# NCERT Solutions Class 12

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## NCERT Solutions Class 12

### Exercise 4.1

Evaluate the following determinants in Exercise 1 and 2.

1. Ans. = = = 18

2. (i) (ii) Ans. (i) = = = 1

(ii) =  = ### 3. If A = then show that Ans. Given: A = then 2A =  L.H.S. = = R.H.S. =  = Since L.H.S. = R.H.S.

Hence, proved.

4. If A = then show that Ans. Given: A = then 3A = = L.H.S.   =  = 3 x 36 = 108

R.H.S.   = = 27 [1 (4 – 0)] = 27 x 4 = 108

Since   L.H.S. = R.H.S.

Hence, proved.

5. Evaluate the determinants:

(i) (ii) (iii) (iv) Ans. Evaluate the determinants:

(i) Given: Expanding along first row,   = (ii) Given: Expanding along first row,   = 21 + 20 + 5 = 46

(iii) Given: Expanding along first row,  = 0 + 6 – 6 = 0

(iv) Given: Expanding along first row,   = 5

6. If A = find Ans. Given:     A =   = Expanding along first row,     = 0

7. Find the value of if:

(i) (ii) Ans. (i) Given:             (ii)       8. If then is equal to:

(A) 6

(B) (C) (D) 0

Ans. Given:         Therefore, option (B) is correct. 