Question 1 :
Solve:$\displaystyle \sin { \left( { \tan }^{ -1 }x \right) } ,\left| x \right| <1$ is equal to
Question 3 :
Simplify ${\cot ^{ - 1}}\dfrac{1}{{\sqrt {{x^2} - 1} }}$ for $x <  - 1$
Question 5 :
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 6 :
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 7 :
The value of $\sin^{-1} \left( \dfrac{2 \sqrt 2}{3} \right ) + \sin^{-1} \left( \dfrac{1}{3}\right )$ is equal to
Question 8 :
$\quad \sin ^{ -1 }{ x } +\sin ^{ -1 }{ \cfrac { 1 }{ x } } +\cos ^{ -1 }{ x } +\cos ^{ -1 }{ \cfrac { 1 }{ x } = } $
Question 9 :
$\sin ^ { - 1 } 5 + \cos ^ { - 1 } 5 = \ldots \ldots$
Question 10 :
The value of $\cos^{-1} (\cos 12) - \sin^{-1} (\sin 12)$ is 
Question 11 :
<i></i>What is the determinant of the matrix $\left [\begin{matrix} 3& 6\\ -1 & 2\end {matrix} \right]$?<br/>
Question 12 :
Find the value of the following determinant:<br/>$\begin{vmatrix}3\sqrt{6} & -4\sqrt{2}\\ 5\sqrt{3} & 2\end{vmatrix}$
Question 13 :
If $A$ is a skew symmetric matrix, then $\left| A \right| $ is
Question 14 :
Find the values of x, if <br>$\begin{vmatrix} 2 & 4 \\ 5 & 1 \end{vmatrix}$= $\begin{vmatrix} 2x & 4 \\ 6 & x \end{vmatrix}$
Question 15 :
If $\begin{bmatrix} x & 1 & 1\\ 2 & 3 & 4\\ 1 & 1 & 1\end{bmatrix}$ has no inverse, then $x=$
Question 16 :
$D=\begin{vmatrix} 18 & 40 & 89 \\ 40 & 89 & 198 \\ 89 & 198 & 440 \end{vmatrix}=$
Question 17 :
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 18 :
If $\displaystyle{\left| {_2^{4\,}\,\,_1^1} \right|^2} = \left| {_1^3\,\,_x^2} \right| - \left| {_{ - 2}^x\,\,_1^3} \right|,$ then $x$=
Question 19 :
If $\begin{vmatrix} x & y\\ 4 & 2 \end{vmatrix}=7$ and $\begin{vmatrix} 2 & 3\\ y & x \end{vmatrix}=4$ then<br>
Question 20 :
If $\begin{vmatrix} 6i & -3i & 1\\ 4 & 3i & -1 \\ 20 & 3 & i\end{vmatrix}=x+iy$, then<br>