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51. The value of: limx→2 (x3 − 8)/(x − 2) is _______. (in integer) Evaluate the Limit of (x³ − 8)/(x − 2) as x Tends to 2 Understanding the Given […]

50. Three vectors are as follows: a⃗ = 3î − 10ĵ + 7k̂ b⃗ = −9î + 6ĵ − 47k̂ c⃗ = 11ĵ − 17k̂ The value of (a⃗ + […]

49. The value of: limn→∞ (3n + 5n + 4)/(4 + 2n²) is _______. (A) 0 (B) 0.75 (C) 1.5 (D) 3 Evaluate the Limit of (3n + 5n + 4)/(4 […]

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

47. Select the value(s) of x for which the determinants of the two matrices are equal. (A) √3 (B) 3 (C) −1 (D) −√3 Reconstructing a Mathematically Consistent Determinant Equation […]

46. Let N be the set of natural numbers and f : N → N be defined by: f(x) = x/2, if x is even f(x) = 3x + 1, if […]

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

44. 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 […]

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

42. Simplify: sin A/(1 + cos A) + (1 + cos A)/sin A (A) 2 sec A (B) 2 cosec A (C) sec A (D) cosec A Simplify sin A/(1 + […]