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41. In how many ways can one write the elements 1, 2, 3, 4 in a sequence x1, x2, x3, x4 with xi G i 6i? (A) 9 (B) 10 […]

40. Let a = (√5 + 1)/2 and b = (√5 − 1)/2. Then, evaluate: limn→∞ (an + bn)/(an − bn) (A) is 1 (B) is 1/2 (C) is 0 (D) […]

39. Let U = {1, 2, 3, 4, 5}. A subset S is chosen uniformly at random from the non-empty subsets of U. What is the probability that S does […]

38. Which one of the points P = (3/2, 1/2), Q = (1/2, 3/2), R = (3/2, 11/2), and S = (11/2, 3/2) lies above the parabola y = 2x² and […]

37. Let a⃗ = 4î − 2ĵ + 6k̂ and b⃗ = 7î + ĵ − 12k̂. If a⃗ × b⃗ = αî + βĵ + γk̂, then the value of […]

36.  In a geometric progression, the 3rd term is 36 and the 5th term is 324. The 7th term of the same progression will be _______. (in integer) Geometric Progression […]

35. Let N be the set of natural numbers and let f : N → N be defined by: f(x) = x/2, if x is even and f(x) = 3x […]

34. Let XYZ be an equilateral triangle and let P, Q, and R be the midpoints of YZ, XZ, and XY, respectively. If r = Area(△PQR) / Area(△XYZ), then the […]

33. Let ƒ(x) = (x — 1)(x — 2)(x — 3)(x — 4) and let α = ƒ(3/2), β = ƒ (5/2) and γ = ƒ(7/2). Which of the following […]

32. Let U = {1, 2, … , 15}. Let P ⊆ U consist of all prime numbers, Q ⊆ U consist of all even numbers and R ⊆ U […]