List-I | List-II | ||
(A) | Kinetic energy of Earth | (I) | $-\frac{GM_sM_e}{a}$ |
(B) | Potential energy of Earth and Sun | (II) | $\frac{GM_sM_e}{2a}$ |
(C) | Total energy of Earth and Sun | (III) | $\frac{GM_e}{ R}$ |
(D) | Escape energy from surface of Earth per unit mass | (IV) | $\frac{GM_sM_e}{2a}$ |
The largest $ n \in \mathbb{N} $ such that $ 3^n $ divides 50! is:
The term independent of $ x $ in the expansion of $$ \left( \frac{x + 1}{x^{3/2} + 1 - \sqrt{x}} \cdot \frac{x + 1}{x - \sqrt{x}} \right)^{10} $$ for $ x>1 $ is: