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MT1 1. 2. 3. 4. 5. 6. 7. 8. A = {x: x is a natural number less then 1} is the set of: (a) Empty (b) Void (c) Hull (d) All of the above If a A a B then: (a) A B (b) A B (c) A B (d) A B If cardinal number of set A is 5 then number of proper subset of A is: (a) 32 (b) 31 (c) 36 (d) 64 If set of elements that belongs to A but not B is: (a) B–A (b) A–B (c) A B (d) A B If A A = A, refers to the law of: (a) Associative (b) Commulative (c) Idempotent (d) None of the above (A B)’ = A’ B’ refers: (a) Additional rule (b) Bay’s rule (c) De’morgan’s rule (d) None of the above The representation of set in geometrical is called _______ diagram: (a) Hasse (b) Venn (c) Organd (d) None of the above Intersection of with A is: (a) A (b) (c) (d) None of the above XIX 9. 10. 11. 12. 13. 14. 15. 16. {(p, q): p p, q q} belongs to: (a) P Q (b) P Q (c) P – Q (d) P × Q If order pairs (x+2, 4) = 4, y–2) then value of x, y is respectively: (a) 2, 4 (b) 2, 2 (c) 2, 6 (d) 6, 2 The set of all second elements in a relation R from a set A to B is called the _______ of R. (a) Domain (b) Range (c) Codomain (d) None of the above If R = {(4, 2), (6, 3) (8, 4)} then range is: (a) {4, 6, 8} (b) {2, 3, 4} (c) {2, 2, 2} (d) None of the above A relation R in a set A is called _______ relation a A. (a) Symmetric (b) Transitive (c) Reflective (d) None of the above If f is a function of A to B and (a, b) f then: (a) f (b) = 0 (b) f (a) = a (c) f (b) = b (d) f (a) = b If f (x) = x2, g (x) = x then (f + g) x is: (a) x2 x (b) x + x2 (c) x2/x (d) None of the above If f: x y if f (x1) = f (x2) x1 = x2 then function is: (a) One-one (b) Injective (c) Both (a) and (b) (d) None of the above (1) MT1 17. A function f : x y s said to be 18. 19. 20. 21. 22. 23. 24. _______ if it is both one-one and onto: (a) One-one (b) Onto (c) Bijective (d) Many one h (x) = 2x – 5is a function that is (h : R R): (a) Injunctive (b) Not injunctive (c) Bijective (d) All of the above If f : R R, f (x) = x5 + 4 then f is: (a) One-one (b) Onto (c) Both (A, and B) (d) None of the above The range of Signum function is: (a) R = {R} (b) R = {– 1, 1} (c) R = {– 1, 0, 1} (d) {– 1, 0} The greatest integer value of 35 is [3 5] (a) 4 (b) 3 (c) 7 (d) 1 If f (x) and g (x) is polynomial of x then f (x)/ g (x) is _______ function: (a) Polynomial (b) Modulus (c) Rational (d) Signum A function is invertible if and only if f is _______ (a) Injunctive (b) Surjunctive (c) Bijective (d) None of the above If a * b = e = b* a then, a, b are _______ of each other: (a) Identify (b) Inverse (c) Commulative (d) None of the above XIX 25. If the value of radian is: (a) 90o (b) 2 (c) 180o (d) 45o 26. The circular measure of 112o 30 is _______ radian: 8 5π (b) 8 3 (c) (a) 8 7 (d) 8 27. The ratio of hypotenuse to base is called: (a) Cos (b) Sec (c) Cosec (d) Sin 28. The ratio of sin to cos is called: (a) Cot (b) Tan (c) Sec (d) Cosec 29. The periodicity of tan x is: (a) (b) /2 (c) 2 (d) 3 /4 30. If sin x = 5/13 then tan x is: (a) 15/5 (b) 5/12 (c) 12 5 (d) None of the above 31. The value of cos 72o is equal to: (a) (b) (c) 5 1 4 5 1 4 52 4 (d) None of the above (2) 32. 