Two cells $$E_1$$ and $$E_2$$ having equal EMF '$$E$$' and internal resistances $$r_1$$ and $$r_2\left(r_1>r_2\right)$$ respectively are connected in series. This combination is connected to an external resistance '$$R$$'. It is observed that the potential difference across the cell $$\mathrm{E}_1$$ becomes zero. The value of '$$R$$' will be

Which one of the following represents correctly the variation of volume (V) of an ideal gas with temperature $$(\mathrm{T})$$ under constant pressure conditions?

Using variation of force and time given below, final velocity of a particle of mass $$2 \mathrm{~kg}$$ moving with initial velocity $$6 \mathrm{~m} / \mathrm{s}$$ will be

$$\mathrm{dQ}$$ is the heat energy supplied to an ideal gas under isochoric conditions. If $$\mathrm{dU}$$ and $$\mathrm{dW}$$ denote the change in internal energy and the work done respectively then