Question 1 :
The value of $\sin^{-1} \left( \dfrac{2 \sqrt 2}{3} \right ) + \sin^{-1} \left( \dfrac{1}{3}\right )$ is equal to
Question 2 :
Calculate the value of $\displaystyle \sin^{-1} \cos \left ( \sin^{-1} x\right ) + \cos^{-1} \sin \left ( \cos^{-1} x \right ) $. where $\displaystyle\left | x \right | \leq 1$
Question 3 :
The value of $\cos^{-1} (\cos 12) - \sin^{-1} (\sin 12)$ is 
Question 4 :
Solve $\cos { \left[ \tan ^{ -1 }{ \left[ \sin { \left( \cot ^{ -1 }{ x }  \right)  }  \right]  }  \right]  } $
Question 5 :
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 7 :
Solve:$\displaystyle \sin { \left( { \tan }^{ -1 }x \right) } ,\left| x \right| <1$ is equal to
Question 10 :
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 11 :
Solve ${\cos ^{ - 1}}\left( {\frac{4}{5}} \right) + {\cos ^{ - 1}}\left( {\frac{{63}}{{65}}} \right) = $
Question 14 :
${ 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 16 :
Simplify ${\cot ^{ - 1}}\dfrac{1}{{\sqrt {{x^2} - 1} }}$ for $x <  - 1$
Question 17 :
$\quad \sin ^{ -1 }{ x } +\sin ^{ -1 }{ \cfrac { 1 }{ x } } +\cos ^{ -1 }{ x } +\cos ^{ -1 }{ \cfrac { 1 }{ x } = } $
Question 18 :
$\sin ^ { - 1 } 5 + \cos ^ { - 1 } 5 = \ldots \ldots$
Question 20 :
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 21 :
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 22 :
If two angles of a triangle are $\tan ^{ -1 }{ (2) } $ and $\tan ^{ -1 }{ (3) } $, then the third angle is
Question 23 :
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 25 :
The value of $\sin ^{ -1 }{ \left( \cos { \cfrac { 53\pi }{ 5 } } \right) } $ is
Question 26 :
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 27 :
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 28 :
What is $\tan ^{ -1 }{ \left( \dfrac { 1 }{ 2 } \right) } +\tan ^{ -1 }{ \left( \dfrac { 1 }{ 3 } \right) } $ equal to?
Question 29 :
$ \sin \left( 2 \sin^{-1} \sqrt{\dfrac{63}{65}} \right) $<br/>is equal to :
Question 30 :
The value of $ \cos \left( \sin^{-1} \left( \dfrac {2}{3} \right) \right) $ is equal to :
Question 31 :
The value of<b></b>$\left( {{{\tan }^{ - 1}}\pi + {{\tan }^{ - 1}}\left( {\frac{1}{\pi }} \right)} \right) + {\tan ^{ - 1}}\sqrt 3 - {\sec ^{ - 1}}( - 2)$ is equal to
Question 32 :
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 33 :
$\tan { ^{ -1 }\left( 3/5 \right) } +\tan { ^{ -1 }\left( 1/4 \right) } =$
Question 34 :
The value of $sin^{-1} x + cos^{-1} x (|x| \geq 1)$ is
Question 35 :
If $a<\cfrac { 1 }{ 32 } $, then the number of solutions of ${ \left( \sin ^{ -1 }{ x } \right) }^{ 3 }+{ \left( \cos ^{ -1 }{ x } \right) }^{ 3 }=a{ \pi }^{ 3 }$, is<br>
Question 36 :
The value of $a$ for which $\displaystyle ax^{2}+sin^{-1}(x^{2}-2x+2)+cos^{-1}(x^{2}-2x+2)=0$ has areal solution is
Question 37 :
Let $\displaystyle f:A\rightarrow B$ be a function defined by $\displaystyle y=f(x)$ where f is a bijective function, means f is injective (one-one) as well as surjective (onto), then there exist a unique mapping $\displaystyle g:B\rightarrow A$ such that $\displaystyle f(x)=y$ if and only if $\displaystyle g(y)=x\forall x \epsilon A,y \epsilon B $ Then function g is said to be inverse of f and vice versa so we write $\displaystyle g=f^{-1}:B\rightarrow A[\left \{ f(x),x \right \}:\left \{ x,f(x) \right \}\epsilon f^{-1}] $when branch of an inverse function is not given (define) then we consider its principal value branch.<br/><br/>If $\displaystyle -1<x<0$,then $\displaystyle \tan^{-1}x $ equals?<br/>
Question 38 :
Let $a, b, c$ be a positive real numbers $\theta = \tan^{-1} \sqrt{\dfrac{a(a + b +c)}{bc}} + \tan^{-1} \sqrt{\dfrac{b(a + b+ c)}{ca}} + \tan^{-1} \sqrt{\dfrac{c(a + b + c)}{ab}}$, then $\tan \theta$<br>
Question 39 :
The number of solution of the equation $ 1+x^{2}+2x\:\sin \left ( \cos^{-1}y \right )= 0 $ is :
Question 40 :
$\displaystyle \sum _{ k=1 }^{ k=n }{ \tan ^{ -1 }{ \frac { 2k }{ 2+{ k }^{ 2 }+{ k }^{ 4 } }  }  } =\tan ^{ -1 }{ \left( \dfrac { 6 }{ 7 }  \right)  } $, then the value of '$n$' is equal to