Hello Students! In this post, you will find the complete** ****NCERT Solutions for Maths Class 12 Exercise 4.1.**

You can download the **PDF of NCERT Books Maths Chapter 4** for your easy reference while studying **NCERT Solutions for Maths Class 12 Exercise 4.1**.

All the schools affiliated with CBSE, follow the NCERT books for all subjects. You can check your syllabus from **NCERT Syllabus for Mathematics Class 12**.

If you want to recall **All Maths Formulas for Class 12**, you can find it by clicking this link.

If you want to recall **All** **Maths Formulas for Class 11**, you can find it by clicking this link.

**NCERT Solutions for Maths Class 12 Exercise 4.2**

**NCERT Solutions for Maths Class 12 Exercise 4.3**

**NCERT Solutions for Maths Class 12 Exercise 4.4**

**NCERT Solutions for Maths Class 12 Exercise 4.5**

**NCERT Solutions for Maths Class 12 Exercise 4.1**

**Maths Class
12 Ex 4.1 Question 1.**

**Evaluate the following determinant:**

**Solution:**

= 2 × (–1) – (–5) × (4)

= –2 + 20

= 18

**Maths Class
12 Ex 4.1 Question 2.**

**Evaluate the
following determinants:**

**(i) **

**(ii) **

**Solution:**

**(i)**

= cos Î¸ × cos Î¸ – (sin Î¸) × (–sin Î¸)

= cos² Î¸ + sin² Î¸

= 1

**Maths Class
12 Ex 4.1 Question 3.**

**If**

**, then show that |2A|= 4|A|**

**Solution:**

**Maths Class
12 Ex 4.1 Question 4.**

**If**

**, then show that |3A| = 27|A|**

**Solution:**

**Maths Class
12 Ex 4.1 Question 5.**

**Evaluate the following determinants:**

**Solution:**

**Maths Class
12 Ex 4.1 Question 6.**

**If**

**, find |A|**

**Solution:**

|A| =

= 1(–9 + 12) – 1(–18 + 15) – 2(8 – 5)

= 0

**Maths Class
12 Ex 4.1 Question 7.**

**Find the values of x, if**

**Solution:**

**(i)**

⇒ 2 – 20 = 2x² – 24

⇒ x² = 3

⇒ x = ±√3

⇒ 2 × 5 – 4 × 3 = 5 × x – 2x × 3

⇒ 10 – 12 = 5x – 6x

⇒ x = 2

**Maths Class
12 Ex 4.1 Question 8.**

**If**

**, then x is equal to**

**(A) 6**

**(B) ****±6**

**(C) -6**

**(D) 0**

**Solution:**

**(B)**

⇒ x² – 36 = 36 – 36

⇒ x² = 36

⇒ x = ± 6

Hence, option (B) is correct.

**Related Links:**

**NCERT Solutions for Maths Class 12 Exercise 4.2**

**NCERT Solutions for Maths Class 12 Exercise 4.3**