Question 1 :
Let $\omega\neq{1}$ be a cube root of unity and $S$ be the set of all non-singular matrices of the form $ \begin{bmatrix} 1 & a & b \\ \omega & 1 & c \\ { \omega }^{ 2 } & \omega & 1 \end{bmatrix}$Where each of $a,\ b$ and $c$ is either $\omega$ or ${\omega}^{2}$. Then the number of distinct matrices in the set $S$ is
Question 2 :
Find the value of the following determinant:<br/>$\begin{vmatrix}\displaystyle \frac{-4}{7} & \displaystyle \frac{-6}{35}\\ 5 & \displaystyle \frac{-2}{5}\end{vmatrix}$
Question 3 :
Find the value of the following determinant:<br/>$\begin{vmatrix}3\sqrt{6} & -4\sqrt{2}\\ 5\sqrt{3} & 2\end{vmatrix}$
Question 4 :
Find the values of x, if <br>$\begin{vmatrix} 2 & 4 \\ 5 & 1 \end{vmatrix}$= $\begin{vmatrix} 2x & 4 \\ 6 & x \end{vmatrix}$
Question 5 :
If $\displaystyle{\left| {_2^{4\,}\,\,_1^1} \right|^2} = \left| {_1^3\,\,_x^2} \right| - \left| {_{ - 2}^x\,\,_1^3} \right|,$ then $x$=
Question 6 :
If $A=\begin{bmatrix}\alpha &2 \\2 &\alpha \end{bmatrix}$ and $|A^3|=125$, then $\alpha$ is equal to<br>
Question 7 :
lf $\alpha,\ \beta$ are the roots of the equation$x^{2}+x+1=0$ and $S_k={\alpha}^k+{\beta}^k ; k=1,2,3,4$ , then<br>$\left| \begin{matrix} 3 & 1+{ S }_{ 1 } & 1+{ S }_{ 2 } \\ 1+{ S }_{ 1 } & 1+{ S }_{ 2 } & 1+{ S }_{ 3 } \\ 1+{ S }_{ 2 } & 1+{ S }_{ 3 } & 1+{ S }_{ 4 } \end{matrix} \right| =\\$<br>
Question 8 :
The value of $det\ A$, where $A = \begin{pmatrix}1& \cos \theta& 0\\ -\cos \theta& 1 & \cos \theta\\ -1& -\cos \theta& 1\end{pmatrix}$ lies<br>
Question 9 :
$f(x)=\begin{vmatrix} \cos { x }  & x & 1 \\ 2\sin { x }  & { x }^{ 2 } & 2x \\ \tan { x }  & x & 1 \end{vmatrix}$. The value of $\displaystyle \lim _{ x\rightarrow 0 }{ \cfrac { f(x) }{ x }  } $ is equal to<br/>
Question 10 :
For a positive numbers $x, y$ and $z$ the numerical value of the determinant $\begin{bmatrix}1 & \log_{x} y & \log_{x} z \\ \log_{y} x & 1 & \log_{y} z\\ \log_{z} x & \log_{z} y & 1\end{bmatrix}$ is:
Question 11 :
$\quad \sin ^{ -1 }{ x } +\sin ^{ -1 }{ \cfrac { 1 }{ x } } +\cos ^{ -1 }{ x } +\cos ^{ -1 }{ \cfrac { 1 }{ x } = } $
Question 12 :
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 13 :
Solve $\cos { \left[ \tan ^{ -1 }{ \left[ \sin { \left( \cot ^{ -1 }{ x }  \right)  }  \right]  }  \right]  } $
Question 14 :
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 16 :
Simplify ${\cot ^{ - 1}}\dfrac{1}{{\sqrt {{x^2} - 1} }}$ for $x <  - 1$
Question 17 :
Solve:$\displaystyle \sin { \left( { \tan }^{ -1 }x \right) } ,\left| x \right| <1$ is equal to
Question 18 :
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 19 :
${ 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 21 :
