n(A∪B) = n(A) + n(B) − n(A∩B)

Q.

If 30% of 140 = x% of 840, then the value of x is

Q.

$5\%$ of which number is $12$?

Q.

Find the value of each of the following:

$3.75\%$ of $1000$ litres.

Q.

In-class $VI$$,$ $14$ students out of $30$ are girls and in-class $VII$$,$ $18$ students out of $38$ are girls. Which grade has more percentage of girls.

Q. Two newspapers $A$ and $B$ are published in a city. It is known that $25\%$ of the city population reads $A$ and $20\%$ reads $B$ while $8\%$ reads both $A$ and $B$. Further, $30\%$ of those who read $A$ but not $B$ look into advertisements and $40\%$ of those who read $B$ but not $A$ also look into advertisements, while $50\%$ of those who read both $A$ and $B$ look into advertisements. Then the percentage of the population who look into advertisements is :

1. $12.8$
2. $13$
3. $13.5$
4. $13.9$

Q.

Find the number which is $40\%$ more than $60$.

Q.

Find the number of students in your class if its $45\%$ is $18$

Q.

Out of $25$toffees , $4$toffees are coffee bite. The percentage of coffee bite is.

1. $12\%$

2. $16\%$

3. $32\%$

4. $23\%$

Q. A survey conducted in a city reveals that $48$% children like cricket while $77$% children like football. Then the percentage of children who like both cricket and football can be

1. $23$
2. $31$
3. $51$
4. $65$

Q.

Find the value of:

$40\%\text{of}1year$

Q.

In a class of 30 students, 18 students play cricket, 15 students play football 12 play both the games. How many students in the class don't play both the games?

__

Q.

$150$ workers were engaged to finish a job in a certain number of days. $4$ workers dropped out on second day, $4$ more workers dropped out on third day and so on. It took $8$ more days to finish the work. Find the number of days in which the work was completed.

Q. If A and B are not disjoint sets, then $n(A\cup B)$is equal to

1. n(A) + n(B)
2. n(A) + n(B) - n(A $\cap$ B)
3. n(A) + n(B) + n(A $\cap$ B)
4. n(A) - n(B)

Q. In a class of $70$ students, $38$ students like physics, $21$ students like mathematics and $15$ students like both the subjects, then the number of students who like neither of the subjects is

1. $27$
2. $24$
3. $11$
4. $26$

Q. According to a survey of $500$ people, $300$ preferred tea while $100$ preferred coffee. $50$ people preferred both tea and coffee. how many people didn't prefer any of the drinks?

1. $350$
2. $150$
3. $400$
4. None of the above

Q. Let $X=\{n\in N:1\le n\le 50\}$. If $A=\{n\in X:n\text{is a multiple of 2}\}$ and $B=\{n\in X:n\text{is a multiple of 7}\}$, then the number of elements in the smallest subset of $X$ containing both $A$ and $B$ is

Q. $100$ students of class $12th$ opted for Mathematics while $90$ students opted for Biology. $170$ students opted for Mathematics or Biology. How much students opted for Mathematics and Biology?

1. $360$
2. $190$
3. $20$
4. None of the above

Q. If $U$ is the universal set with 100 element; $A$ and $B$ are two set such that $n\left(A\right)=50,n\left(B\right)=60,n(A\cap B)=20$, then $n(A^{\prime }\cap B^{\prime })=$

1. $90$
2. $40$
3. $10$
4. $20$

Q.

In a group of $70$ people, $37$ like coffee, $52$ like tea and each person like at least one of the two drinks. The number of persons liking both coffee and tea is:

1. $16$

2. $13$

3. $19$

4. $20$

Q.

In a class of 30 students, 18 students play cricket, 15 students play football 12 play both the games. How many students in the class don't play both the games?

__

Q.

In a school, 40% of the students draw and paint. 40% of those who draw do not paint. If the students do one of the two, then what % of students paint?

1. 70

2. 82.3

3. 73.33

4. 50.54

Q. In a group of $800$ people, $500$ can speak Hindi and $320$ can speak English. Let $\alpha$ be the number of people who speak both languages. Then

1. $320\le \alpha \le 500$
2. $20\le \alpha \le 320$
3. $\alpha \le 320$
4. $\alpha \ge 320$

Q. If two sets $A$ and $B$ are such that $n\left(A\right)=20$, $n(A\cap B)=4$, and $n(A\cup B)=42$, then

1. $n\left(B\right)=22$
2. $n(B-A)=22$
3. $n\left(B\right)=26$
4. $n(A-B)=16$

Q.

For universal set $U$, and sets $A,B$ which are subsets of $U$, the following information is given

$n\left(U\right)=47,$

$n\left(A\right)=18,$

$n\left(B\right)=11,n(A\cap B)=10$

Then, the number of elements that are neither in $A$ nor $B$ is__

Q. If $U$ is the universal set with 100 element; $A$ and $B$ are two set such that $n\left(A\right)=50,n\left(B\right)=60,n(A\cap B)=20$, then $n(A^{\prime }\cap B^{\prime })=$

1. $90$
2. $40$
3. $10$
4. $20$

Q. Let $A=\{1,2,3,4,...,40\}$ be the set of registration number of students of class $12$. Students having registration number as multiple of $4$ play cricket but do not play football, students having even registration number play either cricket or football or both and students having registration number as multiple of $10$ play both cricket and football. Find the number of students who play football.

1. $6$
2. $14$
3. $16$
4. $10$

Q. In a community it is found that $52\%$ people like prime video and $73\%$ like Netflix and $x\%$ like both, then

1. $x\ge 25$
2. $x\le 25$
3. $25\le x\le 52$
4. $x=36$

Q. Let $n\left(U\right)=700,n\left(A\right)=200,n\left(B\right)=300$ and $n(A\cap B)=100$, then $n(A^c\cap B^c)$ equals to

1. $400$
2. $600$
3. $300$
4. $20$

Q. In a group of $50$ students, the number of students studying French, English, Sanskrit were found to be as follows:
French $=17,$ English $=13,$
Sanskrit $=15$
French and English $=09,$
English and Sanskrit $=4$,
French and Sanskrit $=5$,
English, French an Sanskirt $=3$.
Find the number of students who study

$\left(i\right)$ French only

$\left(ii\right)$ English only

$\left(iii\right)$ Sanskrit only

$\left(iv\right)$ English and Sanskrit but not French

$\left(v\right)$ French and Sanskrit but not English

$\left(vi\right)$ French and English but not Sanskrit

$\left(vii\right)$ at least one of the three languages

$\left(viii\right)$ none of the three languages

Q. A set A contains $3$ elements and set $B$ contains $4$ elements. The maximum number of elements in $AUB$ is

1. $3$
2. $4$
3. $7$
4. $12$