RD Sharma Class 12 Exercise 5.2 Determinant Solutions Maths - Download PDF Free Online

The RD Sharma Solution books are the best form of tutors for the class 12 students at their home. Mathematics is a subject that gives chances for a lot of doubts to arise. Every mark that a student scores in the public exam is essential; students should not risk losing their marks. RD Sharma class 12th exercise 5.2, Determinants, is a part where students can score easily. Hence utmost care should be taken in solving the problems. With the help of the RD Sharma Class 12th exercise 5.2, students can do their homework effortlessly.

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

RD Sharma Class 12 Solutions Chapter 5 Determinants - Other Exercise

• Chapter 5 - Determinants Ex 5.1
• Chapter 5 - Determinants Ex 5.3
• Chapter 5 - Determinants Ex 5.4
• Chapter 5 - Determinants Ex 5.5
• Chapter 5 - Determinants Ex FBQ
• Chapter 5 - Determinants Ex MCQ
• Chapter 5 - Determinants Ex VSA

determinants Exercise 5.2 Question 1

Answer:
Hint: We will solve the determinant with respect to row one.
Given:
Solution:

determinants Exercise 5.2 Question 1 Sub Question 2

Answer:

Answer:

Hint: First we will use column operation to get a simple determinant.

Given:

Solution:

on expanding w.r.t row

determinants Exercise 5.2 Question 1 Sub Question 3

Answer:
Hint: We will expand it w.r.t
Given:
Solution:
Expanding w.r.t

determinants Exercise 5.2 Question 1 sub question 4

Answer:
Hint: First we will use row operation to make some element 0
Given:
Solution:

determinants Exercise 5.2 Question 1 sub question 5

Answer:
Hint: We will expand it w.r.t
Given:
Solution:
Expanding w.r.t

determinants Exercise 5.2 Question 1 sub question 6

Answer:
Hint: In this question we will convert some elements into 0
Given:
Solution:


On expanding it w.r.t

Hence

determinants Exercise 5.2 Question 1 sub question 7

Answer:

Hint: First we will make a column with same elements

Given:

Solution:

On changing all rows into columns

If the rows and columns of a determinant are interchanged, the value of the determinant remains the same.
Expanding the determinant w.r.t

Hence,

determinants Exercise 5.2 Question 1 Sub Question 8

Answer:
Hint: We will solve the determinant w.r.t
Given:
Solution:

Hence

determinants Exercise 5.2 Question 2

Answer:
Hint: We will try to do any two column or row equal
Given:
Solution:

If any two rows or columns of a determinant are identical.
The value of the determinant is zero

Hence

determinants Exercise 5.2 Question 2 Sub Question 2

Answer:
Hint: We will try to do any two column or row equal
Given:
Solution:

If any two rows or columns of a determinant are identical.
The value of the determinant is zero

Hence

determinants Exercise 5.2 Question 2 Sub Question 3

Answer:
Hint: We will try to do any two column or row equal
Given:
Solution:

If any two rows or columns of a determinant are identical.
The value of the determinant is zero

Hence,

determinants Exercise 5.2 Question 2 Sub Question 5

Answer:
Hint: We will try to do any two column or row equal
Given:
Solution:

If any two rows or columns of a determinant are identical.
The value of the determinant is zero

Hence

determinants Exercise 5.2 Question 2 Sub Question 6

Answer:
Hint: First we will split the determinant into two determinant
Given:
Solution:

We will multiply and divide by abc in second determinent



If any two rows or columns of a determinant are interchanged,
then sign of the determinant is changed.

