If a polygon of $n$ sides has $275$ diagonals,then $n$ is equal to

Three non-zero non-collinear vectors $\vec{a}, \vec{b}$ and $\vec{c}$ are such that $\vec{a}+3\vec{b}$ is collinear with $\vec{c}$,and $3\vec{b}+2\vec{c}$ is collinear with $\vec{a}$. Then $\vec{a}+3\vec{b}+2\vec{c}$ equals to

$f(x) = (20 - x^4)^{1/4}$ for $0 < x < \sqrt{5}$,then $f(f(1/2))$ is equal to

The square of the difference of the slopes of the lines represented by the equation $x^2(\sec^2 \theta - \sin^2 \theta) - 2xy \tan \theta + y^2 \sin^2 \theta = 0$ is:

Verdigris is

Two pendulums have time periods $T$ and $5T/4$. They start $SHM$ at the same time from the mean position. After how many oscillations of the smaller pendulum will they be again in the same phase?