# NCERT Solutions Class 12 maths Chapter-4 (Determinants)

**NCERT Solutions Class 12 Maths**from class

**12th**Students will get the answers of

**Chapter-4 (Determinants)Exercise 4.1**This chapter will help you to learn the basics and you should expect at least one question in your exam from this chapter.

We have given the answers of all the questions of

**NCERT Board Mathematics Textbook**in very easy language, which will be very easy for the students to understand and remember so that you can pass with good marks in your examination.

**NCERT Question-Answer**

**Class 12 ****Mathematics**

**Chapter-4 ****(****Determinants****)**

**Questions and answers given in practice**

**Chapter****-4 ****(Determinants)**

### Exercise 4.1

**Evaluate the determinants from the following
Questions.**

**Question 1. **

**Solution:**

The determinant of a 2 x 2 matrix

Hence,

**Question 2. (i) **

**Solution:**

from trigonometric identities

**(ii) **

**Solution:**

**Question 3. If show that **

**Solution:**

**LHS=>**

Matrix,

Hence, determinant,

**RHS=>**

Determinant,

Now,

**Hence, proved, LHS = RHS**

**Question 4. If then show that |**

**Solution:**

**LHS=>**

Matrix,

Hence, determinant,

**RHS =>**

Determinant,

Now,

**Hence, proved, LHS = RHS**

**Question 5. Evaluate the determinants**

**(i) **

**Solution:**

Since the maximum number of zeroes are in the second row, we will expand the determinant along row 2.

(ii)

**Solution:**

(iii)

**Solution:**

**Note: This matrix is skew symmetric i.e. **

**For every skew symmetric matrix of “odd dimension”, the determinant vanishes i.e. determinant is zero.**

(iv)

**Solution:**

Since the maximum number of zeroes are in the second row, we will expand the determinant along row 2.

**Question 6. If find |A|**

**Solution:**

**Question 7. Find the values of x if**

**(i) **

**Solution:**

Solving determinants on both sides,

**(ii) **

**Solution:**

Solving determinants on both sides

**Question 8. If then
x is equal to**

**(A) 6 (B) ±6
(C) -6 (D) 0**

**Solution:**

Solving determinants on both sides

Hence, Option (B)

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