Let `f(x)=(1+x)/(1-x)` . If `A` is matrix for which `A^3=O ,t h e nf(A)` is (a)`I+A+A^2` (b) `I+2A+2A^2` (c) `I-A-A^2` (d) none of these

Let f(x)=(1+2x)(1+2x+4x^(2)+8x^(3)+...oo) If A is a matrix for which A^(3)=0, then f(A) equals (I is identity matrix of order equivalent to order of A).

If for the matrix A ,\ A^3=I , then A^(-1)= A^2 (b) A^3 (c) A (d) none of these

If A^(3)=O, then I+A+A^(2) equals I-A b.(I+A^(1))=^(-1) c.(I-A)^(-1) d.none of these

If f(x)="cos"((log)_e x),t h e nf(x)f(y)-1/2[f(x/y)+f(x y)] has value (a) -1 (b) 1/2 (c) -2 (d) none of these

Let f(x)=max. {2-x,2,1+x} then int_(-1)^1 f(x)dx= (A) 0 (B) 2 (C) 9/2 (D) none of these

Let A be a 3x3 matrix such that |A|=-2, then det(-2A^(-1))=-4 (b) 4(c)8(d) none of these

If f(x)= e^(coscos^-1x^2+tancot^-1 x^2), then minimum value of f(x) is (A) e (B) e^2 (C) e^(2/3 (D) none of these

f(x)=(1n(x^2+e^x))/(1n(x^4+e^(2x)))dotT h e n lim_(x->oo)f(x) is equal to (a) 1 (b) 1/2 (c) 2 (d) none of these

If B is an idempotent matrix,and A=I-B then a.A^(2)=A b.A^(2)=I c.AB=O d.BA=O

Let A=[1 2 3-5] and B=[1 0 0 2] and X be a matrix such that A=B X , then X is equal to 1/2[2 4 3-5] (b) 1/2[-2 4 3 5] (c) [2 4 3-5] (d) none of these