JEE Main 2018 — Trigonometry

If $\tan A$ and $\tan B$ are the roots of the quadratic equation, $3 x^2-10 x-25=0$ then the value of $3 \sin ^2(A+B)-10 \sin (A+B) \cdot \cos (A+B)-25 \cos ^2$ $(A+B)$ is

The number of solutions of $\sin 3 x=\cos 2 x$, in the interval $\left(\frac{\pi}{2}, \pi\right)$ is

If sum of all the solutions of the equation $8\mathrm{cos}x\cdot (\mathrm{cos}(\frac{\pi }{6}+x)\cdot \mathrm{cos}(\frac{\pi }{6}-x)-\frac{1}{2})=1$ in $[0, \pi ]$ is $k\pi$, then $k$ is equal to: