If |z| < sqrt(2)-1,t h e n|z^2+2zcosalpha|i s a. less than 1 b. sqrt(2)+1 c. sqrt(2)-1 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 x^2+y^2+z^2=r^2,t h e ntan^(-1)((x y)/(z r))+tan^(-1)((y z)/(x r))+tan^(-1)((x z)/(y r)) is equal to pi (b) pi/2 (c) 0 (d) none of these

If y=cos^(-1)((5cosx-12sinx)/(13)),w h e r ex in (0,pi/2), then (dy)/(dx) is. (a)1 (b) -1 (c) 0 (d) none of these

I= int_(-pi)^(pi) (e^sinx)dx)/(e^sinx +e^(-sinx) then I equals

int_(-1)^2[([x])/(1+x^2)]dx ,w h e r e[dot] denotes the greater integer function, is equal to (a) -2 (b) -1 (c) 0 (d) none of these

Which of the following is true for z=(3+2isintheta)(1-2sintheta)w h e r ei=sqrt(-1) ? (a) z is purely real for theta=npi+-pi/3,n in Z (b)z is purely imaginary for theta=npi+-pi/2,n in Z (c) z is purely real for theta=npi,n in Z (d) none of these

int_(-pi/2)^(pi/2)(e^(|sinx|)cosx)/(1+e^(tanx))dx is equal to (a) e+1 (b) 1-e (c) e-1 (d) none of these

If int_1^2e^(x^2)dx=a ,t h e nint_e^(e^4)sqrt(1n x)dx is equal to (a) 2e^4-2e-a (b) 2e^4-e-a (c) 2e^4-e-2a (d) e^4-e-a

The domain of the function f(x)=x/(sqrt(sin(lnx)-cos(lnx))),(n in Z) is (a) (e^(2npi),e^((3n+1/2)pi)) (b) (e^((2n+1/4)pi),e^((2n+5/4)pi)) (c) (e^((2n+1/4)pi),e^((2n-3/4)pi)) (d) none of these