Chemical $A$ is used for the removal of temporary hardness of water. Compound $A$ reacts with $Na_2CO_3$ to produce caustic soda. When $CO_2$ gas is passed through $A$,it turns milky. What is the chemical formula of $A$?

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

The work done by a force $\vec F = (-6x^3 \hat i) \text{ N}$,in displacing a particle from $x = 4 \text{ m}$ to $x = -2 \text{ m}$ is .............. $J$.

$\int_0^\pi \frac{\theta \sin \theta}{1+\cos ^2 \theta} d \theta$ is equal to

The ratio of the ionization energy of a Bohr hydrogen atom to that of a Bohr hydrogen-like lithium atom is:

Enzymes are