Sample question paper

Value of cot⁻¹(2 cos (1/2 sin⁻¹(√3/2)))

1. Aπ/6
2. Bπ/4
3. Cπ/3
4. Dπ/2

If A = [2 1 −2; 3a 0 4; b 2c 1] is a symmetric matrix, then value of √(6a + 2b + 3c) is:

1. A−2
2. B2
3. C±2
4. D4

If P and Q are matrices of same order such that P = [2 1; 0 1], |Q| = 3, then find |adj(PQ)|

1. A-3
2. B1
3. C6
4. D36

If [1 x][1 0; 0 2][4; −1] = O, then value of x is

1. A−2
2. B−1
3. C1
4. D2

The derivative of cos⁻¹(2x² − 1) with respect to cos⁻¹(x) is

1. A2
2. B±1
3. C1/2
4. D−3

If a, b, c are arbitrary constants such that the function defined by f(x) = {ax² + b, b ≠ 0, x ≤ 1; bx² + ax + c, x > 1} is differentiable at x = 1, then which of the following could be a triplet for (a, b, c)?

1. A(3,2,0)
2. B(0,0,3)
3. C(3/2, 2,0)
4. D(3, 3/2, 0)

If y = a {x + 2a sin (x/a)}, a > 0, x ∈ [0, πa]; is a decreasing function, then the interval in which x lies is

1. A(5π/6, π]
2. B(2π/3, π]
3. C(5πa/6, πa]
4. D(2πa/3, πa]

The values of x for which the derivative of the function y = x⁴ is greater than the value of the function are

1. A0 < x < 4
2. B0 < x ≤ 4
3. Cx < 0 or x > 4
4. Dx < 0 or x ≥ 4