If $x$ is the specific conductance (in $S \ cm^{-1}$) of the electrolyte solution and $y$ is the molarity of the solution,then $\Lambda_m$ (in $S \ cm^2 \ mol^{-1}$) is given by:

When a point source of monochromatic light is placed at a distance of $0.2 \ m$ from a photoelectric cell,the cut-off voltage and saturation current are $0.6 \ V$ and $18 \ mA$ respectively. If the same source is placed at a distance of $0.6 \ m$ from the photoelectric cell,then:

$A$ cubical block of wood with a side length of $10 \, cm$ floats at the interface between oil and water,with its lower surface horizontal and $4 \, cm$ below the interface. The density of oil is $0.6 \, g \cdot cm^{-3}$ and the density of water is $1 \, g \cdot cm^{-3}$. The mass of the block is ...... $gm$.

$A$ series combination of $n_1$ capacitors,each of value $C_1$,is charged by a source of potential difference $4V$. When another parallel combination of $n_2$ capacitors,each of value $C_2$,is charged by a source of potential difference $V$,it has the same (total) energy stored in it as the first combination has. The value of $C_2$,in terms of $C_1$,is then

$\frac{1+\tanh \frac{x}{2}}{1-\tanh \frac{x}{2}}$ is equal to

Two cylinders $A$ and $B$ fitted with pistons contain equal number of moles of an ideal monoatomic gas at $400 ~K$. The piston of $A$ is free to move while that of $B$ is held fixed. Same amount of heat energy is given to the gas in each cylinder. If the rise in temperature of the gas in $A$ is $42 ~K$, the rise in temperature of the gas in $B$ is (in $~K$)