Question

can a convex mirror burn a paper if not why

Answer 1

No because it is not a concave mirror .
A concave mirror converges all the light rays coming from infinity at its focus. All these light rays (probably you're talking about sunlight) converge and meet at the focus of the mirror.

Hence, all the heat and light is focused at the focus. And when you keep a thing, for example a paper, at the focus, it starts burning as this point is very hot.

Answer 2

A concave mirror concentrates light that reflects from it, at its focal point. With the right amount of light, you can make the temperature at the focal point high enough to make paper ignite.