Let $f(\theta ) = \sin \theta (\sin \theta + \sin 3\theta )$, then $f(\theta )$
$ \ge 0$ only when $\theta \ge 0$
$ \le 0$ for all real $\theta $
$ \ge 0$ for all real $\theta $
$ \le 0$ only when $\theta \le 0$
The domain of the function $f(x)=\frac{1}{\sqrt{[x]^2-3[x]-10}}$ is (where $[x]$ denotes the greatest integer less than or equal to $x$ )
If $x \in [0, 1]$, then the number of solution $(s)$ of the equation $2[cos^{-1}x] + 6[sgn(sinx)] = 3$ is (where $[.]$ denotes greatest integer function and sgn $(x)$ denotes signum function of $x$)-
If the domain of the function $f(x)=\log _e\left(4 x^2+11 x+6\right)+\sin ^{-1}$ $(4 x+3)+\cos ^{-1}\left(\frac{10 x+6}{3}\right) \text { is }(\alpha, \beta]$ Then $36|\alpha+\beta|$ is equal to :
If $y = f(x) = \frac{{ax + b}}{{cx - a}}$, then $x$ is equal to