Use Kepler's laws and Newton's law of gravitation

For a planet of mass $m$ revolving around the sun of mass $M$:

$F = \frac{GMm}{r^2}$

Also, for planetary motion in an ellipse, Kepler's third law gives:

$T^2 \propto a^3$

where $a$ is the semi-major axis.

Check statement A

Statement A says: The force acting on a planet is inversely proportional to square of distance from sun.

From $F = \frac{GMm}{r^2}$ we see that $F \propto \frac{1}{r^2}$

So, A is correct.

Check statement B

Statement B says: Force acting on planet is inversely proportional to product of the masses of the planet and the sun.

But actually, $F \propto Mm$ not inversely proportional.

So, B is incorrect.

Check statement C

Statement C says: The centripetal force acting on the planet is directed away from the sun.

Centripetal force is always directed towards the center of motion. Here gravitational force acts toward the sun, not away from it.

So, C is incorrect.

Check statement D

Statement D says: The square of time period of revolution of planet around sun is directly proportional to cube of semi-major axis of elliptical orbit.

This is exactly Kepler’s third law:

$T^2 \propto a^3$

So, D is correct.

Final selection

Correct statements are A and D only.

Hence, the correct option is:

$\boxed{\text{Option C}}$