What will happen if a black hole appears near our solar system? We know that black hole possesses immense power and can destroy anything coming in front of it's path. If such a black hole appears near our solar system, are we going to survive? Is there any way not to fall in a black hole?
The way not to fall into a black hole is essentially the same as the way not to fall into the Sun.  It's no more dangerous than any other body with the same mass, which is typically a few times the Sun's mass.

The danger of a passing black hole (or other star) is not that it could swallow us but that it could perturb our orbit, with unpredictable effects on climate; as well as stir up the comets of the (hypothetical) Oort Cloud, sending some of them toward the inner planets, with the possibility of an impact that could ruin your whole day.