What is the minimum energy required to launch a satellite of mass $m$ from the surface of a planet of mass $M$ and radius $R$ into a circular orbit at an altitude of $2R$?

Two cylinders $A$ and $B$ fitted with pistons contain equal amounts of an ideal diatomic gas at temperature $T \ K$. The piston of cylinder $A$ is free to move,while that of cylinder $B$ is held fixed. The same amount of heat $dQ$ is given to the gas in each cylinder. If the rise in temperature of the gas in $A$ is $dT_{A}$,then the rise in temperature of the gas in $B$ is (where $\gamma = \frac{C_{p}}{C_{v}}$):

Assertion $(A)$: $NaCl$ is less soluble in heavy water than in ordinary water.
Reason $(R)$: Dielectric constant of ordinary water is more than that of heavy water.
The correct answer is

The eccentricity of the ellipse $9x^2 + 5y^2 - 30y = 0$ is

Two bodies $A$ and $B$ start from the same point at the same instant and move along a straight line. $A$ moves with uniform acceleration $a$ and $B$ moves with uniform velocity $V$. They meet after time $t$. The value of $t$ is:

The maximum possible number of real roots of the equation $x^5 - 6x^2 - 4x + 5 = 0$ is