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SHREE GURU GYAN TUTORIALS, Std 12: MATHS, Chapters:4, Total Marks: 42, Date:14/02/22, PAPER 1 TEXT BOOK BASED MCQ, Time: 03Hour, Section A, Choose correct answer from the given options. [Each carries 1 Mark], [42], a 0 0, 1., If A =0 a 0 then adj A = .. ., 0 0 a, (A) a27, (В) а9, (C) a6, (D) a2, 1, 2, -1], 2., If A =|-1, 1, then det(adj(adj A)), 2, -1, 1, (B) (14)3, If A is a orthogonal matrix, then, (A) (14)4, (C) (14)2, (D) (10)!, 3., (A) det(A) = 0, (B) det(A) = t 1, (C) det(A) = 2, (D) None of these, a1 b C1, A = a2 b2 c2 and A' A2 B2 C2where A1, B1, C, A2, B2.. are respectively the cofactors, a3 bz c3|, A1 B1 C1, 4., A3 B3 C3, of the elements a, b, c, az, b2.. of the determinant then AA' =, (A) 0, (B) 2A, (C) 43, (D) A, The elements of the determinant of order 3 x 3 are {o, 1}. Then the maximum and minimum value, are respectively, 5., (A) 1, -1, (B) 2, -2, (C) 4, -4, (D) 6, -6, O 1 2, 1 1, 2, 6., A =1 2 3 and A-, -4, 3, then a = .........., and c =, %3D, 3 a, (A) 1, 1, (B) 1, -1, (C) 1, 2, (D) -1, 1, x+1 x2 +2 x² +x, 7., x2 + x x2 +1 x² + 2 = ax6 + bx5 + cx + dx + ex? + flx) + g then f = . .,, g =, x x2 +x, x +1, + 2, (A) f = 3, g = -5, (B) f = -3, g = -5, (C) f = -3, g = -9, (D) f = -4, g = 9, 2-i i+1, A = 2+i, 3+i is always, 8., 1-i 3-i, (A) Real, (B) Complex, (C) Imaginary, (D) None of these, x + 2y + 3z = 4, 9., The system of equations 2x + 3y + 4z =5 has, solutions., 3x + 4y +5z = 6, (A) Infinite, (B) unique, (C) None of these, (D) can't say anything, Wish You - All The Best, 1
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7 6 x, 10., The equation 2, x 2 = 0 has one root x = -9 then other roots, x 3 7, (A) 2 and 6, (B) 3 and 6, (C) 2 and 7, (D) 3 and 7, 1, x + 1, If f(x) =, then f(100), 11., 2.x, x(x - 1), (x + 1)x, 3x(x-1) x(x-1)(x-2) (x+1)x(x-1), (A) 0, (В) 1, (C) 100, (D) -100, 12., -1 <x < 0, 0 < y < 1, 1< z < 2 and [] is a greatest integer function then,, [x] +1, [yl, [z], [z], [z] + 1, [x], lyl+1, [x], [y], (A) [x], (B) [y], (C) [z], (D) None of these, 3 5 2, If 1, 3 5, 4, 13., 4 7 = k 1, 4 14 then k =, 2 1, 4 2, 1, (A), (B) 4, (C), (D) 2, 1! 2! 3!, 2! 3! 4!, 14., ! 4! 5!, (A) 5 !, (B) 4 !, (C) 3 !, (D) 2 !, 15., The area of triangle with vertices (3, 2), (8, 12) and (11, 8) is, (A) 50, (B) 25, (C) 74, (D) 37, 7, 9., 16., The sum of the cofactor of the elements in second column in 10, 1 is, 12 10, (A) 1, (В) -4, (C) 0, (D) 5, |sinx cosx, cosx cosx, X E| 0,, then x =, 2, 17., %3D, sin x sinx, cosx sinx, (A), (C) 6, (B), (D), The equation of line passing through (-7, 8) and (5, 2) is, (A) x + 2y 9 0, 18., (В) 5х- у-27%3D 0, (C) x - 2y + 9 0, (D) 5x + y - 27 = 0, x 4 10, 19., If 5 2, 5 = 0 then x e, 7 3, (A) {10}, (В), 2, (C) {10, 7}, (D), 2, a + 2a, D =, 2a +1 1, 20., 2a +1, a + 2, 1 then,, 3, 3, (A) D > 0 If a > 1., (C) D = 0 If a = 1., (B) D < 0 If a < 1., (D) All the given alternates, 21., The given system of equations x - ky – z = 0, kx - y - z = 0, x + y - z = 0 has non zero solution, Wish You - All The Best, 2
