$A$ small square loop of wire of side $l$ is placed inside a large square loop of wire of side $L$ $(L \gg l)$. The loops are coplanar and their centers coincide. The mutual inductance of the system is proportional to

$A$ Carnot engine absorbs an amount $Q$ of heat from a reservoir at an absolute temperature $T$ and rejects heat to a sink at a temperature of $T/3$. The amount of heat rejected is

If $A$ and $B$ are mutually exclusive events with $P(B) \neq 1$,then $P(A \mid \bar{B})$ is equal to (Here $\bar{B}$ is the complement of the event $B$)

Two small spheres,each having an equal positive charge $Q$ (Coulomb),are suspended by two insulating strings of equal length $L$ (metre) from a rigid hook. The whole setup is taken into a satellite where there is no gravity. The two balls are now held by electrostatic forces in a horizontal position. The tension in each string is then:

When $22.4 \ L$ of $H_{2(g)}$ is mixed with $11.2 \ L$ of $Cl_{2(g)}$,each at $S.T.P.$,the moles of $HCl_{(g)}$ formed is equal to

The activation energy for a reaction at the temperature $T \ K$ was found to be $2.303 \ RT \ J \ mol^{-1}$. The ratio of the rate constant to Arrhenius factor is