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

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

Area enclosed by the curve (y-sin^(-1)x)^(2)=x-x^(2), is (A) (pi)/(2) sq.units (B) (pi)/(4) sq.units (C) (pi)/(8) sq.units (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

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

If x,y in[0,2 pi] and sin x+sin y=2, then the value of x+y is pi(b)(pi)/(2)(c)3 pi(d) none of these

The value of c in Lagranges theorem for the function f(x)=log sin x in the interval [(pi)/(6),(5 pi)/(6)] is (pi)/(4) (b) (pi)/(2)(2 pi)/(3) (d) none of these

The principal value of sin^(-1)(sin((2 pi)/(3))) is (a)-(2 pi)/(3) (b) (2 pi)/(3) (c) (4 pi)/(3) (d) (5 pi)/(3) (e) none of these

int_(0)^(oo)(xdx)/((1+x)(1+x^(2))) is equal to (A)(pi)/(4) (B) (pi)/(2)(C)pi(D) none of thesel

int_-1^1 sin^-1(x/(1+x^2))dx= (A) pi/4 (B) pi/2 (C) pi (D) 0