The value of $\sin ^{ -1 }{ \left( \cos { \cfrac { 53\pi }{ 5 } } \right) } $ is
Question 23 :
If $\sin ^{ -1 }{ \left( \cfrac { x }{ 13 } \right) } +co\sec ^{ -1 }{ \left( \cfrac { 13 }{ 12 } \right) } =\cfrac { \pi }{ 2 } $, then the value if $x$ is
Question 24 :
$ \sin \left( 2 \sin^{-1} \sqrt{\dfrac{63}{65}} \right) $<br/>is equal to :
Question 25 :
The number of solutions for the equation $2\sin ^{ -1 }{ \sqrt { { x }^{ 2 }-x+1 }  } +\cos ^{ -1 }{ \sqrt { { x }^{ 2 }-x }  } =\dfrac { 3\pi }{ 2 } $ is
Question 26 :
If two angles of a triangle are $\tan ^{ -1 }{ (2) } $ and $\tan ^{ -1 }{ (3) } $, then the third angle is
Question 27 :
The value of $\tan { \left[ \dfrac { 1 }{ 2 } \cos ^{ -1 }{ \left( \dfrac { 2 }{ 3 } \right) } \right] } $ is
Question 28 :
What is $\sin { \left[ \sin ^{ -1 }{ \left( \cfrac { 3 }{ 5 } \right) } +\sin ^{ -1 }{ \left( \cfrac { 4 }{ 5 } \right) } \right] } $ equal to?
Question 29 :
If $\dfrac {(x + 1)^{2}}{x^{3} + x} = \dfrac {A}{x} + \dfrac {Bx + C}{x^{2} + 1}$, then $\csc^{-1}\left (\dfrac {1}{A}\right ) + \cot^{-1}\left (\dfrac {1}{B}\right ) + \sec^{-1}C =$ ____
Question 30 :
The value of $ \cos \left( \sin^{-1} \left( \dfrac {2}{3} \right) \right) $ is equal to :
Question 31 :
If order of a matrix is $3 \times 3$, then it is a
Question 32 :
$\displaystyle { A=\left[ { a }_{ ij } \right] }_{ m\times n}$ is a square matrix , if
Question 33 :
A square matrix A has 9 elements. What is the possible order of A?
Question 34 :
If $\displaystyle A = \begin{bmatrix} 1 & -2 & 4 \\ 2 & 3 & 2 \\ 3 & 1 & 5 \end{bmatrix}$ and $\displaystyle B = \begin{bmatrix} 0 & -2 & 4 \\ 1 & 3 & 2 \\ -1 & 1 & 5 \end{bmatrix}$, then $A + B$ is
Question 35 :
Matrix $A$ is given by $A=\begin{bmatrix} 6 & 11 \\ 2 & 4 \end{bmatrix}$ then the determinant of ${A}^{2015} -6{A}^{2014} $ is.
Question 36 :
The matrix A satisfies the matrix equation if $A=\begin{bmatrix} 1 & 2 & 2 \\ 2 & 1 & 2 \\ 2 & 2 & 1 \end{bmatrix}$<br/>
Question 37 :
If $A$ is a square matrix of order $3$ such that $A^{2} + A + 4I = 0$, where $0$ is the zero matrix and $I$ is the unit matrix of order $3$, then
Question 38 :
Let $\quad A=\begin{pmatrix} { x }^{ 2 } & 6 & 8 \\ 3 & { y }^{ 2 } & 9 \\ 4 & 5 & { z }^{ 2 } \end{pmatrix}$ and $B=\begin{pmatrix} 2x & 3 & 5 \\ 2 & 2y & 6 \\ 1 & 4 & 2z-3 \end{pmatrix}$ be two matrices and if $Tr(A)=Tr(B)$, then the value of $(x+y+z)$ is equal to<br/>(Note: $Tr(P)$ denotes trace of matrix $P$)
Question 40 :
If $A=\left[ \begin{matrix} 1 & -2 & 3 \end{matrix} \right] $     $B=\left[ \begin{matrix} -1 \\ 2 \\ -3 \end{matrix} \right] $, then $A + B$:<br/>
