TOPICS
Miscellaneous

Question-1 :-  determinant

Solution :-
        determinant
    

Question-2 :-  determinant

Solution :-
        determinant
    

Question-3 :-  determinant

Solution :-
        determinant
    

Question-4 :-  determinant

Solution :-
        determinant
    

Question-5 :-  determinant

Solution :-
    determinant
    

Question-6 :-  determinant

Solution :-
        determinant
    

Question-7 :-  determinant

Solution :-
        determinant
        determinant
    

Question-8 :-  determinant

Solution :-
        determinant
    
(i)        determinant
    
        determinant
    
(ii)        determinant
    

Question-9 :-  determinant

Solution :-
        determinant
    

Question-10 :-  determinant

Solution :-
        determinant
    

Question-11 :-  Using properties of determinants, prove that: determinant

Solution :-
        determinant
    

Question-12 :-  Using properties of determinants, prove that: determinant

Solution :-
        determinant
    

Question-13 :-  Using properties of determinants, prove that: determinant

Solution :-
        determinant
    

Question-14 :-  Using properties of determinants, prove that: determinant

Solution :-
        determinant
    

Question-15 :-  Using properties of determinants, prove that: determinant

Solution :-
        determinant
    

Question-16 :-  Solve the system of equations: determinant

Solution :-
  Let 1/x = a, 1/y = b, 1/z = c

  2a + 3b + 10c = 4
  4a – 6b + 5c = 1
  6a + 9b – 20c = 2
  determinant
  a = 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 determinant (A) 0    (B) 1    (C) x    (D) 2x

Solution :-
  determinant
  The correct answer is A.
    

Question-18 :-  determinant

Solution :-
  determinant
  The correct answer is A.
    

Question-19 :-  determinant (A) Det(A) = 0   (B) Det(A) ∈ (2, ∞)   (C) Det(A) ∈ (2, 4)   (D) Det(A) ∈ [2, 4]

Solution :-
  |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.
    
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