The number of molecules of $CO_2$ liberated by the complete combustion of $0.1 \text{ mol}$ of graphite in air is:

$10$ cells,each of emf $E$ and internal resistance $r$,are connected in series to a variable external resistance. The figure shows the variation of the terminal potential difference of their combination with the current drawn from the combination. The emf of each cell is ............. $V$.

For one mole of a van der Waals gas,when $b = 0$ and $T = 300 \ K$,the plot of $PV$ versus $1/V$ is shown below. The value of the van der Waals constant $a \ (atm \ L^2 \ mol^{-2})$ is:

The apparent frequency of a sound wave as heard by an observer is $10\%$ more than the actual frequency. If the velocity of sound in air is $330 \, m/s$,then:
$(i)$ The source may be moving towards the observer with a velocity of $30 \, m/s$
$(ii)$ The source may be moving towards the observer with a velocity of $33 \, m/s$
$(iii)$ The observer may be moving towards the source with a velocity of $30 \, m/s$
$(iv)$ The observer may be moving towards the source with a velocity of $33 \, m/s$

Work done in time $t$ on a body of mass $m$ which is accelerated from rest to a speed $v$ in time $t_1$ as a function of time $t$ is given by

If $x_1$ and $x_2$ are the real roots of the equation $x^2-kx+c=0$,then the distance between the points $A(x_1, 0)$ and $B(x_2, 0)$ is