Union and intersection of sets - class-XI

Question 1 Multiple Choice (Single Answer)

If A = {5, 6, 7, 8} and B = {6, 8, 10} ; find :

$A \cap B$

$\{5\}$
$\{7,6\}$
$\{6,8\}$
$\{6,8,10\}$

Question 2 Multiple Choice (Single Answer)

A and B are two sets such that $A\displaystyle\cup B$ has $18$ elements If A has $8$ elements and B has $15$ elements then the number of elements in $A\displaystyle\cap B$ will be:

$5$
$8$
$7$
$4$

Question 3 Multiple Choice (Single Answer)

Let A = { even number} B = {prime numbers} Then A $\displaystyle\cap $ B equals:

{odd number}
{composite number}
{2}
{whole numbers}

Question 4 Multiple Choice (Single Answer)

Let $A = { x | x$ $\displaystyle \in $ $N$, $x$ is a multiple of 2$ }$
$ B = { x | x$ $\displaystyle \in $ $N$, $x$ is a multiple of 5$}$
$C = {x | x$ $\displaystyle \in $ $N$, $x$ is a multiple of 10$}$
The set $\displaystyle\left ( A\cap B \right )\cap C$ is equal to:

$A$
$\displaystyle A \cap C$
$B$
$C$

Question 5 Multiple Choice (Single Answer)

There are $19$ hockey players in a club. On a particular day $14$ were wearing the prescribed hockey shirts while $11$ were wearing the prescribed hockey paints. None of them was without a hockey pant or a hockey shirt. How many of them were in complete hockey uniform ?

$8$
$6$
$9$
$7$

Question 6 Multiple Choice (Single Answer)

If $\displaystyle A\cap B=A$ and $\displaystyle B\cap C=B$ then $\displaystyle A\cap C$ is equal to :

$B$
$C$
$\displaystyle B\cup C$
$A$

Question 7 Multiple Choice (Single Answer)

In a group of $500$ people $200$ can speck Hindi alone while only $125$ can speck English alone The number of people can speck both Hindi and English is

$175$
$325$
$300$
$375$

Question 8 Multiple Choice (Single Answer)

Given $A={a,b,c,d,e,f,g,h}$ and $B={a,e,i,o,u}$ then $A\cap B$ is equal to

$\{a,e\}$
$\{f,g\}$
$\{g,h\}$
$\{i,u\}$

Question 9 Multiple Choice (Single Answer)

If X=(multiples of $2$ ), Y = ( multiples of $5$) , Z= (multiples of $10$), then $ \displaystyle X \cap(Y\cap Z) $ is equal to

Multiples of $10$
Multiples of $5$
Multiples of $2$
Multiples of $7$

Question 10 Multiple Choice (Single Answer)

If $A={x:x^2-3x+2=0}$ and $B={x:x^2+4x-5=0}$ then the value of $A-B$ is

$\{1,2\}$
$\{2\}$
$\{1\}$
$\{5,2\}$

Question 11 Multiple Choice (Single Answer)

There are $19$ hockey players in a club. On a particular day $14$ were wearing the prescribed hockey shirts, while $11$ were wearing the prescribed hockey pants. None of them was without hockey pant or hockey shirt. How many of them were in complete hockey uniform?

$8$
$6$
$9$
$7$

Question 12 Multiple Choice (Single Answer)

Out of $450$ students in a school, $193$ students read Science Today, $200$ students read Junior Statesman, while $80$ students read neither. How many students read both the magazines?

$137$
$80$
$57$
$23$

Question 13 Multiple Choice (Single Answer)

In a community of $175$ persons, $40$ read the Times, $50$ reads the Samachar and $100$ do not read any. How many persons read both the papers?

$10$
$15$
$20$
$25$

Question 14 Multiple Choice (Single Answer)

In a group of $15, 7$ have studied, German, $8$ have studied French, and $3$ have not studied either. How many of these have studied both German and French?

$0$
$3$
$4$
$5$

Question 15 Multiple Choice (Single Answer)

In a class consisting of $100$ students, $20$ know English and $20$ do not know Hindi and $10$ know neither English nor Hindi. The number of students knowing both Hindi and English is

$5$
$10$
$15$
$20$

Question 16 Multiple Choice (Single Answer)

If $A = \left {1, 2, 3, 4, 5, 6, 7, 8\right }$ and $B \left {1, 3, 5, 7\right }$, then find $A - B$ and $A \cap B$

$\left \{3, 5\right \}$ and $\left \{2, 4, 6\right \}$
$\left \{2, 4, 6\right \}$ and $\left \{1, 5\right \}$
$\left \{2, 4, 6, 8\right \}$ and $\left \{1, 3, 5, 7\right \}$
$\left \{1, 3, 5, 8\right \}$

Question 17 Multiple Choice (Single Answer)

In a certain group of $36$ people, $18$ are wearing hats and $24$ are wearing sweaters. If six people are wearing neither a hat nor a sweater, then how many people are wearing both a hat and a sweater?

