A small square loop of wire of side $l$ is placed inside a large square loop of wire of side $L$ ($L > l$). The loop are coplanar and their centre coincide. The mutual inductance of the system is proportional to

Take current $I$ in the large square loop. Since the small loop is much smaller in comparison to the large one for proportionality, the magnetic field over the small loop scales as the field at the center of the large square loop, so $B \propto \dfrac{I}{L}$. The flux linked with the small loop is then proportional to field times its area, so $\Phi \propto \dfrac{I}{L} \cdot l^2$. Therefore mutual inductance $M = \dfrac{\Phi}{I}$ scales as $$M \propto \dfrac{l^2}{L}.$$ Comparing with the given options, this matches option $\dfrac{l_2}{L}$, where $l_2$ denotes $l^2$.