The compressibility factor for an ideal gas is

If $a \neq 0, b \neq 0, c \neq 0, a \times b = 0$ and $b \times c = 0$,then $a \times c$ is equal to

The number of hydroxide ions produced by one molecule of sodium carbonate $(Na_2CO_3)$ on hydrolysis is

An insulated cylindrical vessel is fitted with an insulated piston of negligible weight and negligible thickness at the midpoint of the vessel. The cylinder contains a gas at $0^{\circ} C$. When the gas is heated to $100^{\circ} C$,the piston moves through a length of $5 ~cm$. The total length of the cylindrical vessel in $cm$ is:

Bhutia is a breed of:

The set of all points for which $f(x) = x^2 \cdot e^{-x}$ strictly increases is