## NCERT Solutions for Class 12 Maths Exercise 4.1 Chapter 4 Determinants â€“ FREE PDF Download

NCERT Solutions for Class 12 Maths Chapter 4 â€“ Determinants is a sure-shot way of obtaining the complete marks in the particular chapter for Board Exam . CoolGyan provides you with Free PDF download of the same solved by Expert Teachers as per NCERT (CBSE) Book guidelines. They provide the students with precise and to the point answers which fetch very good marks in Board Exams. Download today the NCERT CBSE Solutions for Class 12 Maths Chapter 4 â€“ Determinants to achieve your goal score. Class 12 Maths Chapter 4 â€“ Determinants solved by Expert Teachers as per NCERT (CBSE) Book guidelines.

# NCERT Solutions for Class 12 Maths Chapter 4 â€“ Determinants

Evaluate the following determinants in Exercise 1 and 2.

1.Â

1.Â

**Ans.**Â Â Â =Â Â =Â Â = 18

### 2. (i)Â

(ii)Â

**Ans.**Â (i)Â Â =Â Â =Â Â = 1

(ii)Â Â =Â

=Â Â =Â

### 3. If A =Â Â then show thatÂ

**Ans.**Â Given: A =Â Â then 2A =Â

=Â

L.H.S. =Â Â =Â

R.H.S. =Â

=Â Â =Â

Since L.H.S. = R.H.S.

Hence, proved.

### 4. If A =Â Â then show thatÂ

**Ans.**Â Given: A =Â Â then 3A =Â Â =Â

L.H.S.Â Â =Â

=Â Â = 3 x 36 = 108

R.H.S.Â Â =Â

= 27 [1 (4 â€“ 0)] = 27 x 4 = 108

SinceÂ Â L.H.S. = R.H.S.

Hence, proved.

### 5. Evaluate the determinants:

(i)Â

(ii)Â

(iii)Â

(iv)Â

**Ans.**Â Evaluate the determinants:

(i)Â Given:Â

Expanding along first row,Â Â Â

=Â

=Â Â =Â

(ii)Â Given:Â

Expanding along first row,Â Â Â

=Â

=Â

= 21 + 20 + 5 = 46

(iii)Â Given:Â

Expanding along first row,Â Â Â

=Â

= 0 + 6 â€“ 6 = 0

(iv)Â Given:Â Â Â Â Â Â

Expanding along first row,Â Â Â

=Â

=Â Â = 5

### 6. If A =Â Â findÂ

**Ans.**Â Given:Â Â Â Â A =Â

Â Â =Â

Expanding along first row,Â Â Â

=Â

=Â

=Â

=Â Â = 0

### 7. Find the value ofÂ Â if:

(i)Â

(ii)Â

**Ans.**Â (i)Â Given:Â

Â

Â

Â

Â

Â

Â

(ii)Â

Â

Â

Â

### 8. IfÂ Â thenÂ Â is equal to:

(A) 6

(B)Â

(C)Â

(D) 0

**Ans.**Â Given:Â

Â

Â

Â

Â

Therefore, option (B) is correct.