7)
Out of 200 students; 35 students failed in
MHT-CET, 40 in AIEEE and 40 in IIT
entrance, 20 failed in MHT-CET and
AIEEE, 17 in AIEEE and IIT entrance, 15
in MHT-CET and IIT entrance and 5 failed
in all three examinations. Find how many
students.
i) did not fail in any examination.
ii) failed in AIEEE or IIT entrance.
Answers
Answer:
I)37 students
II}40 students
i)The number of students did not fail in any examination is 132
ii) The number of students failed in AIEEE or IIT entrance is 63
Solution:
Let n(M) be the number of students who failed in MHT-CET
n(M) = 35
Let n(A) be the number of students who failed in AIEEE,
n(A) = 40
Let n(I) be the number of students who failed in IIT,
n(I) = 40
Given 20 failed in MHT-CET and AIEEE,
n( M ∩ A) = 20
Given 17 failed in AIEEE and IIT entrance,
n(A ∩ I) = 17,
Given 15 failed in MHT-CET and IIT entrance
n(M ∩ I) = 15
Given 5 failed in all three examinations,
n(A ∩ M ∩ I) = 5
i) To find number of student who did not fail in any of the examination
= [n(A ∪ M ∪ I)']
= n(x) - n(A ∪ M ∪ I)
n(A ∪ M ∪ I) = n(A) + n(M) + n(I) - n(A∩M) - n(A∩I) - n(M∩ I) + n(A∩M∩I)
= 35 + 40 + 40 - 20 - 17 - 15 + 5
= 68
So n(A∪M∪I) = 68
Number of students who did not fail in any examination will be
200 - 68
= 132
ii) Students failed in AIEEE or IIT
= n(A∪I)
= n(A) + n(I) - n(A∩I)
= 40 + 40 - 17
= 63
Hence the students failed in AIEEE or IIT is 63