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Maths MCQ Class 12 Ch- 3 | Matrices

  

Mathematics

Multiple Choice Questions (MCQ)
MCQ | Class 12 | Chapter 3
MATRICES

  • MCQ Based on the different types of Matrices
  • MCQ  Based on the Addition, Subtraction and Multiplication of Matrices.
  • MCQ Based on the Transpose, Symmetric and Skew Symmetric of Matrices
  • MCQ Based on the general problems  of Matrices.

Features

  • In this pdf given below you find the important MCQ which are strictly according to the CBSE syllabus and are very useful for the CBSE Examinations. 
  • Solution Hints are also given to some difficult problems. 
  • Each MCQ contains four options from which one option is correct. 
  • On the right hand side column of the pdf Answer option is given.

Action Plan

  • First of all students should Learn and write all basic points and Formulas related to the Matrices.
  • Start solving  the NCERT Problems with examples.
  • Solve the important assignments on the Matrices.
  • Then start solving the following MCQ.

MCQ | CHAPTER 3 | CLASS 12

MATRICES

Question 1
If A and B are symmetric matrices of the same order, then

a) AB is a symmetric matrix  

b) A – B is a skew-symmetric matrix

c) AB + BA is a symmetric matrix            

d) AB – BA is a symmetric matrix

Answer: c

Question 2

If a matrix A is symmetric as well as skew symmetric  then

a) A is a diagonal matrix                              

b) A is a null matrix

c) A is a unit matrix                                      

d) A is a triangular matrix

Answer: b

Question 3

If A = equation is a symmetric matrix, then x =

a) 4                      

b) 3                                 

c) -4                     

d) -3

Answer: c

Question 4

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

Question 5

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

Question 6

If  A =  equation then  (A – 2I)(A – 3I) =

a)  A       

b) I

c) O

d) 5I

Answer c

Question 7

If  A = equation  and  A2equation , then 

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

Question 8

If  A = equation  and B = equation  and  AB = I3, then  x + y equals

a) 0                          

b) -1                   

c) 2              

d) None of these

Answer a

Question 9

If A = equation and f(x) = (1 + x)(1 - x), then f(A) is 

equation                                            

equation               

equation          

equation                         

Answer: a

Question: 10

Total number of possible matrices of order 2 X 3 with each entry 1 or 0 is

a)  6                          

b)  36                        

c)  32                          

d)  64

Answer: d

Question 11

If  A = equation  and A2 – KA – 5I = 0, then k =

a) 5           

b) 3           

c) 7           

d) None of these

Answer: a

Question 12

equation  is equal to 

equation

equation

equation

equation
Answer a

Question 13
If A = equation  and  B = equation , then  (AB)T is equal to 

equation

equation

equation

equation
Answer b

Question 14

If matrix A = equation

where a, b, c are real positive numbers, abc = 1 and ATA = I, 

then the value of a3 + b3 + c3 is

a) 1                         

b) 2                               

c) 3                         

d) 4

Answer d

Solution Hint: A’A = I A2 = I

Comparing these two matrices we get

a2 + b2 + c2 = 1,         

ab + bc + ca = 0,         

ac + ba + bc = 0,       

bc + ac + ab = 0

Now using  (a + b + c)2 and find the value of (a + b + c) we get (a + b + c) = 1

Using identity:   a+  b+ c3 - 3abc find the value of  a3 + b3 + c3

Question 15

The order of the matrix A is  3 x 5 and that of matrix B is  2 x 3. Then order of the matrix BA is

a)  2 x 3                       

b) 3 x 2                    

c) 2 x 5                      

d) 5 x 2

Answer: c

Question 16

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 x n                    

d) a rectangular matrix.

