Question 1 :
The $\left( A\cup B\cup C \right) \cap \left( A\cap { B }^{ C }\cap { C }^{ C } \right) ^{ C }\cap { C }^{ c }$ is equal to
Question 2 :
Let R = {(1, 3), (4, 2), (2, 3), (3, 1)} be a relation on the set A = (1, 2, 3, 4). The relation R is
Question 3 :
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 4 :
$If\,\,A = \left\{ {x:{x^2} = 1} \right\}\,\,\,and\,B = \left\{ {x:{x^4} = 1} \right\},\,then\,A\Delta B\,\,\,is\,\,equal\,to\,$
Question 5 :
Find all values of a for which all solutions of the inequation $ \\ { ax }^{ 2 }-2\left( { a }^{ 2 }-3 \right) x-12a\quad \ge \quad 0$<br>are the solutions of the ineqaution $ \\ { x }^{ 2 }-49\ge 0$<br>
Question 6 :
Let x= {1, 2, 3, 4, 5} The number of different ordered pairs (y, z) that can be formed such ordered pairs (y , z) that can be formed such that $y\sqsubseteq x,z\sqsubseteq x$ and $y\cap z$ is empty is
Question 8 :
Suppose ${ A }_{ 1 },{ A }_{ 2 },....{ A }_{ 30 },$ are thirty sets each with five elements and ${ B }_{ 1 },{ B }_{ 2 },....B_{ A },$ are n sets each with three elements such $\overset { 30 }{ \underset { i-1 }{ U } } \quad { A }_{ 1 }=\overset { n }{ \underset { j-1 }{ U } } \quad =s$ If each element of belongs to exactly ten of the ${ A }_{ 1 }$ exactly 9 of the ${ A }_{ 1 }$,then value of n is:
Question 9 :
Let $A_{1}, A_{2}, ........., A_{m}$ be m sets such that $O(A_{i}) = p \forall i = 1, 2, ......... m$ and $B_{1}, B_{2}, .........., B_{n}$ be n sets such that $O(B_{j}) = q \forall j = 1, 2, ........., n$. If $\bigcup_{i=1}^{m} A_{i}$ = $\bigcup_{j=1}^{n} B_{j} = S$ and each element of S belongs to exactly $\alpha$ number of $A_{i}'s$ and $\beta$ number of $B_{j}'s$, then
Question 10 :
The value of $'c'$ for which the set $[(x, y)|x^{2} + y^{2} + 2x \leq 1]\cap [(x, y)|x - y + c\geq 0]$ contains only one point in common is :
Question 11 :
$A = \{1,2,4\}, B = \{2, 4,5\}, C = \{2, 5\}, $then $(A - B) \cup (B- C)$ is
Question 12 :
The set $\{x/| x L|< K\}$ is the same for all $K > 0$ and for all L, as
Question 14 :
Which of the following statements is true (if N, W and I are sets of Natural, Whole and <span>Integer numbers respectively ?</span>
Question 16 :
State which of the following is total number of reflexive relations form set $A = \left \{a, b, c\right \}$ to set $B = \left \{d, e\right \}$ is
Question 18 :
If $A=\left [ \frac{5}{111} \frac{-3}{336}\right ]$ and det $(-3A^{2013}+A^{2014})=\alpha ^{\alpha }\beta ^{2}(1+\gamma +\gamma ^{2})$ then, where $\alpha ,\beta ,\gamma $ are integers
Question 19 :
Let $U=R$. If $A=(x\epsilon R : 0 < x < 2), B=(x\epsilon R: 1 < x \leq 3)$, which of the following is false?
