Consider a small segement dx of the rod at a distance x from mass m
$F=\int \limits_d^{d+h} \large\frac{G(\lambda dx)m}{x^2}$
Where $\lambda dx$ is the mass of the small segment of the rod.
$\therefore F=Gm\lambda \bigg[\large\frac{-1}{x}\bigg]_d^{d+l}$
$F=Gm\lambda \bigg[\large\frac{l}{d}-\frac{l}{d+l}\bigg]$
$\quad=\large\frac{Gm\lambda l}{d(d+l)}$
Hence a is the correct answer.