Sample question paper

If the matrix A = [0 r −2; 3 p t; q −4 0] is skew-symmetric, then value of (q+t)/(p+r) is….

1. A−2
2. B0
3. C1
4. D2

If A is a square matrix of order 4 and |adj A| = 27, then A (adj A) is equal to

1. A3
2. B9
3. C3 I
4. D9 I

The inverse of the matrix [3 0 0; 0 2 0; 0 0 5] is…

1. A[0 0 3; 0 2 0; 5 0 0]
2. B[1/3 0 0; 0 1/2 0; 0 0 1/5]
3. C[−1/3 0 0; 0 −1/2 0; 0 0 −1/5]
4. D[−3 0 0; 0 −2 0; 0 0 −5]

If f(x) = x tan⁻¹ x, then f′(1)is equal to

1. Aπ/4 − 1/2
2. Bπ/4 + 1/2
3. C−π/4 − 1/2
4. D−π/4 + 1/2

A function f(x) = 10 − x − 2x² is increasing on the interval

1. A(−∞, −1/4]
2. B(−∞, 1/4)
3. C[−1/4, ∞)
4. D[−1/4, 1/4]

The solution of the differential equation xdx + ydy = 0 represents a family of

1. Astraight lines
2. Bparabolas
3. CCircles
4. DEllipses

If ∫ x³ sin⁴(x⁴) cos(x⁴) dx = a sin⁵(x⁴) + C, then a is equal to

1. A−1/10
2. B1/20
3. C1/4
4. D1/5

A bird flies through a distance in a straight line given by the vector î + 2ĵ + k̂ . A man standing beside a straight metro rail track given by r⃗ = (3 + λ)î + (2λ − 1)ĵ + 3λk̂ is observing the bird. The projected length of its flight on the metro track is

1. A6/√14 units
2. B14/√6 units
3. C8/√14 units
4. D5/√6 units