Question 20 :
Let $A$ and $B$ be two sets containing 4 and 2 elements respectively. Then the number of subsets of the set $A\times B$, each having at least three elements is
Question 21 :
Let S = {x $\epsilon$ $R$ : x 0 and 2$\left | \sqrt{x} 3 \right |$ + $\sqrt{x}$($\sqrt{x}$ 6) + 6 = 0} .<br>Then S :
Question 22 :
<span>If $A$ $=\{(n,2n);n\epsilon Z\}$ and </span><span>B $=\{(2n,3n);n\epsilon Z\}$,then find $A\cap B$</span>
Question 23 :
If the probabilities for A to fail in an examination is $0.2$ and that for B is $0.3$, then the probability that either A or B fails, is
Question 24 :
${ A }_{ 1 },{ A }_{ 2 },.....{ A }_{ n }\quad $ are thirty sets, each with five elements and ${ B }_{ 1 },{ B }_{ 2 },....{ B }_{ n }$ are $n$ sets, each with three elements.<br>Let $\bigcup _{ i=1 }^{ 30 }{ { A }_{ i } } =\bigcup _{ j=1 }^{ n }{ { B }_{ j } } =S$. If each element of $S$ belongs to exactly ten of ${A}_{i}$'s and exactly nine of the ${B}_{j}$'s, then $n$ is<br>
Question 25 :
If $A=[x:x$ is a multiple of $3]$ and $B=[x:x$ is a multiple of $5]$, then $A-B$ is $(\bar { A }$ means complements of $A)$
Question 26 :
Let $n\left( U \right) =700,n\left( A \right) =200,n\left( B \right) =300$ and $n\left( A\cap B \right) =100,$ then $n\left( { A }^{ c }\cap { B }^{ c } \right) =$
Question 27 :
<u></u>Consider that $n(S)$ represented the number of elements in set S. If $n(A\cup B\cup C)=40, n(A\cap B'\cap C')=5, n(B\cap A'\cap C')=10, n(C\cap B' \cap A')=6$ then number of element which belongs to at least two of the set is
Question 28 :
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?
Question 29 :
For a set { 1, 2, {1, 2, 3}}. which of the following statement is false?
Question 30 :
X and Y are two sets and $f:X\rightarrow Y$. If $f(c)=\left\{ y;c\subset X,y\subset Y \right\} $ and ${ f }^{ 1 }(d)=\left\{ x;d\subset Y,x\subset X \right\} $, then the true statement is
Question 31 :
Let A={1, 2, 3, 4), B={2, 3, 4, 5}, then $n\{ (A\times B)\cap (B\times A)\} =$?
Question 34 :
The number of real solutions of $tan^-$ <br> $^1$ $\sqrt{x (x - 1)}$ + $sin^-$ <br> $^1$ $\sqrt{x^2 + x + 1}$ = $\frac{\pi}{2}$ is
Question 35 :
If $A = \{ 4,5,8,12 \} , B = \{ 1,4,6,9 \} \text { and } C = \{ 1,2,3,4 \}$ then $A - ( C - B ) =$
Question 36 :
If $A=\left \{ x:x\in I,-2\leq x\leq 2 \right \}$,<br>$B=\left \{ x:x\in I,0\leq x\leq 3 \right \}$,<br>$C=\left \{ x:x\in N,1\leq x\leq 2 \right \} $ and<br>$D=\left \{ (x,y):x,y\in N,x+y=8 \right \}$, then
Question 37 :
Suppose $A_1, A_2, ....., A_{30}$ are thirty sets each with five elements and $B_1, B_2, ....., B_n$ are $n$ sets each with three elements such that $\bigcup _{ i=1 }^{ 30 }{ { A }_{ i }= } \bigcup _{ j=1 }^{ n }{ { B }_{ j }= } S$ and each element of $S$ belongs to exactly $10$ of the $A_{i}$'s and exactly $9$ of the $B_j$'s. Then $n=$
Question 38 :
$B = \{ \frac{x}{x} + 3 = 6\} ,B = ......$
Question 39 :
An investigator interviewed $100$ students to determine their preferences for the three drinks: milk (M), coffee(C) and tea (T). He reported the following: $10$ students had all the three drinks M, C, T; $20$ had M and C only; $30$ had C and T; $25$ had M and T; $12$ had M only; $5$ had C only; $8$ had T only. Then how many did not take any of the three drinks is?
Question 40 :
If $A_{1}, A_{2},..., A_{100}$ are sets such that $n(A_{i}) = i + 2,$ $A_{1}\subset A_{2}\subset A_{3}........A_{100}$ and $\bigcap_{i=3}^{100}A_{i}=A,$ then $n(A)=$<br>
Question 41 :
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 42 :
The probability that $A$ can solve a problem is $\dfrac {2 }{ 3}$ and that $B$ can solve is $\dfrac {3 }{4}$. If both of them attempt the problem. What is probability that the problem act solved?
Question 43 :
If $aN=\left\{ ax:x\epsilon N \right\}$, then the set $3N\cap 7N$ is
Question 44 :
If $A=\left \{ \left ( x, y \right )\mid x^{2}+y^{2}\leq 4 \right \}$ and $B=\left \{ \left ( x, y \right )\mid \left ( x-3 \right )^{2}+y^{2}\leq 4 \right \}$ and the point $\displaystyle P\left ( a, a-\frac{1}{2} \right )$ belongs to the set $B-A$, then the set of possible real values of $a$ is:
