milk. Calculate the volume of milk that is needed to fill the container completely. (p = 3.142)
(A) 117.45 ml
(B) 107.40 ml
(C) 127.45 ml
(D) 127 ml
35. Without using trigonometric tables, evaluate the following :
cos2 20° + cos2 70° sec2 50° − cot 2 40° (A) 1
+ 2 cosec2 58° – 2 cot 58° tan 32° – 4 tan 13° tan 37° tan 45° tan 53° tan 77° (B) 2
(C) – 1
(D) – 2
36. If x, y and z are real numbers such that x + y + z = 5 and xy + yz + zx = 3, what is the largest value that x can have ?
5 3
(A)
37. If
(B)
(C)
19
13 3
(D) None of these
2 3 + 5 + 7 + ..... + n terms units , then the = Volume of cylinder with diameter 7 units and height 11 5 + 8 + 11 + ..... + 10 terms
value of n is _____.
(A) 35
(B) 36
(C) 37
(D) 40
38. A bag contains tickets marked with numbers 179, 180, 172, 127, 155, 115, 143, 122, 175, 222, 232, 162, 112, 132, 192, 182, 174, 132, 32, 131. A ticket is drawn at random. Find the probability that
the ticket drawn has an even digit at ten’s place. (A) 7/19 (B) 3/20 (C) 7/20
(D) 6/19
39. Point A is on x-axis, point B is on y-axis and the point P lies on line segment AB, such that P=
(
)
(2n + 1)2 − (2n − 1)2 , 3 50n + 5 n ; where n = 2 and AP : PB = 5 : 3. Find the coordinates of
points A and B.
32 (A) , 0 ,( 0, 8 ) 3
32 (B) ( 3, 0 ), 0, 3
(C) (4, 0), (0, 3)
32 (D) , 0 , ( 0, 3 ) 3
40. In the right triangle shown here, AB + AD = BC + CD, if AB = x, BC = h and CD = d, then x is equal to _____.
A B C
hd (A) 2h + d
(B) d – h
D
(C) h + d
(D)
1 h 2
Section III : Everyday Mathematics 41. A girl calculates that the probability of her winning the first prize in a lottery is 0.08. If 6000 tickets
are sold, how many tickets has she bought ? (A) 40 (B) 240
(C) 480
Copyright©2015. Science Olympiad Foundation (SOF)
(D) 750
7
5th IMO - 2011
42. Raghav buys a watch for ` 1,20,000. He pays half of the amount in cash and agrees to pay the balance in 12 annual instalments of ` 5000 each. If the rate of interest is 12% and he pays with the instalment the interest due on the unpaid amount, find the total cost of the watch.
(A) 1,27,750
(B) 1,27,000
(C) 1,28,000
(D) None of these
43. A, B and C start at the same time in the same direction to run around a circular stadium. A completes a round in 252 seconds, B in 308 seconds and C in 198 seconds, all starting at the same point. After what time will they meet again at the starting point ?
(A) 26 minutes 18 seconds
(B) 42 minutes 36 seconds
(C) 45 minutes
(D) 46 minutes 12 seconds
44. Assume that a mango and its seed, both are spherical. The radius of the seed is 2/5 of the thickness of the pulp. The seed lies exactly at the centre of the fruit. What per cent of the total volume of the mango is its pulp ?
(A) 90%
(B) 92%
(C) 97.66%
(D) 93%
45. One fourth of a herd of cows is in the forest. Twice the square root of the herd has gone to mountains, and of the remaining, 15 are on the bank of a river. The total number of cows is ____.
(A) 6
(B) 100
(C) 63
(D) 36
46. Vidushi and Sanya distributed ` 100 each in charity. Vidushi distributes money to 5 more people than Sanya and Sanya gives ` 1 more than Vidushi to each person. How many people are recipients of the charity ?
(A) 45
(B) 60
(C) 90
(D) None of these
47. Rahman bought 30 stamps consisting of 20 paise and 30 paise stamps. Given that the stamps cost ` 7.80 altogether, how many 20 paise stamps did he buy ?
(A) 12
(B) 14
(C) 16
(D) 18
2 3 of the votes cast. If, after of the votes have been 3 4 5 of what he needs, then what part of the remaining ratio does he still counted, a candidate has 6 need ?
48. To win an election, a candidate needs
(A)
1 10
(B)
1 8
(C)
1 4
(D)
3 8
49. Raju has 64 small cubes of 1 cm3. He wants to arrange all of them in a cuboidal shape, such that the surface area will be minimum. What is the diagonal of this larger cuboid ?
(A) 4 3 cm
(B) 2 3 cm
(C) 4 cm
(D) 2 cm
50. The Gurgaon office of Microsoft has 1500 executives. Of these 900 subscribe to the Hindustan Times and 750 subscribe to The Hindu. 150 subscribe to both Hindustan Times and The Hindu. If an executive is picked at random, what is the probability that he has subscribed to Hindustan Times?
(A)
2 5
(B)
3 5
(C)
4 5
Copyright©2015. Science Olympiad Foundation (SOF)
(D)
1 5
Class 10 6th
SET A Year 2012
Copyright©2015. Science Olympiad Foundation (SOF)
2
6th IMO - SET A Section I : Logical Reasoning
1.
Some of the letters are missing which are given in that order as one of the options below it. Choose the correct option.
a __ n __ b __ __ ncb __ __ ncb (A) abbbcc
(B) abcbcb
(C) abcaba
(D) bcabab
2. Two ladies and two men are playing bridge a card game and seated at North, East, South and West of a table. No lady is facing East. Persons sitting opposite to each other are not of the same sex.
One man is facing South. Which directions are the two ladies facing? (A) East and West (B) South and East (C) North and West
(D) North and East
3. If 'sand' is called 'air', 'air' is called 'plateau', 'plateau' is called 'well', 'well' is called 'island' and
'island' is called 'sky', then from where will a woman draw water? (A) Well (B) Island (C) Sky
(D) Air
4.
K is brother of N and X, Y is the mother of N, and Z is the father of K. Which of the following
statements is not definitely true ? (A) K is the son of Z (B) Y is the wife of Z
5.
Read the following information carefully and answer the question given below.
(i) There are five types of cards viz. A, B, C, D and E. There are three cards of each type. These
(C) X is the son of Y
(D) Z is the father of X
are to be inserted in envelopes of three colours - Red, Yellow and Brown. There are five envelopes of each colour.
(ii) B, D and E type cards are inserted in red envelopes. A, B and C type cards are to be inserted in yellow envelopes and C, D and E type cards are to be inserted in brown envelopes.
(iii) Two cards each of B and D type are inserted in red envelopes.
Which of the following combinations of colour of the envelope and the number of cards is definitely
correct in respect of E - type cards? (A) Red-1, Yellow- 2 (B) Yellow -1, Brown-2
(C) Red - 1, Brown-2
(D) None of these
6. The given question is based on the symbols/numeric/alphabets as given below:
A & f t Y↑ P Q n * M ≠ r @ Z & C £ ? 8 7 R u V B e
If the first half of the above series is written in the reverse order, then which letter/symbol will be
7 th letter from the left of 15th letter from right end. (A) M (B) n (C) f
7. If
means '×', D means '+',
means '+',
means '–',
(D) Q means '=',
means 'more' and
means
'less', then which one of the options is incorrect?
(A) 10
3
7
(C) 10
7
5
8.
At an office where an interview was conducted to select persons for clerical posts, they came to
4D2 9D3
5
5
4
2
(B) 10 8
2
(D) 10
3 4
15 D 3 8D4
5 7
7 8
9 2
2 5
know that out of 20 persons, 12 knew only typing and 5 knew only shorthand and the rest knew both typing and shorthand. Which of the following diagrams represents this fact?
(A)
(B)
(C)
Copyright©2015. Science Olympiad Foundation (SOF)
(D)
3
6th IMO - SET A 9.
Find the missing number from amongst the given options at the
4 5 7 3 6 4 (B) 42 9 6 (D) 45
place of sign of interrogation (?).
(A) 34
(C) 44
3 4 4 5
2 4 5 5
0 21 22 ?
10. A college starts from 10 a.m. and continues till 1.30 p.m. In this duration there are 5 periods. If 5 minutes are provided before each period to leave the room and enter the other, then what is the
duration of each period? (A) 41 mins (B) 38 mins
(C) 40 mins
(D) 42 mins
11. If in each of the following groups of numbers, last two digits are interchanged and after that they are arranged in descending order, then what will be the first digit of the middle group?
(A) 7
257, 491, 623, 846, 738 (C) 8
(B) 4
(D) 6
12. In a certain code language, (i) 'pit na som' means 'bring me water'; (ii) 'na jo tod' means 'water is life'; (iii) 'tub od pit' means 'give me toy'; (iv) 'jo lin kot' means 'life and death'; Which of the following represents 'is' in that language ? (A) jo (B) na (C) tod (D) lin 13. How many triangles are there in the figure below?
(A) 5
(B) 6
(C) 8
(D) 10
14. The question consists of a set of three figures X, Y and Z showing a sequence of folding of a piece of paper. Fig. (Z) shows the manner in which the folded paper has been cut. These three figures are followed by options from which you have to choose a figure which would most closely resemble the unfolded form of fig. (Z).
X
(A)
(B)
Y
Z (C)
(D)
15. Which of the following options does not have the same relationship between them as is there between
DH : EG ? (A) VZ : XY
16.
Find the missing term. (A) 10 (B) 13 (C) 12 (D) 14
(B) LP : MO
(C) BG : CF
Copyright©2015. Science Olympiad Foundation (SOF)
(D) QT : RS F
I
D
M
4
? 6
9
4
6th IMO - SET A
17. Select a figure from the options which satisfies the same conditions of placement of the dots as in figure (X) ?
(A)
(B)
(C)
(D)
18. On a peculiar clock shown here, the hands move in an unusual way. Discover the system as revealed from the five positions, (i to v) shown below, and find the next position to be formed in fig (vi) from the options given below. 1 1 9
3 5
2 (A) 9
10
8
6 (iv)
10
?
(v)
(vi)
10 3
(B)
3
9
3 7 6 (iii)
6 (ii)
(i)
10
(C) 9
10 (D) 9
3
12
6
6
19. Machine 'A' produces 60% cloth and remaining is produced on machine 'B'. 25% of each machine's production is defective. Choose the diagram that best represents the situation. The shaded portion depicts defective cloth.
(A)
(B)
(C)
(D)
20. Select a figure from the options, which is not embedded in the given figure (X).
(A)
(B)
(C)
(D)
Section II : Mathematical reasoning 21. If
a 2 x 2 + b2 y 2 + c 2 z 2 x y z = = , then 3 3 3 a b c a x + b y + c z
(A)
xyz abc
(B)
xyz abc
3/2
= _______ . (C)
xyz (abc )2
Copyright©2015. Science Olympiad Foundation (SOF)
(D)
( xyz )2 abc
5
6th IMO - SET A
22. A sports club has 130 members. An increase of 10% in the number of men and 20% in the number of women brought up the membership to 148. How many men and women were there originally?
(A) 90 men, 40 women
(B) 80 men, 50 women
(C) 60 men, 70 women
(D) 50 men, 80 women
23. Radhika draws the figure of an aeroplane as given in the figure. Here the wings ABCD and GHIF forms a parallelogram. The tail DEF is an isosceles triangle, the cockpit CKI is a semi-circle and middle-part DCIF is a square. The measurements (in cms) are given in the figure. The area of the plane figure if BP ^ CD and HQ ^ FI is _____.
