Mathematics-5.Unit-3.03-Matrices and Determinants Test

1. The value of is : (A) ( − 5) (B) 5 ( − 5) (C) 5 ( + 5) (D) 5 ( − 5) 2. is equal to : (A) constant other than zero (B) zero (C) 100 (D) –1997 3. If a + b +c > 0 and a ≠ b ≠ c ≠ 0, then Δ = then : (A) Δ > 0 (B) Δ < 0 (C) Δ = 0 (D) Data insufficient 4. The determinant is equal to zero if : (A) a, b, c are in A.P. (B) a, b, c are in G.P. (C) a, b, c are in H.P. (D) none of these 5. The determinant is divisible by : (A) 1 + x (B) (1 + x)2 (C) x2 (D) none of these 6. is equal to : (A) a positive number (B) a negative number (C) Zero (D) none of these 7. If f(x) = , then dx is equal to : (A) 1/4 (B) –1/3 (C) 1/2 (D) 1 8. For positive numbers x, y, z, the numerical value of the determinant is : (A) 0 (B) 1 (C) 2 (D) none of these 9.  = is equal to : (A) p + q (B) a + b + c (C) x + y + z (D) 0 10. is equal to : (A) abc (B) a2b2c2 (C) ab + bc + ca (D) 0 11. is equal to : (A) 0 (B) 1 (C) –1 (D) none of these 12. If f (x) = then f (100) is equal to : (A) 0 (B) 1 (C) 100 (D) –100 13. is equal to : (A) 1 + ∑a2 (B) ∑a2 (C) (∑a)2 (D) ∑a 14. If A, B, C are the angles of a triangle and , then  is equal to: (A) constant other than zero (B) not a constant (C) 0 (D) none of these 15. If [.] denotes the greatest integer less than or equal to the real number under consideration and –1 ≤ x < 0; 0 ≤ y < 1 and 1 ≤ z < 2, then the value of the determinant is : (A) [z] (B) [y] (C) [x] (D) none of these 16. If  = = 0, then the non zero root of the equation is : (A) a+b +c (B) abc (C) – a – b –c (D) None of these 17. If f (x) = then the value of f(x) dx is equal to : (A) 0 (B) 1 (C) 2 (D) none of these 18. If A = , then A2 is equal to (A) unit matrix (B) null matrix (C) A (D) –A 19. If A′ is the transpose of a square matrix A, then (A) |A| ≠ |A′| (B) |A| = |A′| (C) |A| + |A′| = 0 (D) |A| = |A′| only when A is symmetric 20. If I = , J = and B = , then B equals (A) I cos + J sin (B) I sin + J cos (C) I cos – J sin (D) – I cos + J sin 21. If In is the identity matrix of order n, then (In)–1 (A) does not exist (B) equal to In (C) equals to O (D) nIn 22. If for a matrix A, A2 + I = O where I is the identity matrix, then A equals (A) (B) (C) (D) 23. If A = , then A40 equals (A) (B) (C) (D) none of these 24 If A [aij] is a square matrix of order n  n such that aii = k for all i, then trace of A is equal to (A) kn (B) (C) nk (D) none of these 25. If A = and I = , then the value of k so that A2 = 8A + kI is (A) 7 (B) − 7 (C) 0 (D) 5 26. If A = , then the value of |adj A| is (A) a27 (B) a9 (C) a6 (D) a2 27. If A and B are symmetric matrices of order n (A ≠ B), then (A) A + B is skew symmetric (B) A + B is symmetric (C) A + B is a diagonal matrix (D) A + B is a zero matrix 28. If A = and B = then AB = (A) A3 (B) B2 (C) O (D) I 29. If A = the A is (A) idempotent (B) nilpotent (C) symmetric (D) none of these 30. If A = , then 19A–1 is equal to (A) A′ (B) 2A (C) (D) A

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