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 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

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

If the line xcostheta+ysintheta=P is the normal to the curve (x+a)y=1, then show theta in (2npi+pi/2,(2n+1)pi)uu(2npi+(3pi)/2,(2n+2)pi),n in Z

If the straight line lx+my+n=0 touches the : circle x^(2)+y^(2)=a^(2) , show that a^(2)(l^(2)+m^(2))=n^(2)

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

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

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 expression cos3theta+sin3theta+(2sin2theta-3)(sintheta-costheta) is positive for all theta in (a) (2npi-(3pi)/4,2npi+pi/4),n in Z (b) (2npi-pi/4,2npi+pi/6),n in Z (c) (2npi-pi/3,2npi+pi/3),n in Z (d) (2npi-pi/4,2npi+(3pi)/4),n in Z

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

The sum of all the solutions of cottheta=sin2theta(theta!=npi, n integer) , 0lt=thetalt=pi, is