Question 1 :
Let $P$ be the set of points inside the square, $Q$ be the set of points inside the triangle and $R$ be the set of points inside the circle. If the triangle and circle intersect each other and are contained in the square then,<br/>
Question 2 :
In a certain office, $\dfrac{1}{3}$ of workers are women, $\dfrac{1}{2}$ of the women are married and $\dfrac{1}{3}$ of the married women have children. If $\dfrac{3}{4}$ of the men are married and $\dfrac{2}{3}$ of the married men have children, what part of the workers are without children ?
Question 3 :
Set $A$ has $3$ elements and set $B$ has $6$ elements. What can be the minimum number of elements in $A\cup B$?
Question 4 :
If $X=\{ { 4 }^{ n }-3n-1:n\in N\}$ and<br> $Y=\{ 9(n-1):n\in N\},$ then $X\cup Y$ is equal to
Question 5 :
Let $A$ and $B$ have $3$ and $6$ elements respectively. What can be the minimum number of elements in $A\cup B$?
Question 6 :
For two sets $A$ and $B$, $ A\cap \left( A\cup B \right)=$
Question 8 :
If X $=$ (multiples of 2), Y $=$ (multiples of 5), Z $=$ (multiples of 10), then $X \cap ( Y \cap Z )$ is equal to<br>
Question 10 :
If $S$ and $T$ are two sets such that $S$ has $21$ elements, $T$ has $32$ elements and $\displaystyle S\cap T$ has $11$ elements, then<br/>find the number of elements in $\displaystyle S\cup T$.
Question 11 :
Let $A_1, A_2$ and $A_3$ be subsets of a set $X$. Which one of the following is correct?
Question 12 :
In a community of $ 175$ persons, $40$ read TOI, $50$ read the Samachar Patrika and $100$ do not read either. How many persons read both the papers?
Question 13 :
Let U = {all digits of our number system}; A = { set of prime numbers }; B = { factors of $36$. Then A $\displaystyle\cup$ B includes:
Question 14 :
In an examination $70\%$ students passed both in Mathematics and Physics $85\%$ passed in Mathematics and $80\%$ passed in Physics If $30$ students have failed in both the subjects then the total number of students who appeared in the examination is equal to :
Question 15 :
If A = $\{ 1, 2, 3, 4\}$, B = $\{2, 4, 5, 6\}$ and C = $\{1, 2, 5, 7, 8,\}$ then $\displaystyle \left ( A\cup C \right )\cap B$ is equal to:
Question 16 :
For any two sets A and B, $A = B$ is equivalent to
Question 17 : <div>If $A = \{5, 6, 7, 8\}$ and $B =\{6, 8, 10\}$ find $A \cup B$.</div>
Question 18 :
Let $P = \{ x | x$ is a multiple of $3$ and less than $100 $ ,$x$ $\displaystyle \in $ $N \}$<br/>$Q = \{ x | x$ is a multiple of $10$ and less than $100$, $x$ $\displaystyle \in$ $N\}$<br/>
Question 19 :
If $A$ and $B$ are non empty sets and A' and B' represents their compliments respectively then
Question 20 :
If $X$ and $Y$ are any two non empty sets then what is $\displaystyle \left ( X-Y \right )'$ equal to?
Question 21 :
Let $P =$ Set of all integral multiples of $3 $; $Q =$ Set of integral multiples of $4 $; $R =$ Set of all integral multiples of $6$. Consider the following relations :<br/>$1 $ $\displaystyle P\cup Q=R$<br/>$2.$ $\displaystyle P\subset R$<br/>$3.$ $\displaystyle R\subset \left ( P\cup Q \right )$<br/>Which of the relations given above is/are correct ?
Question 22 :
If $n(A) = 65, n(B) = 32$ and $\displaystyle n\left ( A\cap B \right )=14 $, then $\displaystyle n\left ( A\Delta B \right ) $ equals
Question 23 :
If $n(A) = 115$, $n(B) = 326$, $n(A - B) = 47$ then $\displaystyle n\left ( A\cup B \right )$ is equal to
Question 24 :
If $\displaystyle \xi =\left \{ 2,3,4,5,6,7,8,9,10,11 \right \}$<br/>$\displaystyle A =\left \{ 3,5,7,9,11 \right \}$<br/>$\displaystyle B =\left \{ 7,8,9,10,11 \right \}$, then find $(A - B)'$<br/>
Question 25 :
If $P(A) = 0.8 , P(B) = 0.5 $ & $P(B/A) =0.4 $ find (i) $P(A \cap B) $ (ii) $P(A/B)$ (iii) $P(A\cup B)$.
