Matrices Class-12 MCQ Type Questions for ISC Class-12 Maths. These MCQ / Objective Type Questions is based on latest reduced syllabus according 2021-22 session on bifurcated pattern. Main motto of MCQ Type Question is cracking the next upcoming exam of council. Visit official website CISCE for detail information about ISC Board Class-12 Maths.
ISC Class-12 Maths Matrices Class-12 MCQ Type Questions
Board | ISC |
Class | 12th (XII) |
Subject | Maths |
Ch-Name | Matrices |
Syllabus | on bifurcated syllabus (after reduction) |
Bifurcated pattern |
Semester-1 |
Session | 2021-22 |
Topic | MCQ / Objective Type Question |
MCQ Type Questions for Class-12 of Matrices
Question 1: If a matrix A is both symmetric and skew symmetric then matrix A is
(a) a scalar matrix
(b) a diagonal matrix
(c) a zero matrix of order n × n
(d) a rectangular matrix.
Answer: (c) a zero matrix of order n × n
Question 2: If A = and A = A’ then
(a) x = 0, y = 5
(b) x = y
(c) x + y = 5
(d) x – y = 5
Answer: (b) x = y
Question 3: f A and B are symmetric matrices of the same order, then
(a) AB is a symmetric matrix
(b) A – Bis askew-symmetric matrix
(c) AB + BA is a symmetric matrix
(d) AB – BA is a symmetric matrix
Answer: (c) AB + BA is a symmetric matrix
Question 4: For any unit matrix I
(a) I² = I
(b) |I| = 0
(c) |I| = 2
(d) |I| = 5
Answer: (a) I² = I
Question 5: A matrix A = [aij]m×n is said to be symmetric if
(a) aij = 0
(b) aij = aji
(c) aij = aij
(d) aij = 1
Answer: (b) aij = aji
Question 6: A = [aij]m×n is a square matrix if
(a) m = n
(b) m < n
(c) m > n
(d) None of these
Answer: (a) m = n
Question 7: If A and B are square matrices then (AB)’ =
(a) B’A’
(b) A’B’
(c) AB’
(d) A’B’
Answer: (a) B’A’
Question 8: The number of all possible matrices of order 3 × 3 with each entry 0 or 1 is
(a) 27
(b) 18
(c) 81
(d) 512.
Answer: (d) 512.
Question 9: Assume X, Y, Z, W and P are matrices of order 2 × n, 3 × 1, 2 × p, n × 3 and p × k respectively. Now answer the following (4-5):
The restrictions on n, k and p so that PY + WY will be defined are
(a) k = 3, p = n
(b) k is arbitrary, p = 2
(c) p is arbitrary
(d) k = 2,p = 3.
Answer: (a) k = 3, p = n
Question 10: If n =p, then the order of the matrix 7X – 5Z is:
(a) p × 2
(b) 2 × n
(c) n × 3
(d) p × n.
Answer: (b) 2 × n
Question 11: For a skew symmetric even ordered matrix A of integers, which of the following will not hold true:
(a) det(A) = 9
(b) det(A) = 81
(c) det(A) = 7
(d) det(A) = 4
Answer: (c) det(A) = 7
Question 12: If A any square matrix then which of the following is not symmetric ?
(a) A−At
(b) A+At
(c) AAt
(d) AtA
Answer: (a) A−At
Question 13: For what value of λ the following system of equations does not have a solution ? x + y + z = 6, 4x + λy – λz = 0, 3 x + 2y – 4 z = – 5
(a) 0
(b) 3
(c) -3
(d) 1
Answer: (b) 3
Question 14: If a matrix has 6 elements, then number of possible orders of the matrix can be
(a) 2
(b) 4
(c) 3
(d) 6
Answer: (b) 4
Question 15: Total number of possible matrices of order 2 × 3 with each entry 1 or 0 is
(a) 6
(b) 36
(c) 32
(d) 64
Answer: (d) 64
Question 16: If A is a square matrix such that A²=A, then (I + A)² – 3A is
(a) I
(b) 2A
(c) 3I
(d) A
Answer: (a) I
Question 17: If A is a square matrix, then A – A’ is a
(a) diagonal matrix
(b) skew-symmetric matrix
(c) symmetric matrix
(d) none of these
Answer: (b) skew-symmetric matrix
Question 18: For any square matrix A, AAT is a
(a) unit matrix
(b) symmetric matrix
(c) skew-symmetric matrix
(d) diagonal matrix
Answer: (b) symmetric matrix
Question 19: If a matrix A is both symmetric and skew-symmetric, then
(a) A is a diagonal matrix
(b) A is a zero matrix
(c) A is a scalar matrix
(d) A is a square matrix
Answer: (b) A is a zero matrix
Question 20: If A2 – A + I = O, then the inverse of A is
