In a nearly saturated solution, the solubility increases with increase in temperature, then $\Delta \mathrm{H}$ sol. is

We know that

$\Delta \mathrm{H}$ represents the change in enthalpy which means amount of heat evolved or absorbed during the dissolving process (at constant pressure).

In simple terms,

 Enthalpy is the measurement of energy and is the sum of Internal energy and the product of $P$ and $V$ as;

$\Delta H=\Delta E+P\Delta V$

and

we know that is positive for endothermic reaction and negative for exothermic reaction.

In a nearly saturated solution, solute takes energy from the surroundings to get dissolved in a solvent and the enthalpy of solution is positive. So, thus, on increasing temperature, if Solubility increases, the reaction will be endothermic and $\Delta H=$ positive.

Hence, option(a) is correct.