If in a regular polygon,the number of diagonals is $54$,then the number of sides of the polygon is:

If the points with position vectors $60 \hat{i}+3 \hat{j}$, $40 \hat{i}-8 \hat{j}$, and $a \hat{i}-52 \hat{j}$ are collinear, then $a$ is equal to

The equation $\sqrt{3} \sin x + \cos x = 4$ has

The energy $(E)$,angular momentum $(L)$,and universal gravitational constant $(G)$ are chosen as fundamental quantities. The dimensions of the universal gravitational constant in the dimensional formula of Planck's constant $(h)$ is

$\sqrt[4]{17 + 12\sqrt{2}} = $

Sertoli cells are regulated by the pituitary hormone known as: