JEE Mathematics Determinants MCQs

Question. The system of simultaneous equations kx + 2y – z = 1, (k – 1) y – 2z = 2 and (k + 2) z = 3 have a unique solution if k equals:
(a) – 1
(b) – 2
(c) 0
(d) 1

Answer: A

Question. If A and B are square matrix of the same order such that AB = A and BA = B, then A and B are both :
(a) non-singular
(b) involutory
(c) idempotent
(d) singular

Answer: A

Question. x + ky – z = 0, 3x – ky – z = 0 and x – 3y + z = 0 has non-zero solution for k is equal to :
(a) 1
(b) – 1
(c) 0
(d) 2

Answer: A

Question. The value of a for which the system of equations x + y + z = 0, x + ay + az = 0, x – ay + z = 0, possesses nonzero solutions, are given by :
(a) 1, – 1
(b) none
(c) 1, 2
(d) 1, 0

Answer: A

Question. System of equation : x + 3y + 2z = 6 ; x + λy + 2z = 7 ; x + 3y + 2z = μ has
(1) infinitely many solution if λ= 4, μ = 6
(2) no solution if λ= 5, μ = 7
(3) no solution if λ = 3, μ = 5
(4) unique solution if λ= 2, μ ≠6
(a) 1, 2 and 3 are correct
(b) 2 and 4 are correct
(c) 1 and 2 are correct
(d) 1 and 3 are correct

Answer: A