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Choose the most appropriate option (a, b, c ord)., , 1-2 4, , 1. IfA =2, , -2, , 3 2 and B=, , L3, , 1, , -1, , 1 5, , 41, , 3 2 then A+B is, , 15, , 1-2 41, , (a) 3, , 1-4, , c), , 10J, , 87, (d) none of these, , 2 10J, 10, , If A=8A +kl where A_17, (a) 7, , then k, , (b) -7, , 7, , -2, , 3. The matrix4, , 1, , L2, , -1, , 3, 2, , (a), , d, , a) a b 2, C, , (c) nonexistent, , is, (d) -1, , (c) 1, , if A is, is a singular matrix, , (b), , i t the matrix A =, , a), , 1, , L2, , 6, , L2, 2., , () 3 3 4, , 3 2, 1 5, , L2, , 8, , f1-2, , (d), , (c)-5, , then A*is, a+bc ab + bd, (b) ac +de be +d, (d), , none, , of, , ünese, , none, , of these

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If, 5. If Aaand B=, A1 1, , such that A' =Bthen a is, , (a) 1, , (b) -1, , (c)4, , (d) none of these, , (a) A=3, u =4, (b) A= 4, u = -3, , (c), , real values of , u, (d) none of these, no, , are, , possible, , cos 6 sine, , 7. If AB =0 where A =COS8, cos 6 sin, and B = |, , cos, , Cos, , cos o sin ¢, , sin then 10-ol, sino, , (a) 0, , b), , (c), , (d) T, , 0-4, , 8. If A =| 2, , L1, , 9., , sin e, , 11, , -3 then A, , is equal, , to, , exists (i.e., A is invertible) if, , 2 -1, , (a) A4, , b) A#8, , (c)=4, , (d) none of these, , 10, , The reciprocal matrix of 0, , 1, , 21, , -1is, , l1 2 1, -3-4, , 2, , (a)-1 1 -1, L12 -1, -3-1, , (c)4 1, , 3, , (b), , 1, , 4-2, -1, , 1, , -1-2 1, , 1, , 2, , 2-1 -1, , (d), , none, , of these

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-1, , 11, 0 then the value of, , 2, , 12.ifA=1, , ladj Al, , is, , equalto, , 3 0, , (a) 5, , b) 0, , (c) 1, , (d) none of these, , Sin a - c o Sd, , 11. A, , sin a, , COs, , 0, 0, , then A, , is, , equal to, , 0, , 0, , (a) A, , (b) A, , (c) adjA, , (d) none of these, , 4 -141, 12 IfA= 3, , 0, , then A is equal to, , L3-1-3, a) A, , (b)I, , (c) AT, , (d) none of these, , COSX-sin x 0, 13., , Iffx), , sin, , =, , x, , cos x, , 0, , 0, , 0, 1, , thenf(x + y) is equal to, , (a) fix)+fy), , b) fx)-fy), , (c) fix) fy), , (d) none of these, , 1, 14., , If, , A, , =o, , B=, , 1, 2, , 1, , 4, , 1, , oo, , and C=| o, , o, , 1, , where a is the, 2, , Complex cube root of 1 then (A + B)C is equal to, , 01, , [10 0, , (a) 0, , (b)|0 1 0, , 0J, , LO0 1, , 1, , (c) 0, 1, , 15. 1f* " *, A, , C-b, , --c, b, , (a) 0, (c) 21, , 0, , a, , -a, , 0, , aab, ac, ba, bbe, , and B=|, , ca, , cb, , t h e n ABi se q u a l to, , c, , (b)I, (d), , none, , of these

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16. If Abea matrix such that Ax, , 01,, , A, , (b4 2, , a), , ), , 2, , c, , (d) none of these, , 1, -5, , 3, , 17. The rank ofthematrix3, , 21, , 2-5 is, , 4 -1-3, (a) 3, , (b) 2, , (c)1, , (d) none of these, , 1, , 2 31, 2, , 18. The rank of the matrix| 1, , 4, , is 3 if, , 2-3 1, 8, , 18, , (a) à, , 11, , (d), , () -, , none, , of these, , 4 10 01, 1 0is, L53 00 0 1, , 19. The rank ofthe matrix|, , (d), , (c) 2, , (b) 3, , (a) 4, , none, , of these, , 20. The system of equations, X+y+z=2, , 2x-y+3z =5, x-2y-z+1 =0, written in matrix form is, , 1, , 1, , 11, (c)2 -1 3, 1, , 1, , 1|| 2, , (d), , none, , 1 1, , of these, , -2 -1JL:, 1, , 21., , f[1, , x, , 1 2, , =0 then xis, these, , n, , (a) 2, , (b) -2, , (c) 14, , (d), , o, , n, , of, , e

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+, , jthen, thenx y is equal to, , p2, , (b) 5, , (a)-5, , (d) 6, , (c) 4, , haose, , the correct optio1s. One or n1ore options may be correct., , f1-2 3, 23., , 2 -1 4 | is a, 3, , 4 1, (a) rectangular matrix, , (b) singular matrix, , (C)squarematrix, , (d) nonsingular matrix, , 3, , 5, , 1, , 4 6, , 24. If A=-1 2 and B=41 2, -5 -1 1, 0 6, , then, , (a) A+ B exists, , (b) AB exists, , (c) BA exists, , (d), , 25. If A=, , ii i, (a) A= 9A, (c) A+A = A, , none, , of these, , then, , (b) A=27A, , (d) A, , does not exist