Venn Diagrams

Q.

If lines $4x+3y=1,y=x+5\mathrm{and}5y+bx=3$ are concurrent, then $b$ equals:

1. $1$

2. $3$

3. $6$

4. $0$

Q. If R is a relation on a finite set having n elements, then the number of relations on A is

(a) 2ⁿ
(b) $2^{n^2}$
(c) n²
(d) nⁿ

Q. Which of the following Venn-diagram best represents the sets of males, females and mothers?

1. 
2. 
3. 
4. 

Q. Each student in a class of $40$, studies at least one of the subjects English, Mathematics and Physics. $16$ study English, $22$ study Physics and $26$ study Mathematics, $5$ study English and Physics, $14$ Mathematics and Physics and $2$ study all the three subjects. The number of students who study English and Mathematics but not Physics is

1. $4$
2. $5$
3. $3$
4. $10$

Q. Out of 260 students in a class of a school, 135 like tea, 110 like coffee and 80 like milk, 35 of these like both tea and coffee, 30 like both tea and milk, 20 like both coffee and milk. Also, each student likes atleast one of the three drinks. How many students like all the three drinks?

1. 30
2. 15
3. 20
4. 25

Q. In a class of $400$ students, $150$ are interested in doing a statistics project, $300$ are interested in doing a machine learning project and $25$ are not interested in doing either of the projects. Then the number of students who are interested in doing both the projects, is

1. $50$
2. $75$
3. $125$
4. $65$

Q. For the diagram shown below, $A\cap B=$

1. $\{5,10\}$
2. $\{12,18\}$
3. $\{5,10,12,18\}$

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 $\text{III},$ then the minimum number of persons who know to operate all the three machines is

Q. From the adjoining venn diagram, find $A\cap (B\cap C)$

1. $\{1,3,4,5\}$
2. $\{1,4,5,6\}$
3. $\{5,6\}$
4. $\left\{5\right\}$

Q. In a beauty contest, half the number of experts voted for Miss $A$ and two-third voted for Miss $B$, $10$ voted for both and $6$ did not vote for either. Then how many experts were there?

1. $20$
2. $24$
3. $22$
4. $26$

Q. The correct representation of three sets $A=\{q,w,e,r,t\}$
$B=\{r,t,y,u,i\}\&C=\{u,q,o,p,t\}$ is

1. 
2. 
3. 
4. 

Q. Two sets $M\&N$ are represented as shown below, then

1. $M\subset N$
2. $M=N$
3. $N\subset M$

Q. From the adjoining figure, $A\cap B$ is

1. $\{8,5\}$
2. $\{8,5,0\}$
3. $\{1,5\}$
4. $\{0,1,2,3,5,8,9\}$