If `x , y in [0,2pi]a n dsinx+siny=2,` then the value of `x+y` is `pi` (b) `pi/2` (c) `3pi` (d) none of these

If x, y in [0, 2pi] and sin x + sin y=2 , then the value of x+y is

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

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

Let alphaa n dbeta be any two positive values of x for which 2cosx ,|cosx|, and 1-3cos^2x are in G.P. The minimum value of |alpha-beta| is pi/3 (b) pi/4 (c) pi/2 (d) none of these

If f(x)=sin^(-1)cosx , then the value of f(10)+f^(prime)(10) is (a) 11-(7pi)/2 (b) (7pi)/2-11 (c) (5pi)/2-11 (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"

If 0lt=xlt=2pia n d|cosx|lt=sinx , then then (a) set of all values of x is [pi/4,(3pi)/4] (b) the number of solutions that are integral nultiple of pi/4 is one (c) the number of the largest and the smallest solution is pi (d) the set of all values of x is x in [pi/4,pi/2]uu[pi/2,(3pi)/4]

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

If f(x) satisfies the relation f((5x-3y)/2)=(5f(x)-3f(y))/2AAx ,y in R , and f(0)=3a n df^(prime)(0)=2, then the period of "sin"(f(x)) is (a) 2pi (b) pi (c) 3pi (d) 4pi

If lim_(x->0)[1+x1n(1+b^2)]^(1/x)=2bsin^2theta,b >0 ,where theta in (-pi,pi], then the value of theta is (a) +-pi/4 (b) +-pi/3 (c) +-pi/6 (d) +-pi/2