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.