PG-QP – 29 -4- *PGQP29* PART – A Questions 1 – 10 : Choose the most grammatically correct and meaningful option from those provided at the end of each sentence : 1. One who is incapable of committing a mistake is called A) sure B) certain C) definite D) infallible 2. The opposite of ‘curious’ is A) calm B) indifferent C) undemanding D) provoked 3. Their entire future ____________ on the result of this examination. A) depends B) depending C) resolved D) revolving 4. We haven’t had ________________ rest all of this week. A) many B) some C) any D) no 5. This seems to be the ______________ question to answer right now. A) hardly B) hardest C) very hard D) harder 6. If I ______________ the decision-maker, things would have been much easier. A) had been B) were C) was D) am 7. Everyone was in time for the show, ____________ ? A) wasn’t he B) isn’t it C) weren’t they D) were they 8. He has ______________ all that he had in this gamble. A) lossed B) loosed C) losed D) lost 9. We should refrain ______________ overeating. A) from B) to C) in doingD) over 10. ______________ are we waiting for ? A) Why B) When C) What D) How *PGQP29* -5- PG-QP – 29 11. The highest rank in Indian Air Force is A) Air Chief Marshal B) Air Marshal C) Air Vice-Marshal D) Air Commander 12. Who was the first women to win the Jnanpith Award ? A) Mahadevi Varma B) Subhadra Kumar Chouhan C) Amrita Pritam D) Ashapurna Devi 13. Yuri Gagarin was a A) Nuclear Scientist B) Musician C) Playcont D) Cosmonaut 14. ‘People’s Daily’ is an important newspaper of A) China B) Russia C) Egypt D) Indonesia 15. Find the next term of the series POQ, SRT, VUW A) XYX B) XZY C) ZYX D) YXZ 16. Which of the following States has banned the slaughter of camels ? A) Gujarat B) Punjab C) Haryana D) Rajasthan 17. The first woman Judge of the Supreme Court of India was A) Leela Seth B) Cornelia Sorabjee C) Omna Kunjamma D) M. Fathima Beevi 18. Shelly travelled 9 km to the West and turned right and covered 7 km; then she turned left and covered 8 km; then she turned back and travelled 11 km, finally she turned right and travelled 7 km. How far is she from the starting point ? A) 2 km B) 6 km C) 10 km D) 15 km 19. The ___________ is an instrument used to measure distance travelled on foot. A) Phorometer B) Pedometer C) Micrometer D) Pachymeter PG-QP – 29 -6- *PGQP29* 20. In a row of 21 girls, when Monika was shifted by four places towards the right, she became 12th from the left end. What was her earlier position from the right end of the row ? A) 9th B) 10th C) 12th D) None of these 21. Micheal Corleone is a character from the book A) For Whom the Bells Toll B) Lord of the Rings C) Love Story D) Godfather 22. Who amongst the following are associated with communism ? (i) Karl Marx (ii) Ayn Sue-Khi (iii) Ayn Rend (iv) Mao Tse Tung The correct answer is A) only (i) B) (i) and (iii) C) (i) and (iv) D) only (iv) 23. In covering a distance of 30 km, Abhay takes 2 hours more than Sameer. If Abhay doubles his speed, then he would take 1 hour less than Sameer. Abhay’s speed is A) 5 kmph B) 6 kmph C) 6.25 kmph D) 7.5 kmph 24. The dog breed “Pug” is associated with the advertisement of A) Airtel B) Vodafone C) Aircel D) BSNL 25. “Anokhi” is a brand associated with A) Hand Block Prints B) Pottery C) Antique Furniture D) Organic Food *PGQP29* -7- PG-QP – 29 PART – B 26. Let a be a non-zero real number. Consider the sequence {xn) where a2 xl = 2a and xn = xl – x for n≥ 2. Then xn for n ≥ 2, can be expressed in terms n -1 of a as n n +1 A) x = a B) x = a n n +1 n n n n −1 C) x = a D) x = a n n −1 n n m n 27. Consider the set X = { + : m, n are natural numbers}. Then n m A) X is