\[(a)\;zero \quad (b)\;\frac{-4GM}{r} \quad (c)\;\frac{-6GM}{r} \quad (d)\;\frac{-9GM}{r} \]

Let the point be the position when the gravitational field is zero

$\large\frac{Gm}{x^2}=\large\frac{G(4m)}{(r-x)^2}$

$\large\frac{1}{x}=\frac{2}{(r-x)}$

$r-x=2x$

$x=\large\frac{r}{3}$

the point P is at a distance $\large\frac{r}{3}$ from mass m and $\large\frac{2r}{3}$ from mass 4m

$V= \large\frac{-GM}{\Large\frac{r}{3}}-\frac{G(4m)}{\Large\frac{2r}{3}}$

$\quad= \large\frac{-9GM}{r}$

Hence d is the correct answer.

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