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SHREE GURU GYAN TUTORIALS, Chapters:3, Std 12: MATHS, Date:14/02/22, Total Marks :43, PAPER 1 TEXT BOOK BASED MCQ, Time: 03Hour, Section A, Choose correct answer from the given options. [Each carries 1 Mark], [43], 3 1, If A =, 0 1, 1., then AA' is a, matrix., (A) Symmetric, (B) Skew symmetric, (C) Orthogonal, (D) None of these, O 2B, B, a -B, 2., If a matrix a, -Y is a orthogonal matrix then . ., Y, 1, (A) a = +, V2, 1, (B) B = ±, (C) Y = +, (D) Given all, 1 0 07, 3., If A = 0, 1 0, then A2 + 2A =, 0 0 1, (A) 4A, (В) ЗА, (C) 2A, (D) A, 2 -1, If A =, [2, a, B =, |b -1, 1, and (A + B)2 = A? + B2 + 2AB then . ., 4., 1, (A) a = 2, b = -2, (B) a = 2, b = 2, (C) a = -2, b 2, (D) a = -2, b = -2, [i 0, 5., If A =, ne N then A4" = .. ., (where i is imaginary complex number and 2 = -1), Го, (B), [1, (C), (A), (D), 3, 6., If U = [2 -3 4], V = | 2, X = [0 2 3] and Y = 2 then UV + XY =, 1, 4, (A) 20, (B) [-20], (C) -20, (D) [20], 7., If A is a square matrix then AA' is a .... matrix., (A) Skew symmetric, (B) Symmetric, (C) Diagonal, (D) Orthogonal, 8., For matrices A and B, A + B and AB are defined then. ., (A) A and B are any matrices, (B) A and B are square matrices but not necessary having equal order, (C) A and B are square matrices of some order, (D) No. of coloumn in A = No. of row in B., a, 9., If A = [a b], B [-b -a] and C =, then out of the following, .. . statement is true., -a, (A) A = -B, (B) A + B = A - B, (C) AC = BC, (D) CA = CB, [cosx -sinx], 10., If A(x) =, then A, |· A(n) =, sin x, cosx, 2, 3n, (A) A, (В) А, (C) A, 2, (D) A(- T), Wish You - All The Best, 1

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1 1, then A100, 1 1, 11., If A =, (A) 100 A, (B) 299 A, (C) 2100 A, (D) 99 A, -7, 12., Matrix -5, 11, is a, ....... matrix., 7, -11, (A) Skew symmetric, (B) Symmetric, (C) Diagonal, (D) Zero, 13., Out of the following which statement is false ?, (A) All the diagonal elements of a symmetric matrix are zero., (B) All the diagonal elements of a skew symmetric matrix are zero., (C) For any square matrix A,, (A + A') is a symmetric matrix., (D) For any square matrix A, (A - A') is a skew symmetric matrix., A matrix A has x rows and x + 5 column. A matrix B has y rows and 11 y column. If AB and BA, are exist then the value of x and y are respectively, 14., (A) 3, 9, (В) 8, 3, (C) 3, 8, (D) 4, 8, 2 3k, a, 1, 15., P =- -4kb If PP' = 1 and k = 50 then the value of a, b, c are respectively, * -5k, 16, (A) ±, 13, 1, 1, (В) 7, 3/2', 13, 16, 5/2, 5/2, 3/2, 5/2', 15/2, 13, (C) ±, 16, 1, (D) None of these, 15/2 15/2 * 3/2, 16., C is a skew symmetric matrix of order n. X is a column matrix of order n x 1. then X'CX is a. ., matrix., (A) Square, (B) Identity, (C) Zero, (D) None of these, 17., If A? = A then (I + A)4 =, (A) I + A, (B) I + 4A, (C) I + 15A, (D) None of these, 18., If AB = A and BA = B then A? + B2 =, (A) A + B, (B) - (А + B), (C) (2A + B), (D) (A + 2B), If A is any square matrix then AA' is a .., (A) Symmetric, 19., matrix., (B) Skew symmetric, (C) Identity, (D) Diagonal, If A and B are square matrices of same order then (A-BA)" =, (C) A-1 B" A, 20., ne N., (A) A-" B" A", (В) A" B" А-п, (D) n(A-1 BA), 0 1 2, -1, 21., If A =1 2 3 and A, -4, 3, then the value of a and c are respectively, %3D, 3, a 1, 2., (A) 1, 1, (В) 1, -1, (C) 1, 2, (D) -1, 1, -2, 22., 1, -а 5, then x =, a, 2a, 2а, 2a, (A), 125, (B), 25, (C), 125, (D), 25, Wish You - All The Best, 2

