Matrices VBQs Class 12 Mathematics

VBQs for Class 12

VBQs Matrices Class 12 Mathematics with solutions has been provided below for standard students. We have provided chapter wise VBQ for Class 12 Mathematics with solutions. The following Matrices Class 12 Mathematics value based questions with answers will come in your exams. Students should understand the concepts and learn the solved cased based VBQs provided below. This will help you to get better marks in class 12 examinations.

Matrices VBQs Class 12 Mathematics

Question.

Matrices VBQs Class 12 Mathematics

(a) there cannot exist any B such that AB = BA
(b) there exist more than one but finite number of B’s such that AB = BA
(c) there exists exactly one B such that AB = BA
(d) there exist infinitely many B’s such that AB = BA

Answer

D

Question. If A and B are square matrices of size n × n such that A2 – B2 = (A- B)(A+ B) , then which of the following will be always true?
(a) A = B
(b) AB = BA
(c) either of A or B is a zero matrix
(d) either of A or B is identity matrix

Answer

B

Question.

Matrices VBQs Class 12 Mathematics

(a) 10
(b) 135
(c) 15
(d) 9

Answer

A

Question.

Matrices VBQs Class 12 Mathematics

and B = A20. Then the sum of the elements of the first column of B is?
(a) 211
(b) 210
(c) 231
(d) 251

Answer

C

Question.

Matrices VBQs Class 12 Mathematics

then which one of the following statements is not correct?
(a) A2 + I = A(A2 – I)
(b) A4 – I = A2 + I
(c) A3 + I = A(A3 – I)
(d) A3 – I = A(A – I)

Answer

A

Question. If

Matrices VBQs Class 12 Mathematics

is a matrix satisfying the equation AAT = 9I, where I is 3 × 3 identity matrix, then the ordered pair (a, b) is equal to:
(a) (2, 1)
(b) (–2, – 1)
(c) (2, – 1)
(d) (–2, 1)

Answer

B

Question. Let A and B be two symmetric matrices of order 3.
Statement-1: A(BA) and (AB)A are symmetric matrices.
Statement-2: AB is symmetric matrix if matrix multiplication of A with B is commutative.
(a) Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
(b) Statement-1 is true, Statement-2 is false.
(c) Statement-1 is false, Statement-2 is true.
(d) Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.

Answer

A

Question. The number of all 3 × 3 matrices A, with enteries from the set {–1, 0, 1} such that the sum of the diagonal elements of AAT is 3, is _______.

Answer

672

Question. Let A and B be any two 3 × 3 matrices. If A is symmetric and B is skewsymmetric, then the matrix AB – BA is:
(a) skewsymmetric
(b) symmetric
(c) neither symmetric nor skewsymmetric
(d) I or – I, where I is an identity matrix

Answer

B

Question.

Matrices VBQs Class 12 Mathematics

(a) y = 2x
(b) y = – 2x
(c) y = x
(d) y = – x

Answer

A

Question. If

Matrices VBQs Class 12 Mathematics

then AB equals
(a) I
(b) A
(c) B
(d) 0

Answer

A

Question. Let a be a root of the equation x2 + x + 1 = 0 and the matrix

Matrices VBQs Class 12 Mathematics

then the matrix A31 is equal to:
(a) A
(b) I3
(c) A2
(d) A3

Answer

D

Question. For two 3 × 3 matrices A and B, let A + B = 2BT and 3A + 2B = I3, where BT is the transpose of B and I3 is 3 × 3 identity matrix. Then :
(a) 5A + 10B = 2I3
(b) 10A + 5B = 3I3
(c) B + 2A = I3
(d) 3A + 6B = 2I3

Answer

B

Question. The number of 3 × 3 non-singular matrices, with four entries as 1 and all other entries as 0, is
(a) 5
(b) 6
(c) at least 7
(d) less than 4

Answer

C

Question.

