In which direction, the force of gravity directed towards? I am not being able to answer, where is actually the force of gravity directed towards ?
Look at this picture.

This is a planet with the centre ‘C’. And O is an object. Every point of the planet is attracting the object,The points A and B are also pulling it towards themselves, then why do we say, the force is directed towards the centre?
Also, If i drop the object, will it move towards A , B or towards the centre ? 
 A: You have to think of the symmetry of the situation.  For each point A and B, there is a point A' and B' opposite the center line that has an attractive force pulling in such a way that the components perpendicular to the center line are canceled.  Therefore, the net force is along the center line.
A: As @tmwilson26, said the net force is directed along the center, here's the mathematics of it
if there is a small differential mass at A, there also exists another point A' laying just opposite to the center line(making a same angle $\theta$ with the center line)
The force $F$ experienced at point O has 2 components $F_x$ and $F_y$ where
where $F_y$ is along the radial direction and $F_x$ perpendicular to it
due to symmetry the $x$ components cancel out since they have equal and opposite directions, which leaves behind the $y$-component which is the radial component
A: If the planet is spherically symmetric, the gravitational field is the same as if all the mass were concentrated at the center, so the attraction will be along the line toward the center.  If it is not, it is not really fair to talk of the center.  Imagine if there were a huge mountain at point A.  This could change the gravitational field (a small bit) to pull the object more toward A.  The equatorial bulge of the earth tends to pull satellites into the equatorial plane.  You get a more complicated gravity model, which matters to some things and not to others.