(A) 97.24 cm2
(B) 98.14 cm2
(C) 96.82 cm2
(D) 90 cm2
24. The average of five consecutive natural numbers is m. If the next three natural numbers are also
included, how much more than m will the average of these 8 numbers be ? (A) 1 (B) 1.4 (C) 1.5 (D) 2
25. How many sides does a regular polygon have, whose interior angle is eight times its exterior
angle ? (A) 16
(B) 24
(C) 18
(D) 20
26. In the given figure, BD is the diameter of the circle with centre O,
∠COD = 92° and ∠ABD = 65°. Then y equals ______. (A) 65° (B) 46° (C) 44° (D) 21°
27. The incomes of A, B and C are in the ratio 7 : 9 : 12 and their spendings are in the ratio 8 : 9 : 15. If A saves (1/4)th of his income, then the savings of A, B and C are in the ratio _____.
(A) 56 : 99 : 69
(B) 69 : 56 : 99
(C) 99 : 56 : 69
(D) 99 : 69 : 56
28. The given pie chart shows the hourly distribution of all the major activities of a student.
Find the difference between the time (in percent) the students spends in games and sleeping. Also, what is the difference in time (in hours) spent in school and in homework.
(A) 30%, 2 hrs
(B) 40%, 3 hrs
(C) 25%, 4 hrs
(D) None of these
29. A conical vessel of radius 6 cm and height 8 cm is filled with water. A sphere is lowered into the water and its size is such that when it touches the sides of the conical vessel, it is just immersed. How much water will remain in the cone after the overflow ?
(A) 188.57 cm3
(B) 160 cm3
(C) 181.30 cm3
(D) 175.46 cm3
Copyright©2015. Science Olympiad Foundation (SOF)
6
6th IMO - SET A
30. A circle of radius 'r' has been inscribed in a triangle of area A. If the semi-perimeter of the triangle be S, then ____.
(A) S = Ar
(B) r 2 =
S A
(C) r =
A S
(D) r =
A2 S
31. A group of girls planned a picnic. The budget for food was ` 2400. Due to illness, 10 girls could not go to the picnic and cost of food for each girl increased by ` 8. How many girls had planned
the picnic? (A) 60
(B) 50
(C) 65
(D) 57
32. There are two examination rooms A and B. If 10 candidates are sent from A to B, the number of students in each room is the same. If 20 candidates are sent from B to A, the number of students
in A is double the number of students in B. Find the number of students in each room. (A) A = 60, B = 40 (B) A = 110, B = 60 (C) A = 95, B = 70 (D) A = 100, B = 80
33. A number x is selected from the numbers 1, 2 & 3 and then a second number y is randomly selected from the numbers 1, 4 & 9. What is the probability that the product xy of the two numbers will be
less than 9? 5 (A) 9
(B)
9 10
(C)
2 9
(D)
7 10 E
34. The given diagram represents some beams which supports part of a roof.
If AC = 8 metres, ∠BAC = 60°, ∠ACD = 30°, ∠ADC = 90° and ∠CAE = 90°, then the length of the beam AD is ______. (A) 5 cm (B) 8 cm (C) 4 cm (D) 12 cm
A
D
60° 8
30°
B
C
35. The sum of n terms of the three arithmetical progressions are S1, S2 and S3. The first term of each is unity and the common differences are 1, 2 and 3 respectively, then _____.
(A) S1 + S 3 = 2S 2
(B) S1 – S 3 = S 2
(C) S1 + S 2 = S 3
(D) S1 + S 3 = S 2
36. Three men, four women and six children can complete a work in seven days. A woman does double the work a man does and a child does half the work a man does. How many women alone can complete the work in 7 days ? (A) 14 (B) 8 (C) 7 (D) 12 37. In the adjoining figure, M is the midpoint of BC and AE is half of BE, then AD is _____.
(A) (B) (C) (D)
12.44 17.36 16.27 15.65
cm cm cm cm
38. If 47.2506 = 4 A +
(A) 53.6003
7 5 + 2C + + 6E, then the value of 5A + 3B + 6C + D + 3E is ______. B D (B) 53.603 (C) 153.6003 (D) 213.0003
39. Kruti took a loan at simple interest at 6 % in the first year with an increase of 0.5 % in each
subsequent year. She paid ` 3375 as interest after 4 years. How much loan did she take? (A) ` 12500 (B) ` 15800 (C) ` 33250 (D) ` 30000 Copyright©2015. Science Olympiad Foundation (SOF)
7
6th IMO - SET A
40. What is more favourable for a buyer - discount series P of 20%, 15% and 10% or a discount series
Q of 25%, 12% and 8% ? (A) P (B) Q
(C) Both (P) and (Q)
(D) None of these
Section III : Everyday Mathematics 41. Garima purchased a briefcase with an additional 10% discount on the reduced price after deducting 20% on the labelled price. If the labelled price was ` 1400, at what price did she purchase the briefcase? (A) ` 980 (B) ` 1008 (C) ` 1056 (D) ` 1120 42. A plot of land in the form of a rectangle has a dimension 240 m × 180 m. A drainlet 10 m wide is dug all around it (on the outside) and the earth dug out is evenly spread over the plot, increasing
its surface level by 25 cm. The depth of the drainlet is _______. (A) 1.375 m (B) 1.5 m (C) 1.227 m
(D) None of these
43. There are three pipes fitted in a tank. First two pipes when operated simultaneously, fill the tank in the same time as filled by the third pipe alone. The second pipe fills the tank 7 hours faster than the first pipe and 3 hours slower than the third pipe. The approximate time required by each pipe to fill the tank simultaneously is _____.
(A) 12 hrs, 7 hrs, 3 hrs
(C) 15 hrs, 10 hrs, 6 hrs
1 1 1 hrs, 8 hrs, 5 hrs 2 2 2 (D) 35 hrs, 30 hrs, 26 hrs
(B) 15
44. Two customers are visiting a particular shop in the same week (Monday to Saturday). Each is equally likely to visit the shop on any one day as one another. Find the probability that both will
visit the shop on (i) the same day, (ii) consecutive days. 1 3 1 5 1 5 (A) (B) (C) , , , 6 18 5 18 6 18
(D)
1 3 , 5 18
45. A cake of 6 cm radius is divided into 3 sectors with central angles 120°, 150° and 90° respectively. The ratio of the areas of the three sectors is ____.
(A) 4 : 3 : 5
(B) 5 : 3 : 4
(C) 3 : 4 : 5
(D) 4 : 5 : 3
46. A, B and C starts cycling around a circular path in the same direction at same time. The circumference of the path is 2400 m. If the speed of A is 300 m/min, speed of B is 480 m/min and C is 150 m/min and they start from the same point, then after what time interval they will be together
at the starting point ? 2 (A) 1 hrs 3
1 (B) 1 hrs 3
(C) 3
1 hrs 3
(D) 3
2 hrs 3
47. A trader marks his goods at 20% above the cost price. He sold half the stock at the marked price, one quarter at a discount of 20% on the marked price and the rest at a discount of 40% on the
marked price. His total gain is ______. (A) 2 % (B) 4.5 %
(C) 13.5 %
(D) 15 %
48. Mohit went from Delhi to Shimla via Chandigarh by car. The distance from Delhi to Chandigarh is 3/4 times the distance from Chandigarh to Shimla. The average speed from Delhi to Chandigarh was one and a half times that from Chandigarh to Shimla. If the average speed for the entire
journey was 49 km/hr, what was the average speed from Chandigarh to Shimla ? (A) 39.2 km/hr (B) 63 km/hr (C) 42 km/hr (D) 35 km/hr Copyright©2015. Science Olympiad Foundation (SOF)
8
6th IMO - SET A
49. In a Printing House, machine P can print one lakh books in 8 hours, machine Q can print the same number of books in 10 hours while machine R can print them in 12 hours. All the machines are started at 9 a.m. While machine P is closed at 11 a.m. and the remaining two machines complete the work. Approximately at what time will the work be finished ?
(A) 11 : 30 a.m.
(B) 12 noon
(C) 12 : 30 p.m.
(D) 1 p.m.
50. A railway half ticket costs half the full fare. But, the reservation charges are the same on the half ticket as on the full ticket. One reserved first class full ticket from Mumbai to Ahmedabad costs ` 216 while one full and one half reserved ticket costs ` 327. What is the value of the first class
full ticket and what is the reservation charge respectively? (A) ` 3, ` 210 (B) ` 210, ` 210 (C) ` 6, ` 220 SPACE FOR ROUGH WORK
Copyright©2015. Science Olympiad Foundation (SOF)
(D) ` 210, ` 6
Class 10 6th
SET B Year 2012
Copyright©2015. Science Olympiad Foundation (SOF)
2
6th IMO - SET B Section I : Logical Reasoning
(A) D
2 A C 3 4
L
(B) D
DL2CA34 L A 4 (C) D C 3 2
L2 A 4 C 3
(D) D
2L
Find the water image of the given combination. A C 3
4
1.
2. The different positions of a dice has been shown. What digit will be opposite to digit 4?
3.
(A) 6
(B) 1
(C) 5
(D) 2
Find out the figure from amongst the options which can be formed from the pieces given in Fig. (X).
(A)
4.
Find out the wrong term in the given number series.
(B)
(C)
1236, 2346, 3456, 4566, 5686 (B) 3456 (C) 4566
(D)
(A) 1236
(D) 5686
5.
Read the following letter-number sequence carefully and answer the question. J K P D F G H 6 9 2 8 Q E M 7 4 3 Z Y B T 5 4 2 3
If all the odd numbers are dropped from the above sequence, which of the following element would
be seventh to the right of twelfth element from the right end? (A) B (B) Z (C) Y
6.
Mohit walks 6 km to the east and then turns to the south and walks 5 km. Again he turns to the
(D) 4
east and walks 6 km. Next, he turns northwards and walks 10 km. How far is he now from his
starting point? (A) 5 km
(B) 12 km
(C) 13 km
(D) 17 km
7. Eight friends P, Q, R, S, T, U, V and W are sitting around a circle facing the centre. V is third to the right of Q and is second to the left of R. Q is second to the left of T and on the immediate right of S. U is between Q and T. P is not on the left of R.
Which of the following is the correct position of W?
(A) On the immediate left of V
(B) On the immediate right of V
(C) Between U and V
(D) On the immediate right of R
8.
Pointing to a photograph a woman says : "He is the only son of the wife of my husband's father". How is the man related to the woman?
(A) Son
(B) Son-in-law
(C) Brother-in-law
Copyright©2015. Science Olympiad Foundation (SOF)
(D) Husband
3
6th IMO - SET B 9.
Which of the following option figures will continue the same series as established by the Problem Figures?
(A)
+ + +
(B)
(C)
+ + +
+ + +
+ + (D) +
10. Find the mirror image of Fig. (X) from amongst options, if the mirror is placed to the right of Fig. (X).
(A)
(B)
(C)
(D)
11. In a certain code language 'you require more concentration' is written as 'tig seeg loog roog'; 'stress require for arithmetic' is written as 'miya lota loog kota'; 'non-verbal is more easy' is written as 'seeg yoog beeg laa' and 'stress more on non-verbal' is written as 'seeg mota yoog miya'. Then
what is the code for 'require'? (A) yoog (B) loog
(C) miya
(D) seeg
12. Following question is based on the 5 three-digit numbers given below: 517 394 823 976 465
If the position of the first and the second digits in each of the above numbers are interchanged,
which of the following will be the third digit of the highest number? (A) 7 (B) 4 (C) 3
(D) 6
13. Nihal is taller than Sumit, who is shorter than Rohit. Vipin is taller than Akash. Anshu is shorter than Vivek. Neither Vipin nor Vivek is the tallest. If Rohit is standing second in decreasing order
of height, who will stand in the middle in the group of these seven persons? (A) Vipin (B) Vipin or Vivek (C) Anshu (D) Can't be determined
14. Fig. (i) & (ii) of the Problem Figures bears a certain relationship. Select a Fig. (iii) from the options which bears the same relationship to the Fig. (iv) of the Problem Figures.
