Question 3 :
${\tan ^{ - 1}}2 + {\tan ^{ - 1}}3$ is equal to
Question 5 :
Solve $\cos { \left[ \tan ^{ -1 }{ \left[ \sin { \left( \cot ^{ -1 }{ x }  \right)  }  \right]  }  \right]  } $
Question 6 :
If $\sin^{-1}\left(x-\dfrac {x^{2}}{2}+\dfrac {x^{3}}{4}-...\infty \right)+\cos^{-1}\left(x^{2}-\dfrac {x^{4}}{2}+\dfrac {x^{6}}{4}-...\infty \right)=\dfrac {\pi}{2}$ for $0 < |x| < \sqrt {2}$,then $x$ equal
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 9 :
If $\sec^{-1} x+ \sec^{-1}y + \sec^{-1}z = 3\pi$, then $xy + yz + zx =$ _______.
Question 12 :
If $f ( x ) = \sin ^ { - 1 } \left( \dfrac { 2 \times 3 ^ { x } } { 1 + 9 ^ { x } } \right) ,$ then $f ^ { \prime } \left( - \frac { 1 } { 2 } \right)$
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 :
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 18 :
The value of $\cos^{-1} (\cos 12) - \sin^{-1} (\sin 12)$ is 
Question 20 :
Simplify ${\cot ^{ - 1}}\dfrac{1}{{\sqrt {{x^2} - 1} }}$ for $x <  - 1$
Question 21 :
Solution of the equation $\displaystyle \tan { \left( \cos ^{ -1 }{ x }  \right)  } =\sin { \left( \cot ^{ -1 }{ \frac { 1 }{ 2 }  }  \right)  } $ is
Question 23 :
If $\sin^{-1}\dfrac{1}{3} + \sin^{-1}\dfrac{2}{3} = \sin^{-1}x$, then $x$ is equal to-
Question 24 :
Number of triplets $\left ( x, y, z \right )$ satisfying $\sin ^{-1}x+\sin ^{-1}y+\cos ^{-1}z=2\pi$ is<br>
Question 25 :
The equation $2\cos ^{ -1 }{ x } +\sin ^{ -1 }{ x } =\cfrac { 11\pi }{ 6 } $ has-
Question 27 :
The set of values of $x$ for which<br>$\tan ^{ -1 }{ \cfrac { x }{ \sqrt { 1-{ x }^{ 2 } } } } =\sin ^{ -1 }{ x } $ holds, is
Question 28 :
The greatest and least value of ${\left( {{{\sin }^{ - 1}}x} \right)^2} + {\left( {{{\cos }^{ - 1}}x} \right)^2}$ are respectively
Question 29 :
Assertion: The number of solutions ofthe equation $\sin ^{-1}x+\sin ^{-1}2x=\frac{\pi}{3}$ is only one.
Reason: The sum of two positive angles cannot be negative.
Question 30 :
If $\cos^{-1}\left (\dfrac {1 - x^{2}}{1 + x^{2}}\right ) + \cos^{-1}\left (\dfrac {1 - y^{2}}{1 + y^{2}}\right ) = \dfrac {\pi}{2}$, where $xy < 1$, then
Question 31 :
The value of $\displaystyle \tan^{-1} \left( \frac{\sin{  2} - 1}{\cos {2}} \right )$ is equal to
Question 32 :
<b>If $2\sinh ^{ -1 }{ \left( \dfrac { a }{ \sqrt { 1-{ a }^{ 2 } }  }  \right)  } =\log { \left( \dfrac { 1+x }{ 1-x }  \right)  }$, then $x=$</b>
Question 34 :
If $(\sin ^{-1 }x)^2+(\sin ^{-1 }y)^2+2(\sin ^{-1 }x)(\sin ^{-1 }y)=\pi ^2$, then $x^2+y^2$ is equal to -<br/>
Question 38 :
${\text{If}}\;{\tan ^{ - 1}}\left( {\dfrac{a}{x}} \right) + {\tan ^{ - 1}}\left( {\dfrac{b}{x}} \right) = \dfrac{\pi }{2},{\text{then}}\;x\;{\text{is}}\;{\text{equal}}\;{\text{to}}:$
Question 39 :
If $\cos ^{ -1 }{ x } -\cos ^{ -1 }{ \cfrac { y }{ 2 }  } =\alpha $, then $4{ x }^{ 2 }-4xy\cos { \alpha  } +{ y }^{ 2 }\quad $ is equal to
Question 40 :
$2\cot ^{ -1 }{ 7 } +\cos ^{ -1 }{ \dfrac { 3 }{ 5 }  } $ is equal to 
Question 41 :
The value of $\cot \left( \dfrac{\pi}{4} - 2 \cot^{-1} 3\right)$, is:
