`2sin^2x+sin^2(2x)=2`, `-piltxltpi` `then x equals (A) ` `+- pi/2` (B) `+- pi/4` (C) `+-(3pi)/4` (D) none of these

If cos^2 2x+2cos^2x=1,\ x in (-pi,pi), then x can take the values : +-pi/2 (b) +-pi/4 +-(3pi)/4 (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"

sqrt(3)int_0^pi dx/(1+2sin^2x)= (A) -pi (B) 0 (C) pi (D) none of these

int_0^pi (sin((n+1)/2)x)/sinxdx= (A) 0 (B) pi/2 (C) pi (D) none of these

If a , b in [0,2pi] and the equation x^2+4+3sin(a x+b)-2x=0 has at least one solution, then the value of (a+b) can be (a) (7pi)/2 (b) (5pi)/2 (c) (9pi)/2 (d) none of these

If a , b in [0,2pi] and the equation x^2+4+3sin(a x+b)-2x=0 has at least one solution, then the value of (a+b) can be (7pi)/2 (b) (5pi)/2 (c) (9pi)/2 (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

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

int_1^(e^(17))(pi"sin"(pi(log)_e x))/x dx is equal to (A) 2 (B) -2 (C) 2//pi (D) none of these

The exhaustive set of values of a such that, x^2+a x+sin^(-1)(x^2-4x+5)+cos^(-1)(x^2-4x+5)=0 (A) {-2-pi/4} (B) {-oo,-2-pi/4} (C) {-oo,-2-pi/4} (D) none of these