Question 3 :
Solve $\cos { \left[ \tan ^{ -1 }{ \left[ \sin { \left( \cot ^{ -1 }{ x }  \right)  }  \right]  }  \right]  } $
Question 4 :
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 6 :
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 7 :
The value of $\cos^{-1} (\cos 12) - \sin^{-1} (\sin 12)$ is 
Question 10 :
The value of $\sin^{-1} \left( \dfrac{2 \sqrt 2}{3} \right ) + \sin^{-1} \left( \dfrac{1}{3}\right )$ is equal to
Question 11 :
Solve ${\cos ^{ - 1}}\left( {\frac{4}{5}} \right) + {\cos ^{ - 1}}\left( {\frac{{63}}{{65}}} \right) = $
Question 12 :
Solve:$\displaystyle \sin { \left( { \tan }^{ -1 }x \right) } ,\left| x \right| <1$ is equal to
Question 13 :
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 14 :
$\sin ^ { - 1 } 5 + \cos ^ { - 1 } 5 = \ldots \ldots$
Question 15 :
Simplify ${\cot ^{ - 1}}\dfrac{1}{{\sqrt {{x^2} - 1} }}$ for $x <  - 1$
Question 18 :
$\quad \sin ^{ -1 }{ x } +\sin ^{ -1 }{ \cfrac { 1 }{ x } } +\cos ^{ -1 }{ x } +\cos ^{ -1 }{ \cfrac { 1 }{ x } = } $
Question 19 :
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 20 :
${ 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 :
What is $\sin { \left[ \sin ^{ -1 }{ \left( \cfrac { 3 }{ 5 } \right) } +\sin ^{ -1 }{ \left( \cfrac { 4 }{ 5 } \right) } \right] } $ equal to?
Question 22 :
The value of $ \cos \left( \sin^{-1} \left( \dfrac {2}{3} \right) \right) $ is equal to :
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 24 :
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 25 :
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 26 :
The value of $\sin ^{ -1 }{ \left( \cos { \cfrac { 53\pi }{ 5 } } \right) } $ is
Question 27 :
If two angles of a triangle are $\tan ^{ -1 }{ (2) } $ and $\tan ^{ -1 }{ (3) } $, then the third angle is
Question 28 :
$ \sin \left( 2 \sin^{-1} \sqrt{\dfrac{63}{65}} \right) $<br/>is 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 :
What is $\tan ^{ -1 }{ \left( \dfrac { 1 }{ 2 } \right) } +\tan ^{ -1 }{ \left( \dfrac { 1 }{ 3 } \right) } $ equal to?
Question 32 :
The value of $sin^{-1} x + cos^{-1} x (|x| \geq 1)$ is
Question 33 :
<b>Statement I :</b>  The equation $(sin^{-1}x)^3+(cos^{-1}x)^3-a\pi^3=0$ has a solution for all $a\geqslant \dfrac {1}{32}.$<br/><b>Statement II :</b> For any $x\epsilon R, sin^{-1}x+cos^{-1}x=\dfrac {\pi}{2}$ and $0\leq (sin^{-1}x-\dfrac {\pi}{4})^2\leq \dfrac {9\pi^2}{16}$.<br/>
Question 35 :
$\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
Question 36 :
If $sin^{-1} \left( tan \dfrac {17\pi} {{4}}  \right )- sin^{-1} \left ( \sqrt{ \dfrac {3}{x}} \right ) - \left (\dfrac {\pi}{6} \right ) = 0$, then x is a root of the equation
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 39 :
$\tan { ^{ -1 }\left( 3/5 \right) } +\tan { ^{ -1 }\left( 1/4 \right) } =$
Question 40 :
If $\alpha$ and $\beta$ are two real values of x which satisfy the equation $sin^{-1} x + sin^{-1} (1 - x) = cos^{-1} x$, then
