The function `(sin(x+a))/(sin(x+b))` has no maxima or minima if (a) `b-a=npi,n in I` (b) `b-a=(2n+1)pi,n in I` (c) `b-a=2npi,n in I` (d) none of these

The straight line xcostheta+ysintheta=2 will touch the circle x^2+y^2-2x=0 if (a) theta=npi,n in I Q (b) A=(2n+1)pi,n in I (c) theta=2npi,n in I (d) none of these

The domain of the function f(x)=1/(sqrt({sinx}+{sin(pi+x)})) where {dot} denotes the fractional part, is (a) [0,pi] (b) (2n+1)pi/2, n in Z (c) (0,pi) (d) none of these

The general solution of cosxcos6x=-1 is x=(2n+1)pi,n in Z x=2npi,n in Z x=npi,n in Z (d) none of these

Which of the following set of values of x satisfies the equation 2^(2sin^2x-3sinx+1)+2^(2-2sin^2x+3sinx)=9? (a) x=npi+-pi/6,n in I (b) x=npi+-pi/3, n in I (c) x=npi,n in I (d) x=2npi+pi/2,n in I

Which of the following is not the general solution of 2^(cos2x)+1=3. 2^-sin^(2x)? (a) npi,n in Z (b) (n+1/2)pi,n in Z (n-1/2)pi,n in Z (d) none of these

Which of the following is true for z=(3+2isintheta)(1-2sintheta)w h e r ei=sqrt(-1) ? (a) z is purely real for theta=npi+-pi/3,n in Z (b)z is purely imaginary for theta=npi+-pi/2,n in Z (c) z is purely real for theta=npi,n in Z (d) none of these

If cot^(-1)n/pi>pi/6,n in N , then the maximum value of n is 6 (b) 7 (c) 5 (d) none of these

The general solution of the equation sin^(100)x-cos^(100)x=1 is 2npi+pi/3,n in I (b) n pi+pi/2,n in I npi+pi/4,n in I (d) 2npi=pi/3,n in I

The value of int_0^pi (sin(1+1/2)x)/(sin (x/2)) dx is, (a) n in I, n >= 0 pi/2 (b) 0 (c) pi (d) 2pi

The domain of the function f(x)=sqrt(log(1/(|sinx|))) (a) R-{-pi,pi} (b) R-{npi|npiZ} (c) R-{2npi|n in z} (d) (-oo,oo)