NTSE Maths Challenges

NTSE Maths Challenges Following are the typical problems asked in NTSE Maths and other Mathematical based aptitude tests (best viewed in Chrome or Firefox). Q1: Ramesh walks from his home to Railway station at the rate of 5 kmph, he misses the train by 7 minutes. However, if he walks at the rate of 6 kmph, he reaches the station 5 minutes before the arrival of the train. Find the distance of the station from his home. Answer: Let 'd' be the distance between Ramesh's house to Station. We know that distance = speed x time. If he walks at speed 5kmph, let time taken be

Let the time

is taken when he walks with a speed of 6kmph.

Since the time gap between two cases is

Q2: Roma travels from place A to B and then from B to C. From A to B Distance is 55 km which she covers with an average speed of 22 km per hour It takes her 1 hour 30 minutes moving from B to C with an average speed 30 km per hour Calculate her average speed over the whole of her journey from A to C. Answer: We know that Time taken from A to B =

= 2 Hrs and 30 mins

Distance from A to B = Speed x Time = 20 x 1.5 = 45 km. (note time taken from B to C is given as 1 Hrs 30 minutes i.e. 1.5 Hrs) Average Speed = Total Distance

Total Time

Q4: What is the difference between the sum of the first 2008 even numbers and the sum of the first 2008 odd numbers? (Singapore Maths Olympiad for Primary) Answer: Let us try to identify the pattern an try for small set. Sum of first 5 even numbers N(Even) = 2 + 4 + 6+ 8 + 10 Similarly, sum of first 5 odd numbers will be: N(Odd) = 1 + 3 + 5 + 7 + 9 If we subtract Odd list from Even list, i.e. N(Even) - N (Odd) = (2+4+8+10+12) - (1+3+5+7+9) = (2-1) + (4-3) + (6-5) + (8-7) + (10-9) = 1 + 1 + 1 + 1 + 1 = 5 (or 5 ones)

Similarly, the answer for the first 2008 numbers would be? 2008 Q5: The pages of a book are numbered consecutively, beginning with 1. The digit 7 is printed 25 times in numbering the pages. What is the largest number of pages the book can have? Answer: Count number of 7 appears how many times between 1 and 100 pages numbers = 20 (e.g. 7, 17, 27, 37, 47, 57, 67, 77, 87, 97, 70, 71, 72, 73, 74, 75, 76, 78, 79 = 20, 77 has two 7 digits) Count next five time 7 digit appears from page 101 onwards i.e. 107, 117, 127, 137, 147. Thus the largest number of pages the book will have: 157-1 = 156

Chemical Formula for daily used subtsances Compound Name Formula Uses Acetaminophen Acetic acid Ammonia Ascorbic acid Aspartame Aspirin Baking soda Caffeine Calcium carbonate Carbon dioxide Ethanol Ethylene glycol Hydrochloric acid Magnesium hydroxide Methane Phosphoric acid Potassium tartrate Propane Salt Sodium carbonate Sodium hydroxide Sucrose Sulfuric acid Water Water gas Gypsum

pain reliever tart ingredient in vinegar fertilizer, household cleaner when dissolved in water vitamin C artificial sweetener pain reliever cooking stimulant in coffee, tea, some soda antacid carbonating agent in soda disinfectant, alcoholic beverages antifreeze called muriatic acid, cleans mortar from brick antacid natural gas, fuel (also called Masrh Gas) flavoring in soda cream of tartar, cooking fuel for cooking flavoring (table salt), freezing washing soda drain cleaner sweetener battery acid washing, cooking, cleaning heating and lighting plaster of paris

NTSE SAT Quiz-6 (Geography) Q1: Chilka is the name of: a. a lake in the eastern coast of India. b. the mountain in the Himalayas c. a river in Maharashtra d. an industrial town in Jharkhand.

