Board exam

If A = [[−1, 0, 0], [0, 1, 0], [0, 0, 1]], then A⁻¹ is

1. A[ [−1, 0, 0], [0, −1, 0], [0, 0, −1] ]
2. B[ [1, 0, 0], [0, −1, 0], [0, 0, −1] ]
3. C[ [−1, 0, 0], [0, −1, 0], [0, 0, 1] ]
4. D[ [−1, 0, 0], [0, 1, 0], [0, 0, 1] ]

If vector a⃗ = 3î + 2ĵ − k̂ and vector b⃗ = î − ĵ + k̂, then which of the following is correct?

1. Aa⃗ ∥ b⃗
2. Ba⃗ ⟂ b⃗
3. C|b⃗| > |a⃗|
4. D|a⃗| = |b⃗|

∫₋₁¹ |x|/x dx, x ≠ 0 is equal to

1. A−1
2. B0
3. C1
4. D2

Which of the following is not a homogeneous function of x and y?

1. Ay² − xy
2. Bx − 3y
3. Csin²(y/x) + y/x
4. Dtan x − sec y

If f(x) = |x| + |x − 1|, then which of the following is correct?

1. Af(x) is both continuous and differentiable, at x = 0 and x = 1.
2. Bf(x) is differentiable but not continuous, at x = 0 and x = 1.
3. Cf(x) is continuous but not differentiable, at x = 0 and x = 1.
4. Df(x) is neither continuous nor differentiable, at x = 0 and x = 1.

If A is a square matrix of order 2 such that det (A) = 4, then det (4 adj A) is equal to :

1. A16
2. B64
3. C256
4. D512

If E and F are two independent events such that P(E) = 2/3, P(F) = 3/7, then P(E/F̄) is equal to :

1. A1/6
2. B1/2
3. C2/3
4. D7/9

The absolute maximum value of function f(x) = x³ − 3x + 2 in [0, 2] is :

1. A0
2. B2
3. C4
4. D5