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

Which of the following is not the general solution of 2^(cos2x)+1=3. 2^(-sin^2 x)? (a) npi,n in Z (b) (n+1/2)pi,n in Z (c) (n-1/2)pi,n in Z (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

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

Consider the system of linear equations in x , ya n dz : ""(sin3theta)x-y+z=0 , (cos2theta)x+4y+3z=0 , 2x+7y+7z=0 Which of the following can be the value of theta for which the system has a non-trivial solution (A) npi+(-1)^npi/6,AAn in Z (B) npi+(-1)^npi/3,AAn in Z (C) npi+(-1)^npi/9,AAn in Z (D)none of these

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

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

The set of values of x satisfying the equation sin3alpha=4sinalphasin(x+alpha)sin(x-alpha) is (a) npi+-pi/4,AAn in Z (b) npi+-pi/3,AAn in Z (c) npi+-pi/9,AAn in Z (d) npi+-pi/(12),AAn in Z

Let tanx-tan^2x >0 and |2sinx| (a) x > npi,n in Z (b) x > npi-pi/6,n in Z (c) x (d) x < npi+pi/6, n in Z

Consider the system linear equations in x ,y ,a n dz given by (sin3theta)x-y+z=0,(cos2theta)x+4y+3z=0,2x+7y+7z=0. the value of theta for which the system has a non-trivial solution : (A) theta = npi/2 (B) theta = (2n+1)pi/6 (C) theta = npi or npi + (-1)^n pi/6 (D) none of these