Class 12th
Chapter wise Most Important MCQ's Type Questions for Board Exams
CBSE CLASS XII
CH : 3 MATRICES (MCQ)
Que 1. If A and B matrices are of same order and A + B = B + A, this law is known as:
A. distributive law
B. commutative law
C. associative law
D. Cramer's law
E. Answer. B
Que 2. A pair of equations to determine the value of 2 variables is called
A. simultaneous linear equations
B. paired equations
C. quadratic equations
D. simple equations
Answer. A
Que 3. If a matrix has equal number of columns and rows then it is said to be a
A. row matrix
B. identical matrix
C. square matrix
D. rectangular matrix
Answer. C
Que 4. If determinant of a matrix is equal to zero, then it is said to be
A. square matrix
B. singular matrix
C. non-singular matrix
D. identical matrix
Answr. B
Que 5. We can add two matrices having real numbers A and B if their
A. order is same
B. rows are same
C. columns are same
D. elements are same
Answer. A
Que 6. If the number of columns and rows are not equal in a matrix, then it is said to be a
A. rectangular matrix
B. square matrix
C. diagonal matrix
D. null matrix
Answer. A
Que 7. The methods to solve a pair of simultaneous linear equations are
A. 3
B. 2
C. 4
D. 5
Answer B
Que 8. In matrices (AB)t equals to
A. B
B. A
C. At Bt
D. Bt At
Answer. D
Que 9. If determinant of a matrix is not equal to zero, then it is said to be
A. non-singular matrix
B. square matrix
C. singular matrix
D. identical matrix
Answer. A
Que 10. A diagonal matrix having equal elements is called a
A. square matrix
B. identical matrix
C. scalar matrix
D. rectangular matrix
Answer. C
Que 11. In matrices (A + B)t equals to
A. At
B. Bt
C. At + Bt
D. At Bt
Answer. C
Que 12. If A, B and C matrices are of same order and (A + B) + C = A + (B + C), this law is known as
A. Cramer's law
B. distributive law
C. commutative law
D. associative law
Answer. D
Que 13. If the sum of two matrices A and B is zero matrix, then A and B are said to be
A. multiplicative inverse of each other
B. additive inverse of each other
C. transpose of each other
D. determinant of each other
Answer. B
Que 14. Skew symmetric matrix is also called
A. symmetric
B. identical matrix
C. square matrix
D. anti symmetric
Answer. D
Que 15. The law which does not hold in multiplication of matrices is known as
A. distributive law
B. Inverse law
C. associative law
D. commutative law
Answer. D
Que 16. Generally the matrices are denoted by
A. capital letters
B. numbers
C. small letters
D. operational signs
Que 17. A matrix with only 1 column is called
A. column matrix
B. row matrix
C. identical matrix
D. square matrix
Que 18. We can subtract two matrices A and B if their
A. elements are same
B. order is same
C. rows are same
D. columns are same
Que 19. In matrices, the rows are denoted by
A. A
B. B
C. R
D. C
Que 20. Vertically arranged elements in a matrix are called
A. columns
B. rows
C. determinants
D. transpose
Que 21. By changing the signs of all the elements of a matrix, we obtained
A. identical matrix
B. negative of a matrix
C. null/zero matrix
D. determinant of a matrix
Ans. B
Que 22. If 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
Que 23. 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
Ans: (b) skew-symmetric matrix
Q24. If A is any square matrix, then which of the following is skew-symmetric?
(a) A + AT
(b) A – AT
(c) AAT
(d) ATA
Answer: (b) A – AT
Que25. 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
Que26. 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
Que27. 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
Que28. Total number of possible matrices of order 3 × 3 with each entry 2 or 0 is
(a) 9
(b) 27
(c) 81
(d) 512
Answer: (d) 512
Que29. If A is a matrix of order m × n and B is a matrix such that AB’ and B’A are both defined, then the order of matrix B is
(a) m × m
(b) n × n
(c) n × m
(d) m × n
Answer: (d) m × n
Que30. If A and B are matrices of the same order, then (AB’ – BA’) is a
(a) skew-symmetric matrix
(b) null matrix
(c) symmetric matrix
(d) unit matrix
Answer: (a) skew-symmetric matrix
Que31. 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
Que32. Question 39. 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
CH : 1 RELATIONS AND FUNCTIONS (MCQ)
Que1. The function f : A → B defined by f(x) = 4x + 7, x ∈ R is
(a) one-one
(b) Many-one
(c) Odd
(d) Even
Answer: (a) one-one Question
Que2. The smallest integer function f(x) = [x] is
(a) One-one
(b) Many-one
(c) Both (a) & (b)
(d) None of these
Answer: (b) Many-one Question
Que3. The function f : R → R defined by f(x) = 3 – 4x is
(a) Onto
(b) Not onto
(c) None one-one
(d) None of these
Answer: (a) Onto
Que4. The number of bijective functions from set A to itself when A contains 106 elements is
(a) 106
(b) (106)2
(c) 106!
(d) 2106
Answer: (c) 106!
Que5. The maximum number of equivalence relations on the set A = {1, 2, 3} are
(a) 1
(b) 2
(c) 3
(d) 5
Answer: (d) 5
Que6. Let us define a relation R in R as aRb if a ≥ b. Then R is
(a) an equivalence relation
(b) reflexive, transitive but not symmetric
(c) symmetric, transitive but not reflexive
(d) neither transitive nor reflexive but symmetric
Answer: (b) reflexive, transitive but not symmetric
Que7. Let A = {1, 2, 3} and consider the relation R = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 3), (1, 3)}. Then R is
(a) reflexive but not symmetric
(b) reflexive but not transitive
(c) symmetric and transitive
(d) neither symmetric, nor transitive
Answer: (a) reflexive but not symmetric
Que8. Let S = {1, 2, 3, 4, 5} and let A = S × S. Define the relation R on A as follows: (a, b) R (c, d) iff ad = cb. Then, R is
(a) reflexive only
(b) Symmetric only
(c) Transitive only
(d) Equivalence relation
Answer: (d) Equivalence relation
Que9. Let R be the relation “is congruent to” on the set of all triangles in a plane is
(a) reflexive
(b) symmetric
(c) symmetric and reflexive
(d) equivalence
Answer: (d) equivalence Question
Que10. Total number of equivalence relations defined in the set S = {a, b, c} is
(a) 5
(b) 3!
(c) 23
(d) 33
Answer: (a) 5
