CBSE Class 12 Mathematics Matrices and Determinants MCQs Set 03

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

Question: If A and B are two square matrices such that B = – A^–1 BA, then (A + B)² =
(a) O
(b) A² + B²
(c) A² + 2 AB + B²
(d) A + B
Answer: b

Question: If A is a square matrix of order m with elements aij, then
(a) A = [a_ij]_{n × n}
(b) A = [a_ji]_{m × n}
(c) A = [a_ij]_{m × m}
(d) A = [a_ji]_{n × n}
Answer: c

Question: If A and B are 2 × 2 matrices, then which of the following is true?
(a) (A + B)² = A² + B² + 2AB
(b) (A – B)² = A² + B² – 2AB
(c) (A – B) (A + B) = A² + AB – BA – B²
(d) (A + B) (A – B) = A² – B²
Answer: c

Question: A square matrix B = [b_ij] _{m × m} is said to be a diagonal matrix, if
(a) all its non-diagonal elements are non-zero i.e., b_ji ≠ 0; i ≠ j
(b) all its diagonal elements are zero, i.e., b_ji = 0, i = j
(c) all its non-diagonal elements are zero i.e, b_ji = 0 when i ≠ j
(d) None of the above
Answer: c

Question: If A² – A + I = O, then the inverse of A is
(a) I – A
(b) A – I
(c) A
(d) A + I
Answer: a

Question: If A is a square matrix such that (A – 2I) (A + I) = 0, then A^–1 =
(a) A–I/2
(b) A+I/2
 (c) 2 (A – I)
(d) 2A + I
Answer: a

 Question: If A is a square matrix such that A² = A, then (I + A)³ – 7A is equal to
(a) A
(b) I – A
(c) I
(d) 3 A
Answer: c

Question: A square matrix B = [b_ji]n × n is said to be a scalar matrix, if
(a) b_ji = 0 for i ≠ j and b_ji = k for i = j, for some constant k
(b) b_ji = 0 for i = j
(c) b_ji ≠ 0 for i = j and b_ji = 0 for i = j
(d) None of the above
Answer: a

Question: For a matrix A, AI = A and AA^T = I is true for
(a) If A is a square matrix.
(b) If A is a non singular matrix.
(c) If A is symmetric matrix.
(d) If A is any matrix.
Answer: a

Question: If A and B are matrices of same order, then (AB’− BA’) is a
(a) skew symmetric matrix
(b) null matrix
(c) symmetric matrix
(d) unit matrix
Answer: a

Question: If A is a 3 × 2 matrix, B is a 3 × 3 matrix and C is a 2 × 3 matrix, then the elements in A, B and C are respectively
(a) 6, 9, 8
(b) 6, 9, 6
(c) 9, 6, 6
(d) 6, 6, 9
Answer: b

Question: If A and B are two matrices such that A + B and AB are both defined, then
(a) A and B are two matrices not necessarily of same order.
(b) A and B are square matrices of same order.
(c) Number of columns of A = Number of rows of B.
(d) None of these.
Answer: b

Question: If A is matrix of order m × n and B is a matrix such that AB’and B’A are both defined, then order of matrix B is
(a) m × m
(b) n × n
(c) n × m
(d) m × n
Answer: d

Question: Each diagonal element of a skew-symmetric matrix is
(a) zero
(b) positive
(c) non-real
(d) negative
Answer: a

Question: A square matrix A = [a_ij]_n×n is called a diagonal matrix if a_ij = 0 for
(a) i = j
(b) i < j
(c) i > j
(d) i ≠ j
Answer: d