Q2: Which Indian state tops in hosiery and woolen goods in India: a. Karnataka b. Bihar c. Punjab d. Maharashtra Q3: Bhubaneswar, capital of Orissa is famous for its: a. Oil Refinery b. shipping industry c. space research centre d. famous lingaraja temple. Q4: The crop sown in the commencement of Monsoon season are a. kharif crops b. rabi crops c. zayad crops d. none of these Q5: Which of the following groups constitutes the basic rock forms? a. Sandy, Igneous, Metamorphic b. Igneous, Sedimentary, Metamorphic c. Lignite, Volcanic, Sedimentary d. Sandy, Volcanic, Igneous Q6: Nepanagar in Madhya Pradesh is famous for which of the following industry? a. Jute b. Textiles c. Rail coach d. Newsprint Q7: The narrow band of land, water and air where all kinds of life is possible is known as: a. Atmosphere b. Biosphere c. Lithosphere d. Hydrosphere Q8: Natural Rubber production is dominated by a. Western Europe b. USA c. South East Asia d. Latin America Q9: Petroleum is found in a. Sedimantry Rocks b. Metamorphic Rocks c. Igneous Rocks d. Lateral Rocks Q10: Tropic of Cancer passes through which state? a. Madhya Pradesh b. Uttar Pradesh

c. Maharashtra d. Andhra Pradesh Answer: 1-a 2-c 3-d

4-a

5-b

6-d 7-b 8-c 9-a 10-a

Wednesday, November 2, 2011 NTSE (SAT Quiz-3) Q1: Which of the following is an antibiotic? a. Aspirin b. Penicillin c. Paracetamol d. Sulphadizine Q2: Digestion of food starts in: a. mouth b. liver c. stomach d. intestines Q3: By taking the pulse rate of the human body, a doctor determines a. heartbeat b. functioning of heart valves c. condition of lever d. functioning of lungs Q4: A thermostat is used to a. purify air b. regulate humidity c. regulate temperature d. regulate air pressur Q5: Heat from the sun reaches the earth by a. reflection b. conduction c. convection d. radiation Q6: Dew forms most readily on nights that are: a. calm and clear b. stormy c. windy d. cloudy Q7: The full moon rises in the a. east b. west c. south d. north Q8: An aeroplane is able to fly because

a. it is lighter than air b. it is heavier than air c. it is made up of very light material d. moving air can lift objects Q9: The souring of milk is caused by the action of a. protozoan b. bacteria c. virus d. fungus Q10. The smallest thing that can cause disease in the human body is a. flea b. bacteria c. protozoa d. virus Q11: The most abundant gas in the air is: a. oxygen b. carbon dioxide c. nitrogen d. hydrogen Q12: Which element is common between brass and bronze a. copper b. Iron c. Zinc d. Aluminium Q13: The densest element known so far is a. gold b. mercury c. osmium d. tungsten Q14: The most ductile element is a. gold b. silver c. iron d. aluminium Q15: The metal having highest melting point is a. chromium b. tungsten c. diamond d. silver Answers: 1-b 2-a 3-a 4-c 5-d 6-a 11-c 12-a 13-c 14-a 15-b

7-a

8-d

9-b

10-d

NTSE MAT Quiz-1 (Series completion) Complete the following series: 1. 6,12,21,___,48,66 (a) 33 (b) 38 (c) 40

(d) 45

2. 125,80,45,20,___ (a) 5 (b) 8 (c) 10

(d)12

3. 22,24,28,___,52,84 (a) 30

(b) 36

(c)

42

(d) 46

4. 1,3,3,7,6,13,10,___,15,31 (a) 25

(b) 27

(c)

21

(d) 30

5. 3,1,7,3,13,7,21,15,31,31,___,63,57 (a)

39

(b) 41

(c) 38

(d) 43

6. a b c d e a b c _ a b _ _ b _ (a) d c d c (b) d c a c (c) d c a a (d) d c c c 7. Pick the right choice which complete the series? DF, JL, PR, ?? (a) ZX (b) VX (c) PQ (d) OR 8. C, F, I, L, ?, R (a) P (b) O (c) Q (d) N 9. PQR, RQP, PQRS, SRQP, PQRST, ? (a) RSPQT (b) TRSQP (c) TSQRP (d) TSRQP Answers: 1. (a) We get next term by adding +6,+9,+12,+15,+18,... 2. (a) We get next term by subtraction -45,-35,-25,-15,.... 3. (b) We get next term by adding +2,+4,+8,+16,+32,....

