The number of integral value $(s)$ of $'p'$ for which the equation $99\cos 2\theta - 20\sin 2\theta = 20p + 35$ , will have a solution is
$8$
$9$
$10$
$11$
The equation $\sin x + \cos x = 2$has
If $K = sin^6x + cos^6x$, then $K$ belongs to the interval
If $5{\cos ^2}\theta + 7{\sin ^2}\theta - 6 = 0$, then the general value of $\theta $ is
If ${\sin ^2}\theta = \frac{1}{4},$ then the most general value of $\theta $ is
If $\sqrt 3 \tan 2\theta + \sqrt 3 \tan 3\theta + \tan 2\theta \tan 3\theta = 1$, then the general value of $\theta $ is