Question 2 :
In a class, $20$ opted for Physics, $17$ for Maths, $5$ for both and $10$ for other subjects. The class contains how many students?
Question 4 :
A and B are two events such that $P(A)\neq 0, P(B/A)$ if.<br/>(i) A is a subset of B<br/>(ii)$A\cap B=\Phi$ are respectively<br/>
Question 5 :
A couple has two children,<br>(i) Find the probability that both children are males, if it is known that at least one of the children is male.<br>(ii) Find the probability that both children are females, if ti is known that the elder child is a female.
Question 6 :
Let $A$ and $B$ be subsets of a set $x$. Then
Question 8 :
Let A and B be two events such that $P(A) =7/20, P(B) = 9/20, P(A\cup B)=11/20$ ,then the value of $P(\bar{A}\cup B)$ is equal to
Question 9 :
If A= {1, 2, 5} and B= {3, 4, 5, 9}, then $A \bigcup B$ is equal to :
Question 10 :
The solution set of $3 x - 4 < 8$ over the set of non-negative square numbers is
Question 11 :
In a town of 10000 families, it was found that 40% families buy a newspaper A, 20% families buy newspaper B and 10% families buy newspaper C. 5% families buy both A and B, 3% buy B and C and 4% buy A and C. If 2% families buy all the three newspapers, then the number of families which buy A only.
Question 12 :
if $X' = Y$ then $\displaystyle \left (X \cap Y \right )'$ is equal to
Question 13 :
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 14 :
If A and B are two disjoint sets and N is the universal set then $\displaystyle A^{c}\cup \left [ \left ( A\cup B \right )\cap B^{c} \right ]$ is
Question 15 :
All the students of a batch opted Psychology, Business, or both. 73% of the students opted Psychology and 62% opted Business. If there are 220 students, how many of them opted for both Psychology and business?<br>
Question 16 :
Let $S$ be the relation on $R$ defined by $S=\left\{(x,y)|\ y/2 \ge x \ge 2y\right\}.$ Then, $S$ is
Question 17 :
If $A$ and $B$ are any two non-empty sets, then prove that $(A\cap B)'=$
Question 18 :
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.
Question 19 :
The solution set of $x+2<9$ over a set of positive even integers is
Question 20 :
In a selection process, a hundred candidate participate in Group Discussion sessions (GD) and Personal Interview (PI). The possibilities of a candidate's good performance in GD and in PI are independent of each other. It was found that $20$ candidates were good in GD and $30$ were good in PI. The number of candidates good in both GD and PI is expected to be about:
Question 21 :
$If\,A = \left\{ {\left( {x,y} \right)\,\left| {{x^2} + {y^2} \le \left. 4 \right\}\,and} \right.} \right.$<br>$B = \left\{ {\left( {x,y} \right)\,\left| {{{(x - 3)}^2} + {y^2}} \right. \le \left. 4 \right\}} \right.\,and\,the$<br>$po{\mathop{\rm int}} \,P\left( {a,\frac{1}{2}} \right)\,belongs\,to\,the\,set\,B - A$ then the set of possible real values of $a$ is<br>
Question 22 :
If $S$ is a set with $10$ elements and $A = \left \{(x, y) : x, y\epsilon S, x\neq y\right \}$, then number of elements in $A$ is
Question 23 :
Let $\displaystyle S=\left\{a\in N,a\le100\right\}$ if the equation $\displaystyle[{\tan}^{2}x]-\tan x-a=0$ has real roots, then the number of elements $S$ is (when $[.]$ is greatest integer function)
Question 24 :
In a party, 70 guests were to be served tea or coffee after dinner. There were 52 guests who preferred tea while 37 preferred coffee. Each of the guests liked one or the other beverage. How many guests liked both tea and coffee?<br>
Question 25 :
If a relation from a finite set A having m elements to a finite set B having n elements, then the number of relations from A to B is
Question 26 :
M $\cup$ N = {1, 2, 3, 4, 5, 6} and M = {1, 2, 4} then which of the following represent set N?
