n(A∪B∪C) = n(A) + n(B) + n(C) − n(A∩B) − n(B∩C) − n(C∩A) + n(A∩B∩C)

Q. In a school three languages English, French and Spanish are taught. $30$ students study English, $25$ study French and $20$ study Spanish. Although no student studies all three languages, $8$ students study both English and French, $5$ students study both French and Spanish and $7$ students study both Spanish and English. How many students study at least one of the three languages?

1. $50$
2. $60$
3. $45$
4. $55$

Q. In a class, there are $200$ students in which $120$ take Mathematics, $90$ take Physics, $60$ take Chemistry, $50$ take Mathematics and Physics, $50$ take Mathematics and Chemistry, $43$ take Physics and Chemistry and $38$ take Mathematics, Physics and Chemistry. Then the number of students who have taken exactly one subject is

Q. In a class of $140$ students numbered $1$ to $140$, all even numbered students opted Mathematics course, those whose number is divisible by $3$ opted Physics course and those whose number is divisible by $5$ opted Chemistry course. Then the number of students who did not opt for any of the three courses is :

1. $1$
2. $102$
3. $38$
4. $42$

Q. A school awards $77$ medals in three sports i.e. $48$ in football, $25$ in tennis and $25$ in cricket. If $7$ students got medals in all the three sports, then the number of students who received medals in exactly 2 sports is

Q. In a class of $80$ students numbered $1$ to $80$, all odd numbered students opt for cricket, students whose numbers are divisible by $5$ opt for football and students whose numbers are divisible by $7$ opt for hockey. The number of students who do not opt any of the three games, is -

1. $13$
2. $24$
3. $28$
4. $52$

Q. In a class of $42$ students, $23$ are studying Mathematics, $24$ are studying Physics, $19$ are studying Chemistry. If $12$ are studying both Mathematics and Physics, $9$ are studying both Mathematics and Chemistry, $7$ are studying both Physics and Chemistry and $4$ are studying all the three subjects, then the number of students studying exactly one subject, is

1. $15$
2. $30$
3. $22$
4. $27$

Q. A factory has $80$ workers and $3$ machines. Each worker knows to operate at least two machines. If there are $65$ persons who know to operate machine $\text{I}$, $60$ for machine $\text{II}$ and $55$ for machine $\text{III}$, what can be the minimum number of persons who know to operate all the three machines ?

1. $15$
2. $20$
3. $30$
4. $40$

Q. In a survey of $200$ students of a higher secondary school, it was found that $120$ studied mathematics; $90$ studied physics and $70$ studied chemistry; $40$ studied mathematics and physics; $30$ studied physics and chemistry; $50$ studied chemistry and mathematics, and $20$ studied none of these subjects. If $M$, $P$ and $C$ represent the set of students who studied mathematics, physics and chemistry respectively, then

1. $n(M\cup P\cup C)=180$
2. $n(M^{\prime }\cap P^{\prime }\cap C^{\prime })=20$
3. $n(M\cap P\cap C)=40$
4. $n(M\cap P\cap C)=20$

Q. In a class of $345$ students, the students who took English, Math and Physics are equal in number. $30$ students took English and Math, $26$ choose Math and Physics, $28$ choose Physics and English and $14$ choose all three subjects. $43$ students didn’t take any of the subjects. How many students have taken English as subject?

1. $108$
2. $124$
3. $246$
4. $286$

Q.

In a class of 58 students, 20 follow cricket, 38 follow hockey and 15 follow basketball. Three students follow all the three games. How many students follow exactly two of these three games?

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Q. In a class of $80$ students numbered $1$ to $80$, all odd numbered students opt for cricket, students whose numbers are divisible by $5$ opt for football and students whose numbers are divisible by $7$ opt for hockey. The number of students who do not opt any of the three games, is -

1. $13$
2. $24$
3. $28$
4. $52$