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MULTIPLE CHOICE QUESTIONS®, , Choose and write the correct option in the following questions., , 10., , 11., , , , , , , , , , , , , , , , , , If A= K 7 , then A*is equal to (NCERT Exemplar], 01 10 01 10, ho ® i 0 «) ( | o c |, 1a [OOF ~ HPO! en At A’nl, if the value of a te (NCERT], sing cosa@, @ = w > (x w =, If A and B are square matrices of the same order, then (A + B)(A - B) is equal to, (a) A?-B? (b) A?-BA-AB-B? = (c) A?-B? + BA-AB (d) A?-BA+B*+ AB, Total number of possible matrices of order 3 x 3 with each entry 2 or 0 is, (a) 9 (b) 27 () 81 (a) 512, 0-5 8, The matrix | 5 0 12/ isa INCERT Exemplar], -8 -12 0, (a) diagonal matrix (b) symmetric matrix, (c) skew symmetric matrix (d) scalar matrix, , Assume X, Y, Z, W and P are matrices of order 2 x n,3 x k, 2 x p, 1 x 3 and p x k respectively., Choose the correct option in (6) and (7), , The restriction on n, k and p so that PY + WY will be defined are, , , , , , , , (a) k=3,p=n (b) kis arbitrary, p = 2, (c) pis arbitrary, k =3 (d) k=2,p=3, If n = p, then the order of the matrix 7X — 5Z is, (a) px2 (b)2xn (ec) nx3 (d) pxn, 2x+y 4x]_[7 7y-13 , ., If su axl” iy =€e , then the value of x and y is INCERT Exemplar], (a) x=3,y=1 (b) x=2y=3 (c) x=2,y=4 (@) x=3,y=3, , If A is matrix of order m x n and B is a matrix such that AB’ and B’A are both defined, the order, of matrix B is, , (a) mxm (b) nxn (ec) nxm (d) mxn, If A and B are matrices of same order, then (AB’ — BA’) is a [NCERT Exemplar], (a) skew-symmetric matrix (b) null matrix, (c) symmetric matrix (d) unit matrix, IfA= (¢ B | . such that A? =I, then, Y -«, , , , (a) 1+a?+By=0 (b) 1-0? +By=0 (c) 1-a?-By=0 (d) 1+a°-By=0, , Scanned with CamScanner

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12., , 13., , 14,, , 15., , 16., , 17., , 18., , 19., , 21., , 22., , , , , , , , , , , , , , , , , , , , a, If A -|t ‘ then A" (where #¢N) equals, , na 1 wa 1 ma n na, |p "| |," Jo 0 Mion, If A is square matrix such that A? = I, then (A - 1) + (A + 1) -7A is equal to, , INCERT Exemplar|, , (a) A (b) I-A (c) I+A (d) 3A, If the matrix AB is zero, then, (a) Itis not necessary that either A = O or B=O, (b) A=OorB=O0, (c) A=OandB=O0 (d) All the statements are wrong, , 2 <1 3 2 3, IfA= | and B=|4 -2|, then (NCERT Exemplar}, , 45 1 15, (a) only AB is defined (b) only BA is defined, (c) AB and BA both are defined (d) AB and BA both are not defined., , 0 5 -7, The matrix |-5 0 I1/is INCERT Exemplar], 7 -11 0, , (a) a skew-symmetric matrix (6) asymmetric matrix, (c) a diagonal matrix (@) an upper triangular matrix., If A and B are two matrices of the order 3 x m and 3 x n respectively and m = 1, then the order, , of matrix (5A - 2B) is, , (a) mx3 (b) 3x3 (c) mxn (4) 3xn, IfA= [? ‘| and A=A’, then INCERT Exemplar], (a) x=0,y=5 (b) r+ y=5 (c)x=y (d) none of these, , If A -(3 HI then A’ is, , s {Pal P a), (a) [F ‘| |? Nort |? (d) none of these, 0 1 0, , cos*8 cos OsinO, , The product of the matrix A = cosOsin®@ sin?@, , , , , , d e-| cos*> = cos sind, cospsing sin’, null matrix if 8- equal to, , (@) (n+) (0) nx (c) 2nn (a) n¥, If P and Q are symmetric matrix of same order then PQ- QP isa, , (a) Zero matrix (b) Identity matrix, , (c) Skew Symmetric matrix (d) Symmetric matrix, , Which of the given values of x and y make the following pair of matrix equal, , Scanned with CamScanner