Question 27 :
Consider the non-empty set consisting of children in a family and a relation $R$ defined as $aRb$ if $a$ is brother of $b$. Then $R$ is
Question 28 :
In a survey of brand preference for toothpastes, $82$ of the population (number of people covered for the survey is $100$) liked at least one of the brands: I, II and III. $40$ of those liked brand I, $25$ liked brand II and $35$ liked brand III. If $8$ of those asked, showed liking for all the three brands, then what percentage of those liked more than one of the three brands?<br/>
Question 29 :
Let $S={1,2,3,.....10}$ and $P={1,2,3,4,5}$ The number of subsets $'Q'$ of $S$ such that $p \cup Q=S$, are.....
Question 30 : <div>Find out the number of elements in the following set:</div>$A= \{ x| x \epsilon N, 2 < x <4 \}$.
Question 31 :
In a class 60% of the students were boys and 30% of them had I class. If 50%of the students in the class <span>had I class, find the fraction of the girls in the class who did not have a I class.</span>
Question 32 :
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 33 :
Let $\displaystyle P_{1}$ be the set of all prime numbers, i.e., $\displaystyle P_{1}=(2,3,5,7,11......),$ Let $\displaystyle P_{n}=\left \{ np|p\in P_{1} \right \}$ i.e, the set of all prime multiples of $n$. Then which of the following sets in non empty?
Question 34 :
In a community of 175 persons, 40 read the Times, 50 read the Samachar and 100 do not read any. How many persons read both the papers?<br>
Question 35 :
$A - ( A - B ) $ is equivalent to which expression
Question 36 :
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 $\left( A\cup B \right) \cap \left( A\cup C \right) $
Question 37 :
If $M = \left\{ {x:x \geqslant 7\,\,{\text{and}}\,x \in N} \right\}$ for universal set of natural numbers, then $M'$ is
Question 38 :
If $P(A\cup B)=\dfrac {2}{3}, P(A\cap B)=\dfrac {1}{6}$ and $P(A)=\dfrac {1}{3}$, then
Question 39 :
Find the smallest set $\displaystyle Y$ such that $\displaystyle Y\cup \left \{ 1, 2 \right \}=\left \{ 1, 2, 3, 5, 9 \right \}$
Question 40 :
Let $A$ and $B$ be two sets, then $(A \cup B') \cap (A' \cap B)$ is equal to
Question 41 :
A students appears for tests I,II and III.The student is successful if he passes either in tests I and II or tests I and III.The probabilities of the student passing in test I,II and III are respectively, $p,q,$ and $1/2$.If the probability that the student is successful is $1/2,$ then $p(1+q)=$
Question 42 :
If $A\subset B, n(A) = 5$ and $n(B) = 7$, then $n(A\cup B) =$ ______
Question 43 :
If events $A$ and $B$ are independent and $P(A)=0.15, P(A\cup B)=0.45$, then $P(B)=$
Question 44 :
Let $A$ and $B$ be two sets such that $n(A)=16$, $n(B)=12$, and $n(A\cap B)=8$. Then $n(A\cup B)$ equals
Question 45 :
While preparing the progress reports of the students, the class teacher found that 70% of the students passed in Hindi, 80% passed in English and only 65% passed in both the subjects. Find out the percentage of students who failed in both the subjects.<br>
Question 46 :
If X is a finite set. Let $P(X)$ denote the set of all subsets of X and let $n(X)$ denote the number of elements in X. If for two finite subsets $A, B, n(P(A)) = n(P(B)) + 15$ then $n(B) = $ ____, $n(A) =$ _____
Question 47 :
Given $A=\{x\in N :x<6\} ,B=\{3,6,9\}$ and $C=\{x \in N: 2x-5\le 8\}$
Question 48 :
In order to draw a graph of $f(x) = ax^{2} + bx + c$, a table of values was constructed. These values of the function for a set of equally spaced increasing values of $x$ were $3844, 4096, 4227, 4356, 4489, 4624$, and $4761$. The one which is incorrect is
Question 49 : <div>If universal set $\xi = \{a, b, c, d, e, f, g, h\}, A = \{b, c, d, e, f\}, B =\{a, b, c, g, h\}$ and $C = \{c, d, e, f, g\}$ find <span>$(B - C)'$</span></div>
Question 50 :
If $A$ and $B$ are two equivalence relations defined on set $C$, then