Question 26 :
If $n(A)$ denotes the number of elements in set A and if $n(A)=4, n(B)=5$ and $n(A\cap B)=3$ then $n\left[ \left( A\times B \right) \cap \left( B\times A \right) \right] =$
Question 27 :
If $X$ and $Y$ are two sets, then $X\cap \left( Y\cup X \right)'$ equals
Question 29 :
$A$ and $B$ are two sets having $3$ and $5$ elements respectively and having $2$ elements in common. Then the number of elements in $A\times B$ is
Question 31 :
A survey was carried out to find out the types of shampoo that a group of $150$ women have tried. It was found that $84$ women have used brand A shampoo, $93$ have used brand B, and $69$ have used brand C of these women, $45$ have tried brands A and B, $25$ have tried brands A and C and $40$ have tried brand B and C. Determine the number of women who have tried (a) all three brands, (b) only brand A
Question 32 :
If $X$ and $Y$ are two sets, then $X\cap \left( X\cup Y \right)$ equals
Question 33 :
If $A=\left\{2, 4, 6, 8, 10\right\}, B=\left\{1, 3, 5, 7, 9\right\}$, then $A-B$ =____________
Question 35 :
Let $A$ and $B$ be two sets such that $A\cap B=\phi$. Find the value of $(A\cup B')=$
Question 36 : <div>Given the universal set $B = \{-7,-3,-1,0,5,6,8,9\}$, find :</div>$B = \{x : -4 < x < 6\}$
Question 37 :
Consider the following for any three non empty sets A, B and C<br>1 $\displaystyle A-\left ( B\cup C \right )=\left ( A-B \right )\cup \left ( A-c \right )$<br>2 $\displaystyle A-B=A-\left ( A\cap B \right )$<br>3 $\displaystyle A=\left ( A\cap B \right )\cup \left ( A-B \right )$<br>which of the above is/are correct?
Question 38 :
Let A and B be two non empty subsets of a set X If $\displaystyle \left ( A-B\right )\cup \left ( B-A \right )=A\cup B $, then which one of the following is correct?
Question 39 :
Given $\displaystyle A= \left \{ 1,2,3 \right \}, B= \left \{ 3,4 \right \}, C= \left \{ 4,5,6 \right \}$ find:$\displaystyle A\cup \left ( B\cup C \right )$
Question 40 :
Let A = { letters of the word "IDEA"} and B = {letters of the word "MAN"}.<br>Then the sets A and B are
Question 41 :
If $F(n)$ denotes the set of all divisions of n except $1$ what is the least value of $y$ satisfying $\displaystyle \left [ F\left ( 20 \right )\cap F\left ( 16 \right )\subseteq F\left ( y \right ) \right ] $
Question 42 :
Let $\displaystyle Z_{N}$ be the set of non negative integers, $\displaystyle Z_{P}$ be the set of non positive integers, $Z$ the set of integers, E the set of even integers and P the set of prime numbers, then
Question 43 :
The value of c for which the set {(x, y) | $\displaystyle x^{2}+y^{2}+2x\leq 1$} $\displaystyle \cap $ {$(x, y) | x - y + c$ $\displaystyle \geq 0 $} contains only one point in common is
Question 44 :
Given $A=\left\{ x:x\ is\ a\ root\ of\ { x }^{ 2 }-1=0\right\}$, $B=\left\{ x:x\ is\ a\ root\ of\ { x }^{ 2 }-2x+1=0 \right\}$ then
Question 45 :
If for two sets $A$ and $B$, $A\cup B=A\cap B=A$, then we have
Question 46 :
Let $U=\left\{ 1,2,3,4,5,6,7,8,9,10 \right\}$, $A=\left\{ 1,2,5 \right\}$, $B=\left\{ 6,7 \right\}$ then $A\cap B'$ is
Question 47 :
If A and B be any two sets, then $\displaystyle \left( A \cap B \right) '$ is equal to
Question 48 :
Let $A$ and $B$ be two sets in the universal set. Then $ (A \cup B)'$ equals
Question 49 :
Let $U$ be the set of all people and $M=$(Males), $S=$(College Students), $T=$(Teenagers), $W=$ {People having height more than five feet). Express All people who are neither males nor teenagers nor college students in the notation of set theory.
