Question 1 :
Let $R$ be the relation over the set of all straight lines in a plane such that ${l}_{1}$ $R$ ${l}_{2}\Leftrightarrow {l}_{1}\bot {l}_{2}$. Then, $R$ is
Question 2 :
Find number of all such functions $y = f(x)$ which are one-one?
Question 3 :
The number of reflexive relation in set A = {a, b, c} is equal to
Question 5 :
If the relation is defined on $R-\left\{ 0 \right\} $ by $\left( x,y \right) \in S\Leftrightarrow xy>0$, then $S$ is ________
Question 6 :
Which of the following is not an equivalence relation on $Z$?
Question 7 :
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 8 :
If $f: A \rightarrow B$is a bijective function and if n(A) = 5, then n(B) is equal to
Question 9 :
If $A=\left\{ a,b,c,d \right\} $, then a relation $R=\left\{ \left( a,b \right) ,\left( b,a \right) ,\left( a,a \right) \right\} $ on $A$ is
Question 10 :
The number of reflexive relations of a set with four elements is equal to
Question 11 :
If $\displaystyle \begin{vmatrix} a & b &0\\ 0 & a & b\\b&a&0\end{vmatrix}= 0$, then the order is:
Question 12 :
The entries of a matrix are integers. Adding an integer to all entries on a row or on a column is called an operation. It is given that for infinitely many integers N one can obtain, after a finite number of operations, a table with all entries divisible by N. Prove that one can obtain, after a finite number of operations, the zero matrix.
Question 13 :
If $\displaystyle  \begin{vmatrix} x & y   \\ 1 & 6   \end{vmatrix} $ = $\displaystyle  \begin{vmatrix} 1 & 8   \\ 1 & 6   \end{vmatrix} $ then x+2y=
Question 14 : <p>The possibility for the formation of rectangular matrices in the matrix algebra are</p>
Question 15 :
If $A=\begin{bmatrix} { a }^{ 2 } & ab & ac \\ ab & { b }^{ 2 } & bc \\ ac & bc & { c }^{ 2 } \end{bmatrix}$ and ${a}^{2}+{b}^{2}+{c}^{2}=1$ then ${A}^{2}=$
Question 16 :
If $m[-3\ \ \ 4]+n[4\ \ \ -3]=[10\ \ \ -11]$ then $3m+7n=$
Question 17 :
If $A= [ 1 \ 2\  3 ]$, then the set of elements of A is
Question 18 :
The value of x satisfying the equation 2$\displaystyle \begin{vmatrix} 3 & 1 \\ 1 & 2 \end{vmatrix} $+$\displaystyle \begin{vmatrix} x^{2} & 9 \\ -1 & 0 \end{vmatrix} $=$\displaystyle \begin{vmatrix} 5x & 6 \\ 0 & 1 \end{vmatrix} $+$\displaystyle \begin{vmatrix} 0 & 5 \\ 1 & 3 \end{vmatrix} $are
Question 19 :
If every row of a matrix $A$ contains $p$ elements and its column contains $q$ elements, then the order of $A$ is
Question 20 :
Suppose $A$ and $B$ are two square matrices of same order. If $A,B$ are symmetric matrices and $AB=BA$ then $AB$ is
Question 21 :
Consider $x = 4\tan^{-1}\left (\dfrac {1}{5}\right ), y = \tan^{-1} \left (\dfrac {1}{70}\right )$ and $z = \tan^{-1}\left (\dfrac {1}{99}\right )$.What is $x$ equal to?
Question 23 :
$\sin ^ { - 1 } 5 + \cos ^ { - 1 } 5 = \ldots \ldots$
Question 24 :
$\quad \sin ^{ -1 }{ x } +\sin ^{ -1 }{ \cfrac { 1 }{ x } } +\cos ^{ -1 }{ x } +\cos ^{ -1 }{ \cfrac { 1 }{ x } = } $
Question 25 :
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 26 :
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 28 :
${ tan }^{ -1 }x+{ tan }^{ -1 }y={ tan }^{ -1 }\dfrac { x+y }{ 1-xy } $,      $xy<1$<br/>                                    $=\pi +{ tan }^{ -1 }\dfrac { x+y }{ 1-xy } $,      $xy>1$.<br/> Evaluate:  ${ tan }^{ -1 }\dfrac { 3sin2\alpha  }{ 5+3cos2\alpha  } +{ tan }^{ -1 }\left( \dfrac { tan\alpha  }{ 4 }  \right) $<br/>                                  where $-\dfrac { \pi  }{ 2 } <\alpha <\dfrac { \pi  }{ 2 } $
Question 30 :
Solve:$\displaystyle \sin { \left( { \tan }^{ -1 }x \right) } ,\left| x \right| <1$ is equal to
Question 31 :
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 32 :
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 33 :
<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 34 :
If $f(x)=\displaystyle\frac{\log(1+ax)-log(1-bx)}{x}$ for $x\neq 0$ and $f(0)=k$ and $f(x)$ is continuous at $x=0$, then $k$ is equal to:<br>
Question 35 :
The function $f\left( x \right)=\left[ x \right] ,$  at ${ x }=5$ is:<br/>
Question 36 :
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 37 :
If $f(x) = (1 + 2x)^{\frac{1}{x}}$, for $x \neq 0$ is continuous at $x = 0$, then $f(0) = $_______.
