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

("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 f(x)=0 is a quadratic equation such that f(-pi)=f(pi)=0 and f(pi/2)=-(3pi^2)/4, then lim_(x->-pi)(f(x))/("sin"(sinx) is equal to (a) 0 (b) pi (c) 2pi (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

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

The value of integral int_0^(1/sqrt3) (dx)/((1+x^2)sqrt(1-x^2)) must be (a) 3+2pi (b) 4-pi (c) 2+pi (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)_(xrarr0)(sin(picos^2x)/(x^2)) is equal to (a) -pi (b) pi (c) pi/2 (d) 1

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"

If x_1=2tan^(-1)((1+x)/(1-x)),x_2=sin^(-1)((1-x^2)/(1+x^2)) , where x in (0,1), then x_1+x_2 is equal to 0 (b) 2pi (c) pi (d) none of these

("lim")_(xvec0)1/xcos^(-1)((1-x^2)/(1+x^2)) is equal to (a)1 (b) 0 (c) 2 (d) none of these