The number of solutions of the equation $4 \sin ^2 x-4$ $\cos ^3 \mathrm{x}+9-4 \cos \mathrm{x}=0 ; \mathrm{x} \in[-2 \pi, 2 \pi]$ is :

  • [JEE MAIN 2024]
  • A

    $1$

  • B

    $3$

  • C

    $2$

  • D

    $0$

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Let $A = \left\{ {\theta \,:\,\sin \,\left( \theta  \right) = \tan \,\left( \theta  \right)} \right\}$ and $B = \left\{ {\theta \,:\,\cos \,\left( \theta  \right) = 1} \right\}$ be two sets. Then

  • [JEE MAIN 2013]

The number of solution of the equation,$\sum\limits_{r = 1}^5 {\cos (r\,x)} $ $= 0$ lying in $(0, \pi)$ is :

The number of points in $(-\infty, \infty)$, for which $x^2-x \sin x-\cos x=0$, is

  • [IIT 2013]

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If $m$ and $n$ respectively are the numbers of positive and negative value of $\theta$ in the interval $[-\pi, \pi]$ that satisfy the equation $\cos 2 \theta \cos \frac{\theta}{2}=\cos 3 \theta \cos \frac{9 \theta}{2}$, then $mn$ is equal to $.............$.

  • [JEE MAIN 2023]