Question 1 :
The relation $R=\left\{ \left( 1,1 \right) ,\left( 2,2 \right) \left( 3,3 \right)  \right\} $ on the set $A=\left\{ 1,2,3 \right\} $ is
Question 2 :
If $A=\left\{ 1,2,3 \right\} $, then a relation $R=\left\{ \left( 2,3 \right) \right\} $ on $A$ is
Question 3 :
The number of reflexive relation in set A = {a, b, c} is equal to
Question 4 :
Let $f: N\rightarrow R$ such that $f(x)=\dfrac{2x-1}{2}$ and $g: Q\rightarrow R$such that $g(x)=x+2$ be two function. Then $(gof)\left(\dfrac{3}{2}\right)$ is equal to
Question 5 :
Let A={ 1, 2, 3, 4} and R= {( 2, 2), (3, 3), (4, 4), (1, 2)} be a relation on A. Then R is
Question 6 :
Which of the following is not an equivalence relation on $Z$?
Question 7 :
Consider the following two binary relations on the set $A = \left \{a, b, c\right \} : R_{1} = \left \{(c, a), (b, b), (a, c), (c, c), (b, c), (a, a)\right \}$<br>and $R_{2} = \left \{(a, b), (b, a), (c, c), (c, a), (a, a), (b, b), (a, c)\right \}$ Then<br>
Question 9 :
If $R$ is the largest equivalence relation on a set $A$ and $S$ is any relation on $A$, then
Question 10 :
The true set of real value of $x$ for which the function, $f(x)=x\ \mathrm{ln}\ x-x+1$ is positive is
Question 12 :
Solve ${\cos ^{ - 1}}\left( {\frac{4}{5}} \right) + {\cos ^{ - 1}}\left( {\frac{{63}}{{65}}} \right) = $
Question 13 :
The number of real values of x satisfying the equation $\tan^{-1}\left(\dfrac{x}{1-x^2}\right)+\tan^{-1}\left(\dfrac{1}{x^3}\right)=\dfrac{3\pi}{4}$, is?
Question 14 :
Simplify ${\cot ^{ - 1}}\dfrac{1}{{\sqrt {{x^2} - 1} }}$ for $x <  - 1$
Question 16 :
Consider the following statements:<br/>1. $\tan^{-1} 1+ \tan^{-1} (0.5) = \dfrac {\pi}2$<br/>2. $\sin^{-1}{\cfrac{1}{3} }+ \cos^{-1}{\cfrac{1}{3}} =\cfrac{\pi}{2}$<br/>Which of the above statements is/are correct ? 
Question 17 :
$\quad \sin ^{ -1 }{ x } +\sin ^{ -1 }{ \cfrac { 1 }{ x } } +\cos ^{ -1 }{ x } +\cos ^{ -1 }{ \cfrac { 1 }{ x } = } $
Question 18 :
Solve $\cos { \left[ \tan ^{ -1 }{ \left[ \sin { \left( \cot ^{ -1 }{ x }  \right)  }  \right]  }  \right]  } $
Question 20 :
Solve:$\displaystyle \sin { \left( { \tan }^{ -1 }x \right) } ,\left| x \right| <1$ is equal to
Question 21 :
<br/>The function $f(x)=\begin{cases}(1+x)^{\frac{5}{x}}& for \ {x}\neq 0,\\ e^{5} & for \  {x}=0\end{cases}$ is ........ at ${x}=0$<br/>
Question 22 :
The integer $'n'$ for which $\mathop {\lim }\limits_{x \to 0} \dfrac{{\cos 2x - 1}}{{{x^n}}}$ is a finite non-zero number is
Question 23 :
The function $f\left( x \right)=\left[ x \right] ,$  at ${ x }=5$ is:<br/>
Question 24 :
If $f(x)=\displaystyle \frac{\sin x}{x},x\neq 0$ is to be continuous at ${x}=0$ then $\mathrm{f}({0})=$<br/>
Question 25 :
If $f\left( x \right) =\dfrac { 3sinx-sin\left( 3x \right) }{ { 2x }^{ 3 } } ,x\neq 0,f\left( 0 \right) =2,$ at $x=0,f$ is
Question 26 :
If $f(x) = (1 + 2x)^{\frac{1}{x}}$, for $x \neq 0$ is continuous at $x = 0$, then $f(0) = $_______.
Question 27 :
If $ f\left( x \right) =\begin{cases} 1 & x<0 \\ { x }^{ 2 } & x\ge 0 \end{cases}$ then at $x=0$
Question 28 :
Function $f(x) = \left\{\begin{matrix}(\log_{2}2x)^{\log_{x} 8};& x\neq 1\\(k - 1)^{3};& x = 1\end{matrix}\right.$ is continuous at $x = 1$, then $k =$ _______.<br>
Question 29 :
If the function $\displaystyle f(x)=\begin{cases} 2x^{2}-3 & \text{ if } 0<x\leq 1 \\ x^{2}+bx-1 & \text{ if } 1<x<2 \end{cases}$ is continuous at every point of its domain then the value of $b$ is 
Question 30 :
The function $f(x)=\dfrac{1-\sin x+\cos x}{1+\sin x+\cos x}$ is not defined at $x=\pi$. The value of $f(\pi)$ so that $f(x)$ is continuous at $x=\pi$ is
Question 31 :
If $A$ and $B$ are square matrices such that $AB = I$ and $BA = I$, then $B$ is<br/>
Question 33 :
If $A = \begin{bmatrix}1\end{bmatrix}$, then the order of the matrix is