A mass M is split into two parts and kept separated by a distance r then in which of the following pairs the gravitational force between then will be maximum

We have $F=\frac{G{m}_1{m}_2}{r^2}$ 
Substituting the values:

            For option (a) $F=\frac{2}{9}\frac{G{M}^2}{r^2}$

            For option (b) $F=\frac{1}{4}\frac{G{M}^2}{r^2}$

            For option (c) $F=\frac{3}{16}\frac{G{M}^2}{r^2}$

            For option (d) $F=\frac{4}{25}\frac{G{M}^2}{r^2}$

We can see that the maximum gravitational force is between$\frac{M}{2},\frac{M}{2}$ .
Therefore, option B is the correct answer.