Among the following statements,the incorrect one is:

Which of the following is mismatched?

The relation between the coefficient of real expansion $(\gamma_r)$ and coefficient of apparent expansion $(\gamma_a)$ of a liquid and the coefficient of linear expansion $(\alpha_g)$ of the material of the container is

$A$ vessel is filled with an ideal gas at a pressure of $10 \ atm$ and temperature $27^\circ C$. Half of the mass of the gas is removed from the vessel and the temperature of the remaining gas is increased to $87^\circ C$. Then the pressure of the gas in the vessel will be ...... $atm$.

The angle between the lines whose direction cosines are $\left(\frac{\sqrt{3}}{4}, \frac{1}{4}, \frac{\sqrt{3}}{2}\right)$ and $\left(\frac{\sqrt{3}}{4}, \frac{1}{4}, \frac{-\sqrt{3}}{2}\right)$ is:

Which of the following compounds gives oxygen on fast heating?
$(I)$ $AgNO_3$
$(II)$ $CaCO_3$
$(III)$ $Pb(NO_3)_2$
$(IV)$ $Na_2CO_3$