$30$
$22$
$12$
$8$

Question 18 Multiple Choice (Single Answer)

In a class of $80$ children, $35$% children can play only cricket, $45$% children can play only table-tennis and the remaining children can play both the games. In all, how many children can play cricket?

$55$
$44$
$36$
$28$

Question 19 Multiple Choice (Single Answer)

If x belongs to set of integers, A is the solution set of $2(x-1)< 3x-1$ and B is the solution set of $4x-3\leq 8+x$, find A$\cap$B.

$\left\{0, 1, 2\right\}$
$\left\{1, 2, 3\right\}$
$\left\{0, 1, 2, 3\right\}$
$\left\{0, 2, 4\right\}$

Question 20 Multiple Choice (Single Answer)

If $A = {1, 3, 5, 7, 8, 6}$, $B = {2, 4, 6, 8, 9}$ .Find $A\cap B$

$\{8\}$
$\{9\}$
$\{10\}$
None of these

Question 21 Multiple Choice (Single Answer)

If $A = \left {2, 3, 4, 8, 10\right }, B = \left (3, 4, 5, 10, 12\right }, C = \left {4, 5, 6, 12, 14\right }$, then $(A\cap B)\cup (A\cap C)$ is equal to

$\left \{3, 4, 10\right \}$
$\left \{2, 9, 10\right \}$
$\left \{4, 5, 6\right \}$
$\left \{3, 5, 14\right \}$

Question 22 Multiple Choice (Single Answer)

If U = {1, 2, 3, 4, 5, 6}; A = {3, 5}; B = {2, 3, 4} C = {4, 5}, find then A $\cap$ (B $\cup$ C).

{1, 2, 3, 4, 5, 6}
{3, 5}
{2, 3, 4}
{4, 5, 6}

Question 23 Multiple Choice (Single Answer)

Which is the simplified representation of
$\left( {{A^/} \cap ,{B^/} \cap ,C} \right) \cup \left( {B, \cap ,C} \right) \cup \left( {A \cap ,C} \right)$

where A,B,C are subsets of X

A
B
C
$X \cap \,\left( {A \cup B \cup C} \right)$

Question 24 Multiple Choice (Single Answer)

If $aN=\left{ ax:x\epsilon N \right}$, then the set $3N\cap 7N$ is

$21\ N$
$10\ N$
$4\ N$
None of these

Question 25 Multiple Choice (Single Answer)

If $n(U)= 60, n(A)= 35, n(B)= 24$ and $n(A \cup B)' = 10$ ,then $n(A \cap B)$ is

$9$
$8$
$6$
$7$

Question 26 Multiple Choice (Single Answer)

A is a set containing $n$ elements. $A$ subset $P$ of $A$ is chosen. the set $A$ is reconstructed by replacing the elements of $P.A$ subset $Q$ of $A$ is again chosen. the number of ways of choosing $P$ and $Q$ so that $P \cap Q$

$9. ^{n}C _{2}$
$3^{n}- ^{n}C _{2}$
$^{n}C _{2}.3^{n-2}$
$4^{n}-3^{n}$

Question 27 Multiple Choice (Single Answer)

Let $A=\left{ a,b,c,d \right} ,B=\left{ b,c,d,e \right}$. Then $n\left[ \left( A\times B \right) \cap \left( B\times A \right) \right]$ is equal to

$3$
$6$
$9$
$none$

Question 28 Multiple Choice (Single Answer)

Let A={1, 2, 3, 4), B={2, 3, 4, 5}, then $n{ (A\times B)\cap (B\times A)} =$?

13
16
9
10

Question 29 Multiple Choice (Single Answer)

Let $P={ \theta :sin\theta -cos\theta =\sqrt { 2 } cos\theta } $ and $Q={ sin\theta + cos\theta =\sqrt { 2 } sin\theta } $ be two sets. Then:

$P\subset Q\quad and\quad Q-P\neq \emptyset $
$Q\subset P$
$P\subset Q$
$P=Q$

Question 30 Multiple Choice (Single Answer)

If $A = {1, 2, 3, 4, 5}, B = {2, 4, 6, 8}$ and C= ${3,4,5,6}$,

then verify : $A - (B \cup C) = (A - B) \cap (A - C)$.

