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Question-8 :-
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(ii)![]()
Question-9 :-
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Question-11 :-
Using properties of determinants, prove that:
Question-12 :-
Using properties of determinants, prove that:
Question-13 :-
Using properties of determinants, prove that:
Question-14 :-
Using properties of determinants, prove that:
Question-15 :-
Using properties of determinants, prove that:
Question-16 :-
Solve the system of equations:
Let 1/x = a, 1/y = b, 1/z = c 2a + 3b + 10c = 4 4a – 6b + 5c = 1 6a + 9b – 20c = 2a = 1/2; x = 2 b = 1/3; y = 3 c = 1/5; z = 5
Question-17 :-
If a, b, c, are in A.P, then the determinant
(A) 0 (B) 1 (C) x (D) 2x
The correct answer is A.
Question-18 :-
The correct answer is A.
Question-19 :-
(A) Det(A) = 0 (B) Det(A) ∈ (2, ∞) (C) Det(A) ∈ (2, 4) (D) Det(A) ∈ [2, 4]
|A| = 1(1 + sin²θ) - sin θ(-sin θ + sin θ) + 1(sin²θ + 1) = 1 + sin²θ + sin²θ + 1 = 2 + 2sin²θ = 2(1 + sin²θ) Now, 0 ≤ θ ≤ 2π 0 ≤ sin θ ≤ 1 0 ≤ sin²θ ≤ 1 1 ≤ 1+sin²θ ≤ 2 2 ≤ 2(1+sin²θ) ≤ 4 Det(A) ∈ [2, 4] The correct answer is D.