Question 43 :
If $\dfrac{1}{\sqrt{2}} < x < 1$, then $\cos ^{ -1 }{ x } +\cos ^{ -1 }{ \left( \dfrac { x+\sqrt { 1-{ x }^{ 2 } }  }{ \sqrt { 2 }  }  \right)  } $ is equal to :
Question 45 :
The value of $tan(\frac { 1 }{ 2 } { cos }^{ -1 }(\frac { \sqrt { 5 } }{ 3 } ))$ is
Question 48 :
The value of '$a$' for which $ax^2+\sin^{-1} (x^2-2x+2)+\cos^{-1}(x^2-2x+2)=0$ has a real solution, is
Question 49 :
If $x=\cos^{ - 1}\left( \dfrac{2}{3} \right) + \tan^{ - 1}\left( \dfrac{1}{7} \right)$ then $x$=
Question 53 :
The range of the the function, $f(x)=(\cot ^{-1}x+\sec ^{-1}x+cosec ^{-1}x)$ is
Question 56 :
Assertion: Statement 1 : $f'(2) = \dfrac{-3}{5}$
Reason: Statement 2 : $sin^{-1}\Bigg(\dfrac{2x}{1+x^2}\Bigg)=\pi-2\tan^{-1}x,\forall \,x>1$
Question 57 :
If $\tan^{-1}x=\dfrac{\pi}{10}$ for some $x\in R$, then the value of $\cot^{-1}x$ is
Question 58 :
The value of $\cos ^{-1} \left(\cos \dfrac{3 \pi}{2}\right)$ is equal to
Question 59 :
${\cos ^{ - 1}}\dfrac{3}{5} - {\sin ^{ - 1}}\dfrac{4}{5} = {\cos ^{ - 1}}x$ then $x$ is equal to:
Question 60 :
The number of solutions of the equation, $\sin^{-1}x=2\tan^{-1}x$ (in principle value) is:-
Question 61 :
All x satisfying the inequality <br/>$(\cot^{-1} x)^2 - 7 (\cot^{-1} x)  + 10 > 0$, lie in the interval:-
Question 62 :
The solution of equation<br>$\sin ^{ -1 }{ \left( 1-\cfrac { x }{ 2 } \right) } -2\sin ^{ -1 }{ \left( \cfrac { x }{ 2 } \right) } =\cfrac { \pi }{ 2 } $ is
Question 64 :
The value of $\cos { \left\{ \tan ^{ -1 }{ \left( \tan { \cfrac { 15\pi }{ 4 } } \right) } \right\} } \quad $ is
Question 65 :
If $\sin^{-1} x + \sin^{-1} y = \dfrac{2\pi}{3}$, then $  \cos^{-1} x + \cos^{-1}y =$
Question 66 :
The value of $\cos \left[ {{1 \over 2}{{\cos }^{ - 1}}\cos \left( { - {{14\pi } \over 5}} \right)} \right]$ is
Question 70 :
If $\sin ^{ -1 }{ x } +\sin ^{ -1 }{ \left( x\sqrt { 3 } \right) } =-\dfrac { \pi }{ 2 }$, then $x$ is equal to
Question 71 :
The value of $\cos { \left( \tan ^{ -1 }{ \tan { 4 } } \right) } $ is-
Question 73 :
The value of $\tan ^{ -1 }{ \left( 2\sin { \left( \sec ^{ -1 }{ \left( 2 \right) } \right) } \right) } $ is
Question 74 :
${\cot ^{ - 1}}\left( {2 + \sqrt 3 } \right) = $
Question 75 :
The number of real solutions of $tan^{-1} (\sqrt{x(x+1)}+sin^{-1} \displaystyle \sqrt{(x^{2}+x+1)}=\dfrac{\pi}{2}$ is<br>
Question 76 :
If $3\cos ^{ -1 }{ x } +\sin ^{ -1 }{ x } =\pi $, then $x=.....$
Question 77 :
If $\displaystyle \left ( \sin^{-1} x + \sin^{-1} w\right ) \left ( \sin^{-1} y + \sin^{-1} z\right ) = \pi^{2}$, then $\displaystyle D = \begin{vmatrix}x^{N_{1}} & y^{N_{2}} \\ z^{N_{3}} & w^{N_{4}}\end{vmatrix} \left ( N_{1}, \: N_{2}, \: N_{3}, \: N_{4} \: \epsilon \: N \right )$<br>
Question 79 :
Assertion: Consider $\displaystyle f(x) = sin^{-1}(sec(tan^{-1}x) + cos^{-1}(cosec(cot^{-1}x)$<br/><br/>Statement-1: Domain of f(x) is a singleton.
Reason: Statement-2: Range of the function $f(x)$ is a singleton.
Question 80 :
If $\left[ \sin ^{ -1 }{ \cos ^{ -1 }{ \sin ^{ -1 }{ \tan ^{ -1 }{ \theta } } } } \right] =1$, where $[.]$ denotes the greatest integer function, the $\theta$ lies in the interval
Question 81 :
If $\ \cot^{-1}\left(\dfrac{1}{x}\right) + \ \cos^{-1} (-x) + \ \tan^{-1} x = \pi$ and $\ \sin^{-1}x < 0,$ then the value of $\dfrac{(1-x^2)^{3/2}}{x^2}$ is<br/>
Question 82 :
Assertion: $\displaystyle \sin ^{ -1 }{ \left( \sin { \left( \frac { 2\pi  }{ 3 }  \right)  }  \right)  } =\frac { \pi  }{ 3 } $
Reason: $\displaystyle \sin ^{ -1 }{ \left( \sin { \theta  }  \right)  } =\theta ;$ where $\displaystyle \theta \in \left[ -\frac { \pi  }{ 2 } ,\frac { \pi  }{ 2 }  \right] $
Question 83 : <div><span>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.</span><br/></div><div><span><br/></span></div>If $\displaystyle -1<x<0$,then $\displaystyle \tan^{-1}x $ equals?<br/>
Question 84 :
If $\displaystyle \sin ^{ -1 }{ x } +\sin ^{ -1 }{ y } +\sin ^{ -1 }{ z } =\frac { 3\pi  }{ 2 } $, then $\displaystyle \frac { \sum _{ k=1 }^{ 2 }{ \left( { x }^{ 100k }+{ y }^{ 106k } \right)  }  }{ \sum { { x }^{ 207 }.{ y }^{ 207 } }  } $ is
Question 85 :
$\dfrac { { d } }{ { d }x } \left\{ \tan ^{ -1 }{ \dfrac { x }{ 1+{ x }^{ 2 } } +\tan ^{ -1 }{ \dfrac { 1+{ x }^{ 2 } }{ x } } } \right\} =$
Question 86 :
$\tan { ^{ -1 }\left( 3/5 \right) } +\tan { ^{ -1 }\left( 1/4 \right) } =$
Question 87 :
The value of $sin^{-1} x + cos^{-1} x (|x| \geq 1)$ is
Question 88 :
The range of values of <i>p</i> for which the equation $\sin \cos ^{-1}(\cos (\tan ^{-1}x))= p$ has a solution is<br>
Question 89 :
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 90 :
The value of $\displaystyle \tan \left ( \sin ^{-1}\left ( \cos \left ( \sin ^{-1}x \right ) \right ) \right ) \tan \left ( \cos ^{-1}\left ( \sin \left ( \cos ^{-1} x\right ) \right ) \right )$, where $\displaystyle x\:\epsilon \:\left ( 0,1 \right )$, is equal to<br>
Question 91 :
Solve $\displaystyle \int { \cfrac { { e }^{ \tan ^{ -1 }{ x }  } }{ \left( 1+{ x }^{ 2 } <br/><br/>\right)  } \left[ { \left( \sec ^{ -1 }{ \sqrt { 1+{ x }^{ 2 } }  }  <br/><br/>\right)  }^{ 2 }+\cos ^{ -1 }{ \left( \cfrac { 1-{ x }^{ 2 } }{ 1+{ x <br/><br/>}^{ 2 } }  \right)  }  \right] dx } \quad \left( x>0 \right) $<br/><br/>
Question 92 :
If $cosec ^{ -1 }\left(cosec (x) \right)$ and $cosec\left(cosec ^{ -1 }(x) \right) $ are equal functions, then the maximum range of value of $x$ is<br>
Question 93 :
${\sin ^{ - 1}}\dfrac{{\sqrt x }}{{\sqrt {x + a} }}$ is equal to
Question 96 : 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>If 4 $sin^{-1} x + cos^{-1} x = \pi$, then x equals</td><td>1</td><td>ab</td></tr><tr><td>b</td><td>If $\angle C = 90^{0}$, then the value of $tan^{-1}$ $\dfrac{a}{b + c}$ + $tan^{-1}$ $\dfrac{b}{c +a}$ is </td><td>2</td><td>$\pi$</td></tr><tr><td>c</td><td>$tan^{-1}$ 1 + $tan^{-1}$ 2 + $tan^{-1}$ 3 is</td><td>3</td><td>$\pi$/4</td></tr><tr><td>d</td><td>If $sec^{-1}$ $\dfrac{x}{a}$ - $sec^{-1}$ $\dfrac{x}{b}$ = $sec^{-1}$ b - $sec^{-1}$ a, then x equals</td><td>4</td><td>1/2</td></tr></tbody></table>
Question 98 :
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 100 :
$\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 102 :
The value of $\displaystyle sin^{-1}\left ( cot\left ( sin^{-1} \sqrt{\frac{2-\sqrt{3}}{4}}+cos^{-1}\frac{\sqrt{12}}{4}+sec^{-1}\sqrt{2}\right ) \right )$ is
