Question 1 :
For two sets $A$ and $B$, $ A\cap \left( A\cup B \right)=$
Question 2 :
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 3 :
$n \left [ P (A) \right ] = 16$, then $n(A) =$<br/>
Question 4 :
Let $A$ and $B$ have $3$ and $6$ elements respectively. What can be the minimum number of elements in $A\cup B$?
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 6 :
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 7 :
Classify the following set as 'singleton' or 'empty': $A = \{ x | x$ is a negative natural number$\}$
Question 9 :
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 11 :
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
Question 12 :
If $U = \left \{x|x\epsilon N, x < 5\right \}, A = \left \{x|x\epsilon N, x\leq 2\right \}$ then $A' =$ __________.
Question 14 :
If A and B be any two sets, then $\displaystyle \left( A \cap B \right) '$ is equal to
Question 15 :
From a survey of $100$ college students, a marketing research company found that $75$ students owned stereos, $45$ owned cars, and $35$ owned cars and stereos. How many students owned either a car or a stereo?<br>
Question 16 :
If $C = \{p|p \in I, p^3 = -8\}$ then the set $C$ is a
Question 18 : <div>Given the universal set $B = \{-7,-3,-1,0,5,6,8,9\}$, find :</div>$B = \{x : -4 < x < 6\}$
Question 19 :
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 20 :
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 21 :
If $n(A) = 115$, $n(B) = 326$, $n(A - B) = 47$ then $\displaystyle n\left ( A\cup B \right )$ is equal to
Question 25 : <p>Let $n$ be a fixed positive integer. Let a relation $R$ defined on $I$ (the set of all integers) as follows: $aRb$ iff $n/(a-b)$, that is, iff $a-b$ is divisible by $n$, then, the relation $R$ is</p>
Question 26 :
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 28 :
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 29 :
In a group of $15$ women, $7$ have nose studs, $8$ have ear rings and $3$ have neither. How many of these have both nose studs and ear rings?
Question 30 :
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 33 :
The set B= {a|a is a negative integer and a-1=0} is a
Question 34 :
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.
Question 36 :
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 37 :
Let U = {all digits of our number system}; A = { set of prime numbers }; B = { factors of $36$. Then A $\displaystyle\cup$ B includes:
Question 38 :
Which one of the following is an example of non-empty set?
Question 39 :
State whether the following statement is true or false.<br>The set $\{x : x+8=8\}$ is the null set.<br>
Question 40 :
Classify the following set as 'singleton' or 'empty': $D = \{d | d \in N, d^2 \le 0\}$
Question 41 :
If $N_{ a }={ \left\{ an:n\epsilon N \right\} }, then N_{3} \cap N_{4}$ is equal to<br/>
Question 42 :
The number of elements of the set $\left \{ x:x\in Z,x^{2}=1 \right \}$ is :
Question 44 :
The number of subsets of the set $A=\{ { a }_{ 1 },{ a }_{ 2 },.........{ a }_{ n }\} $ which contain even number of elements is
Question 45 :
For any two sets A and B $A\cup B=A\cap B$ if A$=$B.
Question 46 :
State whether the following statements are true(T) or false(F).Justify your answer.<br>A collection of stamps is a set.
Question 48 :
Let $A$ and $B$ be two sets such that $A\cap B=\phi$. Find the value of $(A\cup B')=$
Question 49 :
Given $P(A \cup B)=0.6, P(A\cap B)=0.2$, the probability of exactly one of the event occurs is
Question 50 : <div><div>State true or false.</div><div>Given universal set= $\displaystyle =\left \{ -6,-5\frac{3}{4}, -\sqrt{4}, -\frac{3}{5}, -\frac{3}{8}, 0, \frac{4}{5}, 1, 1\frac{2}{3}, \sqrt{8}, 3.01, \pi , 8.47 \right \}$ </div><div>From the given set, find set of non-negative integers is $\displaystyle \left \{0,1 \right \}$.</div></div>
Question 51 :
The value of $\sin B \cos (90^0-B) + \cos B \sin (90^0 - B)$ is <br/>
Question 52 : <div>State True or False</div><div> $\cos 2{ A } =\cos ^{ 2 }{ A } -\sin ^{ 2 }{ A } $</div>
