Question 1 :
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 ?
Question 2 :
If A = {1, 2, 3, 4, 5, 6, 7, 8} and B = {1, 3, 5, 7}, then find $A - B$ and $A \cap B$<br>
Question 3 :
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 4 :
If $U = \left \{x|x\epsilon N, x < 5\right \}, A = \left \{x|x\epsilon N, x\leq 2\right \}$ then $A' =$ __________.
Question 6 :
Let $n(u)=700,n(A)=200,n(B)=300$<br>$n\left( A\cap B \right) =100,n\left( A^{\prime} \cap B^{\prime} \right) =$
Question 7 : <span>The union of the following pair of sets is:</span><div>$C = \{a, e, i, o, u\}, D = \{a, b, c, d\}$</div>
Question 8 :
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 9 :
If $A=\left\{2, 4, 6, 8, 10\right\}, B=\left\{1, 3, 5, 7, 9\right\}$, then $A-B$ =____________
Question 10 :
Let $A_1, A_2$ and $A_3$ be subsets of a set $X$. Which one of the following is correct?
Question 11 :
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?
Question 12 :
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?
Question 15 :
Find <span>the set of values of x for which it satisfies </span>$- 2 \le \left[ x \right] \le 4.$ (where $\left[ \ \ \right]$ denotes the greatest integer function )
Question 16 :
<span>Classify the following set as 'singleton' or 'empty': </span>$C = \{x | x$ is natural number, $5 < x < 7\}$
Question 17 :
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
Question 19 :
The set of integers is closed with respect to which one of the following?
Question 20 :
Let $A$ and $B$ be two sets such that $A\cap B=\phi$. Find the value of $(A\cup B')=$
Question 22 :
One Hundred Twenty-five $(125)$ aliens descended on a set of film as Extra Terrestrial Beings. $40$ had two noses, $30$ had three legs, $20$ had four ears, $10$ had two noses and three legs, $12$ had three legs and four ears, $5$ had two noses and four ears and $3$ had all the three unusual features. How many were there without any of these unusual features?
Question 23 :
The set of all those elements of A and B which are common to both is called
Question 24 :
Consider the following relations<br/>(1)$A-B=A-\left( A\cap B \right) $<br/>(2)$A=A-\left( A\cap B \right) \cup \left( A-B \right) $<br/>(3)$A-\left( A\cup C \right) =\left( A-B \right) \cup \left( A-C \right) $<br/>Which of these is correct
Question 25 :
If A has 5 elements and B has 8 elements such that $\displaystyle A\subset B,$ then the number of elements in $\displaystyle A\cap B,$ and $\displaystyle A\cup B,$ are respectively :
Question 26 :
Is the set $H = \{t | t$ is a triangle having four sides$\}$ empty?
Question 27 :
The set $\displaystyle A=\left\{ x:x\in { x }^{ 2 }=16\quad and\quad 2x=6 \right\} $ equals:
Question 28 :
From among the given alternatives select the one in which the set of numbers is most like the set of numbers given in the question.<br>Given set $:$ $(7, 15, 31)$<br>
Question 30 :
In a science talent examination, $50$% of the candidates fail in Mathematics and $50$% fail in Physics. If $20$% fail in both these subjects, then the percentage who pass in both Mathematics and Physics is
Question 31 :
The set B= {a|a is a negative integer and a-1=0} is a
Question 32 :
If X $=$ (multiples of 2), Y $=$ (multiples of 5), Z $=$ (multiples of 10), then $X \cap ( Y \cap Z )$ is equal to<br>
Question 34 : If $A, B$ and $C$ are any three set, then $A \cup (B\cap C) =$<div><br/></div>
Question 35 :
If $A=\{\theta :\tan \theta -\tan^2\theta > 0\}, B=\{\theta :|\sin \theta | < 1/2\}$ find $A\cap B$.
Question 37 :
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 38 :
Let A = { letters of the word "IDEA"} and B = {letters of the word "MAN"}.<br>Then the sets A and B are
Question 40 :
<span>Classify the following set as 'singleton' or 'empty': </span>$A = \{ x | x$ is a negative natural number$\}$
Question 42 :
The set of two digit numbers greater than 98 is a/an
Question 43 : <p>Suppose ${ A }_{ 1 },{ A }_{ 2 },...,{ A }_{ 30 }$ are thirty sets, each with five elements and ${ B }_{ 1 },{ B }_{ 2 },...,{ B }_{ 30 }$ are $n$ sets ecah with three elements. Let $\displaystyle \bigcup _{ i=1 }^{ 30 }{ { A }_{ i }= } \bigcup _{ j=1 }^{ n }{ { B }_{ j } } =S$</p><p>If each element of $S$ belongs to exactly ten of the ${ A }_{ i }'s$ and exactly none of the ${ B }_{ j }'s$ then $n=$</p>
Question 44 :
Given $K=\left \{B, A, N, T, I\right \}$. Then the number of subsets of K, that contain both A, N is
Question 45 :
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:
Question 46 :
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?
Question 48 : <p>Suppose ${ A }_{ 1 },{ A }_{ 2 },...,{ A }_{ 30 }$ are thirty sets, each with five elements and ${ B }_{ 1 },{ B }_{ 2 },...,{ B }_{ 30 }$ are $n$ sets ecah with three elements. Let $\displaystyle \bigcup _{ i=1 }^{ 30 }{ { A }_{ i }= } \bigcup _{ j=1 }^{ n }{ { B }_{ j } } =S$</p><p>If each element of $S$ belongs to exactly ten of the ${ A }_{ i }'s$ and exactly none of the ${ B }_{ j }'s$ then $n=$</p>
Question 49 :
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?