(A)
(B)
(C)
(D)
15. How many pairs of letters are there in the word GOALKEEPER which have the same number of
letters between them as in English alphabet? (A) Five (B) Four
(C) Seven
Copyright©2015. Science Olympiad Foundation (SOF)
(D) Six
4
6th IMO - SET B
16. In the question, two Problems Figures, followed by four Answer Figures (A), (B), (C) and (D) are given. The two Problem Figures have some common characteristics/features. Find out one figure out of the four Answer Figures which has the same features/characteristics. Problem Figures
(A)
(B)
+ +
(C)
+
×
(D)
17. Select a figure from the options which completes the Fig. (X)?
(A)
(B)
(C)
(D)
18. The question is based on the following information:
'A @ B' means 'A is added to B'.
'A * B' means 'A is multiplied by B'.
'A # B' means 'A is divided by B'.
'A $ B' means 'B' is subtracted from A'.
In the question below, some information is given. You have to find out which expression correctly represents the statement.
Number of boys (B) in a class is equal to one-fourth of three times the number of girls (G) in the
class. (A) B = (3 # G) * 4
(B) B = (3 * G) @ 4
(C) B = (3 * G) # 4
(D) B = (3 $ G) # 4
19. '2' is subtracted from each odd digit and '1' is added to each even digit in the number 7652348. Which of the following will be the sum of the second digit from the right and the third digit from
the left of the new number thus formed? (A) 10 (B) 8
(C) 4
(D) 6
20. The question below is based on the given diagram. You have to take the given diagram to be true even if it seems to be at variance from commonly known facts and then decide which of the given options logically follows the given diagram. BPO employees
A
E
C D B
Population earning more than ` 10,000 per month
Graduate population
Which of the following represents the population which is graduate, employed in BPO and earning
more than ` 10,000 a month? (A) Only C (B) C and D
(C) A, C and D
Copyright©2015. Science Olympiad Foundation (SOF)
(D) Only B
5
6th IMO - SET B Section II : Mathematical reasoning
21. H.C.F. of 3240, 3600 and a third number is 36 and their L.C.M. is 2 4 × 35 × 52 × 72. The third number
is ______. (A) 22 × 35 × 72
(B) 22 × 53 × 72
(C) 25 × 52 × 72
(D) 23 × 35 × 72
22. In the given figure, BC = AC = AD, ∠EAD = 81°. Find the value of x.
(A) 45°
(B) 54°
(C) 63°
(D) 36°
23. If x = 21/3 + 2–1/3, then the value of 2x 3 – 6x will be ______. (A) 5 (B) –5 (C) 1
(D) 0
3 , find the value of cotq + cosecq. 5 (B) 2
(D) 0
24. If cosq =
(A) 1
(C) 3
25. The following table gives weekly wages in rupees of workers in a certain commercial organization. The frequency of class 49 - 52 is missing. It is known that the mean of the frequency distribution is 47.2. Find the missing frequency. Weekly wages (`)
40 - 43
43 - 46
46 - 49
49 - 52
52 - 55
31
58
60
?
27
Number of workers (A) 40
(B) 38
(C) 44
(D) 42
26. ABCD is a parallelogram. The diagonals AC and BD intersect at a point O. If E, F, G, and H are the mid-points of AO, DO, CO and BO respectively, then the ratio of (EF + FG + GH + HE) to (AD + DC + CB + BA) is _____. (A) 1 : 1 (B) 1 : 2 (C) 1 : 3 (D) 1 : 4 27. If the 3rd and 7th terms of an A.P. are 17 and 27 respectively. Find the first term of the A.P. (A) 9 (B) 12 (C) 14 (D) None of these 28. What must be subtracted from the polynomial f(x) = x4 + 2x 3 – 13x 2 – 12x + 21 so that the resulting
polynomial is exactly divisible by x 2 – 4x + 3? (A) 2x – 3 (B) 2x + 3
(C) x + 3
(D) 3x – 2
29. If –5 is a root of the quadratic equation 2x 2 + px – 15 = 0 and the quadratic equation p(x 2 + x) + k = 0 has equal roots, find the value of k. 4 7 7 8 (B) (C) (D) (A) 7 4 8 7 30. In the given figure, AB is diameter of the circle. C and D lie on the semicircle. If ∠ABC = 65° and ∠CAD = 45°, then ∠DCA is ______.
(A) 45°
(B) 25°
(C) 20°
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(D) 10°
6
6th IMO - SET B
31. Find the value of a for which the following system of equations has infinitely many solutions.
2x + 3y = 7
(a – 1)x + (a + 2)y = 3a (C) a = 5
(A) a = 4
(B) a = 7
(D) a = 6
32. In the given figure, ∠A = ∠CED. Find the value of x.
(A) 8 cm
(B) 5 cm
(C) 7 cm
(D) 6 cm
33. If 5 5 × 53 ÷ 5 −3/2 = 5 a +2 , then the value of a is ______.
(A) 4
(B) 5
(C) 9
(D) 16
34. If x be a rational number and y be an irrational number, then _____.
(A) Both x + y and xy are necessarily irrational.
(B) Both x + y and xy are necessarily rational.
(C) xy is necessarily irrational, but x + y can be either rational or irrational.
(D) x + y is necessarily irrational, but xy can be either rational or irrational.
35. If the sum of the zeroes of the quadratic polynomial f(t) = kt 2 + 2t + 3k is equal to their product, find the value of k.
(A) 5
(B) −
36. If sin θ =
(A)
2 3
(C) 7
(D) 0
3 cosec2 θ − cot 2 θ , find . 4 sec2 θ − 1
7 3
5 3
(B)
(C)
2 3
5 3
(D)
37. The following is the distribution of height of students of a certain class in a certain city. Height (in cms)
160 - 162
Number of students
Find the median height.
(A) 172.94
163 - 165
15
166 - 168
169 - 171
172 - 174
142
127
18
118
(B) 161.36
(C) 150.53
(D) 167.13
38. Which of the following statements is TRUE?
(A) The value of tan A is always less than 1.
(C) sinq =
4 , for some angle q . 3
(B) sec A =
12 , for some value of angle A. 5
(D) cot A is the product of cot and A.
39. Two dice are tossed. The probability that the total score is a prime number is _____.
(A)
1 6
(B)
5 12
(C)
1 2
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(D)
7 9
7
6th IMO - SET B
40. A spherical ball of lead 6 cm in radius is melted and recast into three spherical balls. The radii of
two of these balls are 3 cm and 4 cm. What is the radius of the third ball? (A) 4.5 cm (B) 5 cm (C) 6 cm (D) 7 cm
Section III : Everyday Mathematics 41. Shubham travels 760 km to his home partly by train and partly by car. He takes 8 hours if he travels 160 km by train and the rest by car. He takes 12 minutes more if he travels 240 km by train and the rest by car. Find the speed of the train and the car respectively (in km/hr).
(A) 40, 80
(B) 60, 120
(C) 80, 100
(D) 100, 120
42. Titan sells a wrist watch to a wholesaler making a profit of 10%. The wholesaler, in turn, sells it to the retailer making a profit of 10%. A customer purchases it by paying ` 990. Thus the profit of retailer is 2
(A) ` 768
3 % . What is the cost incurred by the Titan to produce it? 11 (B) ` 750 (C) ` 800 (D) ` 820
43. A cell-phone is available for ` 2500 cash or ` 520 cash down payments followed by 4 equal monthly instalments. If the rate of interest charged is 25% per annum, calculate the monthly instalment.
(A) ` 520
(B) ` 480
(C) ` 550
(D) None of these
44. A well with 14 m inside diameter is dugout 15 m deep. The earth taken out of it has been evenly spread all around it to a width of 21 m to form an embankment. What is the height of the
embankment? (A) 2 m
(B) 1 m
(C) 3 m
(D) 4 m
45. Two trains starting at the same time from two stations 300 km apart and going in opposite directions, cross each other at a distance of 160 km from one of them. The ratio of their speeds is _____.
(A) 7 : 9
(B) 16 : 20
(C) 8 : 7
(D) None of these
46. The monthly salary of Megha and Beena together is ` 28,000. The salary of Megha and Beena is increased by 25% and 12.5% respectively, then the new salary of Beena becomes 120% of the new salary of Megha. The new (or increased) salary of Megha is ______.
(A) ` 15,000
(B) ` 18,000
(C) ` 14,000
(D) ` 16,000
47. Latika, Garima and Priya are three sisters. Latika and Garima are twins. The sum of the ages of Latika and Garima is same as that of Priya alone. Three years earlier the ratio of age of Latika and Priya was 2 : 7. What will be the age of Garima 3 years hence?
(A) 21 years
(B) 16 years
(C) 8 years
(D) 12 years
48. Two pencils are 24 cm and 42 cm. If we want to make them of equal size then minimum number of similar pencils is _____.
(A) 6
(B) 11
(C) 12
(D) None of these
49. I know a two digit number, but when its digits interchanges their places, we get another two digit number. But when these two digit numbers are added, it amounts to 99. Further if I just consider the difference between these numbers, it comes out to be 45. What is the number which I know?
(A) 27
(B) 38
(C) 72
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(D) Data insufficient
8
6th IMO - SET B
50. Samay has a right circular cylinder which he inserted completely into a right circular cone of height 30 cm. The vertical angle of the cone is 60° and the diameter of the cylinder is 8 3 cm. What is the volume of the cone?
(A)
3000 π cm3 7
(B) 3000p cm3
(C) 4860p cm3
SPACE FOR ROUGH WORK
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(D) Can't be determined
Class 10 7th
SET A Year 2013
Copyright©2015. Science Olympiad Foundation (SOF)
2
7th IMO - Set A
logical reasoning 1.
Choose the correct option that will continue the same pattern and replace the question mark in the given series. 3, 12, 27, 48, 75, 108, ?
A. B. C. D.
2.
147 162 183 192
A.
In a certain code, PLEADING is written as FMHCQMFB. How is SHOULDER written in that code?
B.
A. B. C. D.
C.
3.
Q's mother is sister of P and daughter of M. S is daughter of P and sister of T. How is M related to T?
KCDQTIPV QDCKVPIT QDCKTIPV TIPVQDCK
A. B. C. D.
4.
Read the following information carefully and answer the question that follows :
(i) Five friends P, Q, R, S and T travelled to five different cities; Chennai, Kolkata, Delhi, Bangalore and Hyderabad by different modes of transport; Bus, Train, Aeroplane, Car and Boat from Mumbai. (ii) The person who travelled to Delhi did not travel by boat. (iii) R went to Bangalore by car and Q went to Kolkata by aeroplane. (iv) S travelled by boat whereas T travelled by train. (v) Mumbai is not connected by bus to Delhi and Chennai. Which of the following combinations of place and mode is not correct ? A. Delhi-Train B. Kolkata-Aeroplane C. Hyderabad-Car D. Chennai-Boat
5.
Aunt Father Sister Maternal Grandfather or Maternal Grandmother
The given question consists of five figures marked P, Q, R, S and T called the Problem Figures. Select a figure from the options which will continue the same series as established by the five Problem Figures.
D.
6.
Find the number of triangles in the given figure.
A. B. C. D.
7.
The door of Aditya's house faces East. From the back side of his house, he walks straight 50 metres, then turns to the right and walks 50 metres again. Finally, he turns towards left and stops after walking 25 metres. Now, Aditya is in which direction from the starting point ?
A. B. C. D.
8.
Forty boys are standing in a row facing the North. Arun is eleventh from the left and Deepak is thirtyfirst from the right end of the row. How far will Shreya, who is third to the right of Arun in the row, be from Deepak ?
