Dear Prathik,

Your score in Exam 2 is 82 out of 100

Everything was right except

#5: You integrated over the WHOLE sphere rather
than the portion (one-eight of it) that lies in 
x,y,z>0:
-4 points

#6: you integrated over [0,Pi] rather than [Pi/2,Pi]:
-4 points

#9: wrong ans, started right (but EXTREMELY comlicated
way, not the way that I taught). Also (more seriously)
you forgot to multiply by -1 (I said DOWNWARD diretion):

-6 points

#10: You answered (correctly) a DIFFERENT question
I asked for the POINT, not the value:
-4 points

MORAL: READ THE QUESTIONS. MAKE SURE THAT
THE INTEGRATION DOMAIN IS CORRECT.

Best wishes,

  Dr. Z.