n(A∪B) = n(A) + n(B) − n(A∩B)

Q.

If $AandB$ are disjoint sets, then $n(A\cup B)$ is equal to

1. $n\left(A\right)+n\left(B\right)$

2. $n\left(A\right)+n\left(B\right)–n(A\cap B)$

3. $n\left(A\right)+n\left(B\right)+n(A\cap B)$

4. $n\left(A\right)+n\left(B\right)+n(A+B)$

5. $n\left(A\right)–n\left(B\right)$

Q.

If ${\mathrm{P}}_{\mathrm{m}}$ stands for ${}^{\mathrm{m}}{\mathrm{P}}_{\mathrm{m}}$, then $1+1{\mathrm{P}}_1+2{\mathrm{P}}_2+3{\mathrm{P}}_3+\dots +{\mathrm{nP}}_{\mathrm{n}}$ is equal to:

1. $1!$

2. $(n+3)!$

3. $(n+2)!$

4. $(n+1)!$

Q.

If $A$ and $B$ be two sets such that $n\left(A\right)=15$, $n\left(B\right)=25$, then the number of possible values of $n(A△B)$ (symmetric difference of $A$ and $B$) is

1. $30$

2. $16$

3. $26$

4. $40$

Q. In a examination, $45\%$of the candidates have passed in English, $40\%$ have passed in Hindi, while $30\%$ have passed in both the subjects. find the total number of candidates, if $90$ of them have failed in both the subjects.

1. $100$
2. $200$
3. $50$
4. None of the above

Q.

If$a+2b+3c=0,$ then $a\times b+b\times c+c\times a=ka\times b,$ Where $k$ is equal to ?

1. $0$

2. $1$

3. $2$

4. $3$

Q.

If A and B are 2 sets such that A U B has 40 elements, A has 18 elements and B has 29 elements, how many elements does A ∩ B have? __

Q.

Sets A and B have 3 and 6 elements respectively. What can be the minimum number of elements in (A U B )

1. 3

2. 6

3. 9

4. 18

Q. The number of $4-$digit numbers which are neither multiple of $7$ nor multiple of $3$ is

Q. Out of all the patients in a hospital $89\%$ are found to be suffering from heart ailment and $98\%$ are suffering from lungs infection. If $K\%$ of them are suffering from both ailments, then $K$ can not belong to the set:

1. $\{84,87,90,93\}$
2. $\{84,86,88,90\}$
3. $\{79,81,83,85\}$
4. $\{80,83,86,89\}$

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. 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. If two sets $A\&B$ are disjoint sets, then $n(A\cup B)=n\left(A\right)+n\left(B\right).$

1. False
2. True

Q. If $n\left(U\right)=60,n\left(A\right)=21,n\left(B\right)=43,$ then minimum and maximum value of $n(A\cup B)$ is

1. $43,60$
2. $50,64$
3. $44,60$
4. $38,60$

Q.

In a survey of 200 students from 7 different schools, 50 people do not play NFS, 40 people do not play Dota and 10 people play no online game. Then find the no. of people out of 200 people who do not play both the games provided these are the only two games on offer.

1. 80

2. 70

3. 60

4. 50

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. Let $A$ and $B$ be two sets containing $4$ and $7$ elements respectively. If the minimum and maximum number of elements in $A\cup B$ are $m$ and $n$ respectively, then $m+n$ is

1. $18$
2. $19$
3. $20$
4. $21$

Q. For any two sets $A$ and $B$,
$n\left(AUB\right)\ge n\left(A\right)+n\left(B\right)$
where, $n\left(P\right)$ represents the number of elements in set $P$.

1. False
2. True

Q.

A survey shows that 63% of the people watch news whereas 76% watch sports. If $x$% of people watch both sports and news, then

1. $x=39$

2. $x=63$

3. $39\le x\le 63$

4. $0\le x\le 39$

Q.

In a factory 70% of the workers like oranges and 64% likes apples. If each worker likes at least one fruit, What is the minimum percentage of workers who like both the fruits?

__

Q. A survey shows that 63% of the Indians like Paneer whereas 76% like Tofu. If x% of the Indians like both Paneer and Tofu, then which of the following is/are correct?

1. Maximum value of x is 63.
2. Maximum value of x is 76.
3. Minimum value of x is 39.
4. Minimum value of x is 0.