A. B. C. D.
12 15 14 None of these
South-east North-east West North-west
2nd 3rd 4th 5th
Copyright©2015. Science Olympiad Foundation (SOF)
3
7th IMO - Set A 9.
If 'Q' denotes '+', 'J' denotes '×', 'T' denotes '–' and 'K' denotes '÷', then 30 K 2 Q 3 J 6 T 5 = ?
A. B. C. D.
18 28 31 103
10. Which of the following is the mirror image of the given word, if the mirror is placed vertically left? N otification
A. B. C. D.
15. If the third, fourth, fifth, seventh and tenth letters of the word PERSONALITY forms a meaningful word then first letter of the word is the answer. If no word is possible, then 'X' is the answer and if more than one such word is formed, then 'M' is the answer.
A. B. C. D.
R X O M
16. Find the missing character.
T W 3
11. Find out how many such pairs of letters are there in the given word each of which has as many letters between them in the word as in the English alphabet. ADVERTISEMENT A. Three B. Four C. Five D. More than five
J
A. B. C. D.
T
10
15
S
D
? P G
5 9 11 13
17. The number of cubes required to make the given figure is ______.
12. The triangle represents females, rectangle represents housewife and circle represents school teachers, then the number representing females who are school teachers but unmarried is
A. B. C. D.
2 4 3 8
13. How many 8's are there in the following number series each of which is exactly divisible by its immediately preceding and also divisible by its immediately succeeding number?
A. B. C. D.
31 32 33 34
18. Select the figure from the options which is embedded in the given Fig. (X).
824517284842282698454832843183
A. B. C. D.
1 4 3 2
14. Choose the group which is different from the rest.
A. B. C. D.
MEWGN PBQTX DRYSN CGHKV
A.
B. C.
D.
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4
7th IMO - Set A
19. In the given question, two rows of numbers are given. The resultant number in each row is to be worked out separately based on the following rules and the question below the rows of numbers is to be answered. The operations of numbers progress from left to right.
Rules
I.
If an odd number is followed by a two-digit even number, then they are to be added. II. If an odd number is followed by a two-digit odd number, then the second number is to be subtracted from the first number. III. If an even number is followed by a number which is a perfect square of a number, then the second number is to be divided by the first number. IV. If an even number is followed by a two-digit even number, then the first number is to be multiplied by the second number. 13 11 4 17 13 12
A. B. C. D.
48 69 75 96
20. Which of the following options will complete the figure matrix?
A.
B. C.
If the resultant of the first set of numbers is multiplied by the resultant of the second set of numbers, what will be the outcome?
D.
MATHEMATICAL REASONING 21. If one root of the equation a(b – c)x2 + b(c – a)x + c(a – b) = 0 is 1, then the other root is ___. b (c − a ) a (b − c) B. A. a (b − c) c ( a − b) a (b − c) c ( a − b) C. D. b (c − a ) a (b − c) 22. If H.C.F of (x – 5)(x2 – x – a) and (x – 4) (x2 – 2x – b) is (x – 4)(x – 5), find the values of a and b respectively.
A. B. C. D.
15, 10, –8, 12,
18 7 10 15
24. ABCD is a cyclic quadrilateral. AE is drawn parallel to CD and BA is produced. If ∠ ABC = 92° and ∠FAE = 20°, then ∠BCD =
A. B. C. D.
88° 108° 115° 72°
25. If xcos3q + ysin3q = sinqcosq and xcosq = ysinq, then x2 + y 2 =
23. What is the sum of an A.P. whose first term is a, the second term is b and the last term is c? (b + c − 2a )(a + c) A. 2(b − a ) (b + c + a)(a + c) B. 2b − a 2(a + c)(b − c + 2a ) C. b+a (b + c − 2a )(a − c) D. b+a
A. B. C. D.
0 4 1 2
26. Find the coordinates of the points which trisect the line joining (–3, 5) and (6, –7).
A. B. C. D.
(0, 1) and (3, –3) (–1, –1) and (0, 3) (2, 0) and (1, 1) (2, 2) and (0, 1)
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5
7th IMO - Set A
31. The product of 12% of an integer and 20% of the next integer is 61.2. Find the integer.
x8 − a 8 27. Express in lowest terms : 6 x − a6 2 2 2 2 ( x + a )( x − a ) A. ( x 2 + ax + a 2 )2
B.
C.
D.
( x 2 + a 2 )( x 4 + a 4 ) ( x 2 + ax + a 2 )( x 2 − ax + a 2 ) 2
2
4
A.
( x + a )( x + a ) ( x 2 − ax + a 2 )2 ( x 2 + a 2 )( x 4 + a 4 )
( x 2 + ax − a 2 )( x 2 − ax + a 2 )
33. Find the value of x in the given figure, where O is the centre of the circle.
(3 x 2 − 14)
B.
C.
D.
50 –51 63 Both A and B
32. Find the values of p and q respectively for which the following system of linear equations has infinite solutions. 2x + 3y = 7 (p + q)x + (2p – q)y = 21 A. 2, 6 B. –7, 3 C. –3, –5 D. 5, 1
4
28. Express as a rational expression. 1 1 2 4 − − − x − 1 x + 1 x2 + 1 x4 + 1
A. B. C. D.
x2 − 1 ( x 2 + 3) x4 + 1 8 8 ( x − 1) 2( x + 4) x +1
29. A point D is on the side BC of an equilateral DABC 1 such that DC = BC. Then AD 2 = 4 A. 13 CD2 B. 9 AB2 C. 6 CD2 D. 12 BC 2 30. In the given figure, AB, EF and CD are parallel lines. Given that EG = 5 cm, GC = 10 cm and DC = 18 cm, then EF = A. 9 cm B. 25 cm C. 13 cm D. 16 cm
A. B. C. D.
80° 160° 100° 105°
34. If sinq + cosq =
A.
B.
2 −1
C. D.
2 +1 –1
2 sin(90° – q), then cotq =
1
35. Find k, so that 4k + 8, k3 + 3k + 6 and 3k2 + 4k + 4 are three successive terms of an A.P.
A. C.
0 –1
B. D.
2 Both A and B
EVERYDAY MATHeMATICS 36. A lot of 24 bulbs contains 25% defective bulbs. A bulb is drawn at random from the lot. It is found to be not defective and it is not put back. Now, one bulb is drawn at random from the rest. What is the probability that this bulb is not defective?
A. B. C. D.
18/23 15/24 17/23 20/23
37. The mean height of the 10 girls of a class is 1.4 m and the mean height of the 30 boys of the class is 1.45 m. Find the approximate mean height of the 40 students of the class.
A. B. C. D.
1.39 1.46 1.42 1.44
m m m m
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6
7th IMO - Set A
38. A man sold a chair and a table together for ` 760 thereby making a profit of 25% on chair and 10% on table. By selling them together for ` 767.50, he would have made a profit of 10% on chair and 25% on table. Find the cost price of the table.
A. B. C. D.
` ` ` `
300 315 325 350
39. 15 pastries and 12 biscuit packets have been donated for a school fete. These are to be packed in several smaller identical boxes with the same number of pastries and biscuit packets in each. How many biscuit packets and how many pastries respectively will each box contain?
A. B. C. D.
3, 3, 4, 5,
3 4 5 4
40. A person was asked to state his age in years. His reply was, "Take my age three years hence, multiply it by 3 and then subtract three times my age three years ago and you will know how old I am." What was the age of the person?
A. B. C. D.
18 20 24 32
years years years years
41. A girl of height 90 cm is walking away from the base of a lamp-post at a speed of 1.2 m/sec. If the lamp is 3.6 m above the ground, find the length of her shadow after 4 seconds.
A. 1.6 m B. 1.4 m
C. D.
4.2 m 3.6 m
42. A person can row boat at the rate of 5 km/hr in still water. He takes thrice as much time in going 40 km upstream as in going 40 km downstream. Find the speed of the stream.
A. B. C. D.
3.4 km/hr 2 km/hr 5 km/hr 2.5 km/hr
43. A man repays a loan of ` 3250 by paying ` 20 in the first month and then increases the payment by ` 15 every month. How long will it take him to clear the loan?
A. B. C. D.
60 20 15 25
months months months months
44. A tree 12 m high, is broken by the wind in such a way that its top touches the ground and makes an angle 60° with the ground. At what height from the bottom the tree is broken by the wind?
A. B. C. D.
5.569 1.732 5.916 2.456
m m m m
45. Along a yard 225 metres long, 26 trees are planted at equal distances, one tree being at each end of the yard. What is the distance between two consecutive trees?
A. B. C. D.
8 metres 9 metres 10 metres 15 metres
Achievers Section 46. There is a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statements is/are sufficient to answer the given question.
statement II alone are not sufficient to answer the question.
B.
If the data in statement II alone are sufficient to answer the question, while the data in statement I alone are not sufficient to answer the question.
C.
If the data either in statement I or in statement II alone are sufficient to answer the question.
D.
If the data even in both statements I and II together are not sufficient to answer the question.
What is the volume of a cube?
I.
The area of each face of the cube is 64 square metres. II. The length of one side of the cube is 8 metres. A. If the data in statement I alone are sufficient to answer the question, while the data in
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7
7th IMO - Set A
(iv) a4 + b4 =
p be a rational number, such q that the prime factorisation of q is not of the form 2m × 5n , where m, n are non-negative integers. Then, x has a decimal expansion which is non terminating repeating.
A. B. C. D.
Statement 2 : 64 is a terminating repeating. 455 A. Statement 1 is true but statement 2 is false. B. Statement 1 is false but statement 2 is true. C. Both the statements is true. D. Both the statements is false.
47. Which of the following options hold? Statement 1 : Let x =
48. Match the column-I with column-II. If a and b are the zeroes of the quadratic polynomial f(x) = x2 – 3x – 2, then
Column-I
(i) a2b + ab2 = 1 1 + = α β (iii) α − β + 1 = 2αβ (ii)
Column-II
4 17 − 1 4 (b) –6 (a)
(c) 161
(i)→(b), (i)→(d), (i)→(b), (i)→(b),
(ii)→(a), (ii)→(b), (ii)→(d), (ii)→(d),
3 2 (iii)→(d), (iv)→(c) (iii)→(c), (iv)→(a) (iii)→(c), (iv)→(a) (iii)→(a), (iv)→(c) (d) −
49. Which of the following statements is incorrect? A. The abscissa of every point on y-axis is zero. B. The ordinate of a point is its perpendicular distance from x-axis. C. The coordinates of any point on y-axis are of the form (0, y). D. If points A(x1, y 1), B(x 2, y 2) and C(x 3, y 3) are collinear, then x1(y 2 – y 3) + x 2(y1 – y 3) + x 3(y1 – y 2) = 0. 50. Fill in the blank : ______ times the sum of the squares of the sides of a triangle is equal to four times the sum of the squares of the medians of the triangle.
A. B. C. D.
Two Three Five One and half
SPACE FOR ROUGH WORK
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Class 10 7th
SET B Year 2013
Copyright©2015. Science Olympiad Foundation (SOF)
2
7th IMO - Set B
logical reasoning 1.
2.
A person is asked to put in a basket one apple when ordered ‘One’, one guava when ordered ‘Two’, one orange when ordered ‘Three’ and is asked to take out from the basket one apple and one guava both when ordered ‘Four’. The order sequence executed by the person is as follows: 1 2 3 3 2 1 4 2 3 1 4 2 2 3 3 1 4 1 1 3 2 3 4 How many fruits will be there in the basket at the end of the above order sequence? A. 10 B. 11 C. 12 D. 13
4.
