@SamyakMarathe No-one enjoys the JEE preparation. Every student I've chatted to here finds it depressing. This probably doesn't make you feel better, but maybe it's some comfort that you are not alone.
You can imagine a cone with the apex at the +5q charge and the axis along the line between the two charges, and the solid angle subtended by the cone is ⁴⁄₅𝜋, then all the field lines inside the cone go to the -q charge.
@satan29 When the hardest part of a question is figuring out what the examiner had been smoking when they set it, that's usually an indication it is not a good question :-)
Now we think quantum mechanics is true because so far it has never been disproved, but quantum mechanics is less than a hundred years old. Give it another two hundred years and who knows?
Most of us don't worry too much about what entropy really is. We just use the equations for the change in entropy and carry on with our lives. I recommend this approach :-)
"Why" questions are always tricky in physics. Quantum field theory gives us a way to calculate how charges interact, but once you start asking yes, but what really happens? we're moving away from physics and towards philosophy.
And even though it's a terrible thing to say, the way you get a good rank in the JEE isn't by being great at physics, it's by being great at answering JEE questions.