Hence

determinants Exercise 5.2 Question 2 Sub Question 7

Answer:
Hint: We will try to do any two column or row equal
Given:
Solution:

If any two rows or columns of a determinant are identical.
The value of the determinant is zero

Hence

determinants Exercise 5.2 Question 2 Sub Question 8

Answer:
Hint: We will try to do any two column or row equal
Given:
Solution:


If any two rows or columns of a determinant are identical.
The value of the determinant is zero

Hence

determinants Exercise 5.2 Question 2 Sub Question 9

Answer:
Hint: We will try to do any two column or row equal
Given:
Solution:

If any two rows or columns of a determinant are identical.
The value of the determinant is zero

Hence

determinants Exercise 5.2 Question 10

Answer:
Hint: We will try to do any two column or row equal
Given:
Solution:

If any two rows or columns of a determinant are identical.
The value of the determinant is zero

Hence

determinants Exercise 5.2 Question 12

Answer:
Hint: We will try to do any two column or row equal
Given:
Solution:





If any two rows or columns of a determinant are identical.
The value of the determinant is zero

Hence

determinants Exercise 5.2 Question 13

Answer:
Hint: We will try to do any two column or row equal
Given:
Solution:

If any two rows or columns of a determinant are identical.
The value of the determinant is zero

Hence

deteminants Exercise 5.2 Question 15

Answer:
Hint: We will try to do any two column or row identical
Given:
Solution:




If any two rows or columns of a determinant are identical.
The value of the determinant is zero

Hence

deteminants Exercise 5.2 Question 16

Answer:
Hint: We will try to make all the elements of two row or column zero
Given:
Solution:



If all the elements of a row or column are zero
The value of the determinant is zero

Hence

deteminants Exercise 5 .2 Question 17

Answer: where A,B,C are the angles of ΔABC
Hint: We will try to convert some elements of determinant zero or 1
Given:
Solution:






Hence

deteminants Exercise MCQs Question 2 sub question 3

Answer:-
Hint: We will try to make some elements of the determinant into zero
Given:-
Solution :-





Hence

determinants Exercise 5.2 Question 2 sub question 4

Answer:-
Hint: We will try to make some elements of the determinant into zero
Given:
Solution :



Hence

determinants Exercise 5.2 Question 2 sub question 5

Answer:
Hint: We will try to make some elements of the determinant into zero
Given:
Solution:




Hence

determinants Exercise 5.2 Question 2 sub question 6

Answer:
Hint :We will try to make some elements of the determinant into zero
Given :
Solution:



Hence

determinants Exercise 5.2 Question 2 sub question 7

Answer:
Hint: We will try to make some elements of the determinant into zero
Given:
Solution:



Hence

determinants Exercise 5.2 Question 2 sub question 8

Answer:
Hint:We will take common from
Given:
Solution:


Hence

determinants Exercise 5.2 Question 2 sub question 9

Answer:
Hint:We will try to make some elements of the determinant into zero
Given :
Solution:




Hence

deteminants Exercise 5.2 Question 10

Answer:-

Hint: First we solve and after we solve for
We will try to make some elements of the determinant zero
Given:
Solution:Let us solve for




If we convert all columns into rows
then the value of determinant does not change


Now Lets us Solve for



On expanding w.r.t

Now L.H.S

From equation (1) and (2)

Hence it is proved that

determinants Exercise 5.2 Question 11

Answer:
Hint: We will try to make some elements of the determinant zero
Given:
Solution: L.H.S





Hence it is proved that

determinants Exercise 5.2 Question 12

Answer:
Hint:We will try to make some elements of the determinant zero
Given:
Solution:L.H.S



=RHS
Hence it is proved that

deteminants Exercise 5.2 Question 13

Answer:
Hint: We will make of L.H.S according to R.H.S
Given:
Solution:L.H.S




Hence it is proved that

deteminants Exercise 5.2 Question 14

Answer:
Hint We will try to make some elements of the determinant zero
Given:
Solution:





Hence it is proved that

determinants Exercise 5.2 Question 15

Answer:
Hint:We will try to make some elements of the determinant zero
Given:
Solution:







Hence it is proved that

determinants Exercise 5.2 Question 16

Answer:

Answer:
Hint : We will try to make some elements of the determinant zero
Given:
Solution:

If the rows and columns of a determinant are interchanged, the value of the determinant remains the same.