The following question consist of a set of three figures X, Y and Z showing a sequence of folding of a piece of paper. Figure (Z) shows the manner in which the folded paper has been cut. Choose a figure from the given options which would most closely resemble the unfolded form of paper.
A.
Select a figure from amongst the given options which will continue the series as established by the five problem figures. Problem Figures
B.
C.
D.
5.
Five children were administered psychological tests to know their intellectual levels. In the report, psychologists pointed out that the child P is less intelligent than the child Q. The child R is less intelligent than the child S. The child Q is less intelligent than the child R and child P is more intelligent than the child T. Which child is the most intelligent?
A. B. C. D.
6.
A square field PQRS of side 90 m is so located that its diagonal PR is from north to south and the corner Q is to the west of S. Rohan and Rahul start walking along the sides from Q and R respectively in the clockwise and anti-clockwise directions with speeds of 8 km/hr and 10 km/hr respectively. Where shall they cross each other the second time?
A. B. C. D.
7.
If the positions corresponding to the multiples of 5 in the English alphabet are replaced by symbols and that of multiples of 7 by digits, how many letters will be left?
A.
B.
C.
D.
3.
Choose the Venn diagram which best illustrates the relationship amongst three given classes "Teacher, Graduate, Player".
A.
B.
C.
D.
P Q S T
PQ QR PS None of these
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3
7th IMO - Set B
A. B. C. D.
15 17 18 21
12. There is a definite relationship between figures 1 and 2. Establish a similar relationship between figures 3 and 4 by selecting a suitable figure that would replace the question mark (?) in figure (4).
8.
In the following question, a set of figures is carrying certain numbers. Assuming that the numbers in each set follow a similar pattern, find the missing number.
A. B. C. D.
9.
What number is opposite to 3, if four different positions of a dice are shown below?
A. B. C. D.
2 3 4 5
A.
B.
C.
D.
6 4 3 2
Figure (X) A.
B.
C.
D.
A. B. C. D.
1.
The number of males equals that of females.
2.
A and E are sons of F.
3.
D is the mother of two, one boy and one girl.
4.
B is the son of A.
5. There is one married couple in the family at present.
Which one of the following is true from the above information? A. A, B and C are all females. B. A is the husband of D. C. D is the grand daughter of F. D. E and F are children of D.
14. Select the correct mirror image of Figure (X).
A.
Figure (X)
11. Between two book-ends in your study are displayed your five favourite puzzle books. If you decide to arrange the five books in every possible combination and move just one book every minute, how long would it take you?
13. Examine the following relationships among members of a family of six persons—A, B, C, D, E and F.
10. In the following question, find out how will the Figure (X) look like after rotation?
1 2 3 4
hour hours hours hours
B.
C.
D.
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4
7th IMO - Set B
15. If + means ÷ , ÷ means –, – means ×, × means +, then 12 + 6 ÷ 3 – 2 × 8 =
A. B. C. D.
–2 2 4 8
16. In a class, among the passed students, Amisha is twenty-second from the top and Sajal, who is 5 ranks below Amisha, is thirty-fourth from the bottom. All the students from the class appeared for the exam. If the ratio of the students who passed in the exam to those who failed is 4 : 1 in that class, how many students are there in the class?
A. B. C. D.
60 75 90 Data inadequate
17. If SCOTLAND is written as 12345678, LOAN is written as 1435, LOTS is written as 8124, DAN is written as 537 and SON is written as 458, then what will be the code for ‘C’?
A. B. C. D.
0 4 5 6
18. A family consists of six members P, Q, R, S, T and U. There are two married couples. Q is a doctor and the father of T. U is grandfather of R and is a contractor. S is grandmother of T and is a housewife. There is one doctor, one contractor, one nurse, one housewife and two students in the family. Who is the sister/brother of T?
A. B. C. D.
R U T Information insufficient
19. Study the given information carefully to answer the following question. M K K I D N E T T Q O B F H AA G T U U X W L S R I Each of these letters gets a numerical value based on its position in the above arrangement, such as, 1 for M, 2 for K, 4 for I and so on. Value of A is exactly equal to the total value of which of the following pairs? 1. DO 2. QE 3. MH
A. B. C. D.
Only 1 Only 2 Only 3 Both 1 and 3
20. In the given figure, if the centres of all the circles are joined by horizontal and vertical lines, then find the number of squares that can be formed.
A. B. C. D.
16 17 18 14
Mathematical reasoning 21. ABCD is a quadrilateral with right angles at A and C. Points E and F are on the diagonal AC such that DE and BF are both perpendicular to AC. If AE = 3 cm, DE = 5 cm and CE = 7 cm then the length of BF is _______ cm.
22. The value of
2
l +m
xl
A. B. C. D.
xm 2 –1 0 1
2
´ m+ n
xm xn
2
2
´ n+l
xn xl
2
2
=
23. If (aa + b)–2 + (ab + b)–2 = 1, where a, b are the roots of ax2 + bx + c = 0, then ac (ac + 2) = _____
A. B. C. D.
3.2 3.4 4 4.2
A.
B. C. D.
b2 2 b3 2b b2
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5
7th IMO - Set B 24. Two candidates attempt to solve a quadratic equation of the form x 2 + px + q = 0. One starts with a wrong value of p and finds the roots to be 2 and 6. The other starts with a wrong value of q and finds the roots to be 2 and –9. Find the correct roots.
A. B. C. D.
2, 6 2, –9 4, 8 –3, –4
25. In the diagram, PQ and QR are tangents to the circle, with centre O at P and R respectively. Find the value of x.
29. I f A i s 1 / 4 o f a c o m p l e t e r e v o l u t i o n , t h e n æ 3 + 2 cos A ö÷-3 æ 1+ 2 sin A ö-3 çç ÷÷ = ç ÷ çè 1- 2 sin A ÷ø + ççè 3 - 2 cos A ÷ø
A.
1
B. C. D.
3 0 –1
30. The sums of n terms of two arithmetic series are in the 7n +1 ratio of . Find the ratio of their 11th terms. 4n + 27
A. B. C. D.
4:3 5:4 7:4 None of these
31. Points A(6, 6), B(2, 3) and C(4, 7) are the vertices of a triangle which is _______.
A. B. C. D.
25° 30° 55° 65°
26. Let Sn denote the sum of the first ‘n’ terms of an A.P. and S2n = 3Sn. Then the ratio S3n is to Sn is equal to_____.
A. B. C. D.
4 6 8 3
: : : :
2 1 2 1
27. The L.C.M. of two numbers is 45 times their H.C.F. If one of the numbers is 125 and the sum of H.C.F. and L.C.M. is 1150, then the sum of two numbers is _____.
A. B. C. D.
215 220 225 350
A.
( AD + BC ) 2
B.
( AB + CD) 2
C.
DF ´ CF AE ´ BE
D.
AD + EF + BC 2
Right angled Acute angled Obtuse angled None of these
32. If cosec q – sin q = a3 and sec q – cos q = b 3, then a 2 b 2 (a 2 + b 2) =
A. B. C. D.
1 –1 2 0
33. Each observation in a raw data is first multiplied by 3, then 6 is added. It is then divided by 3 and subsequently reduced by 6, then ____
A. B. C. D.
The The The The
new new new new
mean mean mean mean
is equal to the original mean. is 4 more than the original mean. is 4 less than the original mean. is 2 more than the original mean.
34. If N is the sum of first 13986 prime numbers, then N is always divisible by
28. ABCD is a trapezium, in which AD||BC, E and F are the mid-points of AB and CD respectively, then EF is
A. B. C. D.
A. B. C. D.
6 4 8 None of these
35. In a right triangle ABC is right-angled at B. If P and Q are points on the sides AB and BC respectively, then
A.
AQ2 + CP2 = 2(AC2 + PQ2)
B.
2(AQ2 + CP2) = AC2 + PQ2
C.
D.
AQ2 + CP2 = AC2 + PQ2 1 AQ + CP = (AC + PQ) 2
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6
7th IMO - Set B
everyday Mathematics 36. Bag I contains 4 chips numbered 1, 3, 5 and 7 respectively. Bag II contains 3 chips numbered 2, 4 and 6 respectively. A chip is drawn at random from each bag. Find the probability that the sum of the two chips drawn is odd.
A. B. C. D.
7/12 0 1 5/12
37. The income of a bank on the n th day is ` (n 2 + 2) and the expenditure of the bank on the n th day is ` (2n + 1). Also income = expenditure + savings In how many days his total savings will be ` 1240?
A. B. C. D.
10 12 15 16
38. A test has 50 questions. A student scores 1 mark 1 for a correct answer, - for a wrong answer, and 3 1 for not attempting a question. If the net score 6 of a student is 32, the number of questions answered wrongly by that student cannot be less than
A. 6
B.
12
C.
3
D. 9
A. B. C. D.
216.50 215.25 212.25 210.25
m m m m
40. A tank 4 m long, 2.5 m wide and 1.5 m deep is dug in a field 31 m long and 10 m wide. If the earth dug out is evenly spread out over the field, the rise in level of the field is _____.
A. B. C. D.
3.1 cm 4.8 cm 5 cm 6.2 cm
A. B. C. D.
1 m/s 2 m/s 1.87 m/s None of these
42. A box contains 25 tickets, numbered 1, 2, 3, …, 25. A ticket is drawn and then another ticket is drawn without replacement. Find the probability that both tickets will show odd numbers.
A.
B.
37 50
13 50 13 C. 25 D. None of these
43. Ayesha’s father was 38 years of age when she was born while her mother was 36 years old when her brother four years younger to her was born. What is the difference between the ages of her parents?
39. A kite is flown with a thread of 250 m length. If the thread is assumed to be stretched and makes an angle of 60° with the horizontal, then the height of the kite above the ground is (approx.) _____.
41. An elephant of length 4 m is at one corner of a rectangular cage 16 m × 30 m and facing towards the diagonally opposite corner. If the elephant starts moving towards the diagonally opposite corner it takes 15 seconds to reach the opposite corner. Find the speed of the elephant.
A. B. C. D.
2 4 6 8
years years years years
1 44. 33 % of a man’s daily output is equal to 50% of a 3 second man’s daily output. If the second man turns out 1500 screws daily, then the first man’s output in terms of making screws is ______.
A. B. C. D.
500 1000 2000 2250
45. A man bought some fruits at the rate of 16 for ` 24 and sold them at the rate of 8 for ` 18. What is the profit percent?
A. B. C. D.
25% 40% 50% 60%
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7
7th IMO - Set B
ACHIEVERS SECTION 46. There are six faces in a cube. Rajeev fix one cube on each of the faces. The dimensions of all the cubes are same. What is the ratio of total surface area of the newly formed solid to the area of a single cube?
A. B. C. D.
7:1 6:1 5:1 41 : 9
48. A plane left 40 minutes late due to bad weather and in order to reach its destination, 1600 km away in time, it had to increase its speed by 400 km/hr from its usual speed. Find the usual speed of the plane.
600 km/hr 800 km/hr
B. D.
750 km/hr None of these
49. Which of the following is correct?
47. In the given figure, a circle is inscribed in a q u a d r i l a t e r a l A BCD i n w h i c h ∠ B = 9 0 ° . I f AD = 23 cm, AB = 29 cm, BC = 25 cm and DS = 5 cm, then match the columns.
Statement II : If a constant number is added to each term of an A.P., then the resulting pattern of numbers is also an A.P.
A. Both statement I and statement II are true and statement II is the correct explanation of statement I. B. Both statement I and statement II are true but statement II is not the correct explanation of statement I. C. Statement I is true but statement II is false. D. Statement I is false but statement II is true.
(a) (b) (c) (d)
Column-I AQ radius, r CD PC
Column-II (p) 19 cm (q) 14 cm (r) 18 cm (s) 11 cm
(a) → r, (b) → s, (c) → p, (d) → q
B.
