A body of mass '$$\mathrm{m}$$' kg starts falling from a distance 3R above earth's surface. When it reaches a distance '$$R$$' above the surface of the earth of radius '$$R$$' and Mass '$$M$$', then its kinetic energy is

In the case of NAND gate, if A and B are the inputs and $$\mathrm{Y}$$ is the output then

A monoatomic gas at pressure '$$\mathrm{P}$$', having volume '$$\mathrm{V}$$' expands isothermally to a volume '$$2 \mathrm{~V}$$' and then adiabatically to a volume '$$16 \mathrm{~V}$$'. The final pressure of the gas is (Take $$\gamma=5 / 3$$ )

In potentiometer experiments, two cells of e. m. f. '$$E_1$$' and '$$E_2$$' are connected in series $$\left(E_1>E_2\right)$$, the balancing length is $$64 \mathrm{~cm}$$ of the wire. If the polarity of $$E_2$$ is reversed, the balancing length becomes $$32 \mathrm{~cm}$$. The ratio $$\mathrm{E}_1 / \mathrm{E}_2$$ is