`sintheta+sqrt(3)costheta=6x-x^2-11 ,0lt=thetalt=4pi,x in R ,` (a) hold for no values of `x and theta` (b) one value of `x` and two values of `theta` (c) two values of `x` and two values of `theta` (d) two point of values of `(x ,theta)`

Minimum value of cos2theta+costheta for all real value of theta is

If sin theta =sqrt(3) cos theta, -pi lt theta lt 0 , then the value of theta is

Find the values of p if it satisfy, cos theta = x + p/x, x in R for all real values of theta .

If f(x)=3^x+4^x+5^x-6^x, then f(x)ltf(3) for (A) only one value of x (B) no value of x (C) only two value of x (D) infinitely many value of x

Equation 1+x^2+2x"sin"(cos^(-1)y)=0 is satisfied by exactly one value of x exactly two value of x exactly one value of y exactly two value of y

The maximum values of 3 costheta+5sin(theta-(pi)/(6)) for any real value of theta is:

If x=cos^2theta+sin^4theta then for all real values of theta

If the equation (lamda-1)x^2+(lamda+1)x+lamda-1=0 has real roots then lamda= (sintheta)/(costheta).(cos3theta)/(sin3theta) for (A) only one value of theta (B) for infinitely many values of theta (C) for no value of theta (D) of only two values of theta

Find maximum and minium value of 5costheta+3sintheta(theta+pi/6) for all real values of theta .

If hat u and hat v are unit vectors and theta is the acute angle between them, then 2 hat uxx3 hat v is a unit vector for (1) exactly two values of theta (2) more than two values of theta (3) no value of theta (4) exactly one value of theta