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MCQs are a great way to test students' knowledge of an entire chapter by combining questions from all sections. This is why RD Sharma class 12th exercise MCQ can be highly beneficial to students preparing for board exams. The RD Sharma class 12 chapter 4 exercise MCQ is based on the chapter Algebra of Matrices, which covers addition, multiplication, division, and subtraction of Matrices. You will also learn about skew-symmetric matrices, null matrices, symmetric matrices, and so on. RD Sharma class 12th exercise MCQ part of the textbook will have 46 questions that you will answer.

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**Also Read - **RD Sharma Solution for Class 9 to 12 Maths

- Chapter 4 - Algebra of Matrices Ex 4.1
- Chapter 4 - Algebra of Matrices Ex 4.2
- Chapter 4 - Algebra of Matrices Ex 4.3
- Chapter 4 - Algebra of Matrices Ex 4.4
- Chapter 4 - Algebra of Matrices Ex 4.5
- Chapter 4 - Algebra Matrices Ex FBQ
- Chapter 4 - Algebra Matrices Ex VSA

Given:

Solution:

Answer: The correct option is

Given:

Solution:

It is Given that,

....(1)

....(2)

Now from Equation (2),

Again from Equation (2),

So, the option (B) is correct.

Given:

Solution:

....(1)

....(2)

Now from Equation (2),

Again from Equation (2),

Now from Equation (1),

Again from Equation (1),

So,

Hence, the correct option is (B).

4 Algebra of Matrices Exercise MCQs Question 5

Answer: The correct option isGiven:

Solution:

.....(1)

.....(2)

Now from Equation (2),

Again from Equation (2),

Now from Equation (1),

Again from Equation (1),

So,

So, the option (C) is the correct option.

4 Algebra of Matrices Exercise MCQs Question 6

Answer: The correct option is (D), k = 7Given:

Solution:

Let

Then

{k cab be anything}

Now,

Similarly,

Hence,

Now, multiplying and to LHS and RHS,

Then,

Hence,k=7

So, the option (D) is correct.

4 Algebra of Matrices Exercise MCQs Question 7

Answer: The correct option is (A),Given: The matrix AB is zero.

Solution:

If the matrix AB is zero, then, it is not necessary that either A = 0 or B = 0.

So, the option (A) is correct

4 Algebra of Matrices Exercise MCQs Question 8

Answer: The correct option is (C).Given:

Solution:

So, the correct option is option (C).

4 Algebra of Matrices Exercise MCQs Question 9

Answer: The correct option is (A), B is a null matrix.

Given: AB = 0

Solution:

As, AB = 0 and the order of the matrices is A and B is 3,

So, the matrix B has to be a null matrix.

Thus, the correct option is (A)

Answer: The correct option is (B), AB = nB

Given:

Solution:

Now

So, the option (B) is correct.

Given:

Solution:

Now

So, the option (B) is correct.

4 Algebra of Matrices Exercise Multiple Choice Questions Question 11

So, the correct option is (A).

4 Algebra of Matrices Exercise Multiple Choice Questions Question 12

Hence,

x + y = 0

So, the correct option is (A).

4 Algebra of Matrices Exercise Multiple Choice Questions Question 13

**Answer:** The correct option is (B).**Given:****Solution: **

As,

So, the correct option is (B).

So,

Hence, the correct option is (C).

4 Algebra of Matrices Exercise Multiple Choice Questions Question 15

**Answer: **The correct option is (C).

**Given:**

**Solution: **

** (Square Matrix)**

Hence,

So, the correct option is (C).

4 Algebra of Matrices Exercise Multiple Choice Questions Question 16

(‘I’ stands for Identity Matrix)

So, the correct option is (C).

4 Algebra of Matrices Exercise Multiple Choice Questions Question 17

If a matrix A is both Symmetric and Skew-Symmetric,

and

Comparing both the equations,

Then A is a Zero Matrix.

So, the correct option is (B).

4 Algebra of Matrices Exercise Multiple Choice Questions 18

**Answer:** The correct option is (A).**Given:** Matrix = **Solution: **

Therefore, the given matrix is a Skew-Symmetric matrix.

