In a class of 100 students, 55 students have passed in Mathematics and 67 students have passed in Ph

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1.Set Theory

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In a class of $100$ students, $55$ students have passed in Mathematics and $67$ students have passed in Physics. Then the number of students who have passed in Physics only is

A

$22$

B

$33$

C

$10$

D

$45$

Solution

(d) $n\,(M) = 55,n\,(P) = 67,n\,(M \cup P) = 100$

Now, $n\,(M \cup P) = n\,(M) + n\,(P) – n\,(M \cap P)$

$100 = 55 + 67 – n\,(M \cap P)$

$\therefore n\,(M \cap P) = 122 – 100 = 22$

Now $n$ ($P$ only) =$n\,(P) – n(M \cap P)$$ = 67 – 22 = 45$.

Standard 11

Mathematics

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