Answer; c

Question: 17

If A = equation and  A2 – 4A + 10 I = A, then k =

a) – 4                     

b) 0                    

c) 1 or 4                        

d) 4 and not 1

Answer: d

Question:18

equation   if the value of x is

a)  - 7                                

b)  - 11

c)  - 2                          

d)  14

Answer: c

Question:19

If A = equation and  A-1equation, then x equals

a)  2                         

b)  -1/2          

c) 1                           

d) 1/2

Answer: d

Question:20

For any square matrix A, AAT is a
a) unit matrix                     

b) symmetric matrix

c) skew-symmetric matrix                    

d) diagonal matrix

Answer: b



Question:21

If the matrix A = equation  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

Question:22

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

Question:23

The matrix A = equation  is a

a) unit matrix                                            

b) diagonal matrix         

c) symmetric matrix                                  

d) skew-symmetric matrix

Answer: d

Question: 24

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: 25

If  equation  then the value of  x, y, z are respectively

a) 5, 2, 2                                                    

b) 1, -2, 3                       

c) 0, -3, 3                                                    

d) 11, 8, 3

Answer: b

Question: 26

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

Question: 27

The matrix  equation  is  a

a) diagonal matrix                                         

b) symmetric matrix      

c) skew symmetric matrix                            

d) scalar matrix

Answer: c

Question: 28

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

Question: 29

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

Question: 30

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

Question: 31

If A2 = A, then (I + A)4  is equal to

a)  I + A                                               

b) I + 4A               

c)  I + 15 A                                          

d) None of these

Answer: c

Question: 32

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

Question: 33

Which of the given values of x and y make the following pairs of matrices equal

equation

a)  x = -1/ 3, y = 7                                             

b) Not possible to find

c)  y = 7,      x = -2/ 3                                         

d) x = -1/ 3,   y = -2/ 3

Answer: b

Question 34

If A is a symmetric matrix then, then  A2  is a

a)  symmetric matrix                                     

b) Identity matrix

c) skew symmetric matrix                             

d) null matrix

Answer: a

Question: 35

Suppose P and Q are two different matrices of order  3 x n and n x p, then the order of the matrix  P x Q is  ?

a)  3 x p                                

b) p x 3                         

c)  n x n                  

d)  3 x 3

Answer: a

Question: 36

Find the order of the following 

equation

a)  2 x 3                               

b) 2 x 2                           

c)  3 x 2                    

d) 3 x 3

Answer: d

Question: 37

Matrices  A and  B will be inverse of each other only if

a)  AB = BA                                 

b)  AB = BA = 0

c)  AB = 0, BA = 1                      

d) AB = BA = I

Answer: d

Question: 38

Total number of possible matrices of order 2 X 3 with each entry 1 or 0 is

a)  6                 

b)  36                    

c)  32                   

d)  64

Answer: d

Question: 39

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 x n                                

d) a rectangular matrix.

Answer: c

Question: 40

equation

Then  find AB + XY 

a)  [28]                 

b) [24]                       

c)  [32]                 

d) None of these

Answer: a

Question: 41

If A = equation then  A100  is equal to

a) 2100A            

b)  299 A                  

c) 100A                 

d) 299 A

Answer: b

Solution Hint

We have, A = equation

A2 = A x A = equation = 2 equation = 2A

A4 = A2 . A2 = 2A . 2A = 4 A2 = 4 x 2A = 8A = 23A

Similarly  A8 = 27A          A100 = 299 A

Question: 42

The matrix  equation  is a

a) Identity Matrix                                          

b) Symmetric Matrix

c) Skew – Symmetric Matrix                        

d)  None of these

Answer: b

Question: 43

Each diagonal element of a skew symmetric matrix is

a) zero                                                         

b) positive

c) non-real                                                    

d) negative

Answer: a

Question: 44

If A and B are symmetric matrix of same order, then  AB – BA is a :

a) Skew – Symmetric Matrix                                  

b) Symmetric Matrix

c) Zero Matrix                                                           

d) Identity Matrix

Answer: a

Question: 45

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)  3 A

Answer a

Question: 46

equation

Then the values of x are

a)  1, 5                          

b) -1, -5                       

c)  1,6                       

d) -1, -6

Answer: d

Question 47

If A = equation is upper triangular matrix, then  x + y is

a) 3                                 

b) -3                             

c)  0                            

d)  1

Answer: c

Question 48

Sum of two symmetric matrix is always

a)  symmetric matrix                                      

b) Identity matrix

c) skew symmetric matrix                             

d) None of these

Answer c

Question 49

Which of the following matrices both symmetric  and skew symmetric matrix  ?

a)  Identity matrix                                           

b)  Unit matrix

c) Null matrix                                                 

d) None of these

Answer: c

Question 50

If A = equation and  B =equation, then find the value of x for which  A2 = B

a) 1                             

b)  -1                       

c) 4                         

d) None of these

Answer: d




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