A Carnot engine, whose efficiency is 40% takes heat from a source maintained at temperature 600K. To have an efficiency 60%, the intake temperature for the same exhaust temperature should be

The heat energy that must be supplied to 14 g of nitrogen at room temperature to raise its temperature by $48\ ^\circ\text{C}$ at constant pressure is ($R$ = gas constant, Molecular weight of nitrogen $(\text{N}_2)$ = 28)

The speeds of the seven molecules are 1, 3, 5, 7, 2, 4 and 6 km/s respectively. The ratio of their r.m.s. velocity and average velocity will be

Two simple pendulums of lengths $L_1$ and $L_2$ have periodic time $T_1$ and $T_2$ respectively $(T_1 > T_2)$. The time period of the pendulum of length $(L_1-L_2)$ is
$[(L_1-L_2) > 60\text{ cm}]$