neither bounded below nor bounded above B) X is bounded above and sup X = 4 C) X is bounded below and inf X = 2 D) X is bounded below and inf X = 1 ⎧ n ⎫ 28. Consider the sequence ⎨ ⎬ . This sequence ⎩2n ⎭ A) is bounded but not convergent B) is not bounded C) is convergent and converges to 1 D) is convergent and converges to 0. PG-QP – 29 -8- *PGQP29* ∞ 1 3 29. The series ∑ =+Sin Cos + n11 2n 2 n 1 1 A) converges to Sin 1 B) converges to Sin 1 2 1 C) converges to Cos 1 D) converges to Cos 1 2 ⎛ π ⎞ Cos⎜ Cosx ⎟ ⎝ 2 ⎠ 30. The lim exists and its value is x→0 Sin (Sin x) A) –1 B) 0 C) 1 D) 2 1 31. Consider the function f(x) = for real numbers x≠ 0. Denote by e1/ x +1 lim lim − f(x) the left hand limit and + f(x) the right hand limit x→0 x→0 of f(x) at x = 0. Then lim lim A) − f(x) exists but not + f(x) x→0 x→0 lim lim B) + f(x) exists but not − f(x) x→0 x→0 lim lim C) both − f(x), + f(x) exist and their values are not equal x→0 x→0 lim lim D) both − f(x), + f(x) exist and their values are equal x→0 x→0 32. Let f : 3 → 3 be given by ⎪⎧x2 −1, if x isirrational f(x) = ⎨ ⎩⎪ 0, if x isrational Then f is continuous A) only at x = – 1 and x = 1 B) only at x = – 1 C) only at x = 1 D) at no point of 3 *PGQP29* -9- PG-QP – 29 33. Let f :3 → 3 be a function given by ⎧4x, if x ≤ 0 ⎪ f(x) = ⎨ax 2 + bx + c, if 0 < x <1 ⎪ ⎩⎪3 − 2x, if x ≥1 Then f is differentiable on 3 if A) a = b = 3 and c = l B) a = – 3, b = 4 and c = 0 C) a = – 3, b = – 4 and c= 0 D) a = 3, b= – 4 and c = 0 34. The polynomial p(x) = x13 + 7x3 – 5 has A) no real root B) two real roots C) only one real root D) more than two real roots π x Sin x 35. Value of the integral ∫ dx is + 2 0 1 Cos x π2 π2 π2 A) π 2 B) C) D) 2 3 4 36. Let f be a continuous function on [0, 1] such that f (x) > 0 for all x ∈[0, 1]. Then the 1 f(x) value of ∫ + − dx is 0 f(x) f(1 x) 1 1 1 A) 1 B) C) D) 2 3 4 PG-QP – 29 -10- *PGQP29* 37. Let f : 32→ 3 be a function of two real variables given by ⎧x ⎪ , y ≠0 f(x, y) = ⎨y ⎩⎪ 0, y =0 Determine which one of the following facts about f is not correct ? ∂f ∂f A) Partial derivatives and at (0, 0) exist ∂x ∂y B) Directional derivative of f at (0, 0) in the direction of the vector (a, b), where ab≠ 0, does not exist C) f is bounded on some neighbourhood of (0, 0) D) f is not continuous at (0, 0) 2 2 38. The value of the double integral ∫∫(x + y ) dxdy, where S is the square S with vertices (0, 0), (1, 1), (2, 0), (1, – 1) is 1 2 4 8 A) B) C) D) 3 3 3 3 ⎛ ⎞ ⎜ 4 2 1 3⎟ ⎜ ⎟ ⎜ 6 3 4 7⎟ ⎜ ⎟ 39. The rank of the matrix ⎜ 2 1 0 1⎟ is ⎜ ⎟ ⎝ 2 1 1 2⎠ A)4 B)3 C)2 D)1 *PGQP29* -11- PG-QP – 29 40. The general solution of y′′− 2y′ + y = x + ex is 1 A) y = c x + c ex + x + x2ex + 2, c , c are arbitrary constants 1 2 2 l 2 1 B) y = (c x + c )ex + x + x2ex + 2, c , c are arbitrary constants 1 2 2 l 2 x C) y = (c1x + c2)e + x + 2, cl, c2 are arbitrary constants 1 D) y = (c + c x)ex + x + x2ex, c , c are arbitrary constants 1 2 2 l 2 41. Eight people P1, P2, ... , P8, are arranged randomly in a line, the probability that Pl and P2 are not next to each other is 3 1 1 3 A) B) C) D) 4 4 8 8 42. Of all row arrangements of 6 boys and girls, the number of arrangements with at least two boys is A) 47 B) 37 C) 57 D) 27 43. A class contains 10 boys and 20 girls of which half the girls have brown eyes, the probability that a person chosen at random is a boy or has brown eyes is 3 7 5 4 A) B) C) D) 9 6 6 6 44. The mean of 16 numbers is 27 and their median is 21. Suppose the largest number is increased by 6 and the smallest number is reduced by 9, the mean and median of the modified numbers are, respectively A) 26.81, 21 B) 27.00, 19.75 C) 26.81, 19.75 D) 27.00, 21 45.