Correct option is D
Concept:
n(A ∪ B) = n(A) + n(B) - n(A ∩ B)
Solution:
Given in a class of 84 students, 29 failed in Science (S), 43 failed in Maths (M) and 17 students passed in both.
Total number of students who failed in either maths or science is 84 - 17 = 67
⇒ n(M ∪ S) = 67.
We know that
n(M ∪ S) = n(M) + n(S) - n(M ∩ S)
⇒ 67 = 43 + 29 - n(M ∩ S)
⇒ n(M ∩ S) = 72 - 67
⇒ n(M ∩ S) = 5
∴ Students who failed in only Science = 29 - 5 = 24.
Students who failed in only maths = 43 - 5 = 38.
Required venn diagram is:
