The number of solutions of the equation $\sin (9 x)+\sin (3 x)=0$ in the closed interval $[0,2 \pi]$ is
$7$
$13$
$19$
$25$
The number of values of $\alpha $ in $[0, 2\pi]$ for which $2\,{\sin ^3}\,\alpha - 7\,{\sin ^2}\,\alpha + 7\,\sin \,\alpha = 2$ , is
If the equation $\cos ^{4} \theta+\sin ^{4} \theta+\lambda=0$ has real solutions for $\theta,$ then $\lambda$ lies in the interval
The number of elements in the set $S =\left\{\theta \in[0,2 \pi]: 3 \cos ^4 \theta-5 \cos ^2 \theta-2 \sin ^2 \theta+2=0\right\}$ is $...........$.
The number of solution of the given equation $a\sin x + b\cos x = c$ , where $|c|\, > \,\sqrt {{a^2} + {b^2}} ,$ is
The number of distinct solutions of the equation $\frac{5}{4} \cos ^2 2 x+\cos ^4 x+\sin ^4 x+\cos ^6 x+\sin ^6 x=2$ in the interval $[0,2 \pi]$ is