Hence it is proved that

determinants Exercise 5.2 Question 17

Answer:
Hint We will try to make some elements of the determinant zero
Given :
Solution:





Hence it is proved that

deteminants Exercise 5.2 Question 18

Answer:
Hint We will make column (3) of L.H.S abc
Given:
Solution:



If any two rows or columns of a determinant are interchanged, then sign of the determinant is changed.

Hence it is proved that

deteminants Exercise 5.2 Question 19.

Answer:

Hint:We will prove all the determinant equal by using interchange column or row property
Given:
Solution:
Let us first solve for

If any two rows or columns of a determinant are interchanged, then sign of the determinant is changed.





.....2
(3)




From equation (1), (2),(3) and (4)
Hence it is proved that

determinants Exercise 5.2 Question 20

Answer:
Hint We will try to make and any two elements of determinant
Given:
Solution:





Taking common(a+b+c)from



Hence it is proved that

deteminants Exercise 5.2 Question 22

Answer:

Answer:
Hint
Given:
Solution:






Hence it is proved that

determinants Exercise 5.2 Question 23

Answer:
Hint We will make some elements of the determinant zero
Given:
Solution:






(2)

From (2)


Hence it is proved that

determinants Exercise 5.2 Question 24

Answer:
Hint We will convert some elements of the determinant into zero
Given:
Solution:








Hence it is proved that

determinants Exercise 5.2 Question 25

Answer:

Answer:
Hint First we will try to convert some elements into zero
Given:
Solution:





Hence it is proved that

determinants Exercise 5.2 Question 26

Answer:

Answer:
Hint we will convert element of into zero
Given:
Solution:


Hence it is proved that

determinants Exercise 5.2 Question 27

Answer:
Hint First we will make elements of
Given:
Solution:




Hence it is proved that

deteminants Exercise 5.2 Question 28

Answer:

Answer:
Hint First we will try to make some elements of
Because from R.H.S
Given:
Solution:





Hence it is proved that

determinants Exercise 5.2 Question 29

Answer:

Answer:
Hint We will try to convert some elements of determinant into zero
Given:
Solution:





Hence it is proved that

determinants Exercise 5.2 Question 30

Answer:
Hint We will try to convert some elements of determinant into zero
Given:
Solution:





Hence it is proved that

determinants Exercise 5.2 Question 31

Answer:
Hint Use determinant formula
Given:
Solution:

determinants Exercise 5.2 Question 32

Answer:
Hint: Use determinant formula
Given:
Solution:

determinants Exercise 5.2 Question 33

Answer:
Hint: Use determinant formula
Given:
Solution:

deteminants Exercise 5.2 Question 34

Answer:
Hint Use determinant formula
Given:
Solution:

determinants Exercise 5.2 Question 35

Answer:
Hint Use determinant formula
Given :
Solution:

determinants Exercise 5.2 Question 36

Answer:
Hint Use determinant formula
Given:
Solution:

determinants Exercise 5.2 Question 37

Answer:
Hint: Use determinant formula
Given:
Solution:

deteminants Exercise 5.2 Question 38

Answer:
Hint Use determinant formula
Given:
Solution:




Expanding w.r.t

deteminants Exercise 5.2 Question 39

Answer:
Hint Use determinant formula
Given:
Solution:



Expanding w.r.t

determinants Exercise 5.2 Question 40

Answer:
Hint Use determinant formula
Given:
Solution:



Expanding w.r.t

Question:41.1

determinants Exercise 5. 2 Question 41

Answer:
Hint Use determinant formula
Given:
Solution:



Expanding w.r.t

determinants Exercise 5.2 Question 41 sub question 2

Answer:

Answer:
Hint Use determinant formula
Given:
Solution:

deteminants Exercise 5.2 Question 42

Answer:
Hint Use determinant formula
Given:

Solution:


Expanding w.r.t

determinants Exercise 5.2 Question 43

Answer:
Hint Use determinant formula
Given:
Solution:


Expanding w.r.t

determinants Exercise 5.2 Question 44

Answer:
Hint Use determinant formula
Given:
Solution:

deteminants Exercise 5.2 Question 45

Answer:
Hint Use determinant formula
Given:
Solution:

determinants Exercise 5.2 Question 46

Answer: Proved
Hint Use determinant formula
Given:
Solution:


For interchanging R2↔R3
negative sign will be added

Now convert rows in columns and column in row

deteminants Exercise 5.2 Question 47

Answer: 0
Hint
Given:
Solution:

As
Substituting the value in the denominator,

Expanding along

deteminants Exercise 5.2 Question 48

Answer:
Hint
Given:
Solution:
...(1)


Expanding along ,
..hence proved

determinants Exercise 5.2 Question 49

Answer:
Hint Use determinant formula
Given:
Solution:




Hence,

deteminants Exercise 5.2 Question 50

Answer:
Hint Use determinant formula
Given:
Solution:

determinants Exercise 5.2 Question 51

Answer:
Hint Use determinant formula
Given:
Solution:

determinants Exercise 5.2 Question 52

Answer:
Hint Use determinant formula
Given:
Solution:

deteminants Exercise 5.2 Question 52 sub question 2

Answer:
Hint: Use determinant formula
Given:
Solution:

deteminants Exercise 5.2 Question 52 sub question 3

Answer:
Hint: Use determinant formula
Given:
Solution:

deteminants Exercise 5.2 Question 52 sub question 4

Answer:
Hint Use determinant formula
Given:
Solution:



Expand from

deteminants Exercise 5.2 Question 52 sub question 5

Answer:

Answer:
Hint: Use determinant formula
Given:
Solution:

deteminants Exercise 5.2 Question 52 Sub Question 6

Answer:
Hint: Use determinant formula
Given:
Solution:

deteminants Exercise 5.2 Question 52 Sub Question 7

Answer:
Hint: Use determinant formula
Given:
Solution:

deteminants Exercise 5.2 Question 52 Sub Question 8

Answer:
Hint: Use determinant formula
Given:
Solution:

deteminants Exercise 5.2 Question 52 Sub Question 9

Answer:
Hint: Use determinant formula
Given:
Solution:

deteminants Exercise 5.2 Question 52.1

Answer:
Hint: Use determinant formula
Given:
Solution:

determinants Exercise 5.2 Question 53

Answer:
Hint Use determinant formula
Given:
Solution:

determinants Exercise 5.2 Question 5

Answer:
Hint: Use determinant formula
Given:
Solution:

The class 12 chapter 5, Determinants, is where the tendency to score marks easily as possible. The students need to make use of this opportunity to the best level. The concepts present in the RD Sharma class 12th exercise 5.2, are to evaluate the determinants, prove the determinant's value is zero, Arithmetic Progression in Determinants, and prove using the properties of determinants. A total of eighty-eight questions, including its subparts, are present in this exercise. It would take much time to solve or recheck the answers. Hence a copy of the RD Sharma Class 12 Chapter 5 Exercise 5.2 solutions book is a must.

Every answer here is provided and verified by experts. And the solutions follow the NCERT method, which gives a good reason for the CBSE students to adapt to it. An abundance of students has scored high marks in this chapter by preparing with the help of the Class 12 RD Sharma Class 12 Solutions Determinant Ex 5.2. Not only can students prepare for exams, but they can also use it to complete their daily homework and assignments.

For the welfare of the students, they can download the RD Sharma class 12th exercise 5.2 solution books for free of cost from the Career360 website. So they need not pay even a single penny for it. All you need is to visit the Career 360 website, search for the Class 12 RD Sharma Chapter 5 Exercise 5.2 Solution, and click the download button. It saves you hundreds to thousands of rupees that you would spend on other solution books.

If you strive to cross your benchmark score in the Determinants chapter, download the RD Sharma Class 12 Solutions Chapter 5 ex 5.2 and start preparing your exams with it. As the problems given in the RD Sharma books are solved in various methods, the students get the opportunity to decide which way they can follow. It clears the air for the people who are confused and also helps in rechecking their solutions.

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