CBSE Class 12 Mathematics Matrices and Determinants MCQs Set C

Question: If (Image 80) then values of x, y, z, w are:
(a) 2, 2, 3, 4
(b) 2, 3, 1, 2
(c) 3, 3, 0, 1
(d) None of the options

Answer: a

Question: The system of equations x+Y+3z=1, 2x+y+2z=3 nad 3x+2y+5z=3 have
(a) unique solution
(b) infinite solution
(c) inconsistent
(d) None of the options

Answer: c

Question: If A is skew-symmetric and B= (I -A)-1 (I+ A), then B is
(a) singular
(b) symmetric
(c) skew-symmetric
(d) orthogonal

Answer: d

Question: 10.//10 If adj B =A and |p|= |Q|=1, then adj (Q^-1 BP^-1))is equal
(a) APQ
(b) PAQ
(c) B
(d) A

Answer: b

Question: The system of simultaneous equations kx+ 2y- z = 1 (k-1) y-2z=2 and (k+2) z=3 has a unique solution, if k is equal to
(a) – 2
(b) – 1
(c) 0
(d) 1

Answer: b

Question: If In is the identity matrix of order n, then (In) -1 is equal to
(a) does not exist
(b) In
(c) 0
(d) n I n

Answer b

Question: Matrix A such that A²=2A-I is the identity matrix. Then, for n ≥ 2,Aⁿ is equal to
(a) n A -(n-1)1
(b) n A -I
(c) 2n-1 A- (n-1) I
(d) 2n-1A-1

Answer: a

Question: The values of λ and μ for which the system of equations.
x+ y+z = 6, x+ 2y+3z = 10 and x+ 2y + λz =μ have no solution are
(a) λ =3
(b) μ = 10
(c) λ ≠ 3
d) λ ≠10 .

Answer: a,b

Question: Let A be an orthogonal non-singular matrix of order n, then the determinant of matrix ‘A -In’I,e.,| A- I -n | is equal to
(a) |In-A|
(b) | A |
(c) |A|| In -A|
(d) (-1 )n |A | |In-A|
Answer: c

Question: The values of x, y, z in order, if the system of equations 3x +y 2z=3, 2x-3y-z=-3 and x + 2y+ z = 4 has unique solution, are
(a) 2, 1, 5
(b) 1, 1, 1
(c) 1, -2, -1
(d) 1, 2, -1

Answer: d

Question: The system of equations
(aα +b)x + ay +bz=0
(bα +c)x + by + cz=0
(aα+b)+ (bα+c)z=0
has a non-trival solution, if
(a) a, b, c are in AP
(b) a, b, c are in GP
(c) a, b, c are in HP
(d) α is not a root of ax²+ 2bx+c=0

Answer: b

Question: The system of equations
αx +y +z= α-1
x+α y + z=α-1
x+ y +α z= α-1
has no solution, if a is
(a) not -2
(b) 1
(c) -2
(d) either -2 or 1

Answer: c

Question: The values of a for which the system of equations
x +y +z=1
x+2y+4z=α
x +4y + 10z=α2
is consistent, are
(a) 1, 2
(b) – 1, 2
(c) 1, 2
(d) None of the options

Answer: c

Question: Total number of possible matrices of order 3 x 3 with each entry 2 or 0 is
(a) 9
(b) 27
(c) 81
(d) 512

Answer: d

Question: If I is a unit matrix of order 10,then the determinant of I is equal to
(a) 10
(b) 1
(c) 1/10
(d) 9

Answer: b

Question: The system of linear equation x +y + z =2 , 2x + y − z = 3, 3x + 2y + k z = 4 has unique solution if:
(a) K ≠ 0
(b) –1 < K < 1
(c) –2 < K < 2
(d) K = 0

Answer: a

Question: The rank of the matrix (Image 80) is:
(a) 1 if a = 6
(b) 2 if a =1
(c) 3 if a = 2
(d) 1 if a = – 6

Answer: b,d

Question: If one of the Eigen values of a square matrix A order 3×3 is zero, then prove that det A = 0?
(a) A = 0
(b) A ≠ 0
(c) A < 2
(d) K = 0

Answer: a

Question: If A and B are square matrices of order n×n, then 2 (A − B) is equal to :
a. A2 − B2
b. A2 − 2AB + B2
c. A2 + 2AB + B2
d. A2 − AB − BA + B2

Answer: d

Question: A square matrix A = [aij] in which aij = 0 for i ≠ j and a_e = k (constant) for i = j is called a:
a. Unit matrix
b. Scalar matrix
c. Null matrix
d. Diagonal matrix

Answer: b

Question: Inverse of diagonal matrix (if it exists) is a:
a. Skew-symmetric matrix
b. Diagonal matrix
c. Non invertible matrix
d. None of the options

Answer: b

Question: If A and B are square matrices of same order then:
a. (AB)′ = A′B′
b. (AB)′ = B′A′
c. AB = 0, if | A|= 0 or | B |= 0
d. AB = 0, if | A|= I or B = I

Answer: b

Question: In an upper triangular matrix n × n, minimum number of zeros is:
a. n(n–1)/2
b. n(n+1)/2
c. 2n(n–1)/2
d. None of the options

Answer: a

Question: Let p be a non-singular matrix, 1 + p + p²+. . .pⁿ = 0 (0 denotes the null matrix), then 1 p− = ?
a. pⁿ
b. − pⁿ
c. (1 ….. ) n − + p + + p
d. None of the options

Answer: a

Question: Matrix A is such that 2 A = 2A− I where I is the identity matrix. Then for 2, n n ≥ A = ?
a. nA− (n −1)I
b. nA− I
c. 2^n-1 A − (n −1)I
d. 2^n-1 A−I

Answer: a