Dear Kishan

 Please consult

https://sites.math.rutgers.edu/~zeilberg/Hist21/q2S.pdf

for the full solutions.

You got 8 points (out of 10). Good job!

#2 was wrong.

In theexam I expect you to expain more in #4, #5 but this time I did not take any points off for these.

 Best wishes,

   Dr. Z.