(a) → r, (b) → p, (c) → s, (d) → q
C.
(a) → r, (b) → q, (c) → s, (d) → p
D.
(a) → p, (b) → q, (c) → r, (d) → s
1 1 1 Statement I : If a, b, c are in A.P., then , , bc ca ab are also in A.P.
A.
A. C.
50. For the following grouped frequency distribution, which of the following options is INCORRECT? Class Frequency
A. B.
C. D.
3-6
6-9
9-12
12-15
15-18
18-21
21-24
2
5
10
23
21
12
3
Lower limit of modal class is 12 Frequency of the class preceding the modal class = 10 Mode = 14.6 and width of the modal class is 4 All of these
SPACE FOR ROUGH WORK
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Class 10 8th
Set A Year 2014
Copyright©2015. Science Olympiad Foundation (SOF)
8th IMO - Set A
2
logical reasoning 1.
Two rows of numbers are given. The resultant number in each row is to be worked out separately based on the following rules and the question below the rows of numbers is to be answered. The operations of numbers progress from left to right. Rules:
If an even number is followed by another even number, they are to be added. (ii) If an even number is followed by a prime number, they are to be multiplied. (iii) If an odd number is followed by an even number, the even number is to be subtracted from the odd number. (iv) If an odd number is followed by another odd number, the first number is to be added to the square of the second number. (v) If an even number is followed by a composite odd number, the even number is to be divided by the odd number. 36 13 39 77 30 7 Which will be the outcome if the resultant of the second row is divided by the resultant of the first row? A. 12 B. 16 C. 8 D. 6 2.
(i)
A dealer sold six cars – M, N, O, P, Q and R– during a period of Monday to Saturday, one car on each day.
(i) The car O was sold at least before three cars. (ii) The car R was sold on Tuesday. (iii) Both the cars N and Q were sold at least before one car. (iv) The car P was sold immediately after the car O. (v) At least four cars were sold after the car Q.
If Mr. Jindal is purchased a car sold on Wednesday, then the car purchased by him is
A. B. C. D.
4.
'X + Y means 'Y is brother of X'; 'X × Y' means 'Y is husband of X'; 'X – Y' means 'X is mother of Y'; and 'X ÷ Y' means 'X is father of Y'. Then which of the following expressions indicates 'P is grandmother of T'?
A. B. C. D.
5.
A trader in order to code the cost price of an article used the letters of psicholazy in the form of '0 to 9' respectively. If an article was sold for ` 1015.58 to earn the 16% gain, then which of the following code stands for cost price?
A. AIL.HP B. AIL.HS C. ZYA.HO D. ZAO.OP
6.
Find the missing figure from the options which will continue the series in given Problem Figures.
The given square grid shows the plan of a playground. The bench is North of the toy car. Bench
R
Q Toy-car
P
S
Swing
Slide
A. C.
P R
M N O P
Q – P + R ÷ T P×Q÷R–T P × Q ÷ R + T P+Q÷R–T
See-saw
The town council wants to plant a tree in the playground. The location of the tree is to be North of the swing and South-West of the slide. Identify the position where the tree will be planted.
3.
B. D.
Q S
A.
B.
C.
D.
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8th IMO - Set A
3
7.
An enterprising businessman earns an income of ` 1 on the first day of his business. On every subsequent day, he earns an income which is just double of that made on the previous day. On the 10th day of business, his income is _______.
A. B. C. D.
8.
There is a certain rule followed in all the three figures. Identify the rule and find the missing number.
` ` ` `
12. Count the number of circles used to draw the given figure.
29 210 10 102
A. C.
20 25
B. D.
21 17
13. Select the figure from the options in which Fig.(X) is exactly embedded as one of its part.
A. C.
6 540
B. D.
90 60
9.
Identify the wrong figure in the given series.
A.
B.
C.
A. C.
Q R
B. D.
S T
10. In a shop, the items were arranged in a shelf consisting of six rows. Biscuits are arranged above tins of chocolates but below the rows of packets of chips, cakes are at the bottom and the bottles of peppermints are below the chocolates. The topmost row had the display of jam bottles. Where exactly are the bottles of peppermints from the top?
A. C.
2nd 4th
B. D.
A.
C.
D.
14. There are three figures X, Y and Z showing a sequence of folding of a sheet of paper. Figure (Z) shows the manner in which the folded sheet has been cut. Select the figure from the options which would resemble the unfolded form of paper.
A.
B.
C.
D.
15. A cube of side 10 cm is coloured red with a 2 cm wide green strip along all the sides on all the faces. The cube is cut into 125 smallest cubes of equal size. How many cubes have at least two green faces?
B.
D.
3rd 5th
11. There is a certain relationship between figures P and Q. Identify the same relationship between figures R and S and find the missing figure from the options.
A. B. C. D.
8 27 44 63
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8th IMO - Set A
4
mathematical Reasoning 16. The given figure is created by using the arcs of quadrants with radii 1 cm, 2 cm and 3 cm. Find the total area of the shaded region. (Take p = 3.14)
A. 31.93 cm2 C. 63.84 cm2
B. D.
20. In the given figure (not drawn to scale), OABC is a quadrilateral with ABC on horizontal ground and O is vertically above A. M is the mid-point of BC. If ∠BAC = 90°, AB = AC = 16 cm and OA = 12 cm, calculate the length of OB.
15.96 cm2 13.68 cm2
17. In the given figure (not drawn to scale), AG is parallel 2 to CD and AG = CD. The point B on AC is such 7 2 that BC = AC . If the line BG meets AD at F and 7 the line through C is parallel to BG which meets AD FG at E, then find the value of . EC
A. C.
25 cm 20 cm
B. D.
15 cm 28 cm
21. The given figure shows sector OAB with centre O and radius 54 cm. Another circle XYZ with centre P, is enclosed by the sector OAB. If ∠AOB = 60°. Find the area of OXPY.
1 7 4 C. 7
A.
B. D.
3 7 2 7
18. In the given figure (not drawn to scale), BD is a diameter of the circle with centre O. C and A are two points on the circle. BA and CD, when produced, meet at E. If ∠DOC = 60° and ∠ABD = 23°, then find ∠OBC.
A.
161 cm2
B.
461 cm2
C. 324 cm2
D.
561.2 cm2
22. If two zeroes of the polynomial x 4 – 6x 3 – 26x 2 + 138x – 35 are 2 − 3 and 2 + 3 , then find all the zeros.
A. 60° C. 45°
B. D.
30° 67°
19. Which of the following have non-terminating repeating decimal?
A.
2 25
C.
2
B.
231 2
2 ×5 ×7
D.
2 7 3
1323
6 × (35)
2
A.
–5, 7
B.
–7, 5
C.
3, –5
D.
5, –3
23. Solve : (sin4 q – cos4 q + 1) cosec2q
A.
1
B.
–2
C.
2
D.
0
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8th IMO - Set A
5
24. What is the value of the median of the data using the graph in the figure given below, of less than ogive and more than ogive?
A. C.
8 5
B. D.
4 17.5
25. The number of zeroes for the given graph is ____.
28. Swati folded the three corners of a triangle. She managed to measure four of the angles as shown below before breaking her protractor. She needs help to figure out what the named angles are. Help her find f , g and h.
f A. 52° B. 44° C. 44° D. 47°
g 44° 52° 47° 44°
h 47° 47° 52° 52°
29. Kunal arranged some metal blocks at the bottom of a tank as seen in the figure below. Then he filled the 30 cm by 25 cm by 25 cm tank with water. If each block is 4 cm long, 3 cm wide and 5 cm tall, then how much water is needed to fill the tank to 80% of the tank's height?
A. C.
3 4
B. D.
2 1
26. Find the mode (approx.) from the given frequency distribution. Expenditure on food (in `) in a month 300-309 310-319 320-329 330-339 340-349 350-359 360-369 370-379 Total
A. C.
336.41 343.22
Number of workers 10 20 24 38 48 27 17 6 190 B. D.
307.20 342.72
A. 15000 cm3 C. 12720 cm3
B. D.
2280 cm3 16470 cm3
30. A number is chosen at random from 1 to 120. The probability of the number chosen being a multiple of 3 and 15 both is _____.
A. C.
1/15 1/17
B. D.
1/16 1/19
31. In the given figure, TAS is a tangent to the circle, with centre O, at the point A. If ∠OBA = 32°, then find the values of x and y respectively.
2 27. If the roots of the quadratic equation x + px + q = 0 are tan 30° and tan 15° respectively, then the value of 2 + q – p is ______.
A. B. C. D.
0 1 2 3
A. C.
32°, 58° 58°, 58°
Copyright©2015. Science Olympiad Foundation (SOF)
B. D.
58°, 48° 42°, 58°
8th IMO - Set A
6
32. In the given graph, line APB meets the x-axis at A and y-axis at B. P is the point (–4, 2) and AP : PB = 1 : 2. Find the coordinates of A and B respectively.
34. If x 2 + px + q = 0 and x 2 + qx + p = 0 have a common root, then ______.
A. B. C. D.
p = q 1+p+q=0 p + q = 0 Both A and B
35. If the area of the triangle given below is 20 sq. units, then what are the co-ordinates of point C?
A. (–5, 0), (0, 5) C. (–6, 0), (0, 5)
B. D.
(–6, 0), (0, 6) (6, –6), (–6, 6)
33. Let S n denote the sum of the first 'n' terms of an A.P. S 2n = 3S n. Then, the ratio S3n /S n is equal to _____.
A. B. C. D.
4 6 8 10
A.
40 0, a
B.
(a2 + b2, 0)
C.
20 , 0 b
D.
40 , 0 b
Everyday mathematics 36. A man walks a distance of 48 km in a given time. If he walks 2 km an hour faster, he will perform the journey 4 hours before. Find his normal rate of walking.
A. 4 km/hr C. 3 km/hr
B. D.
6 km/hr 8 km/hr
37. Mohan ate half a pizza on Monday. He ate half of what was left on Tuesday and so on. He followed this pattern for one week. How much of the pizza would he have eaten during the week?
A. C.
99.22% 98.22%
B. D.
95% 100%
38. The price of commodity X increases by 40 paise every year, while the price of commodity Y increases by 15 paise every year. If in 2014 the price of commodity X was ` 4.20 and that of Y was ` 6.30, in which year commodity X will cost 40 paise more than the commodity Y?
A. C.
2024 2022
B. D.
2021 2023
40. The members in a welfare committee decided to collect as many paise from each member of the committee as is the number of members. If the total collection amounts to ` 96.04, then the number of members in the committee is _______.
A. C.
84 102
B. D.
98 92
41. A company produces on an average 4000 items per month for the first 3 months. How many items it must produce on an average per month over the next 9 months, to average 4375 items per month over the whole?
A. C.
4500 4680
B. D.
4600 4710
42. A housewife saved ` 2.50 in buying an item on sale. If she spent ` 25 for the item, then how much percent she saved in the transaction approximately?
A. C.
8% 10%
B. D.
9% 11%
39. The total monthly salary of 4 men and 2 women is ` 46,000. If a woman earns ` 500 more than a man, what is the monthly salary of a woman?
43. Rajeev buys goods worth ` 6650. He gets a rebate of 6% on it. After getting the rebate, he pays sales tax @ 10%. Find the amount he will have to pay for the goods.
A. C.
` 6500 ` 8000
B. D.
` 7500 ` 9000
A. C.
` 6876.10 ` 6654
Copyright©2015. Science Olympiad Foundation (SOF)
B. D.
` 6999.20 ` 7000
8th IMO - Set A
7
44. Twenty women can do a work in sixteen days and sixteen men can complete the same work in fifteen days. What is the ratio between the capacity of a man and a woman?
