Degree of dissociation, when molar conductivity of X at its concentration C is 24.14 and its limiting molar conductivity is 48.28 will be:

The correct option is 0.5.

To find the degree of dissociation (represented by $\alpha$), we use the relation between the molar conductivity of an electrolyte at a given concentration (${\Lambda }_c$) and its limiting molar conductivity (${\Lambda }_0$).

The formula for the degree of dissociation is given by:

$$\alpha =\frac{{\Lambda }_c}{{\Lambda }_0}$$

From the given data:
Molar conductivity at concentration C, ${\Lambda }_c=24.14$
Limiting molar conductivity, ${\Lambda }_0=48.28$

Substituting these values into the formula:

$$\alpha =\frac{24.14}{48.28}$$

Simplifying the fraction:

$$\alpha =0.5$$

Therefore, the degree of dissociation of the electrolyte X is 0.5.