If `A^3=O ,t h e nI+A+A^2` equals a.`I-A` b. `(I+A^1)^(-1)` c. `(I-A)^(-1)` d. none of these

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

If tan^2theta=2tan^2phi+1,t h e ncos2theta+sin^2phi equals (a) -1 (b) 0 (c) 1 (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 Z is an idempotent matrix, then (I+Z)^n I+2^n Z b. I+(2^n-1)Z c. I-(2^n-1)Z d. none of these

If A^(3)=O , then prove that (I-A)^(-1) =I+A+A^(2) .

If f(1)=3,f^(prime)(1)=2,f''(1)=4,t h e n f^(-1)(3)= a. 1 b. -1/2 c. -2 d. none of these

If b_(n+1)=1/(1-b_n)forngeq1a n db_1=b_3, t h e nsum_(r=1)^(2001)b r^ 2001 is equal to 2001 b. -2001 c. 0 d. none of these

If z(1+a)=b+i ca n da^2+b^2+c^2=1, then [(1+i z)//(1-i z)= A. (a+i b)/(1+c) B. (b-i c)/(1+a) C. (a+i c)/(1+b) D. none of these

If tan^(-1)(a+x)/a+tan^(-1)(a-x)/a=pi/6,t h e nx^2= (a) 2sqrt(3)a (b) sqrt(3)a (c) 2sqrt(3)a^2 (d) none of these

If k in R_ot h e ndet{a d j(k I_n)} is equal to K^(n-1) b. K^(n(n-1)) c. K^n d. k