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1 3 2 1, 23., [1 x 1]0 5 1, 1, = 0 then x = .........., 0 3 2 x, -9 + 53, (C), (A) 1, (B) -1, (D) None of these, 24., A is a 3 x 4 matrix. A matrix B is such that A'B and BA' are defined. Then the order of B is .., (A) 3 x 4, (В) 3 х 3, (C) 4 x 4, (D) 4 x 3, 25., P is a 2 x 2 matrix. P = Pl then P =, cose, -sine], cose, sine, -cose, sine, (A), -sine, cose, (B), -sine cose, (C), sine, -cose, (D) None of these, 26., A is a 3x3 matrix, then |3A|, |AJ., ......, (A) 3, (B) 6, (C) 9, (D) 27, (ai + a) (n > 1), (C) a diagonal matrix, 27., If A = [aln x n such that, Aij, = 0, for i į then, A is, ....., (A) a column matrix, (B) a row matrix, (D) a scalar matrix, -1, -1, A =, -1, 28., the correct statement is .., (A) A-1 does not exist, (B) A = (-1)I3, (C) A2 = I, (D) A is a diagonal matrix., 29., If A is skew-symmetric 3 x 3 matrix, JA|, %3D, (A) 1, (B) 0, (C) -1, (D) 3, The system of equations ax + y + z a - 1, x+ ay + z a -1 and x + y + az a - 1 does not have, unique solution if a = .., 30., (A) 1 or -2, (B) 3, (C) 2, (D) -1, a b, 31., If A =, b a, and A2 =, Ly x, then, x =, y = ......, (A) x a2 + b2, y = a2 - b2, (B) x 2ab, y = a? + b2, %3D, (C) x = a? + b, y = ab, (D) x = a? + b², y = 2ab, cos?B, sinßcosß, cos?a, cosasina, If a and B are not the multiple of, and, cosa sin a, 32., %3D, sin?a, [sinßcosß sin?, then, a -, B is, (A) any multiple of n, (B) odd multiple of, (C) 0, 2, (D) odd multiple of n, 3 5, 6 3, -4, If, 1 у, 33., then, x = ......, y = ......, -3, 2 1, (A) x = 3, y = 2, (B) x = 3, y = -2, (C) x = -3, y = -2, (D) x = -3, y = 2, [1, If inverse of A = 2, 1, 4, 1, -5, 10, 1, 2, al then, a = ..., -1, 1, 34., 1, -3 is, 1, 1, -2, 3, (A) 5, (B) -5, (C) 2, (D) -2, 35., If AB = BA and A =, then, B = ...., x x, (A), х у, (C), (B), (D), [1 3], 36., If A =, and A? – kA - 51 = 0, then k = .., 3 4, Wish You - All The Best, 3

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(A) 3, (B) 7, (C) 5, (D) 9, 1, 3 2, 1, 37., If [1 x 1], 05, 1, 1, = 0, then x = ......, 03 2, -9 +35, (A), -7± 53, (B), -9t 53, (C), -7±35, (D), 2, 2, 2, 2, [0 2y, 38., Matrix A =x, y, -z if AAT = I then, (x, y, z) = (..., .., .) (x, y, z> 0), x -y, 1, (A), 1, 1, 1, (C), 1, 1, (D), 1, 1, 1, (B), 1, 1, J万, 2 6, V6' 2 3, -1, -8 -10, 1 -2 -5, If A, 3, 39., %3D, 1, -2, -5, then, A =, 4, 22, 15, -2, 2 -1, 1 0, 2 -1, (A), 0 -3 4, (C), -3, -1, (D), (B), 1, 1, 2 -3 4, -3, 4, 4, 2n, -sin, Cos, 3, 2n, sin, 3, 40., If A =, then, A3 =.., 2n, Cos, 3, (A), (B), (C), (D), [1, 1, 1, 1, 11, 2, 8, 2 5, -19 14 is an inverse of A =3 1 1, -5, 41., Check, whether,, if so, then a = ...., 6., 4 2 1, (A) -3, (B) 2, (C) -5, (D) does not exist, 2.x, If A =, -3 -2, 9., and JA| = 3 then x .. .,x e R., 42., (A) 7.5, (B) 6, (C) 15, (D) 12, 43., For A = [alnx p a = 0, i # j then is a .. matrix. (a # a;j), (n > 1), (A) Raw matrix, (B) column matrix, (C) Diagonal matrix, (D) Scalar matrix, Wish You - All The Best, 4