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 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

If f^(prime)(x)=sqrt(2x^2-1)a n dy=f(x^2),t h e n(dy)/(dx)a tx=1 is 2 (b) 1 (c) -2 (d) none of these

If A=[1 2 2 1]a n df(x)=(1+x)/(1-x),t h e nf(A) is [1 1 1 1] b. [2 2 2 2] c. 1-1-1-1 d. none of these

If y=tan^(-1)((2^x)/(1+2^(2x+1))),t h e n(dy)/(dx)a tx=0 is (a)1 (b) 2 (c) 1n 2 (d) none of these

If f(x) is a polynomial satisfying f(x)f(1/x)=f(x)+f(1/x)a n df(3)=28 ,t h e nf(4) is equal to 63 (b) 65 (c) 17 (d) none of these

If af(x+1)+bf(1/(x+1))=x ,x!=-1,a!=b ,t h e nf(2) is equal to (a) (2a+b)/(2(a^2-b^2)) (b) a/(a^2-b^2) (c) (a+2b)/(a^2-b^2) (d) none of these

If (x^2+p x+1) is a factor of (a x^3+b x+c),t h e n a. a^2+c^2=-a b b. a^2-c^2=-a b c. a^2-c^2=a b d. none of these

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 f(x)=|[a,-1, 0],[a x, a,-1],[a x^2,a x, a]|,t h e nf(2x)-f(x) is divisible by (a) a (b) b (c) c ,d ,e (d) none of these

("lim")_(x->oo){(x^3+1)/(x^2+1)-(a x+b)}=2,t h e n (a) a=1,b=1 (b) a=1,b=2 (c) a=1,b=-2 (d) none of these