$0.1 \mathrm{mol}$ of $\mathrm{NaCl}$ is dissolved in$100 \mathrm{g}$ of water. The mole fraction of $\mathrm{NaCl}$ is

We know that Mole Fraction$=\frac{No. of moles of component }{Total no. of moles of all the components}$

Therefore,

 Mole fraction of  $\mathrm{NaCl}$ $=\frac{\text{ Number of mole of }\mathrm{NaCl}}{\text{ Total number of mole of solution }}$

We know that Number of moles= $\frac{Given mass}{Molar Mass}$

Therefore,

Total Number of moles of 

$$\begin{gathered} 100 \mathrm{g}\text{ water }=\frac{100}{18}\text{ mol,water }=5.5 \mathrm{mol} \\ \text{ Mole fraction of }\mathrm{NaCl}=\frac{0.1}{0.1+5.5}=\frac{0.1}{5.6}=0.0178\left(approx\right) \end{gathered}$$

Hence, option(b) is correct.