4. (c) This series is made up of 2 series,having alternate terms We get first series by adding +2,+3,+4,+5,+6 We get second series by adding +4,+6,+8,+10 5. (d)This series is made up of 2 series,having alternate terms We get first series by adding +4,+6,+8,+10,+12,+14 We get second series by adding +2,+4,+8,+16,+32 6 (c) Here the pattern comes out as abcde abcd abc ab a 7 (b) The distance between the letters is 6 i.e. D is 4th alphabet, J is 10th and P is 16th. Similarly, F is 6th, L is 12th and so on. Hence the next term is VX. 8 (b) the difference is 2 between two consecutive letter. 9 (d) (hint see the 1st and 2nd terms, positions are exchanged left to right and so on.)

Sunday, October 30, 2011 English Grammar (Quiz of Verbs and Tenses) Fill in the blanks by writing the appropriate tense form of the verb given in brackets. Also name the tense form filled here. 1. Fashion is important to Shyam, so he always _______________ the latest and most popular poaching style. (to select) 2. While Radha_______________ new clothes, her fashion consultant is busy on the sidelines, recommending stripes and long 'kurtas' to minimize the bulge factor. (to buy) 3. Shyam hopes that the next fashion fad _______________ a more mature, oval figure like his own. (to flatter) 4. She once _______________ a purple suede pantsuit, which clashed with her orange “I Love Motorcycles” tattoo. (to purchase) 5. Two minutes after she received the award, Maya _______________ it on a shelf next to her “Best Dressed, Considering” medal. (to place) 6. Rita _______________ it to me in detail yesterday. (to explain) 7. Rima _______________ an acceptance speech, but the “Leader of the Year” title went to Henna instead. (to prepare) 8. Mike _______________ on thin ice for two hours when he heard the first crack. (to skate) 9. Reema _____________ Shyam for years about his smoking habits, but he just won’t listen. (to warn) 10. Garima _____________ to speak to Mickey ever since he declared that “a little thin ice” shouldn’t scare anyone. (to refuse) Answers: 1. selects (present tense) 2. is buying or buys (present or present continuous) 3. will flatter (future tense, hint: see word next)

4. purchased (simple past). 5. placed (simple past, hint: after she received.) 6. explained (simple past, hint: yesterday) 7. had prepared (past perfect, hint: two events happened in past). 8. had been skating (past perfect continuous) 9. has been warning 10. has refused (present perfect, hint:present past link here) Grammar Quiz (Nouns) Q1: Identify which of the following are abstract noun or a proper noun a. muffin ............ b. violin ............ c. freedom ........... d. elegance ........... e. train Q2: Underline the noun(s) in the sentences below. The sentences may have more than one noun. a. She read the play over again. b. The actions became monotonous. c. He felt that his marriage, his relationship with her,was strong. d. The time had finally come to confess the truth. e. He’s the boy who delivers the paper. Q3: The following sentences have not been edited. Write each sentence in correct form. a. A large number of the fishes died due to pollution of water. b. Many peoples left the place c. Riches have wings. d. No news are released today. e. This five rupees note is a soiled one. Q4: Four parts of each of the following sentences are underlined. One of them is not acceptable in written English. Pick up the unacceptable. If there is no error, pick, mark 'E'. a. My fathers's secretary's wife met with an accident. NO ERROR A B C D E b. It is better to continue your study. NO ERROR A B C D E c. He showered many abuses on me. NO ERROR A B C D E d. The weather of New York is not good. NO ERROR Answers: 1: a-proper b-proper c-abstract d-abstract 2: a-play b-actions c-marriage, relationship 3: a-fish b-people c-has d-is e-five rupee 4. a-A b-D c-B d-A

e-proper d-time, truth

e-boy, paper