(a) I – A
(b) A – I
(c) A
(d) A + I
Answer: (a) I – A
Question 21: If A is a square matrix such that A2 = I, then (A – I)3 + (A + I)3 – 7A is equal to
(a) A
(b) I – A
(c) I + A
(d) 3A
Answer: (a) A
Question 22: If A is an m × n matrix such that AB and BA are both defined, then B is a
(a) m × n matrix
(b) n × m matrix
(c) n × n matrix
(d) m × n matrix
Answer: (b) n × m matrix
Question 23:
(a) A + B = B + A and A + (B + C) = (A + B) + C
(b) A + B = B + A and AC = BC
(c) A + B = B + A and AB = BC
(d) AC = BC and A = BC
Answer: (a) A + B = B + A and A + (B + C) = (A + B) + C
Question 24: If , then A2 – 5A is equal to
(a) 2I
(b) 3I
(c) -2I
(d) null matrix
Answer: (a) 2I
Question 25: The diagonal elements of a skew symmetric matrix are
(a) all zeroes
(b) are all equal to some scalar k(≠ 0)
(c) can be any number
(d) none of these
Answer: (a) all zeroes
Question 26: If = 0, the value of x is
(a) 3
(b) 8
(c) 24
(d) 0
Answer: (b) 8
Question 27: Let A be a non-singular matrix of the order 2 × 2 then |A-1|=
(a) |A|
(b) 1/|A|
(c) 0
(d) 1
Answer: (b) 1/|A|
Question 28: If A = is a symmetric matrix, then x =
(a) 4
(b) 3
(c) -4
(d) -3
Answer: (c) -4
Question 29:
(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
Answer: (b) α = a2 + b2, β = 2ab
Question 30: If a matrix is both symmetric matrix and skew symmetric matrix then
(a) A is a diagonal matrix
(b) A is zero matrix
(c) A is scalar matrix
(d) None of these
Answer: (b) A is zero matrix
Question 31: If A, B are symmetric matrices of same order, then AB – BA is a
(a) Skew-symmetric matrix
(b) Symmetric matrix
(c) Zero matrix
(d) Identity matrix.
Answer: (a) Skew-symmetric matrix
Question 32: Matrices A and B will be inverse of each other only if:
(a) AB = BA
(b) AB – BA = O
(c) AB = O, BA = I
(d) AB = BA = I.
Answer: (d) AB = BA = I.
Question 33: The number of 3 × 3 non-singular matrices, with four entries as 1 and all other entries as 0, is:
(a) less than 4
(b) 5
(c) 6
(d) 7.
Answer: (d) 7.
Question 34: The system of equations, x + y + z = 1, 3 x + 6 y + z = 8, αx + 2 y + 3z = 1 has a unique solution for
(a) α not equal to 0
(b) all integral α
(c) all rational α
(d) all real α
Answer: (b) all integral α
Question 35: The inverse of a matrix is defined for
(a) Only square matrices
(b) Diagonal matrices
(c) all matrices
(d) Rectangular matrices
Answer: (a) Only square matrices
Question 36: The equations x + 2y + 2z = 1 and 2x + 4 y + 4z = 9 have
(a) infinitely many solutions.
(b) only one solution
(c) only two solutions
(d) no solution
Answer: (d) no solution
Question 37: square matrix A = [aij]n×n is called a lower triangular matrix if aij = 0 for
(a) i is less than j
(b) i = j
(c) iis greater than j
(d) None of these
Answer: (a) i is less than j
Question 38: If the system of equationsx + 4 ay + az = 0, x + 3by + bz = 0 andx + 2 cy +cz = 0 have a non-zero solution,then a, b, c are in
(a) H.P.
(b) G.P.
(c) A.P.
(d) None of these
Answer: (a) H.P.
Question 39: Rank of a non-zero matrix is always
(a) ⩾1
(b) 0
(c) greater than 1
(d) equal to 1
Answer: (a) ⩾1
Question 40: The matrix P = is
(a) square matrix
(b) diagonal matrix
(c) unit matrix
(d) None of these
Answer: (a) square matrix
Question 41: If the matrix A = is a symmetric matrix, then find the value of x, y and t respectively.
(a) 4, 2, 3
(b) 4, 2, -3
(c) 4, 2, -7
(d) 2, 4, -7
Answer: (b) 4, 2, -3
Question 42: If A = then A4 – 24 (A – I) =
(a) 5I + A
(b) 5I – A
(c) 5I
(d) 6I
Answer: (b) 5I – A
: End of Matrices Class-12 MCQ Type Questions for ISC Class-12 Maths :-
-: also visit :-
- ISC Class-12 Text book Solutions, Notes , Syllabus, Paper
- MCQ Type Questions ISC Class-12 Semester-1 Session 2021-22
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