So, the correct option is (A).

4 Algebra of Matrices Exercise Multiple Choice Questions Question 19

If A is a Square matrix,

Then, AA is neither of the matrices given in the options of the question.

So, the correct option is (D).

4 Algebra of Matrices Exercise Multiple Choice Questions Question 21

Then

So,

So, the correct option is (C).

4 Algebra of Matrices Exercise Multiple Choice Questions Question 21

Then

So,

So, the correct option is (C).

As and are both defined, the number of columns in B should be equal to the number of rows in A for BA and also, the number of columns in A should be equal to the number of rows in B for BA.

So, the order of the matrix is

Thus, the correct option is (A).

4 Algebra of Matrices Exercise Multiple choice Questions Question 23:

From

So,

So, the correct option is (D).

4 Algebra of Matrices Exercise Multiple Choice Questions Question 24

Now,

So, the correct option is (C).

4 Algebra of Matrices Exercise Multiple Choice Questions Question 25

Answer: The correct option is (A).**Given:****Solution: **

Then

As the sum is expressed as,

So, the correct option is (A).

Thus, the correct option is (A).

4 Algebra of Matrices Exercise Multiple Choice Questions Question 27

No. of elements = 9

Order =

Every item in this matrix can be filled in two ways either by 0 or by 1.

So, the number of possible matrices is =

Thus, the correct option is (D).

4 Algebra of Matrices Exercise Multiple Choice Questions Question 28

**Answer:** The correct option is (D), Not possible to find.**Given:****Solution: **are equal

Then from the matrices,

These values of are not equal to each other, so it is not possible to find.

Thus, the correct option is (D).

4 Algebra of Matrices Exercise Multiple Choice Questions Question 29

From Matrix,

Now comparing the Equations,

So the values are k = -6, a= -4 and b = -9

Thus, the correct option is (C).

4 Algebra of Matrices Exercise Multiple Choice Questions Question 30

From the Matrices,

Thus, the correct option is (C).

4 Algebra of Matrices Exercise Multiple Choice Questions Question 31

1 + 7 + 9 = 17

Trace = 17

Thus, the correct option is (A).

4 Algebra of Matrices Exercise Multiple Choice Questions Question 32

Trace of A, i.e,

Thus, the correct option is (A).

4 Algebra of Matrices Exercise Multiple Choice questionsQuestion 33

Answer: The correct option is (D).Therefore, it is not matching with any of the given matrix options.

Thus, the correct option is (D).

4 Algebra of Matrices Exercise Multiple Choice Questions Question 34

No. of elements = 9

Order =

Every item in this matrix can be filled in two ways either by 0 or by 1.

So, the number of possible matrices is

Thus, the correct option is (D).

4 Algebra of Matrices Exercise Multiple Choice Questions Question 35

Comparing the Equations,

Thus, the correct option is (B).

4 Algebra of Matrices Exercise MCQs Question 36**Answer:** The correct option is (A).**Given: **is a square matrix**Hint:** Using **Solution:**

4 Algebra of Matrices Exercise Multiple Choice Questions Question 37\

**Answer:****Given: **if A and B are two matrices of order and respectively and , then the order of is**Hint:** you must know the subtraction of the matrices**Solution:**

Order of the matrix

Order of the matrix

Now we know in matrices;

Addition or subtraction is possible only if their orders are same

i.e. order of A must be equal to the order or B

[Also ,is given]

Order of is also equal to

4 Algebra of Matrices Exercise Multiple Choice Questions Question 38

Order of the matrix

Order of the matrix

Order of the matrix

We are given exists

Number of columns in A= Number of rows in

Also we are given exists

Number of columns in = Number of rows in A

Order of B becomes

**Given:** If A and B are matrices of same order then is**Hint:** You must know about properties of transpose**Solution:**

Given that order of matrices A and B are same

Then we check it by taking transpose of

i.e.

