Correct Answer - Option 1 : 35

**Given:**

A Class has 100 students with roll number from 101 to 200

**Formula used:**

n(P ∪ C ∪ B) = n(P) + n(P) + n(C) + n(B) – n(P ∩ B) – n(P ∩ C) – n(C ∩ B) + n(P ∩ C ∩ B)

**Calculation:**

Physics students be P

Chemistry students be C

Biology students be B

⇒ (100/2) + (100/5) + (100/7) – [100/LCM(2,7)] – [100/LCM(2,5)] – [100/LCM(5,7)] + [100/LCM(2, 5, 7)]

⇒ [50 + 20 + 14.28 – (100/14) – (100/10) – (100/35) + (100/70)]

⇒ (50 + 20 + 14.28 – 7.14 – 10 – 2.85 + 1.42)

⇒ (50 + 20 + 14 – 7 – 10 – 2 + 1)

⇒ 66

Students do not study any exam = ∪ – n(P ∪ C ∪ B)

⇒ 100 – 66 = 34 in approximately 35

**∴ Students do not study any exam is 35.**