CBSE Class 12 Mathematics Matrices Worksheet

CBSE Class 12 Mathematics Worksheet - Matrices. CBSE issues sample papers every year for students for class 12 board exams. Students should solve the CBSE issued sample papers to understand the pattern of the question paper which will come in class 12 board exams this year. The sample papers have been provided with marking scheme. It’s always recommended to practice as many CBSE sample papers as possible before the board examinations. Sample papers should be always practiced in examination condition at home or school and the student should show the answers to teachers for checking or compare with the answers provided. Students can download the sample papers in pdf format free and score better marks in examinations. Refer to other links too for latest sample papers.

Question. The number of all possible matrices of order 3x3 with each entry 0 or 1 is:
(a) 27
(b) 18
(c) 81
(d) 512
Answer : D

Question. Matrix A and B will be inverse of each other only if
(a) AB = BA
(b) AB = BA = 0
(c) AB = 0, BA = I
(d) AB = BA = I
Answer : D

Question. If A and B are symmetric matrices of same order, then AB-BA is a
(a) Skew-symmetric matrix
(b) Symmetric matrix
(c) Zero matrix
(d) Identity
Answer : A

Question. 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

Question. 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

Question. 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

Question. 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

Question. If matrix A is of order m × n, and for matrix B, AB and BA both are defined, then order of matrix B is
(a) m × n
(b) n × n
(c) m × m
(d) n × m
Answer : D

Question. 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

Question. A matrix has 18 elements, then possible number of orders of a matrix are
(a) 3
(b) 4
(c) 6
(d) 5
Answer : C

CASE STUDY QUESTIONS

1.A manufacture produces three stationery products Pencil, Eraser and Sharpener which he sells in two markets.

If the unit Sale price of Pencil, Eraser and Sharpener are ₹ 2.50, ₹ 1.50 and ₹ 1.00 respectively, and unit cost of the above three commodities are ₹ 2.00, ₹ 1.00 and ₹ 0.50 respectively, then, based on the above information answer the following:

Question. Total revenue of market A
(i) ₹ 64,000
(ii) ₹ 60,400
(iii) ₹ 46,000
(iv) ₹ 40,600
Answer : III

Question. Total revenue of market B
(i) ₹ 35,000
(ii) ₹ 53,000
(iii) ₹ 50,300
(iv) ₹ 30,500
Answer : II

Question. Cost incurred in market A
(i) ₹ 13,000
(ii) ₹ 30,100
(iii) ₹ 10,300
(iv) ₹ 31,000
Answer : IV

Question. Profit in market A and B respectively are
(i) (₹ 15,000, ₹ 17,000)
(ii) (₹ 17,000, ₹ 15,000)
(iii) (₹ 51,000, ₹ 71,000)
(iv) (₹ 10,000, ₹ 20,000)
Answer : I

Question. Gross profit in both market
(i) ₹ 23,000
(ii) ₹ 20,300
(iii) ₹ 32,000
(iv) ₹ 30,200
Answer : III

ASSERTION AND REASON

1.In the following questions, a statement of Assertion (A) is followed by a statement of Reason (R).
Mark the correct choice as.
(A) Both A and R are true and R is the correct explanation of A
(B) Both A and R are true but R is not the correct explanation of A
(C) A is true but R is false
(D) A is False and R is True.

Question. Let A and B be the two symmetric matrices of order 3
Assertion (A) : A(BA) and (AB)A are symmetric matrices
Reason (R) : AB is symmetric matrix if matrix multiplication of A with B is commutative .
Answer : B

Question. Assertion (A) : If A is a square matrix such that A2 = A , then ( I + A )² – 3A = I
Reason (R) : AI = IA  = A
Answer : A

Question. Assertion (A) : (A + B )²≠ A² + 2AB + B²
Reason (R) : Generally AB ≠ BA
Answer : A

Question. Assertion (A) : If A and B are symmetric matrices , then AB – BA is a skew-symmetric matrix.
Reason (R) : (AB)’ = B’ A’
Answer : A

Question. Assertion (A) : If A is a symmetric matrix, then B’AB is also symmetric
Reason (R) : (ABC)’ = C’B’A’
Answer : A

Question. A and B are two matrices such that AB and BA are defined
Assertion (A) : (A + B ) ( A – B ) = A² – B²
Reason (R) : ( A + B ) ( A – B ) = A² – AB + BA – B²
Answer : D

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