Question

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Answer 1

MATHS

There are 100 students in a class. In an examination, 50 of them failed in Mathematics, 45 failed in Physics, 40 failed in Biology and 32 failed in exactly two of the three subjects. Only one student passed in all the subjects. Then, the number of students failing in all the three subjects is

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ANSWER

Given that there are 100 students and only one student passed in all 3 subjects

So the number of students failed in at least one subject is 99

Let a be the number of students failed only in mathematics, b be number of students failed only in physics and c be number of students failed only in Biology.

Let x be number of students failed only in mathematics and physics, y be number of students failed only in physics and biology and z be the number of students failed only in biology and mathematics.

Let p be the number of students failed in all three subjects

By Venn diagram, we get 99=a+b+c+x+y+z+p

Number of students failed in exactly two subjects is 32=x+y+z

Students failed in mathematics is 50=a+x+z+p , students failed in physics is 45=b+x+y+p and students failed in Biology is 40=c+y+z+p

By adding above three equations, we get 135=a+b+c+2(x+y+z)+3p

⇒135=99+32+2p

⇒p=2

Therefore option C is correct