11 Sample Questions SECTION A - MATHEMATICS 1. A. At least one in [0,1] Which one is not periodic 2 B. At least one root in [2, 3] A. |sin3x| + sin x B. cos x + cos 2 C. At least one root in [4, 5] x D. none of these C. cos4x + tan2x 6. D. cos2x + sinx 2. ( ) x ù -1 The domain of sin éêëlog3 is 3 ûú A. 3r A. [1, 9] D. 2r + 1. C. [–9, 1] 3. 7. If an = 7 + 7 + 7 + .... having n radical signs then by methods of mathematical induction which is true 8. A. an > 7 " n ³ 1 B. an > 3 " n ³ 1 C. an < 4 " n ³ 1 D. an < 3 " n ³ 1 9. 4. 13 – 23 + 33 – 43 + ... + 93 = A. 425 B. – 425 C. 475 D. – 475. Sum of infinite number of terms in GP is 20 and sum of their square is 100. The common ratio of GP is A. 5 B. 3/5 C. 8/5 D. 1/5. Difference between the corresponding Two common tangents to the circle x2 + y2 = 2a2 and parabola y 2 = 8ax are roots of x2 + ax + b = 0 and A. x = ±(y + 2a) x2 + bx + a = 0 is same and a ¹b, then A. a + b + 4 = 0 B. a + b – 4 = 0 C. a – b – 4 = 0 5. B. 3r + 1 C. 2r B. [–1, 9] D. [–9, –1]. r and n are positive integers r > 1, n > 2 and coefficient of (r + 2)th term and 3r th term in the expansion of (1 + x)2n are equal, then n equals B. y = ±(x + 2a) C. x = ±(y + a) D. y = ±(x + a). 10. A and B are events such that P (A È B) = 3/4, P (A Ç B) = 1/4, P( A)= D. a – b + 4 = 0. 2/3 then is If 2a + 3b + 6c = 0 (a, b, c Î R) then the quadratic equation ax2 + bx + c = 0 has A. 5/12 B. 3/8 C. 5/8 D. 1/4. P( A ∩ B) 31 11 SECTION B - MENTAL ABILITY 11. If TOUR is written in a certain code as 1234, CLEAR as 56784 and SPARE as 14. In a certain language, (a) 'hupa chip fu pa' stands for the statement 'Ram is very intelligent', (b) 'chip hupa kupa tik' for 'Hari is very smart', (c) 'Luck fu hupa' for 'boy is intelligent' and (d) 'fu tik dop' for 'smart and 90847 what will be the 5 th digit for SCULPTURE in the same code? A. 3 C. 0 intelligent'. Which of the following words stands for 'Hari' ? B. 6 D. 4 A. Chip B. Hupa 12. On another planet, the local terminology for earth, water, light, air and sky are ‘sky’, C. Tik D. Kupa ‘light’, ‘air’, ‘water’ and ‘earth’ respectively. If someone is thirsty there, what would he drink? A. Sky 15. Which one of the answer figure shall complete the given pattern ? B. Water C. Air D. Light 13. A, B, C, D, E, F and G are members of a Problem figure family consisting of four adults and three children, two of whom, F and G are girls. A and D are brothers and A is a doctor. E is an engineer married to one of the Answer figures brothers and has two children. B is married to D and G is their child. Who is C? A. B. C. D. A. G’s brother B. F’s father C. E’s daughter D. A’s son Answers 1. B 6. C 11. C 32 2. A 7. A 12. D 3. B 8. B 13. D 4. A 9. B 14. D 5. A 10. A 15. D