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

$A$ vertical pole subtends an angle $\tan ^{-1}\left(\frac{1}{2}\right)$ at a point $P$ on the ground. If the angles subtended by the upper half and the lower half of the pole at $P$ are respectively $\alpha$ and $\beta$,then $(\tan \alpha, \tan \beta)$ is equal to

The normal at a point on the parabola $y^2=4x$ passes through $(5,0)$. If two more normals to this parabola also pass through $(5,0)$,then the centroid of the triangle formed by the feet of these three normals is

The lowest $O-O$ bond length in the following molecules is:

The osmotic pressure of a $5\% \, w/v$ solution of cane sugar at $150 \, ^\circ C$ is ......... $atm$.

Three liquids of densities $\rho_1, \rho_2$ and $\rho_3$ (with $\rho_1 > \rho_2 > \rho_3$) having same value of surface tension $T$,rise to the same height in three identical capillaries. Angle of contact $\theta_1, \theta_2$ and $\theta_3$ respectively obey