3 cos + sin is equal to: (a) 2 (b) –2 (c) 1 (d) None of the above 33. Sin–1 (sin x) is equal to: (a) x (b) –x (c) 1/x (d) None of the above 34. Sin+1 x + cos–1 x is equal to: (a) (b) /2 (c) 2 (d) 3/2 35. Domain of sin–1 x is: (a) [– 1, 1] (b) (1, –1) (c) (1, 0) (d) (0, 1) 36. tan–1 x + cot–1 x = (a) (b) 2 (c) /2 (d) /3 37. cos–1 (–x) is equal to: (a) (b) – cos–1 x (c) + cos–1 x (d) – sin–1 x 38. If cosec + cot = 2 3 then sin is: (a) 1/3 (b) 2/3 (c) (c) 3/2 (d) None of the above 39. The value of tan 15o is: (a) 2 3 2 (b) 2 3 2 (c) 2 3 (d) None of the above 40. Cos–1 (cos 7/6) is equal to: (a) 7 /6 (b) 5 /6 (c) Both A and B (d) None of the above XIX 41. What is the 11 23 (a) 23 (b) 23 imaging MT1 part of (c) 11 (d) None of the above 42. What is 1 i 3 the additive inverse of (a) 1 1i 3 (b) 1 i 3 (c) 1 i 3 (d) None of the above 43. If z1 = 3 2i + z2 = – 5 + 4 i then (z1 + z2) is: (a) (b) (c) (d) 44. 2 – 6i 2 + 6i –2 + 6i None of the above 2 3i 1 3i a ib then value of a is: (–1) 42 (–1) 43 (–1) 4–1 None of the above 45. If z = a + i b then modulus of z is: (a) (a) ab 2 2 1/2 (b) (a +b ) (a) (b) (c) (d) a 1 / 2 b1 / 2 (c) (c) (d) None of the above 46. If z = a + i b then polar form of complex number: (a) r (cos i sin ) (b) r (cos | i sin ) (c) r cos (d) i r sin 47. The argument of z = a + i b = r (cos + sin ) is: a b b (b) tan 1 a (a) tan 1 (c) tan–1 (a b) (d) tan–1 (c) (3) MT1 48. The value of i4 is: (a) –1 (b) 1 (c) 0 (d) None of the above 49. The value of npr is equal to: (a) Ln Lr Ln r (c) Ln Ln r 50. Solution of 10P4 is: (a) 1080 (b) 5040 (c) 5020 (d) None of the above 51. The numbers of arrangements of letters 56. in the word ‘MATHEMATICS’ L11 2 2 57. 2 L L L (b) (c) (d) L12 L2 L2 L4 L13 L2 L2 L3 58. L11 L2 L2 L2 52. The value of (nco + ncn) is: (a) 1 (b) 0 (c) 0–1 (d) None of the above 53. A bag contains 2 red, 6 p mk, 7 green and 5 black balls are drawn from the bag. Find the numbers of way of selecting 8 balls such that the selection consists of 2 balls of each other. (a) 1024 (b) 3150 (c) 3205 (d) 2025 XIX Ln Lr Ln r (b) Ln Lr Ln r (c) Ln Ln r 55. Arrangement made out of given number L Lr Ln (d) None of the above (a) (a) (d) None of the above n (b) 54. What is the value of nCr = 59. 60. of then is: (a) Combination (b) Permutation (c) Both A and B (d) None of the above Selection made out of given number of things: (a) Combination (b) Permutation (c) Both (a) and (b) (d) None of the above If nC10 = nC15 then value of 27Cn is: (a) 350 (b) 351 (c) 352 (d) None of the above How many words can be formed by using all the letters of word “Allahabad”. (a) 7860 (b) 7560 (c) 6507 (d) None of the above n (n – 1) (n–2) …. 3 2 1 is: (a) npr (b) ncr (c) Ln (d) None of the above n C0 + nC1 + nC2 + …. + nCn–1 + nCn (a) 2n–1 (b) 2n (c) 2n–2 (d) None of the above (4) MT1 2 61. Find the coefficient of x expansion of 1 / 2 x in the 105 32 (c) 101 32 66. An arrangement of number in a definite 67. (d) None of the above 62. The coefficient of x 10 2 1 is: x 6 in can of x 640 230 210 None of the above 63. The binomial theorem discovered by: (a) Einstein (b) Bays (c) Newton (d) Galeleo 64. The sum of indices in the expansion (a + b)n, of a and b is: (a) n (b) n–1 (c) n+1 (d) None of the above 2n 65. In the expansion of x 1 , the middle (a) (b) (c) (d) term is: (a) nth (b) (n+2)th XIX (c) (n+1) (d) None of the above 10 32 (a) 105 (b) th x 68. 69. 70. order following some rule is known as– (a) Term (b) Sequence (c) Series (d) None of the above The 15th term of the sequence 3, –3, –9, – 15, is (a) 81 (b) –81 (c) 85 (d) –85 Find the sum of sequence 3 + 7 + 11 + ….. 79 (a) 830 (b) 850 (c) 820 (d) 720 If a, b, c are in A.P. then: (a) 2b = a + c (b) b = a+c/2 (c) Both (a) and (b) (d) None of the above The arithmetic mean of 18 and 16 is: (a) 18 (b) 16 (c) 17 (d) 18 (5)