Minimum value of $5 \sin^2 \theta + 4 \cos^2 \theta$ is

If $\cos A = \frac{\sqrt{3}}{2},$ then $\tan 3A = $

If $\tan (A-B) = \frac{7}{24}$ and $\tan A = \frac{4}{3}$,where $A$ and $B$ are acute,then $A+B = $

Let $f(x) = \max (\sin x, \cos x)$ and $g(x) = \min (\cos x, \sin x)$. If the equation $f(x)y^2 + ay + g(x) = 0$ has real roots for all $x \in R$,then the complete set of values of $a$ is:

The angle of elevation of the top of a tower is $30^{\circ}$. On walking $100 \ m$ towards the tower,the angle of elevation of the top of the tower becomes $60^{\circ}$. Find the height of the tower (in $m$).

If $\alpha, \beta, \gamma$ are positive numbers such that $\alpha + \beta = \pi$ and $\beta + \gamma = \alpha$,then $\tan \alpha$ is equal to - (where $\gamma \neq n\pi, n \in I$)