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Exercise - 4.1

Determinants

**Question-1 :-**
Evaluate the determinants :

|A| = -2 - (-20) = -2 + 20 = 18

**Question-2 :-**
Evaluate the determinants:

(i) |A| = cos^{2}θ - (-sin^{2}θ) = cos^{2}θ + sin^{2}θ = 1 (ii) |B| = (x^{2}- x + 1)(x + 1) - (x - 1)(x + 1) = x^{3}+ x^{2}- x^{2}- x + x + 1 - (x^{2}- 1) = x^{3}+ 1 - x^{2}+ 1 = x^{3}- x^{2}+ 2

**Question-3 :-**

**Question-4 :-**

**Question-5 :-**
Evaluate the determinants :

(i)

(ii)

(iii)

(iv)

**Question-6 :-**

**Question-7 :-**
Find values of x, if

(i) 2 - 20 = 2x^{2}- 24 -18 + 24 = 2x^{2}6 = 2x^{2}x^{2}= 3 x = ±√3 (ii) 10 - 12 = 5x - 6x -2 = -x x = 2

**Question-8 :-**

(A) 6 (B) ±6 (C) -6 (D) 0

x^{2}- 36 = 36 - 36 x^{2}- 36 = 0 x^{2}= 36 x = ±6 The correct answer is B.

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