The equivalent conductivity of 0.1 M weak acid is 100 times less than that at infinite dilution. The degree dissociation is 

Here given is ,
Conductivity = C= 0.1M
Equivalent conductivity is ${\mathrm{\lambda }}_{\mathrm{m}}=\frac{{\mathrm{\lambda }}_{\infty }}{100}$
Here we need to find out degree of dissociation i.e. $\mathrm{\alpha }=?$
$\mathrm{\alpha }=\frac{{\mathrm{\lambda }}_{\mathrm{m}}}{{\mathrm{\lambda }}_{\infty }}$
By putting values 
$\mathrm{\alpha }=\frac{{\mathrm{\lambda }}_{\infty }}{100\times {\mathrm{\lambda }}_{\infty }}$

$\mathrm{\alpha }=\frac{1}{100}=0.01$
 

Therefore option C is correct.