Question 53 :
If P = cos $\dfrac {\pi } {20} .cos \dfrac {3\pi } {20} .cos\dfrac {7\pi } {20} . cos\dfrac{9\pi } {20} $ & Q = cos$ \dfrac{\pi } {11}. cos\dfrac{2\pi } {11} .cos\dfrac{4\pi } {11} . cos\dfrac {8\pi } {11}. cos \dfrac {16\pi } {11}, then \dfrac {P} {Q} $ is
Question 54 :
The value of ${\cos ^2}{45^ \circ } - {\sin ^2}{15^ \circ }$ is
Question 55 :
If $ \displaystyle \tan \Theta =\frac{3}{4}and 0<\Theta , < 90^{\circ} $ , then the value of $ \displaystyle \sin \Theta \cos \Theta $ is
Question 57 :
If $\displaystyle 0^{0}\leq \theta \leq 90^{0}$, find the value of $\displaystyle \theta $ satisfying $\displaystyle 3\tan \theta +\cot \theta =5\text{cosec} \theta $
Question 58 :
The value of $\sin { \left( {{ 45 }}^{o} +\theta \right) } -\cos { \left( {{ 45 }}^{o} -\theta \right) } $ is
Question 59 :
The value of $4\cos^{2} \dfrac {\pi}{3} + \sec^{2} \dfrac {\pi}{6} - \sin^{2} \dfrac {\pi}{4}$ is
Question 64 : In $\Delta$ $ABC$ the sides opposite to angles $A, B, C$ are denoted by $a, b, c$ respectively, <div>then $\ \displaystyle \frac{b\cos A+a\cos B}{\cos C}$ is equal to<br/></div>
Question 65 :
If $sin\Theta =cos\Theta $, then the value of cosec$ \Theta $ is :<br/>
Question 66 :
Given that A is positive acute angle and $ { sin }^{ }A=\dfrac { \sqrt { 3 } -1 }{ 2 } ,$ then A take the value (s)-
Question 68 :
In a $\triangle ABC,\ \angle A= \dfrac {\pi}{2},$ then $\cos ^{ 2 }{ B } +\cos ^{ 2 }{ C } $ equals :
Question 69 :
Given that $ \displaystyle \cos 50^{\circ}18'=0.6388\ and\ \cos 50^{\circ}42'=0.6334, $ then the possible value of $ \displaystyle \cos 50^{\circ}20' $ is
Question 70 :
If $\theta$ is in the first quadrant and cos $\theta=\frac{3}{5}$, then the value of $\dfrac{5 tan \theta -4cosec \theta}{5 sec\theta-4cot \theta}$ is<br/><br/>
Question 73 :
If $ \displaystyle \sin 50=0.766 $ , then value of $ \displaystyle \sec 40^{\circ} $ is
Question 74 : <div>Change the following radian measure to degree measure:<br/></div>$\cfrac { 3\pi }{ 2 } $
Question 75 :
Value of $ \displaystyle \cos 25^{\circ}\cos 20^{\circ}+\sin 25^{\circ}\sin 20^{\circ} $ is
Question 76 :
The minimum value of $\sec^2 \theta + \cos^2 \theta$ is -<br/>
Question 77 :
Let $\alpha, \beta$ be two distinct roots of a $\cos \theta + b\sin \theta = c$, where $a, b$ and $c$ are three real constants and $\theta \epsilon [0, 2\pi]$. Then $\alpha + \beta$ is also a root of the same equation if
Question 82 :
The least positive root of the function $\sin { x } -\cfrac { \pi }{ 2 } +1=0$ lies in the interval<br><br>
Question 85 :
If range of $f(x)=\cos x, x\in \left(\dfrac {-\pi}{3}, \dfrac {\pi}{6}\right)$ is $(a,b)$, then
Question 86 :
If $(1 - \cos A)/2 = x$, then the value of $x$ is
Question 88 :
The value of $\cos { \left( -1044^{o} \right) } $ is $\dfrac{\left( \sqrt { 5 } +1 \right) }{4}$.
Question 90 :
Find the range if $\left[ 2\sin { x } \right] +\left[ \cos { x } \right] =-3,$ then the range of the function $f\left( x \right) =\sin { x } +\sqrt { 3 } \cos { x } $ in $\left[ 0,2\pi \right] $ (where $[.]$ denotes the greatest integer function)
Question 92 :
If tan A = 4 /3, tanB = 1/ 7,then A - B =
Question 93 :
As $\theta$ increases from $\cfrac { \pi }{ 4 } $ to $\cfrac { 5\pi }{ 4 } $, the value of $4\cos { \cfrac { 1 }{ 2 } \theta } $
Question 94 :
If ${\tan ^2}\theta = 2\,{\tan ^2}\phi + 1$, then the value of $\cos \,2\theta + {\sin ^2}\phi \,is$ is
Question 96 :
If $\displaystyle \tan { \theta } =\frac { 1 }{ 2 } $ and $\displaystyle \tan { \phi } =\frac { 1 }{ 3 } $, then the value of $\displaystyle \theta +\phi $ is:
Question 97 :
The value of $\cot 15^{\circ} \cot 20^{\circ} \cot 70^{\circ} \cot 75^{\circ}$ is equal to
Question 98 :
If $\displaystyle \alpha +\beta =90^{\circ}$ and $ \alpha =2\beta $, then $ \cos ^{2}\alpha +\sin ^{2}\beta $ equals to
Question 99 :
The number of value $x$ in the interval $[0,3\pi]$ satisfying the $eq^n 2\sin^2x+5\sin \,\,x-3=0$ is
