Question

Can  a  convex  mirror  burn  a  paper?  If  not?  Why?

Answer 1

no a convex mirror cannot burn a paper since it is a diverging mirror light rays cannot be focused at a point as in case of concave mirror light rays converge at a point

Answer 2

Burning of paper with the help of convex mirror is not possible.  

This is because of the reason that the convex mirror acts as a divergent medium which forms the virtual image and always a diminished image.

The concave mirror acts as a convergent medium for the recipient rays of light which can focus the ray of light at the focal point of the mirror which causes heating and might burn the paper with increased heat turning into flame.