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24., , 2s., , 26., , 27., , 28., , 29., , 31., , 32., , 33., , 34., , , , 3x47 5 ||. rt, , y+1 2-3x]'|8 4, , @) x=-4,y=7 (b) cannot be determined, 2 1 2, , () x=-F,y=7 (4) x=-Z,y=-F, , The number of all possible matrices of order 3 x 3 with each entry 0 or 1 is, (a) 27 (b) 18 (c) 81 (d) 512, , If matrix A= laily.a where a, = 1, if i # jand a= 0, if i= j, then A’ is equal to, (a) I (b) A (c) 0 (d) None of these, If A= : is such that A* = / (identity matrix) then, , , , , , (a) 1+a?+By=0 (b) 1-a?+By=0 (c) 1-a?-By=0 (a) 1+a*-By=0, , , , , , , , If the matrix A is both symmetric and skew symmetric, then, (a) Ais diagonal matrix. (b) A is zero matrix., (c) Ais square matrix. (d) None of these, If A is square matrix such that A? = A then (I + A)’ =7A is equal to, (a) A (b) -A (cl (d) 3A, A matrix A= [asl , is said to be symmetric if, (a) a= 0 (b) Ay = = a5 (c) ai = a5, (d) ag=1, A matrix A = [a,)], ., is said to be skew symmetric if, (a) a,=0 (0) ay =— ay (c) ay =a, (4) ay=1, 132, If A=|1 1 1] then A*is, 22, (a) 27A (b) 2A (c) 3A (a) 1, If A -[ plana 8 =[3 ‘I then A? = Bis true, (a) fora=-4 (b) fora=4 (c) fora =1 (d) for no value of a, If A and B are two matrices such that AB = B and BA = A, then A? + B? =, (2) 2BA (b) 2AB () A+B (d) AB, 1 |sin" Gx) tan? = 1 |-cos (xz) tant, IfA=> si B=— then A - B is equal to, - 3 -1 n - 3 X +1, sin” = cot” 7x sa" O- tan™ xx, @1 ® 0 (© 21 @ 41, ado, Let A=|0 a 0} then A* is equal to, 00a, 4a 0 0 aoo0 0 0 a a’ at at, (a) |0 4a 0 (v) |0 at O () ]0 at oO (a4) }0 a 0, 0 0 4a 0 0 at ao 0 00a, , , , , , , , , , , , , , , , , , Scanned with CamScanner

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35., , 37., , 39,, , 41., , , , , , , , , , , , , , , , , , , , , , , , , , , , 217, If A=|1 1 1} then Atis, aia, 444 ttt 27 27 27 15 15 15, (a) |444 (by) j111 (c) 27 27 27) (d) 15 15 15, 444 111 27 27 27 15 15 15, _| cosa sing !, Ae) ing =e then A'A is, oo 11 10, (a) 0 al (b) i i| (c) + (d) None of these, v1, If A= 4 & then A’ is equal to, "2 2, 3¥3 1, 2 28 10, (a) 1 3 3 (b) ke al (c) i ‘| (d) None of these, “3 8, 0 — r, If A= 0 and A =A’ then () is equal to, @ = & OF @ F, 010, If A=|0 0 1)then A*-rA?-gA is equal to, rer, (a) pl (b) qi (c) rl (d) None of these, , wef feels ne, , (a) Acos§+Bsin8, (c) Asin@+Bcos6, , , , cos sin@, -sin® cos8, , | then C is equal to, , (b) Acos@-Bsin 6, (d) -Acos6+Bsin8, , If A and B are symmetric matrices, then ABA is, , (a) symmetric matrix, , (c) diagonal matrix, , 13 14, 2 s}e-[3 3} ten, , (a) A™B™ =(AB)", , Let A=, , , , 1-3, Let A= 2s and B=|2 1 |then, -314 3 4, , , , , , (a) Only AB is defined, (c) Both (a) and (b), , (b) BTAT = (AB)", , (b) skew-symmetric matrix, (d) scalar matrix, , (c) (BA)" = BTAT (d) None of these, , (b) Only BA is defined, (d) None of these, , Scanned with CamScanner

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45., , 47., , 49., , , , a2, If A=] 4 {=u 3 -6], then, 5, (a) (AB)'=B'A™ —(b) (AB)" = A™BT (c) AB=BA (d) None of these, , 23, a[2 a] nen, , (a) O(a’) =2x2 (b) O(a’) =4x4 (c) O(a") =9x9 (d) None of these, Let A be a square matrix, then, , (a) (A+ A?) is a symmetric matrix (b) (A + A!) is a skew symmetric matrix, , (c) (A+ A’) is not a square matrix. (d) None of these, , If A be a square matrix, such that, , (A-All=Al-(A)=A'-A, , (a) A-A’ is asymmetric matrix (b) A-A’ is a skew symmetric matrix, (c) A-Al is not a square matrix (d) None of these, , Let A is a diagonal matrix, then, , aoo 100, , 0aod 020, 00a 003, , A= and B=, , , , , , , , , , _ |jafori=j, «) 7 { bani,, , 6 _ |aor different real number fori =j, »4" Ofori #j, (c) a,= {* “ ae i a, \ are real number., (d) None of these, If A is a null matrix then, (a) Aisa square matrix (b) A is not a square matrix, (c) both (a) and (b) (d) None of these, If A is a scalar matrix, if, * Oifi¥j 7 _[k ifi#j keR, (a) A=[aj), where a; |i i¢ i= jforkeR. ©) A= lide =| 9 i¢ i=;, , (c) A= [a], where a, = kVij (d) None of these, , Scanned with CamScanner