45. A sum of money is borrowed and paid back in two annual installments of ` 882 each allowing 5% compound interest. The sum borrowed was _______.
A. C.
3 : 4 5 : 3
B. D.
4:3 Data inadequate
A. C.
` 1620 ` 1680
B. D.
` 1640 ` 1700
Achievers section 46. Which of the following statements is true? Statement-1 : The area of the equilateral triangle described on the hypotenuse of a right angled triangle is equal to the sum of the areas of the equilateral triangles described on the other two sides of the triangle. Statement-2 : The area of the equilateral triangle described on the side of right angled isosceles triangle is half of the area of the equilateral triangle described on its hypotenuse.
A. B. C. D.
Only statement-1 Only statement-2 Both statement-1 and statement-2 Neither statement-1 nor statement-2
(i)
Column-I 2
2
2
(iii) The amount of money in the account of Sanchi at the end of every year when ` 1000 is deposited at simple interest at the rate of 10% per annum.
(iv) The number of bacteria in a certain food item after each second, when they double themselves in every second.
A. Only (i) C. Both (ii) and (iv)
2
(sec q + tan q) – 4sec qtan q = (p) 9 (tan 2 60° + 4 cos 2 45° + 3 sec2 30° + 5 cos 2 90°) cosec30° + sec 60 °− cot2 30 °
(q) 8/17
(ii)
(iii) If secq + tanq = 4, then cosq = (r) 4
(iv) tan5°tan85° + tan10°tan80°
B. D.
Only (ii) Only (iv)
xi
58
59
60
61
62
63
64
65
66
fi
2
3
6
15
10
5
4
3
2
A. B. C. D.
51.72, 62, 61 61, 62, 61 61, 60, 61 61.72, 61, 61
50. Fill in the blanks.
(s) 1
tan35°tan55° + tan25°tan65° = (i) → (s), (ii) → (p), (iii) → (r), (iv) → (q) (i) → (s), (ii) → (p), (iii) → (q), (iv) → (r) (i) → (p), (ii) → (r), (iii) → (q), (iv) → (s) (i) → (q), (ii) → (p), (iii) → (s), (iv) → (r)
48. Which of the following situations do not form an A.P.?
Column-II 2
A. B. C. D.
(ii) The fee charged every month by a school from classes I to XII, when the monthly fee for class I is ` 250 and it increases by ` 50 for the next higher class.
49. Find the mean, mode and median respectively of the following data.
47. Match the columns.
(i) The fee charged from a student every month by a school for the whole session when the monthly fee is ` 400.
p be a rational number such that p and q are q P and the prime factorisation of q is not of the form 2n × 5m , where n and m are whole numbers, then a has a decimal expansion which is Q and R . Let a =
A. B. C. D.
P Prime Co-prime Co-prime Prime
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Q Non-terminating Terminating Non-terminating Non-terminating
R Non-repeating Repeating Repeating Repeating
Class 10 8th
Set B Year 2014
Copyright©2015. Science Olympiad Foundation (SOF)
8th IMO - Set B
1
Logical Reasoning 1.
2.
3.
4.
5.
In the given letter series, some of the letters are missing which are given in that order as one of the options below it. Choose the correct option. mnonopqopqrs A. knopq B. oqrst C. pqrst D. qrstu How many such pair of letters are there in the word PRODUCTION each of which has as many letters between them as in the English alphabet? A. None B. One C. Two D. Three In a certain code 'a friend of mine' is written as '4 9 1 6', 'mine lot of metal' is written as '3 1 0 9' and 'a piece of metal' is written as '7 1 6 3'. How can '8 7 3' be written in same code? A. a metal piece B. metal for friend C. piece of advice D. large metal piece Boys and girls are made to sit in 7 rows and 7 columns all of them facing West. P is at the centre of the arrangement, Q is just behind P, R is on the immediate left of Q, and S is to the West of P. Then R is in which direction with respect to S? A. South-West B. North-West C. South-East D. Data inadequate There is a certain relationship between figures (i) and (ii). Establish a similar relationship between figures (iii) and (iv) by selecting a suitable figure from the options that would replace the question mark in figure (iii).
? (i)
(ii)
(iii)
A.
B.
C.
D.
(iv)
6.
7.
8. 9.
Read the following information and answer the question given below : (i) Four persons A, B, C and D eat Mango, Banana, Orange or Peach from Monday to Thursday. No two persons eat the same fruit on a day. Each of them eats only one fruit on a day and does not repeat it on any other day. (ii) Neither C nor D eats orange or peach on Tuesday. (iii) B eats banana on Wednesday. (iv) A eats peach on Monday. (v) C does not eat mango on Thursday. (vi) D eats banana on Monday. Which fruit does D eat on Thursday? A. Banana B. Peach C. Either banana or mango D. Either peach or orange A, B, C, D, E and F are seated in a circle facing the centre. A and C are seated adjacent to each other and E and B are also seated adjacent to each other. B is to the immediate left of F. There are two persons between D and E. A is not seated adjacent to E. Who is to the immediate left of E? A. C B. B C. F D. Cannot be determined The six faces of a cube are coloured, each with a different colour. I. The white face is between yellow and green. II. The red face is adjacent to brown. III. The green face is opposite the yellow side. IV. The blue face is adjacent to red. V. The yellow face is the top face of the cube. The faces adjacent to white bear the colours A. Yellow, green, brown and red B. Yellow, brown, blue and green C. Yellow, green, blue and red D. None of these Find the correct mirror-image of the given word, if the mirror is placed vertically to the right. disturb A. b r u t s i d B. b r u t s i d C. b r u t s i d D. b i s t u r d
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2
8th IMO - Set B
10. The given Venn diagram represents the students who study Physics, Chemistry and Mathematics. Identify the region which represents the students who study Physics and Mathematics but not Chemistry. X Physics
13. Select a figure from the options which will continue the series established by the problem figures.
Y Q
V
P T
U
Chemistry
A.
B.
C.
D.
R
S
Mathematics
Z
A. B. C. D.
T P+T+S V P+T+S+R+U+V
11. The given set of figures carry certain characters. Assuming that the characters in each set follow a similar pattern, identify the pattern and find the missing character. 29 39
27 72
45
A. B. C. D.
33 43
29
30 73
42 43
31 44
59 ? 39
40 79
10 20
?
49 50 60 69
(i)
12. Three figures X, Y and Z shows a sequence of folding a sheet of paper. Figure Z shows the manner in which the folded sheet has been cut out. Select a figure from the options which most closely resembles the unfolded form of sheet.
X
A.
B.
C.
D.
14. There is a certain relationship between figures (i) and (ii). Establish a similar relationship between figures (iii) and (iv) by selecting a figure from the options that would replace the question mark in figure (iv).
Y
A.
B.
C.
D.
(ii)
(iii)
(iv)
Z
15. How many such 1's are there in the given arrangement, each of which is immediately preceded by a perfect square? 18594712583659276452926412 3514283 A. None B. One C. Two D. Three
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8th IMO - Set B
3
MATHEMATICAL REASONING 16. If one of the zeroes of the cubic polynomial x 3 + ax 2 + bx + c is –1, then the product of the other two zeroes is A. b – a + 1 B. b – a – 1 C. a – b + 1 D. a – b – 1 17. Solve for x and y : bx + ay = a + b, 1 1 2a 1 1 ax − + by − = a − b a + b b − a b + a a + b 2
b +a
2
,y=
A.
x=
B.
x=
C.
x=
D.
x = a2 + b2, y = 2ab + a2
A. B. C. D.
1 2 4 1
: : : :
4, 7, 5, 9,
6 5 7 3
21. The given figure is made up of a large circle ABCDE with centre O, a small circle BQOP, two semi-circles and a sector OED. AC is 28 cm. Find the total shaded area of the figure. B
2a 2b ,y= a −b b−a a 2 + b2 2
a + ab
,y=
2 1 1 4
l2 + m , find m : n. nl
19. In DPQR, point M is on side PQ and point S is on the side PR such that QRSM is a trapezium. If MS : QR = 3 : 5, then find area (DPMS) : area (QRSM). A. 9 : 16 B. 10 : 17 C. 3 : 5 D. 9 : 25 20. The median of the given data is 50. Find the values of p and q respectively, if the sum of all the frequencies is 90. Marks
Frequency
20-30
p
30-40
15
40-50
25
50-60
20
60-70
q
70-80
8
80-90
10
A. B. C. D.
C
O E
−2b a −b
Q
P A
18. If tanq + secq = l, then secq =
A. B. C. D.
2b a+b
ab + b 2
D
(198p – 98) cm2 (49p + 198) cm2 (150p + 100) cm2 (147p – 196) cm2
22. The sum of the remainders obtained when 2x 3 + (p + 2)x + p – 2 is divided by x – 2 and when it is divided by x + 1 is 0. Find the value of p. A. 3 B. –2 C. – 4 D. 8 23. Find the values of p and q respectively for which the equation 2x 2 + px = q has root –3 and factor (x – 5). A. –5, –25 B. – 4, 30 C. 5, –25 D. – 4, –30 24. Find the sum from the sixth term to the twelfth term of the arithmetic progression 6, 10, 14, … A. 266 B. 240 C. 256 D. 276 25. Two dice are thrown simultaneously. Find the probability of getting a multiple of 2 on one dice and a multiple of 3 on the other dice. A. 1/3 B. 11/36 C. 1/4 D. 13/36
Copyright©2015. Science Olympiad Foundation (SOF)
4
8th IMO - Set B
26. In the given diagram, ST is a tangent to the circle with centre O. Find the value of x. A. 25° B. 35° C. 40° D. 45°
R
Q
70°
O x
S
65°
P T
27. In the arithmetic progression 7, 10, 13, … how many terms will add up to a sum of 920? A. 25 B. 16 C. 27 D. 23 28. A solid rectangular block has a square base with side ( 3 − 2 ) m. The volume of the block is (3 18 − 7 3 ) m3 . Find the height of the block in the form (a 2 + b 3 ) m, where a and b are integers.
A.
3 2+ 3
B.
5 3+4 2
C.
15 2 + 3
D.
5 5+3 3
29.
Solve : 3(81)x + 3 = 9x + 1 + 9x. A. 3, 2 B. ±1/2 C. 4, 5 D. ±1
31. Two circles of radii 10 cm and 8 cm intersect each other and the length of common chord is 12 cm. The distance between their centres is A O
O B
A.
7 cm
B.
3 7 cm
C.
4 7 cm
D.
(8 + 2 7 ) cm
B.
3p cm
C. D.
3 p cm 3 p cm
B
O C
33. Given below are the steps of construction of a pair of tangents to a circle of radius 4 cm from a point on the concentric circle of radius 6 cm. Find which of the following step is wrong? Step-I : Take a point O on the plane paper and draw a circle of radius OA = 4 cm. Also, draw a concentric circle of radius OB = 6 cm. Step-II : Find the mid-point A of OB and draw a circle of radius BA = AO. Suppose this circle intersects the circle of radius 4 cm at P and Q. Step-III : Join BP and BQ to get the desired tangents. P
30. For a frequency distribution, mean, median and mode are connected by which of the following relations? A. Mode = 3 Mean – 2 Median B. Mode = 2 Median – 3 Mean C. Mode = 3 Median – 2 Mean D. Mode = 3 Median + 2 Mean
32. O is the centre of a circle of diameter 4 cm and 1 OABC is a square. If the shaded area is area of 3 the square, then the side of the square is A A. p 3 cm
B A
C
O
Q
A. B. C. D.
Only Step-I Only Step-II Both Step-I and Step-II Both Step-II and Step-III
34. The value of
A.
B.
C.
