Consider the reaction at $300\, K$:
$C_6H_{6(l)} + \frac{15}{2} O_{2(g)} \to 6 CO_{2(g)} + 3 H_2O_{(l)}$; $\Delta H = -3271\, kJ$
What is $\Delta U$ for the combustion of $1.5\, mol$ of benzene at $27\, ^\circ C$? .....$kJ$

The maximum tension a rope can withstand is $60 ~kg-wt$. The ratio of maximum acceleration with which two boys of masses $20 ~kg$ and $30 ~kg$ can climb up the rope at the same time is

The resistance in the following circuit is increased at a particular instant. At this instant,the value of resistance is $10 \, \Omega$. The current in the circuit will be now:

$\lim _{x \rightarrow 0} \frac{\sin \left(\pi \cos ^2 x\right)}{x^2}$ is equal to

Which of the following is a redox reaction?

$A$ particle of mass $4 M$ which is initially at rest explodes into three pieces of masses $M$,$M$ and $2 M$. The equal masses move along $X$ and $Y$-axes with velocities $4 ~ms^{-1}$ and $6 ~ms^{-1}$,respectively. The magnitude of the velocity of the heavier mass is