Question 38 :
$f(x)=\left\{\begin{matrix} 2x-1& if &x>2 \\ k & if &x=2 \\  x^{2}-1& if & x<2\end{matrix}\right.$is continuous at $x= 2$ then $k =$
Question 40 :
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 41 :
If $y = 6x -x^3$ and $x$ increases at the rate of $5$ units per second, the rate of change of slope when $x = 3$ is
Question 42 :
Excluding stoppages, the speed of a bus is $72\ kmph$ and including stoppages, it is $60\ kmph$. For how many minutes does the bus stop per hour?
Question 43 :
The radius of a circle is uniformly increasing at the rate of $3cm/s$. What is the rate of increase in area, when the radius is $10cm$?
Question 44 :
The interval in which the function $x^3$ increases less rapidly than $6x^2+15x+15$ is
Question 45 :
The interval in which the function $f(x) = {x^3}$ increases less rapidly than $\,g(x) = 6{x^2} + 15x + 5$ is :
Question 46 :
If the displacement of a particle moving in straight line is given by $x=3t^2+2t+1$ at time $t$ then  the acceleration of the particle at time $t=3$ is
Question 47 :
A ladder, 5 meter long, standing on a horizontal floor, leans against vertical wall. If the top of the ladder slides downwards at the rate of 10cm/sec, then the rate at which the angle between the floor and the ladder is decreasing when lower end of ladder is 2 metres from the wall is:
Question 48 :
A particle moves along a curve so that its coordinates at time $t$ are $\displaystyle x = t, y = \frac{1}{2} t^{2}, z =\frac{1}{3}t^{3}$ acceleration at $ t=1 $ is<br>
Question 50 :
A particle moves along a straight line according to the law $s=16-2t+3t^3$, where $s$ metres is the distance of the particle from a fixed point at the end of $t$ second. The acceleration of the particle at the end of $2$ s is
Question 51 :
If $A = \begin{bmatrix}1& \log_{b}a\\ \log_{a}b& 1\end{bmatrix}$ then $|A|$ is equal to<br>
Question 52 :
If $\omega$ is a non-real cube root of unity and n is not a multiple of 3, then $\displaystyle \Delta =\left | \begin{matrix}<br>1 & \omega^{n} &\omega^{2n} \\ <br>\omega^{2n}&1 &\omega^{n} \\ <br>\omega^{n}&\omega^{2n} &1 <br>\end{matrix} \right |$ is equal to<br>
Question 53 :
If $\begin{bmatrix} x & 1 & 1\\ 2 & 3 & 4\\ 1 & 1 & 1\end{bmatrix}$ has no inverse, then $x=$
Question 54 :
$\displaystyle \Delta = \begin{vmatrix}1 & \log_{x}y  & \log_{x}z \\ \log_{y}x & 1 & \log_{y}z \\ \log _{z}x  &\log _{z}y  & 1\end{vmatrix}$ is equal to <br/> <br/>
Question 55 :
Find the value of the following determinant:<br/>$\begin{vmatrix}1.2 & 0.03\\ 0.57 & -0.23\end{vmatrix}$
Question 56 :
The value of the determinant$\begin{vmatrix} 5 & 1 \\ 3 & 2 \end{vmatrix}$
Question 57 :
For positive numbers $x, y$ and $z$ the numerical value of the determinant $\begin{vmatrix} 1 & \log_x y & \log_x z\\ \log_y x & 1 & \log_y z \\ \log_z x & \log_z y & 1 \end{vmatrix}$ is<br>
Question 58 :
If $\begin{vmatrix} 6i & -3i & 1\\ 4 & 3i & -1 \\ 20 & 3 & i\end{vmatrix}=x+iy$, then<br>
Question 59 :
If the trivial solution is the only solution of the system of equations$x-ky+z=0,kx+3y-kz=0, 3x+y-z=0$. Then the set of all values of k is:<br>
Question 60 :
If $\begin{vmatrix} x & y\\ 4 & 2 \end{vmatrix}=7$ and $\begin{vmatrix} 2 & 3\\ y & x \end{vmatrix}=4$ then<br>
