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 an election the number of candidates is $1$ greater than the persons to be elected. If a voter can vote in $254$ ways, then the number of candidates is?

1. $7$

2. $10$

3. $8$

4. $6$

Q.

A class has , $175$ students. the following table shows the number of students studying one or more of the following subjects in this class. find how many students are enrolled in mathematics alone, physics alone, and chemistry alone? are there students who have not been offered any of these three subjects?

Subject	Number of students
Mathematics	100
Physics	70
Chemistry	46
Mathematics and Physics	30
Mathematics and Chemistry	28
Physics and Chemistry	23
Mathematics, Physics and Chemistry	18

Q.

There was a survey conducted in a city about number of people reading newspaper A, B and C. There are 42% of people read newspaper A; 51% of people read newspaper B and 68% of people read paper C. 30% of people read both newspaper A and B. 28% reads B and C and 36% read C and A. 8% do not read any newspaper. Find the percentage of people who read all the three newspapers.

__

Q. In a group of tourists, $40\%$ liked Goa, $30\%$ liked Kerala and $30\%$ liked Bangalore. $7\%$ liked both Goa and Kerala, $5\%$ liked both Kerala and Bangalore, $10\%$ liked both Bangalore and Goa. If $86\%$ of these liked at least one of the places, then what percentage of people liked all three?

1. $5$
2. $6$
3. $7$
4. $8$

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. A group of $123$ workers went to a canteen for cold drink, ice-cream and tea. $42$ workers took ice-cream, $36$ took tea and $30$ took cold drink. $15$ workers purchased ice-cream and tea, $10$ purchased ice-cream and cold drink, and $4$ purchased cold drink and tea but not ice-cream. Then the number of workers who did not purchase anything is

1. $60$
2. $79$
3. $44$
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 survey of $60$ people, it was found that $25$ people read newspaper $H,26$ read newspaper $T,26$ read newspaper $I,9$ read both $H\&I,11$ read both $H\&T,8$ read both $T\&I,3$ read all three newspapers, then

1. $26$ People read exactly one newspaper
2. $30$ People read exactly one newspaper
3. $19$ People read exactly two of the three newspaper
4. $28$ People read exactly two of the three newspaper

Q.

Of the 200 candidates who were interviewed for a position at a call center, 100 had a two-wheeler, 70 had a credit card and 140 had a mobile phone. 40 of them had both two-wheeler and credit card, 30 had both credit card and mobile phone and 60 had both two wheeler and mobile phone and 10 had all three. How many candidates had none of the three?

1. 0

2. 10

3. 20

4. 18

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. $52$