Question 1 :
If  $B = \{y | y^2 = 36\}$ then the set $B$ is a ______ set.
Question 3 :
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 4 :
The smallest set $A$ such that $A\cup \left\{ 1,2 \right\} =\left\{ 1,2,3,5,9 \right\} $ is 
Question 5 :
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 6 :
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 7 :
A relation $\phi$ from $C$ to $R$ is defined by $x\phi y\Leftrightarrow \left| x \right| =y$. Which one is correct?
Question 9 :
Write explicitly, functions of $y$ defined by the following equations and also find the domains of definition of the given implicit functions:<br/>$x + \mid y \mid = 2y$
Question 12 :
The domain of the function $f(x) = {{log_{3+x}}({x^2} - 1)}$ is
Question 15 :
The value of $4\cos^{2} \dfrac {\pi}{3} + \sec^{2} \dfrac {\pi}{6} - \sin^{2} \dfrac {\pi}{4}$ is
Question 16 :
The value of $\sqrt2 ( \cos 15^o - \sin 15^o ) $ is equal to :
Question 17 :
If $\cos (12 + \theta) = \dfrac{\sqrt{3}}{2}$; $0 < \theta < 20^\circ$, then the value of $\theta$ is <br/>
Question 19 :
If ${ x }_{ 1 }=3sin\omega t$ and ${ x }_{ 2 }=4cos\omega t$ then
Question 20 :
The measure of an angle in degrees, grades and radians be D, G and C respectively, then relation between them $\displaystyle \frac{D}{90}=\frac{G}{100}=\frac{2C}{\pi }$ but $\displaystyle 1^{\circ}=\left ( \frac{180}{\pi } \right )^{\circ}\:\simeq 57^{\circ},17',44.{8}''$ and sum of interior angles of a $n$-sided regular polygon is $\displaystyle \left ( 2n-4 \right )\dfrac {\pi }2$. On the basis of above information, answer the following questions :Which of the following are correct<br/>
Question 21 :
Two complex numbers are represented by ordered pairs $z_1: (2,4)\ \&\ z_2: (-4,5)$, which of the following is real part for $z_1\times z_2=$?
Question 22 :
If $\left(\dfrac {3}{2}+\dfrac {\sqrt 3}{2}\right)^{50} =3^{25} (x-iy)$ where $x, y$ are real, then the ordered pair $(x, y)$ given by