If `Aa n dB` are two non-singular matrices such that `A B=C ,t h e n|B|` is equal to `(|C|)/(|A|)` b. `(|A|)/(|C|)` c. `|C|` d. none of these

if Aa n dB are squares matrices such that A^(2006)=Oa n dA B=A+B ,t h e n"det"(B) equals 0 b. 1 c. -1 d. none of these

If Aa n dB are two matrices such that A B=Ba n dB A=A ,t h e n (A^5-B^5)^3=A-B b. (A^5-B^5)^3=A^3-B^3 c. A-B is idempotent d. none of these

If Aa n dB are symmetric matrices of the same order and X=A B+B Aa n dY=A B-B A ,t h e n(X Y)^T is equal to X Y b. Y X c. -Y X d. none of these

If Aa n dB are two non-singular matrices of the same order such that B^r=I , for some positive integer r >1,t h e nA^(-1)B^(r-1)A=A^(-1)B^(-1)A= I b. 2I c. O d. -I

In triangle A B C ,/_A=30^0,H is the orthocenter and D is the midpoint of B Cdot Segment H D is produced to T such that H D=D Tdot The length A T is equal to a. 2B C b. 3B C c. 4/2B C d. none of these

If Aa n dB are two events such that P(A)>0a n d P(B)!=1, t h e nP( barA / barB ) is equal to (Here barAa n d barB are complements of Aa n dB , respectively. (a) 1-p(A/B) (b). 1-p(( barA )/B) (c). (1-p(AuuB))/(P( barB )) (d). (P( barA ))/(P(B))

If A=[a b c d] (where b c!=0 ) satisfies the equations x^2+k=0,t h e n a+d=0 b. K=-|A| c. k=|A| d. none of these

If Aa n dB are symmetric and commute, then which of the following is/are symmetric? A^(-1)B b. A B^(-1) c. A^(-1)B^(-1) d. none of these

In triangle A B C , if sinAcosB=1/4 and 3t a n A=t a n B ,t h e ncot^2A is equal to (a)2 (b) 3 (c) 4 (d) 5.

If A is non-singular and (A-2I)(A-4I)=O ,t h e n1/6A+4/3A^(-1) is equal to O I b. 2I c. 6I d. I