`("lim")_(xvecoo)"{"x+5")"tan^(-1)(x+5)-(x+1)tan^(-1)(x+1)}` is equal to (a) `pi` (b) `2pi` (c) `pi/2` (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 (a) pi (b) pi/2 (c) 0 (d) none of these

lim_(x->1)(1-x^2)/(sin2pix) is equal to (a) 1/(2pi) (b) -1/pi (c) (-2)/pi (d) none of these

int_0^oo(x dx)/((1+x)(1+x^2)) is equal to (A) pi/4 (B) pi/2 (C) pi (D) none of these"

(lim)_(xrarr0)(sin(picos^2x)/(x^2)) is equal to (a) -pi (b) pi (c) pi/2 (d) 1

tan(pi/4+1/2cos^(-1)x)+tan(pi/4-1/2cos^(-1)x),x!=0, is equal to x (b) 2x (c) 2/x (d) none of these

int_0^oo(pi/(1+pi^2x^2)-1/(1+x^2))logxdx is equal to (a) -pi/2lnpi (b) 0 (c) pi/2ln2 (d) none of these

lim_(xvecoo)((x^2+2x-1)/(2x^2-3x-2))^((2x+1)/(2x-1)) is equal to (a) 0 (b) oo (c) 1/2 (d) none of these

lim_(x->oo) (e^(1/x^2)-1)/(2tan^-1(x^2)-pi) is equal to (a) 1 (b) -1 (c) 1/2 (d) -1/2

tan^(-1)(x/y)-tan^(-1)((x-y)/(x+y)) is (A) pi/2 (B) pi/3 (C) pi/4 (D) pi/4 or (3pi)/4

The value of 2tan^(-1)(cos e ctan^(-1)x-tancot^(-1)x) is equal to (a) cot^(-1)x (b) cot^(-1)1/x (c) tan^(-1)x (d) none of these