Question 1 :
How many elements does following set contain?<br/>$F = \{y | y$ is a point of intersection of two parallel lines$\}$
Question 2 :
Two finite sets have m and n elements. The total number of subsets of the first set is 56 more than the total number of subsets of the second set. Find the values of m and n.
Question 3 :
Let $A =$ {$\phi$ , {$\phi$},$1$, {$1$,$\phi$ },$7$}. Which of the following is true?<br/><br/>
Question 4 :
Say true or false.The collection of rich people in your district is an example of a set.
Question 5 :
State whether the following statement is True or False<br/>If $U=\left\{1,2,3,4,5,6,7\right\}$ and $A=\left\{5,6,7\right\}$, then $U$ is the subset of $A$.
Question 7 :
If  $B = \{y | y^2 = 36\}$ then the set $B$ is a ______ set.
Question 8 :
If $A = \left \{1, 2, 3, 4\right \}$, what is the number of subsets of A with at least three elements?
Question 10 :
A=B for which of the following statements?<br>$(i)A=\{2,4,6,8,10\};$ <br> $B=\{x:x$ is a positive even integer and $x\le10\}$<br>$(ii)A=\{x:x$ is a multiple of $10\};$ <br> $B=\{10,15,20,25,30,.....\}$
Question 12 :
Classify the following set as 'singleton' or 'empty':  $B = \{y | y$ is an odd prime number $< 4\}$
Question 13 :
The set B= {a|a is a negative integer and a-1=0} is a
Question 14 :
State whether the following statements are true(T) or false(F).Justify your answer.<br>A collection of some fruits is a set.
Question 17 :
The set of all those elements of A and B which are common to both is called
Question 21 :
If $X = \left \{1, 2, 3, ..., 10\right \}$ and $A = \left \{1, 2, 3, 4, 5\right \}$. Then, the number of subsets $B$ of $X$ such that $A - B = \left \{4\right \}$ is
Question 22 :
Let $A , B$ and $C$ be pairwise independent events with $P ( C ) > 0$ and $P ( A \cap B \cap C ) = 0$ Then, $P \left( A ^ { C } \cap B ^ { C } / C \right)$ is equal to
Question 23 :
In a survey of 25 students, it was found that 15 had taken mathematics, 12 had taken physics and 11 had taken chemistry, 5 had taken mathematics and chemistry, 9 had taken mathematics and physics, 4 had taken physics and chemistry and 3 had taken all the three subjects.Find the number of students that had taken exactly two of the three subjects.
Question 26 :
In a flight 50 people speak Hindi, 20 speak English and 10 speak both English and Hindi. The number of people who speak atleast one of the two languages is
Question 27 :
Find out the truth sets of the following open sentences replacement sets are given against them.<br>$2(x-3)< 1 ; \{1, 2, 3, 4, .......10\}.$
Question 28 :
Two finite sets have $m$ and $n$ elements. The total number of subsets of first set $56$ more than the total number of subsets of second set. Find the values of $m$ and $n.$
Question 30 :
State whether the following statements is true or false. Justify your answer.<br>The set of all integers is contained in the set of all rational numbers.<br>
Question 31 :
The number of binary operations on the set $\{1, 2, 3\}$ is _________.
Question 33 :
In each of the following, determine whether the statement is true or false. If it is true, prove it. If it is false, give an example.<br>If $x A$ and $A B$, then $x B$<br>
Question 34 :
If $A$ and $B$ are any two non-empty sets, then prove that $(A\cap B)'=$ 
Question 35 :
Let $A=\{x:x\in R\  \&\ x^2+1=0\}$ then $A$ is a null set.
Question 36 :
Let $A=\left\{ \left( x,y \right) :y={ e }^{ x },x\in R \right\}$<br> $B=\left\{ \left( x,y \right) :y={ e }^{ -x },x\in R \right\}$. Then
Question 37 :
The smallest set $A$ such that $A\cup \left\{ 1,2 \right\} =\left\{ 1,2,3,5,9 \right\} $ is 
Question 38 :
The set A = { x : x + 4 = 4} can also be represented by :
Question 40 :
Let $S$ be a non-empty subset of $R$. Consider the following statement:<br>$p$ : There is a rational number $x$ such that $x > 0$.<br>which of the following statements is the negation of the statement P ?
Question 41 :
The set of natural number is subset of set of real numbers.State true or false:<br/>
Question 43 :
Consider the non-empty set consisting of children in a family and a relation $R$ defined as a $Rb$ if $a$ is brother of $b$. Then $R$ is
Question 45 :
Suppose ${ A }_{ 1 },{ A }_{ 2 },,{A }_{ 30 }$ are thirty sets each having $5$ elements and ${ B }_{ 1 },{ B }_{ 2 },..,{B}_{ n }$ are $n$ sets each with $3$ elements, let $\displaystyle \bigcup _{ i=1 }^{ 30 }{ { A }_{ i } } =\bigcup _{ j=1 }^{ n }{ { B }_{ j } =S}$ and each element of $S$ belongs to exactly $10$ of the ${A}_{i}s$ and exactly $9$ of the ${B}_{j}s.$ Then $n$ is equal to
Question 47 :
Suppose $A_1 , A_2,... A_{30}$ are thirty sets each having 5 elements and $B_1, B_2,..., B_n$ are n sets each with 3 elements , let $\underset{i = 1}{\overset{30}{\cup}} A_i = \underset{j = 1}{\overset{n}{\cup}} B_j = S$ and each element of S belongs to exactly 10 of the $A_i's$ and exactly 9 of the $B_j'S$. then n is equal to
Question 48 :
Set of all real value of a such that $f(x) = \frac {(2a - 1)x^2(a + 1)x + (2a - 1)}{x^2 2x + 40}$ always negative is
Question 49 :
Let A and B be two sets containing four and two elements respectively. Then the number of subsets of the set $A \times B$, each having at least three elements is............
Question 50 :
If $X=\left\{ { 4 }^{ n }-3n-1;n\in R \right\} $ and $Y=\left\{ 9\left( n-1 \right) ;n\in N \right\} $, then $X\cap Y=$
Question 51 :
Suman is given an aptitude test containing 80 problems, each carrying I mark to be tackled in 60 minutes. The problems are of 2 types; the easy ones and the difficult ones. Suman can solve the easy problems in half a minute each and the difficult ones in 2 minutes each. (The two type of problems alternate in the test). Before solving a problem, Suman must spend one-fourth of a minute for reading it. What is the maximum score that Suman can get if he solves all the problems that he attempts?
