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M0IITU15 - Determinants qns

# M0IITU15 - Determinants qns - 1 1 a a2 bc 1 b b2 a c = 1 c...

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1 QUEST TUTORIALS Head Office : E-16/289, Sector-8, Rohini, New Delhi, Ph. 65395439 1. 1 1 1 2 2 2 a a bc b b a c c c a b - - - = (A) 0 (B) a 3 + b 3 + c 3 - 3 abc (C) 3 abc (D) (a + b + c) 3 2. The following system of equations, 3x - 2y + z = 0, λ x - 14y + 15z = 0, x + 2y - 3z = 0 has a solution other than, x = y = z = 0 for λ equal to : 1 (B) 2 3 5 3. The roots of the equation, 1 4 20 1 2 5 1 2 5 2 - x x = 0 are : - 1, - 2 - 1, 2 2 4. If 0 0 0 x a x b x a x c x b x c - - + - + + = 0, then the value of x is : 0 1 2 3 5. ω is the cube root of unity, then 1 1 1 2 2 2 ω ω ω ω ω ω = 1 0 ω ω 2 6. If x x x + + + 1 3 5 2 2 5 2 3 4 = 0, then x = 1, 9 - - 9 9 7. The value of the determinant, 7 9 79 4 1 41 5 5 55 - 7 0 15 27 8. a b c a a b b c a b c c c a b - - - - - - 2 2 2 2 2 2 = (a + b + c) 2 + b + c) 3 (a + b + c) (ab + bc + ca) None of these 9. a b a b a b a b a b a b a b a b a b + + + + + + + + + 2 3 2 3 4 4 5 6 = 3 (a + b) 3 ab 3a + 5b 0 10. b c a a b c a b c c a b + + + = abc 2 abc 4 abc 11. One of the roots of the given equation

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2 QUEST TUTORIALS Head Office : E-16/289, Sector-8, Rohini, New Delhi, Ph. 65395439 x a b c b x c a c a a b + + + = 0, is : (A) - (a + b) (B) - (b + c) (C) - a (D) - (a + b + c) 12. If 2x + 3y - 5z = 7, x + y + z = 6, 3x - 4y + 2z = 1, then x = 2 5 7 1 1 6 3 2 1 7 3 5 6 1 1 1 4 2 - + - - - - - - - + - - 7 3 5 6 1 1 1 4 2 2 3 5 1 1 1 3 4 2 7 3 5 6 1 1 1 4 2 2 3 5 1 1 1 3 4 2 - - + - - 13. x + ky - z = 0, 3x - ky - z = 0 and x - 3y + z = 0 has non-zero solution for k = - 1 0 1 2 14. Δ = a b c a b c a b c 1 1 1 2 2 2 3 3 3 and A 1 , B 1 , C 1 denote the co-factors of a 1 , b 1 , c 1 respectively, then the value of the determinant, A B C A B C A B C 1 1 1 2 2 2 3 3 3 is : Δ Δ 2 Δ 3 0 15. The number of solutions of equations x + y - z = 0, 3x - y - z = 0 and 0 1 2 Infinite 16. The number of solutions of the equations, x + 4y - z = 0, 3x - 4y - z = 0 and x - 3y + z = 0 is 0 1 2 17. b c a b a c a b c b a b c a c + - + - + - = a 3 + b 3 + c 3 - 3 abc 3 abc - a 3 - b 3 - c 3 a 3 + b 3 3 2 b - b 2 c - c 2 a (a + b + c) (a 2 + b 2 + c 2 + ab + bc + ca) 18. x = cy + bz, y = az + cx, z = bx + ay, where x, y, z are not all zero, then : a 2 2 2 - 2 abc = 0 a 2 2 2 + 2 a 2 2 2 abc = 1 a 2 2 2 19. ω is a cube root of unity, then a root of the following equation, x x x + + + 1 1 1 2 2 2 ω ω ω ω ω ω
3 QUEST TUTORIALS Head Office : E-16/289, Sector-8, Rohini, New Delhi, Ph. 65395439 (A) 1 (B) ω (C) ω 2 (D) 0 20. In a skew-symmetric matrix, the diagonal elements are all : Different from each other Zero One None of these 21. If A, B, C are three n × n martices, then (ABC) = A B C C B A B C A B A C 22. If M = 1 2 2 3 and M 2 - λ M - I 2 = O, then λ = - 2 2 - 4 4 23. If A = 1 0 0 0 1 0 1 a b - , then A 2 = Unit matrix (B) Null matrix A - A 24. 1 1 0 1 , then A n = 1 0 1 n n n n 0 n n 1 0 1 1 0 n 25. If 1 1 1 1 - - 2 = A 2 A A 26. AB = O, if and only if : A O, B = O A = O, B O A = O or B = O 27. Inverse of the matrix 3 2 1 4 1 1 2 0 0 - - - - is : 1 2 3 3 3 7 2 4 5 - - - 1 3 5 7 4 6 4 2 7 - (C) 1 2 3 2 5 7 2 4 5 - - - (D) 1 2 4 8 4 5 3 5 2 - - - 28.

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M0IITU15 - Determinants qns - 1 1 a a2 bc 1 b b2 a c = 1 c...

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