D.
a2
a + a 2 − b2 a − a 2 − b2
+
a − a 2 − b2 a + a 2 − b2
is
b2 b2
a2 a b 2(2a 2 − b 2 ) b2
35. If the sums of n, 2n and 3n terms of an A.P. are S1, S3 S 2 and S3 respectively, then is ( S2 − S1 ) A. 0 B. 1 C. 2 D. 3
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8th IMO - Set B
5
EVERYDAY MATHeMATICS 36. There is a circular path around a sports field. Priya takes 18 minutes to drive one round of the field, while Ravish takes 12 minutes for the same. Suppose they both start at the same point and at the same time, and go in the same direction. After how many minutes will they meet again at the starting point? A. 54 B. 24 C. 36 D. 72 37. A person invested some amount at the rate of 10% simple interest and some other amount at the rate of 12% simple interest. He received yearly interest of ` 130. But if he had interchanged the amounts invested, he would have received ` 4 more as interest. How much amount did he invest at the rate of 10% and 12% respectively? A. ` 1200, ` 100 B. ` 700, ` 500 C. ` 1000, ` 1200 D. ` 500, ` 700 38. Father is aged three times more than his son Ronit. After 8 years, he would be two and a half times of Ronit's age. After further 8 years, how many times would he be of Ronit's age? A. 2 times 1 B. 2 times 2 3 C. 2 times 4 D. 3 times 39. By selling an article, Mohit earned a profit equal to one-fourth of the price he bought it. If he sold it for ` 375, what was the cost price? A. ` 281.75 B. ` 300 C. ` 312.50 D. ` 350 40. Simran started a software business by investing ` 50,000. After six months, Nancy joined her with a capital of ` 80,000. After 3 years, they earned a profit of ` 24,500. What was Simran's share in the profit? A. ` 9,423 B. ` 10,250 C. ` 12,500 D. None of these
41. 10 women can complete a work in 7 days and 10 children take 14 days to complete the work. How many days will 5 women and 10 children take to complete the work? A. 3 B. 5 C. 7 D. None of these 42. In covering a certain distance, the speeds of A and B are in the ratio of 3 : 4. A takes 30 minutes more than B to reach the destination. The time taken by A to reach the destination is A. 1 hour
B.
C.
D.
1 hours 2 2 hours 1 2 hours 2 1
43. Three containers have their volumes in the ratio 3 : 4 : 5. They are full of mixtures of milk and water. The mixtures contain milk and water in the ratio of (4 : 1), (3 : 1) and (5 : 2) respectively. The contents of all these three containers are poured into a fourth container. The ratio of milk and water in the fourth container is A. 4 : 1 B. 151 : 48 C. 157 : 53 D. 5 : 2 44. Pure ghee costs ` 100 per kg. After adulterating it with vegetable oil costing ` 50 per kg, a shopkeeper sells the mixture at the rate of ` 96 per kg, thereby making a profit of 20%. In what ratio does he mix the two? A. 3 : 2 B. 4 : 3 C. 5 : 2 D. 7 : 6 45. A manufacturer offers a 20% rebate on the marked price of a product. The retailer offers another 30% rebate on the reduced price. The two reductions are equivalent to a single reduction of A. 40% B. 44% C. 46% D. 50%
Copyright©2015. Science Olympiad Foundation (SOF)
6
8th IMO - Set B
Achievers Section 46. The graph of ax 2 + bx + c is shown here and −b D A , − . Identify the signs of a, b and c. 2a 4a y
x P y
A. B. C. D.
a +ve +ve +ve –ve
b +ve –ve –ve +ve
x
O A
c –ve –ve +ve –ve
47. Match the columns. Column-I sin q + (a) (i) sec q + tan q − 1 cos q = cosec q + cot q − 1
(b) sec4q(1 – sin4q) – 2 tan2q = (ii)
(c)
sec q − 1 sec q + 1 + = sec q + 1 sec q − 1
Column-II 2 cosecq
2
(iii) 1
(d) (1 + cotq – cosecq) (iv) 0 (1 + tanq + secq) = A. (a) → (i), (b) → (iii), (c) → (i), (d) → (ii) B. (a) → (ii), (b) → (iii), (c) → (ii), (d) → (iv) C. (a) → (iii), (b) → (iii), (c) → (i), (d) → (ii) D. (a) → (ii), (b) → (iii), (c) → (i), (d) → (ii)
48. Study the statements carefully. Statement-1 : Three times the square of one side of an equilateral triangle is equal to four times the square of one of its altitudes. Statement-2 : Three times the sum of the squares of the sides of a triangle is equal to the three times the sum of the squares of the medians of the triangle. A. Statement-1 is true and statement-2 is false. B. Statement-1 is false and statement-2 is true. C. Both statements are true. D. Both statements are false. 49. Which of the following is incorrect? 9 A. For K = , the equation 2x2 + 3x + K = 0 will 8 have real and equal roots. B. For K = –1, the equation x2 + K(4x + K – 1) + 2 = 0 will have equal roots. C. For K = 2, the equation x2 – 2x(1 + 3K) + 7(3 + 2K) = 0 will have equal roots. D. For K = –3, the equation (K + 1)x2 – 2(K – 1)x + 1 = 0 will have equal roots. 50. Fill in the blanks: Every ____ (a) ____ number can be expressed (factorised) as the product of ____ (b) ____ factors and this factorisation is ____ (c) ____ except for the order in which the prime factor occur. (a) (b) (c) A. Prime Composite Unique B. Composite Prime Unique C. Odd Even Universal D. Even Odd Universal
SPACE FOR ROUGH WORK
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ANSWER KEYS 4 th IMO (2010) 1. (D) 11. (B) 21. (A) 31. (C) 41. (B)
2. (C) 12. (B) 22. (C) 32. (B) 42. (B)
3. (A) 13. (D) 23. (B) 33. (D) 43. (D)
4. (B) 14. (C) 24. (D) 34. (C) 44. (C)
5. (A) 15. (B) 25. (C) 35. (C) 45. (D)
6. (D) 16. (C) 26. (A) 36. (C) 46. (A)
7. (C) 17. (B) 27. (C) 37. (B) 47. (B)
8. (B) 18. (B) 28. (B) 38. (B) 48. (C)
9. 19. 29. 39. 49.
(B) (C) (A) (B) (C)
10. 20. 30. 40. 50.
(D) (D) (D) (C) (B)
7. 17. 27. 37. 47.
(B) (A) (B) (A) (A)
8. 18. 28. 38. 48.
(C) (D) (C) (C) (D)
9. 19. 29. 39. 49.
(D) (D) (A) (A) (A)
10. 20. 30. 40. 50.
(B) (A) (A) (A) (B)
7. 17. 27. 37. 47.
(D) (D) (A) (C) (A)
8. 18. 28. 38. 48.
(C) (D) (C) (C) (C)
9. 19. 29. 39. 49.
(A) (A) (A) (A) (D)
10. 20. 30. 40. 50.
(B) (B) (C) (B) (D)
7. (B) 17. (B) 27. (B) 37. (D) 47. (C)
8. (D) 18. (C) 28. (A) 38. (B) 48. (B)
9. 19. 29. 39. 49.
(B) (B) (B) (B) (D)
10. 20. 30. 40. 50.
(A) (A) (C) (B) (B)
5 th IMO (2011) 1. 11. 21. 31. 41.
(D) (D) (A) (A) (C)
2. 12. 22. 32. 42.
(A) (A) (D) (B) (D)
3. 13. 23. 33. 43.
(D) (B) (C) (B) (D)
4. 14. 24. 34. 44.
(D) (D) (A) (C) (C)
5. 15. 25. 35. 45.
(A) (B) (B) (C) (D)
6. 16. 26. 36. 46.
(A) (A) (C) (B) (A)
6 th IMO (2012) 1. 11. 21. 31. 41.
(D) (D) (B) (A) (B)
2. 12. 22. 32. 42.
(C) (C) (B) (D) (C)
3. 13. 23. 33. 43.
(B) (B) (B) (A) (B)
4. 14. 24. 34. 44.
(C) (C) (C) (C) (C)
5. 15. 25. 35. 45.
SET A (C) 6. (A) 16. (C) 26. (A) 36. (D) 46.
(B) (B) (D) (C) (B)
SET B 1. (A) 11. (B) 21. (A) 31. (B) 41. (C)
2. (B) 12. (B) 22. (B) 32. (D) 42. (C)
3. (C) 13. (D) 23. (A) 33. (A) 43. (A)
4. (D) 14. (A) 24. (B) 34. (D) 44. (B)
5. (C) 15. (D) 25. (C) 35. (B) 45. (C)
6. (C) 16. (A) 26. (B) 36. (A) 46. (A)
7 th IMO (2013)
1. (A) 11. (D) 21. (D) 31. (D) 41. (A)
1. (B) 11. (B) 21. (D) 31. (A) 41. (B)
2. (C) 12. (C) 22. (D) 32. (D) 42. (D)
2. (B) 12. (D) 22. (D) 32. (A) 42. (B)
3. (D) 13. (B) 23. (A) 33. (C) 43. (B)
3. (C) 13. (B) 23. (D) 33. (C) 43. (C)
4. (C) 14. (A) 24. (B) 34. (C) 44. (A)
SET A 5. (C) 6. (B) 15. (D) 16. (B) 25. (C) 26. (A) 35. (D) 36. (C) 45. (B) 46. (C)
7. (D) 17. (A) 27. (B) 37. (D) 47. (A)
8. (C) 18. (C) 28. (C) 38. (D) 48. (D)
9. 19. 29. 39. 49.
(B) (D) (A) (C) (D)
10. 20. 30. 40. 50.
(B) (A) (A) (A) (B)
4. (B) 14. (A) 24. (D) 34. (D) 44. (D)
SET B 5. (C) 6. (B) 15. (C) 16. (B) 25. (B) 26. (B) 35. (C) 36. (C) 45. (C) 46. (C)
7. (C) 17. (D) 27. (D) 37. (D) 47. (A)
8. (C) 18. (A) 28. (A) 38. (C) 48. (C)
9. 19. 29. 39. 49.
(B) (C) (C) (A) (B)
10. 20. 30. 40. 50.
(B) (D) (A) (C) (C)
8 th IMO (2014)
1. (C) 11. (B) 21. (D) 31. (C) 41. (A)
2. (A) 12. (B) 22. (A) 32. (B) 42. (B)
3. (C) 13. (D) 23. (C) 33. (B) 43. (A)
4. (B) 14. (A) 24. (C) 34. (D) 44. (B)
SET A 5. (D) 6. (A) 15. (C) 16. (D) 25. (A) 26. (D) 35. (D) 36. (A) 45. (B) 46. (C)
7. (A) 17. (D) 27. (D) 37. (A) 47. (B)
8. (A) 18. (B) 28. (B) 38. (A) 48. (C)
9. 19. 29. 39. 49.
(D) (B) (C) (C) (D)
10. 20. 30. 40. 50.
(D) (C) (A) (B) (C)
1. (C) 11. (D) 21. (D) 31. (D) 41. (C)
2. (D) 12. (B) 22. (C) 32. (B) 42. (C)
3. (D) 13. (A) 23. (B) 33. (B) 43. (C)
4. (C) 14. (C) 24. (A) 34. (D) 44. (A)
SET B 5. (D) 6. (D) 15. (B) 16. (A) 25. (B) 26. (D) 35. (D) 36. (C) 45. (B) 46. (B)
7. (A) 17. (A) 27. (D) 37. (B) 47. (C)
8. (B) 18. (A) 28. (A) 38. (A) 48. (A)
9. 19. 29. 39. 49.
(A) (A) (B) (B) (D)
10. 20. 30. 40. 50.
(A) (C) (C) (D) (B)
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