Question 1 :
$\sin ^ { - 1 } 5 + \cos ^ { - 1 } 5 = \ldots \ldots$

Question 2 :
The value of $\sin^{-1} \left( \dfrac{2 \sqrt 2}{3} \right ) + \sin^{-1} \left( \dfrac{1}{3}\right )$ is equal to

Question 3 :
If $\cot^{-1} [\sqrt{\cos \alpha}] - \tan^{-1} [\sqrt{\cos \alpha}] = x$, then $\sin x$ is equal to

Question 4 :
Consider the following :<br>1. ${\sin}^{-1}\dfrac{4}{5}+{\sin}^{-1}\dfrac{3}{5}=\dfrac{\pi}{2}$<br>2. ${\tan}^{-1}\sqrt{3}+{\tan}^{-1}1=-{\tan}^{-1}(2+\sqrt{3})$<br>Which of the above is/are correct?

Question 5 :
$\tan { ^{ -1 }\left( 3/5 \right) } +\tan { ^{ -1 }\left( 1/4 \right) } =$

Question 6 :
Match the entries of Column - I and Column - II.<br><table class="wysiwyg-table"><tbody><tr><td></td><td>Column - I</td><td></td><td>Column - II</td></tr><tr><td>a</td><td>x = $cosec^{2}$ $(cot^{-1} 3)$ - $sec^{2}$ $(tan^{-1} 2)$</td><td>p</td><td>x = 2</td></tr><tr><td>b</td><td>$tan^{-1}$ x + $tan^{-1}$ $\dfrac{1}{y}$ = $(tan^{-1} 3)$ and $y^{2}$ + y - 56 = 0</td><td>q</td><td>x = 5</td></tr><tr><td>c</td><td>$cos^{-1}$ x = $tan^{-1}$ y and $y^{2}$ = 3</td><td>r</td><td>$x = \dfrac{1}{2}$</td></tr><tr><td>d</td><td>$sin^{-1}$ $\left (tan \dfrac{\pi}{4} \right )$ - $sin^{-1}$ $\sqrt{\dfrac{3}{y}}$ = $\dfrac{\pi}{6}$ and $x^{2}$ = y<br></td><td>s</td><td>x = - $\dfrac {1}{2}$</td></tr></tbody></table>

Question 7 :
If $A = \begin{bmatrix}2 &amp; 3 &amp; 4 \\ -3 &amp; 4 &amp; 8\end{bmatrix}$ and&#160;$B = \begin{bmatrix}-1 &amp; 4 &amp; 7 \\ -3 &amp; -2 &amp; 5\end{bmatrix}$, Then&#160;$\quad A+B = \begin{bmatrix}1 &amp; a &amp; b \\ c &amp; 2 &amp; 13\end{bmatrix}$<br/>Find the value of $a+b+c=$

Question 9 :
Assertion: The matrix $\begin{bmatrix} a & 0 & 0 & 0 \\ 0 & b & 0 & 0 \\ 0 & 0 & c & 0 \end{bmatrix}$ is a diagonal matrix Reason: $A[{a}_{ij}]$ is a square matrix such that ${a}_{ij}=0$ for all $i\ne j$, then $A$ is called diagonal matrix

Question 10 :
Let $\quad A=\begin{pmatrix} { x }^{ 2 } &amp; 6 &amp; 8 \\ 3 &amp; { y }^{ 2 } &amp; 9 \\ 4 &amp; 5 &amp; { z }^{ 2 } \end{pmatrix}$ and $B=\begin{pmatrix} 2x &amp; 3 &amp; 5 \\ 2 &amp; 2y &amp; 6 \\ 1 &amp; 4 &amp; 2z-3 \end{pmatrix}$ 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 11 :
If $\begin{vmatrix}a &amp; -b &amp; -c\\-a &amp; b &amp; -c \\ -a &amp; -b &amp; -c\end{vmatrix}+\lambda abc=0$, then $\lambda$ is equal to<br>

Question 12 :
$\begin{vmatrix} 2^3 &amp; 3^3 &amp; 3.2^2+3.2+1\\ 3^3 &amp; 4^3 &amp; 3.3^2+3.3+1\\ 4^3 &amp; 5^3 &amp; 3.4^2+3.4+1\end{vmatrix}$ is equal to?

Question 13 :
If $\Delta_1=\begin{vmatrix} 1 &amp; 0\\ a &amp; b\end{vmatrix}$ and $\Delta_2=\begin{vmatrix} 1 &amp; 0\\ c &amp; d\end{vmatrix}$ then $\Delta_2 \Delta_1$ is equal to<br>

Question 14 :
If $A=\begin{bmatrix} 1 &amp; 1 &amp; 1 \\ 1 &amp; 1+x &amp; 1 \\ 1 &amp; 1 &amp; 1+y &#160;\end{bmatrix}$ for $x\neq 0, &#160;y\neq 0$, then $D$ is:<br/>

Question 15 :
Assertion: The determinant of a matrix $\displaystyle A=\begin{bmatrix}0 &amp;1 &amp;2 \\-1 &amp;0 &amp;3 \\-2 &amp;-3 &amp;0 \end{bmatrix}$ is zero Reason: The determinant of every skew symmetric matrix of odd order is zero.

Question 16 :
If $\displaystyle f(x)=\begin{bmatrix}\sin x &amp;\ cosec x &amp;\tan x \\\sec x &amp;x\sin x &amp;x\tan x \\x^{2}-1 &amp;\cos x &amp;x^{2}+1 \end{bmatrix}$ then $\displaystyle \int_{-a}^{a}\left | f(x) \right |dx $ equals<br>

Question 17 :
Value of $\displaystyle \left| \begin{matrix} 3i \\ 5 \\ i \end{matrix}\,\,\,\,\begin{matrix} 2i \\ 4 \\ 2i \end{matrix}\,\,\,\,\begin{matrix} 2i \\ -3i \\ 7 \end{matrix} \right|&#160;$ is