The balancing length for a cell is $560 \, cm$ in a potentiometer experiment. When an external resistance of $10 \, \Omega$ is connected in parallel to the cell, the balancing length changes by $60 \, cm$. The internal resistance of the cell in ohms is:

$\frac{\sin 5 \theta}{\sin \theta}$ is equal to

The middle lamella of a plant cell is primarily composed of which of the following?

At a certain temperature and at infinite dilution,the equivalent conductances of sodium benzoate,hydrochloric acid,and sodium chloride are $240$,$349$,and $229 \ \Omega^{-1} \ cm^2 \ \text{equiv}^{-1}$ respectively. The equivalent conductance of benzoic acid in $\Omega^{-1} \ cm^2 \ \text{equiv}^{-1}$ at the same conditions is:

$A$ small quantity of solution containing $Na^{24}$ radionuclide of activity $1$ $\mu Ci$ is injected into the blood of a person. $A$ sample of the blood of volume $1\, cm^3$ taken after $5\, hours$ shows an activity of $296$ disintegrations per minute. What will be the total volume of the blood in the body of the person? Assume that the radioactive solution mixes uniformly in the blood of the person. (Take $1\, curie = 3.7 \times 10^{10}$ disintegrations per second and $e^{-\lambda t} = 0.7927$; where $\lambda$ is the disintegration constant).

$A$ sample of $0.1 \text{ g}$ of water at $100^{\circ} \text{C}$ and normal pressure $(1.013 \times 10^5 \text{ Nm}^{-2})$ requires $54 \text{ cal}$ of heat energy to convert to steam at $100^{\circ} \text{C}$. If the volume of the steam produced is $167.1 \text{ cc}$,the change in internal energy of the sample is ....... $\text{J}$.