12 Sample Questions SECTION A - MATHEMATICS Compulsory for all 1. 2. A die is tossed 5 times. Getting an odd 7. number is considered a success. Then the variance of distribution of success is A. 8/3 B. 3/8 C. 4/5 D. 5/4. If a > 0 and discriminant of ax2 + 2bx +c 8. a b is –ve, then b c ax + b bx + c is ax + b bx + c A. B. C. D. 3. FOR SCIENCE STREAM STUDENTS 0 9. +ve (ac – b 2)(ax2 + 2bx + c) –ve 0. log x n - [ x ] , [x ] x ®0 Lim n ÎN , ([x] denotes greatest integer less than or equal to x) A. has value – 1 B. has value 0 C. has value 1 D. does not exist 4. The maximum distance from origin of a point at on the curve x = a sint – b sin b at y = a cost - b cos , both a, b > 0 is b A. a – b B. a + b ( ) 5. 6. r r r and b is p6 then (a ´ b ) is equal to A. 48 B. 16 r C. a D. none of these r r r If ar, b , c are vectors r r such that [ar b cr] = 4 then [ar ´ b b ´ cr cr ´ ar] = A. 16 B. 64 C. 4 D. 8. 2 The d.r. of normal to the plane through (1, 0, 0), (0, 1, 0) which makes an angle p/4 with plane x + y = 3 are A. 1, 2, 1 B. 1, 1, 2 C. 1, 1, 2 D. 2, 1, 1. 10. Two systems of rectangular axes have the same origin. If a plane cuts them at distance a, b, c and a ¢, b ¢, c ¢ from the origin, then 1 a2 1 B. 2 a 1 C. 2 a 1 D. 2 a A. + 12 - 12 + 12 + 12 - 1 2 = 0 b c a¢ b¢ c¢ - 12 - 12 + 12 - 12 - 1 2 = 0 b c a¢ b¢ c¢ + 12 + 12 - 12 - 12 - 1 2 = 0 b c a¢ b¢ c¢ + 12 + 12 + 12 + 12 + 1 2 = 0. b c a¢ b¢ c¢ FOR NON SCIENCE STREAM STUDENTS a2 - b2 . 11. Dilip, Ram and Amar started a shop by d 2y -2 x investing Rs. 27000, Rs. 81000 and =e The solution of the equation is dx 2 Rs. 72000 respectively. At the end of one 1 1 A. 4 e -2x B. 4 e -2 x + cx + d year, the profit was distributed. If Ram’s share of profit be Rs. 36000, the total profit 1 -2 x 1 2 -2 x C. 4 e + cx + d D. 4 e + c + d . was: 1 1 A. Rs. 108000 B. Rs. 116000 -1 é 1 cot ë(cos a ) 2 ùû + tan éë(cos a ) 2 ùû = x then C. Rs. 80000 D. None of these sinx = 12. A, B and C enter into partnership by making A. 1 B. cot2(a/2) investments in the ratio 3 : 5 : 7. After a C. tan a D. cot (a/2) year, C invests another Rs. 337600 while C. a2 + b 2 ( ) r r r If a = 4, b = 2 and the angle between a D. 31 12 A withdrew Rs. 45600. The ratio of investments then changes to 24 : 59 : 167. How much did A invest initially? A. Rs. 45600 B. Rs. 96000 C. Rs. 141600 D. None of these 13. In a partnership, A invests (1/6) of the capital for (1/6) of the time, B invests (1/3) of the capital for (1/3) of the time and C, the rest of the capital for the whole time. Out of a profit of Rs. 4600, B’s share is : A. Rs. 800 B. Rs. 1000 C. Rs. 650 D. Rs. 960 14. A person buys a house paying Rs 50,000 in cash and the balance in 20 instalments of Rs. 8000 each at the end of each year. If interest be reckoned at 16%, how much he should have paid if he had purchased it cash down. A. 97435,50 B. 94735.50 C. 93475.50 Answer figure A. B. Geography. D and A were teaching Mathematics and Hindi. E and B were teaching History and French. Who among the teachers was teaching maximum number of subjects? A. A B. B C. C 18. Statements : Conclusions : fit into one of the diagrams at (A), (B), (C), (D). You have to indicate which diagram depicts the correct relationship among the following group of elements. Honesty, intelligence, aptitude. A. B. C. D. 16. Which figure shall come next in the series ? Select your answer from the answer figures. Problem figure 32 D. D All sparrows are koels. No Koel is parrot. I. No sparrow is parrot. II. Some sparrows are parrots SECTION B - MENTAL ABILITY elements may or may not have some interlinkage. Each group of the elements may D. 17. In a school, there were five teachers. A and B were teaching Hindi and English. C and B were teaching English and D. 95743.50 15. Three elements are given below. These C. III. All koels are Sparrows IV. Some parrots are sparrows A. Only I follows B. None follows C. Only II and III follow D. Only II and IV follow 19. If 'TEACHER' and 'HIGHLY' are written as 'X W P B R W M' and 'R S N R D Z' respectively, how will you code the word 'CHARITY' ? A. B P R N S B Z B. B R P M S Z B C. B R P M S D Z D. B R P M S X Z Answers 1. D 6. A 11. C 16. A 2. C 7. B 12. C 17. B 3. D 8. A 13. A 18. A 4. A 9. B 14. A 19. D 5. B 10. C 15. A