Test Codes: SIA (Multiple Choice Type) and SIB (Short Answer Type ...

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$LATEX and Beamer (Arijit Bishnu). - Indian Statistical Institute$

(C) a pair of distinct parallel straight lines(D) a point40. The number of triplets (a, b, c) of integers such that a anda, b, c are sides of a triangle with perimeter 21 is(A) 7 (B) 8 (C) 11 (D) 12.41. Suppose a, b and c are three numbers in G.P. If the equationsax 2 + 2bx + c = 0 and dx 2 + 2ex + f = 0 have a common root, thenda , e b and f are inc(A) A.P. (B) G.P. (C) H.P. (D) none of the above.42. The number of solutions of the equation sin −1 x = 2 tan −1 x is(A) 1 (B) 2 (C) 3 (D) 5.43. Suppose ABCD is a quadrilateral such that ∠BAC = 50 ◦ , ∠CAD =60 ◦ , ∠CBD = 30 ◦ and ∠BDC = 25 ◦ . If E is the point of intersectionof AC and BD, then the value of ∠AEB is(A) 75 ◦ (B) 85 ◦ (C) 95 ◦ (D) 110 ◦ .44. Let R be the set of all real numbers. The function f : R → R definedby f(x) = x 3 − 3x 2 + 6x − 5 is(A) one-to-one, but not onto(B) one-to-one and onto(C) onto, but not one-to-one(D) neither one-to-one nor onto.45. Let L be the point (t, 2) and M be a point on the y-axis such thatLM has slope −t. Then the locus of the midpoint of LM, as t variesover all real values, is(A) y = 2 + 2x 2 (B) y = 1 + x 2(C) y = 2 − 2x 2 (D) y = 1 − x 2 .46. Suppose x, y ∈ (0, π/2) and x ≠ y. Which of the following statementsis true?(A) 2 sin(x + y) < sin 2x + sin 2y for all x, y.(B) 2 sin(x + y) > sin 2x + sin 2y for all x, y.(C) There exist x, y such that 2 sin(x + y) = sin 2x + sin 2y.(D) None of the above.47. A triangle ABC has a fixed base BC. If AB : AC = 1 : 2, then thelocus of the vertex A is(A) a circle whose centre is the midpoint of BC(B) a circle whose centre is on the line BC but not the midpoint ofBC8
(C) a straight line(D) none of the above.48. N is a 50 digit number. All the digits except the 26th from the rightare 1. If N is divisible by 13, then the unknown digit is(A) 1 (B) 3 (C) 7 (D) 9.49. Suppose a < b. The maximum value of the integral∫ ba( )34 − x − x2 dxover all possible values of a and b is(A) 3 4(B) 4 3(C) 3 2(D) 2 3 .50. For any n ≥ 5, the value of 1 + 1 2 + 1 3 + · · · + 12 n − 1lies between(A) 0 and n 2(C) n and 2n(B) n 2 and n(D) none of the above.51. Let ω denote a cube root of unity which is not equal to 1. Then thenumber of distinct elements in the set{(1 + ω + ω 2 + · · · + ω n ) m : m, n = 1, 2, 3, · · · }is(A) 4 (B) 5 (C) 7 (D) infinite.52. The value of the integral∫ 32dxlog e x(A) is less than 2 (B) is equal to 2(C) lies in the interval (2, 3) (D) is greater than 3.9
Page 1 and 2: Test Codes: SIA (Multiple Choice Ty
Page 3 and 4: (A) real and negative,(B) real and
Page 5 and 6: many of these unit squares contain
Page 7: (A)(B)(C)(D)34. If a n =(1 + 1 ) )
Page 11 and 12: 2. Let n > 3 be odd. Then(A) n 2
Page 13 and 14: (A) ∫ b0 2x[f(b) − f(x)]dx (B)
Page 15 and 16: (D) S n > 1 √ 4n+2for all n ≥ 2
Page 17 and 18: Sample Questions for SIB1. How many
Page 19 and 20: (ii) a + b 2 is irrational but ab 2

Test Codes: SIA (Multiple Choice Type) and SIB (Short Answer Type ...

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