Is it true that for a object moving in circular orbit if the radius of the orbit increases then the velocity of the object moving in the circular orbit also increases?
No, that is not true. The velocity actually decreases with increasing radius. This works kind of like a balancing act, the length of the radius versus the velocity the object. You can demonstrate this radius versus velocity yourself, if you get a length of string and tie a weighted object on the end of it. Whirl the object around your hand in a circular orbit, then allow the string to wind on your fingers. Observe what happens to the velocity of the object as the string gets shorter. It gets progressively faster the shorter the string becomes. So the shorter the radius the faster the velocity. This must occur because the pull of gravity becomes stronger as you decrease the distance between the objects. This effect may also be observed with increasing distance of the planets away from the sun. The farther out the planet is, the longer it takes to go around the sun. This is partly due to the increased distance, while also due to decreased velocity.
You can also prove this using the circular motion formula:
This tells you the centripetal force that keeps the object in orbit, if you know the speed, v. Conversely, we know the force and want to find the speed, given the radius, r (what is the force? Think gravity).
So the force is gravity, which is some numbers divided by r^2. Lets say F=A/r^2. (what's A?). So we have two expressions for the force, which must be equal!
A/r^2 = mv^2 / r.
v^2 = A/(m * r)
So if we increase r, we decrease the speed - there is an inverse relationship between r and v (technically, you could say it's an inverse square-root relationship, but that's not important here).