True
False

Question 31 Multiple Choice (Single Answer)

Let $A = {$ multiples of $3$ less than $20 }$
$B = {$ multiples of $5$ less than $20}$
Then $A$ $\displaystyle\cap$ $B$ is

$\{3, 5\}$
$\{5, 9\}$
${15}$
$\displaystyle\phi $

Question 32 Multiple Choice (Single Answer)

Let $P _1$ be the set of all prime numbers, i.e., $P _1=\left {2, 3, 5, 7, 11, ....\right }$, Let $Pn=\left {np|p\epsilon P _1|\right }$, i.e., the set of all prime multiples of n. Then which of the following sets is non empty?

$P _1\cap P _{23}$
$P _7\cap P _{21}$
$P _{12}\cap P _{20}$
$P _{20}\cap P _{24}$

Question 33 Multiple Choice (Single Answer)

If $A={a,b,c,d,e,f}$ and $B={c,e,f,g,h}$, then the number of elements of $(A-B)\cap A$ is

$0$
$1$
$2$
$3$

Question 34 Multiple Choice (Single Answer)

In a group of $760$ persons, $510$ can speak Hindi and $360$ can speak English. Find how many can speak Hindi only.

$250$
$400$
$1270$
$150$

Question 35 Multiple Choice (Single Answer)

There are $25$ trays on a table in the cafeteria. Each tray contains a cup only, a plate only, or both a cup and a plate. If $15$ of the trays contain cups and $21$ of the trays contain plates, how many contain both a cup and a plate?

$10$
$11$
$12$
$13$

Question 36 Multiple Choice (Single Answer)

Let A = {x : x is a square of a natural number and x is less than 100} and B is a set of even natural numbers. What is the cardinality of $ A \cap B$ ?

4
5
9
None of the above

Question 37 Multiple Choice (Single Answer)

If $A = ${1,4,6}, $B = ${3,6}, then find $(A \cap B)$

$({1,3,4,6})$
$\phi$
${6}$
none of these

Question 38 Multiple Choice (Single Answer)

$If\ A = {1, 2, 3}, B = {4, 5}, then\ find\ A \cap B$

${1, 2, 3, 4, 5}$
$\phi $
${4,5}$
${1, 2, 3}$

Question 39 Multiple Choice (Single Answer)

A survey shows that $63%$ of Indians like mangoes whereas $76%$ like apple. If $x%$ of the Indians like both mangoes and apples, then

$x=39$
$x=63$
$39\le x\le 63$
$None\ of\ these$

Question 40 Multiple Choice (Single Answer)

Two set A and B are as under
A = {(a,b) $\epsilon$ R $\times$ R : $\mid a - 5\mid$ < $1$ and $\mid b - 5\mid$ < $1$};
B = {(a,b) $\epsilon$ R $\times$ R : $4(a-6)^2 + 9(b-5)^2$ $\leq 36$. Then,

B $\subset$ A
A $\subset$ B
A $\bigcap$ B = $\phi$ (an empty set)
nither A $\subset$ B nor B $\subset$ A

Question 41 Multiple Choice (Single Answer)

$R$ is the set of all positive odd integers less than $20$; $S$ is the set of all multiples of $3$ that are less than $20$. How many elements are in the set $R$ $\cap$ $S$?

0
1
2
3
4

Question 42 Multiple Choice (Single Answer)

Let $Z$ denotes the set of all integers and $A=\left{ \left( a,b \right) :{ a }^{ 2 }+3{ b }^{ 2 }=28,a,b\in Z \right} $ and $B=\left{ \left( a,b \right) :a < b,a,b\in Z \right} $. Then, the number of elements in $A\cap B$ is

$2$
$4$
$6$
$5$

Question 43 Multiple Choice (Single Answer)

Let $A,B$ be two sets such that $A\cap B=\phi$, then $A=\phi$ and $B=\phi$?

True
False

Question 44 Multiple Choice (Single Answer)

If $A={\theta :\tan \theta -\tan^2\theta > 0}, B={\theta :|\sin \theta | < 1/2}$ find $A\cap B$.

$\left(0 , \cfrac{7\pi}{6}\right)$
$\left(0 , \cfrac{\pi}{6}\right)$
$\left(0 , -\cfrac{\pi}{6}\right)$
None of these

Union and intersection of sets - class-XI

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