Matrices VBQs Class 12 Mathematics

where i = √-1, then which one of the following is not true?
(a) α ≤ α2 + b2 ≤ 1
(b) α2 – d2 = 0
(c) α2 – c2 = 1
(d) α2 – b2 = 1/2

Answer

D

Question. If ω ≠ 1 is the complex cube root of unity and matrix

Matrices VBQs Class 12 Mathematics

(a) 0
(b) –H
(c) H2
(d) H

Answer

D

Question.

Matrices VBQs Class 12 Mathematics

(a) 1/√5
(b) 1/√3
(c) 1/√2
(d) 1/√6

Answer

C

Question. If

Matrices VBQs Class 12 Mathematics

then which one of the following holds for all n ≥ 1, by the principle of mathematical induction
(a) An = nA – (n – 1) I
(b) An = 2n–1 A – (n – 1) I
(c) An = nA + (n – 1) I
(d) An = 2n–1 A + (n – 1) I

Answer

A

Question. If

Matrices VBQs Class 12 Mathematics

be two matrices, then ABT is a non-zero matrix for |α| not equal to
(a) 2
(b) 0
(c) 1
(d) 3

Answer

C

Question.

Matrices VBQs Class 12 Mathematics

then 10A–1 is equal to:
(a) A – 4I
(b) 6I – A
(c) A – 6I
(d) 4I – A

Answer

C

Question. If p, q, r are 3 real numbers satisfying the matrix equation,

Matrices VBQs Class 12 Mathematics

then 2p + q – r equals :
(a) – 3
(b) – 1
(c) 4
(d) 2

Answer

A

Question. The matrix A2 + 4A – 5I, where I is identity matrix and

Matrices VBQs Class 12 Mathematics
Answer

A

Question. If A is a symmetric matrix and B is a skew-symmetrix matrix such that

Matrices VBQs Class 12 Mathematics

then AB is equal to :

Matrices VBQs Class 12 Mathematics
Answer

A

Question.

Matrices VBQs Class 12 Mathematics

is equal to __________.

Answer

10

Question.

Matrices VBQs Class 12 Mathematics

Then a value of α is :
(a) π/32
(b) 0
(c) π/64
(d) π/16

Answer

C

Question.

Matrices VBQs Class 12 Mathematics

(a) 2
(b) 3
(c) 6
(d) 4

Answer

D

Question. If

Matrices VBQs Class 12 Mathematics

and Q = PAPT, then PT Q2015 P is ;

Matrices VBQs Class 12 Mathematics
Answer

C

Question.

Matrices VBQs Class 12 Mathematics

(a) α = 2αb,β = a + b
(b) α = α2 + b , β = αb
(c) α = α2 + b , β = 2αb
(d) α = α2 + b , β = α2 – b2

Answer

C

Question. Let α, b, c ∈ R be all non-zero and satisfy α3 + b3 + c3 = 2. If the matrix

satisfies ATA = I, then a value of αbc can be :
(a) − 1/3
(b) 1/3
(c) 3
(d) 2/3

Answer

B

CASE STUDY QUESTIONS

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

Annual sales are indicated below 

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
(a) ₹ 64,000
(b) ₹ 60,400
(c) ₹ 46,000
(d) ₹ 40,600

Answer

C

Question. Total revenue of market B
(a) ₹ 35,000
(b) ₹ 53,000
(c) ₹ 50,300
(d) ₹ 30,500

Answer

B

Question. Cost incurred in market A
(a) ₹ 13,000
(b) ₹ 30,100
(c) ₹ 10,300
(d) ₹ 31,000

Answer

D

Question. Profit in market A and B respectively are
(a) (₹ 15,000, ₹ 17,000)
(b) (₹ 17,000, ₹ 15,000)
(c) (₹ 51,000, ₹ 71,000)
(d) (₹ 10,000, ₹ 20,000)

Answer

A

Question. Gross profit in both market
(a) ₹ 23,000
(b) ₹ 20,300
(c) ₹ 32,000
(d) ₹ 30,200

Answer

C