Q1.Convex mirror are used as reflector in street lamps whereas concave mirror is used as a reflector in torch and car headlight.why?

Q2.In reflector telescopes the bigger curved mirror is a convex mirror.This sentence is false.Give reason why it is false?

Convex mirror is also called diverging mirror as it diverges the beam of light falling on it. It ia for this purpose that it is used in street lamps as it would diverge the light rays and hence spread the light so that visibility increases.

On the other hand concave mirror is also called converging mirror. It is used for different light rays falling on it to a single point. Now we use search light and torches so that we have a more focused light beam which will not diverge out and hence help in searching. Due to this reason we use concave mirror in torches and search lights.

Case 2

As stated above concave mirrors help to produce more focused beam of light . due to this reason , it is used in reflecting type telescopes. It has large aperture . It is free from chromatic and spherical aberrations . The image formed is much brighter as a result. Also the resolving power of this telescope is much greater than the refracting type telescope. hence the statement is wrong that convex mirrors are used in reflecting type telescope. For further explanation just view the following diagram :

Here as we can see that the primary mirror is the concave mirror with large aperture. It produces inverted image but we know that most of the astronomical bodies are spherical hence it doesn't matter.