Is a skew symmetric matrix

4 Algebra of Matrices Exercise Multiple Choice Questions Question 40

We have

Let A be a square matrix

Now for

And for

4 Algebra of Matrices Exercise Multiple Choice Questions Question 42

4 Algebra of Matrices Exercise Multiple Choice Questions Question 43

Hence order of the matrix

And order of the matrix

Columns of matrix A= Rows of matrix B

AB is defined

Also here column of matrix B= Rows of matrix A

is defined

4 Algebra of Matrices Exercise Multiple Choice Questions Question 44

A is a skew symmetric matrix

4 Algebra of Matrices Exercise Multiple Choice Questions Question 45

Answer: Diagonal matrix

Given:

Hint: You must know about diagonal matrix

Solution:

Here all the elements of the matrix except the diagonal elements are 0

A is a diagonal matrix

4 Algebra of Matrices Exercise Multiple Choice Questions Question 46

**Answer: **Skew symmetric matrix**Given: **A and B are symmetric matrices of same order.**Hint:** You must know about properties of transpose of a matrix**Solution:**

Given that A and B are symmetric matrices

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The RD Sharma class 12 solutions Algebra of Matrices ex MCQ is continuously updated to include the newest syllabus and corresponds to the questions present in the NCERT textbooks of class 12. The book contains simple answers that are easy to follow and will help you test your knowledge at home. Students will be able to practice maths at home and compare their answers with the ones in the book. This will help them mark themselves and concentrate on their weaker areas where they have failed to score well. You might even find common questions from the book appear in your board paper.

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**Chapter-wise RD Sharma Class 12 Solutions**

- Chapter 1 - Relations
- Chapter 2 - Functions
- Chapter 3 - Inverse Trigonometric Functions
- Chapter 4 - Algebra of Matrices
- Chapter 5 - Determinants
- Chapter 6 - Adjoint and Inverse of a Matrix
- Chapter 7 - Solution of Simultaneous Linear Equations
- Chapter 8 - Continuity
- Chapter 9 - Differentiability
- Chapter 10 - Differentiation
- Chapter 11 - Higher Order Derivatives
- Chapter 12 - Derivative as a Rate Measurer
- Chapter 13 - Differentials, Errors and Approximations
- Chapter 14 - Mean Value Theorems
- Chapter 15 - Tangents and Normals
- Chapter 16 - Increasing and Decreasing Functions
- Chapter 17 - Maxima and Minima
- Chapter 18 - Indefinite Integrals
- Chapter 19 - Definite Integrals
- Chapter 20 - Areas of Bounded Regions
- Chapter 21 - Differential Equations
- Chapter 22 - Algebra of Vectors
- Chapter 23 - Scalar Or Dot Product
- Chapter 24 - Vector or Cross Product
- Chapter 25 - Scalar Triple Product
- Chapter 26 - Direction Cosines and Direction Ratios
- Chapter 27 - Straight Line in Space
- Chapter 28 - The Plane
- Chapter 29 - Linear programming
- Chapter 30- Probability
- Chapter 31 - Mean and Variance of a Random Variable

1. How to solve the MCQs in class 12 mathematics chapter 4?

The MCQs in the class 12 maths book chapter 4 can be solved by using RD Sharma solutions. Students can avail the class 12 RD Sharma chapter 4 exercise MCQ solution pdf online and use the solutions in this book to answer the MCQs of Algebra of Matrices.

2. How can MCQs in maths help students?

MCQs are a great way of testing the overall knowledge of students on a topic or topics. For example, in the RD Sharma class 12 solutions Algebra of Matrices ex MCQ, students will be tested on their knowledge on the entire chapter of Algebra of Matrices.

3. Where can I download the class 12 RD Sharma chapter 4 exercise MCQ solution pdf?

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5. Can RD Sharma class 12 solutions Algebra of Matrices ex MCQ help in JEE Mains Preparations?

The RD Sharma class 12 solutions Algebra of Matrices ex MCQ pdf can definitely help students to score well in their JEE mains. Students can use the book for self-practice and self-testing, which would enhance their problem-solving skills

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Application Date:09 September,2024 - 14 November,2024

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