Which of the following statement is correct for a weak electrolytic solution?
${\Lambda }_m$ - Molar conductivity
${\Lambda }_m^0$ - Limiting molar conductivity
$C$ - concentration of electrolyte

The correct option is C ${\Lambda }_m^0$ cannot be found by extrapolation of ${\Lambda }_m$ to zero concentration.
On dilution, the molar conductivity increases for both strong and weak electrolyte.

On dilution of weak electrolyte, the degree of dissociation increases which results in increase in the number of ions in solution. So, there will be overall increase in molar conductance.

Variation in ${\Lambda }_m$ for weak electrolyte:
Weak electrolytes like acetic acid have lower degree of dissociation.
With dilution of an ionic solution, the degree of dissociation ($\alpha$) of the electrolyte increases which result in increase in the number of ions in solution. Near lower concentration, there will be a steep increase in molar conductance.

Plot of ${\Lambda }_{m}vs\sqrt{C}$

From above it is evident that curve for ${\Lambda }_{m}vs\sqrt{C}$ for a weak electrolyte (here acetic acid) is rectangular hyperbola. It does not intercept the y-axis.
Although, the concept of molar conductance at infinite dilution exists for a weak electrolyte.
But graphically, the value cannot be evaluated.

Thus, statement (a) is correct.