If a ball is kept on the table, then what forces are being exerted on it? If a ball is kept on a table then there is gravity acting on it as well as a normal reaction force by the table on the ball. But as both the forces are being exerted on the same object i.e. the ball, then it cannot be called a- action reaction pair under Newton's third law of motion because it requires the forces acting on two different bodies.
So, if it is not an action reaction pair, then how is any force being exerted by the table on the ball? Also, is the ball applying any force on the table?
 A: 
If a ball is kept on a table then there is gravity acting on it as well as a normal reaction force by the table on the ball.

This is correct.

But as both the forces are being exerted on the same object i.e. the ball, then it cannot be called a- action reaction pair under Newton's third law of motion because it requires the forces acting on two different bodies.

This is also correct. The force of gravity and the normal force from the table on the ball are not action-reaction pairs as described by Newton's third law.

So, if it is not an action reaction pair, then how is any force being exerted by the table on the ball? Also, is the ball applying any force on the table?

As you have recognized, both forces in action-reaction force pairs do not act on the same object, so why would you think that in order to have forces acting on an object they have to be part of an action-reaction pair? 
There are two action-reaction force pairs here. 


*

*The force of gravity: Earth on the ball and ball on the Earth

*The normal force: Table on the ball and ball on the table


As you can see, we have our two forces acting on our ball: gravity and normal force. Each of these forces has a corresponding force that it forms an action-reaction pair with, as stated by Newton's third law.

As a small aside, the more I see questions on this site about Newton's third law and actions/reactions, the more I realize how confusing this terminology is to new students to physics. If this is all still confusing to you, may I suggest a different view of Newton's third law? 

All forces arise from interactions

If you want to pick out your action-reaction pairs, just pick out your interactions. Are the ball and Earth interacting? Yes, through gravity. Are the ball and the table interacting? Yes, through the normal force (electrostatic interactions).
A: 
So, if it is not an action reaction pair, then how is any force being
  exerted by the table on the ball? Also, is the ball applying any force
  on the table?

This is the crux of the issue.
There are two completely separate things happening here. One is gravity on the ball, the other is the ball on the table.
The first is Newton's Universal Gravitation. The force is due to mutual attraction. The ball is pulling on the Earth, and the Earth is pulling on the ball. The net result of these interactions is the the "earth part" is so much larger than the "ball part" that the later is best represented by zero. So to you, it looks like a net force downward equal to the mass of the ball.
Now when you have a non-zero force, what happens? Movement. But the ball is not moving. So where did it go?
Well that force on the ball is causing it to press into the table. The table responds by bending until the stress force caused by that bending is equal to the force put on it. Now you have two equal forces, so the motion stops. And since the ball is likely much lighter than the table's maximum weight capacity, the amount of bending is tiny to the point you can't see it.
Now of course the table is sitting on the floor, which similarily bends. And that floor is supported by walls, which are pushed down into the ground which compresses. And now you're at the Earth, so the force it put on the ball is ultimately balanced out.
Invariably when I see people confused in Newtonian examples it's because the experimental setup is being artificially limited by the question - in this case you ask what about the ball and the table and the earth. But if you look at the whole thing, you have earth->foundation->floor->table->ball->earth. So that 100g of mass in the ball that causes .1 N of force from the earth ultimately puts .1 of force on the earth and the cycle is closed. It's not the table that's balancing the force of the earth, it's (ultimately) the earth balancing the force of the earth.
Does that make sense?
