A projectile is thrown with an initial velocity $$(a \hat{i}+b \hat{j}) \mathrm{m} / \mathrm{s}$$, where $$\hat{i}$$ and $$\hat{j}$$ are unit vectors along horizontal and vertical directions respectively. If the range of the projectile is twice the maximum height reached by it, then

To determine the internal resistance of a cell by using a potentiometer, the null point is at $$1 \mathrm{~m}$$ when shunted by $$3 \Omega$$ resistance and at a length $$1.5 \mathrm{~m}$$, when cell is shunted by $$6 \Omega$$ resistance The internal resistance of the cell is

The rms speed of a gas molecule is '$$\mathrm{V}$$' at pressure '$$\mathrm{P}$$'. If the pressure is increased by two times, then the rms speed of the gas molecule at the same temperature will be

A body executes SHM under the action of force '$$\mathrm{F}_1$$' with time period '$$\mathrm{T}_1$$'. If the force is changed to '$$\mathrm{F_2}$$', it executes SHM with period '$$\mathrm{T_2}$$'. If both the forces '$$\mathrm{F_1}$$' and '$$\mathrm{F}_2$$' act simultaneously in the same direction on the body, its time period is