The gravitational force of attraction between two objects of masses M and N with distance d between them is given by $\(F=\frac{(M \times N)}{d^2}\)$; we need to check from the options that which of them is true.

(A) The force doubles if the distance between the two bodies doubles - which is false as $\(2 \mathrm{~F} \neq \frac{(\mathrm{M} \times \mathrm{N})}{(2 \mathrm{~d})^2}=\frac{(\mathrm{M} \times \mathrm{N})}{4 \mathrm{~d}^2}\)$
(B) The force quadruples if each of the masses of the two bodies with the same distance between them double - which is true as $\(4 \mathrm{~F}=\frac{(2 \mathrm{M} \times 2 \mathrm{~N})}{\mathrm{d}^2}=\frac{4(\mathrm{M} \times \mathrm{N})}{\mathrm{d}^2}\)$
(C) The force quadruples if the distance between the two bodies of the same masses reduces by half - which is true as $\(4 \mathrm{~F}=\frac{(\mathrm{M} \times \mathrm{N})}{(\mathrm{d} / 2)^2}=\frac{4(\mathrm{M} \times N)}{\mathrm{d}^2}\)$
(D) The force remains constant if the values of masses of each of the two bodies doubles and the distance between them reduces by half - which is false as $\(\frac{(2 \mathrm{M} \times 2 \mathrm{~N})}{(\mathrm{d} / 2)^2}=\frac{16(\mathrm{M} \times N)}{\mathrm{d}^2}=16 \mathrm{~F}\)$ Hence only options (B) \& (C) are true.