JEE Main 10 Jan 2019 Shift 1 Solved Paper

Let n(A) = number of students opted Mathematics = 70,
n(B) = number of students opted Physics = 46,
n(C) = number of students opted Chemistry = 28,
n (A ∩ B) = 23 ,
n(B ∩ C) = 9,
n(A ∩ C) = 14,
n(A ∩ B ∩ C) = 4,
Now n(A ∪ B ∪ C)
= n(A) + n(B) + n(C) – n(A ∩ B) – n(B ∩ C)
– n(A ∩ C) + n(A ∩ B ∩ C)
= 70 + 46 + 28 – 23 – 9 – 14 + 4 = 102
So number of students not opted for any course
= Total – n(A ∪ B ∪ C)
= 140 – 102 = 38