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then the possible value ofk is, (A) -1 or 2, (B) 1 or 2, (C) 0 or 1, (D) -1 or 1, x b bl, x b, b and A2 =, a, 22., If A = la, are given determinants then,, a a x, d, d, (A) A, = 3(A,)2, (A) = 3A2, (A1) = 3A3, (D) A1 = 3(A2), (B), (C), %3D, dx, dx, 23., If A is a square matrix and JA[ = 2 then A"|, where n is a positive integer., %3D, (A) 0, (B) 2n, (C) 2", (D) n?, 24., If A is a square matrix and A2 = A then JA|, (A) 0 or 1, (B) -2 or 2, (C) -3 or 3, (D) None of these, la -b a- b|, 25., b, b - c = 0 then a, b, c are in, 2, 1, (A) G.P., (B) A.P., (С) Н.Р., (D) None of these, 2, 3, 4, 26., 4x 6x 8x = ......, 7, (A) 18x, (B) 0, (C) 1, (D) 18x3, |2008 2009, is, 27., The value of, 2010 2011, (A) -1, (B) 1, (C) -2, (D) 2, x 1 y+z, y 1, z 1 x+y|, 28., z + x, (A) x + y + z, (B) (x + y) (y+ z) (z + x) (C) 3, (D) 0, sin 40°, 29., sin 50°, -cos 40°, = ......, cos50°, (A) 0, (B) 1, (C) -1, (D) not exist., 2, If D = 5 -1, 3, 1, performing R12(-1) on D; then D will become ., -1, 30., 3, 1, 1, 1, 4, -1, 1, 6., (A), 3, 3, (D), -1, 2, -6 2, -1, 1, (B), (C), 7, 4, -3 -1, 4, 4, 52 53, 51, 53, 53, 54, 55, 31., 52, (A) 59, (B) 512, (C) 50, (D) 0, 1 yz x, 1, 1, 1, 1, y and D2, y, 32., If D,, zx, then, ...., %3D, 1 xy z, ye z, (A) D + 2D, = 0, (B) 2D1, D2, = 0, (C) D, + D, = 0, (D) D, = D2, %3D, Wish You - All The Best, 3, N57
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q+ x D+ x, X-c = 0 then x= ......, 33., If a +0, b 0, c+0 and x - a, -b x2 +c, (A) 1, (B) 0, (C) a+b+ c, (D) -(a +b + c), (x + 1)2 (y + 1)2, (z + 1)2|, If x, y, ze R. x>y>z and D =, 1, 34., then D is ...., y, 1, 1, (A) negative, (B) positive, (C) zero, (D) not real, 1, cose, 1, 35., If D =, -cose, 1, cose, then value of D lies in the interval .., -1, - cose, 1, (A) (2, 0), (В) (2, 4), (C) [2, 4], (D) [-2, 2], ax + by, bx + cy, a, b, 36., If, b, = 0 and ax? + 2bxy + cy2 + 0, then ..., ax + by bx + cy, (A) a, b, c are in A.P., (B) a, b, c are in G.P., (C) a, b, c are in A.P., (D) a, b, c are neither in A.P. nor in G.P., 1, If 1, 3 -1 2, 5, 5 = 0, then x = ......, 37., (A) 2, (B) -2, (C) 5, (D) -5, 1+x 1-x 1-x, The roots of 1-x 1 +x 1-x = 0 are ......, 38., 1- х 1-х 1+x, (A) 0 OR 1, (B) 0 OR -1, (C) 0 OR -3, (D) 0 OR 3, -6, -1, If 2, -3x x- 3 = 0, then x =, -3, 39., 2x, x +2, (А) -3, -2, 1, (В) -3, 2, -1, (С) -3, 2, 1, (D) 3, 2, 1, |V14 + 3, V20 V5, V15 + /28, V25 V10, 40., 3+ 70, V15, (A) 25/3 - 15/2, (B) 15/2 + 25/3, (C) -25/3- 15/2, (D) 15/2- 25/3, b, ax + b|, a, 41., If, bx + c = 0, then a, b, c are in .. (where ax2 + 2bx -c + 0), ......, ax + b bx + c, (A) A.P., (B) G.P., (C) an increasing sequence, (D) a decreasing sequence, Isin 35° -cos 35°, 42., sin 55°, cos 55°, (A) 1, (B) 0, (C) -1, (D) 2, Wish You - All The Best, 4