If D =  for x ≠ 0, y ≠ 0 then D is

a) Divisible by neither x nor y

b) Divisible by both x and y

c) Divisible by x but not y

d) Divisible by y but not x

If A and B are square matrices of side n x n such that A² – B² = (A – B) (A + B) then which of the following will always be true

a) AB = BA

b) Either A or B is a zero matrix

c) Either A or B is an identity matrix

d) A = B

Let A =  and B =, a, b ε ℕ. Then

a) There exist more than one but finite number of B’s such that

AB = BA

b) There exist exactly one B such that AB = BA

c) There exist infinitely many B’s such that AB = BA

d) There cannot exist any B such that AB = BA

If A² – A + I = [0] then the inverse of A is

a) I – A

b) A –I

c) A

d) A + I

If a² + b² + c² = – 2 and
 f(x) = ,
then f(x) is a polynomial of degree

a) 2

b) 3

c) 0

d) 1

If a₁, a₂ . . . . , a_n,. . . . . . are in geometric progression then the determinant
Δ =  is equal to

a) 2

b) 4

c) 0

d) 1

Let A =  

the only correct statement about the matrix A is

a) A is a zero matrix

b) A = (-1) I where I is a unit matrix

c) A^-1 does not exist

d) A² = I

Let A =  and (10) B =.

If B is inverse of the matrix A then α is

a) -2

b) 1

c) 2

d) 5

The system of equations x + 2ay + az = 0, x + 3by + bz = 0 and
x + 4cy + cz = 0 has a non–zero solution, then a, b, c

a) are in arithmetic progression

b) are in geometric progression

c) are in harmonic progression

d) satisfy a+ 2b + 3c =0

If A =  and A² =  then

a) α = a² + b², β = ab

b) α = a² + b², β = 2ab

c) α = a² + b², β = a²  b²

d) α =2ab, β = a² + b²

If 1, ω, ω² are cube roots of unity, then  is equal to

a) 0

b) 1

c) ω

d) ω²

If l, m, n are the p^th, q^th and r^th term of a geometric progression and are all positive then  equals

a) 3

b) 2

c) 1

d) 0

If ω ≠ 1 is a cube root of unity, then
  equals

a) 0

b) 1

c) i

d) ω

If f(x) =   then

   is

a) -2

b)  -1

c) 2

d) 1

The matrix A =  is

a) Unitary

b) Orthogonal

c) Nil potent

d) Involuntary

If f (x) =  then the value of  is

a) 0

b) 1

c) -1

d) 2

Let A =  

where 0 ≤ θ ≤ 2π. Then the range of |A| is

a) 0

b) {2, 4}

c) [2, 4]

d) None of these

If A is a skew–symmetric matrix, then trace of A is

a) 1

b) -1

c) 0

d) None of these

The arbitrary constant on which the value of the determinant
 
does not depend is

a) α

b) p

c) d

d) a

If f(x) =  

then f (100)is equal to

a) 0

b) 1

c) 100

d) -100

If A =  and A. (adj A) = λI then the value of λ is

a) 2

b) 1

c) 3

d) 0

The value of, if U_n =  is

a) 0

b) 1

c) -1

d) None of these

If A and B are orthogonal matrices of the same size then which one of the following is an orthogonal matrix

a) A + B

b) A + iB

c) i(A + B)

d) AB