Question Text
Question 5 :
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 6 :
What is $\tan ^{ -1 }{ \left( \dfrac { 1 }{ 2 } \right) } +\tan ^{ -1 }{ \left( \dfrac { 1 }{ 3 } \right) } $ equal to?
Question 8 :
The value of $ \cos \left( \sin^{-1} \left( \dfrac {2}{3} \right) \right) $ is equal to :
Question 9 :
The value of $\tan { \left[ \dfrac { 1 }{ 2 } \cos ^{ -1 }{ \left( \dfrac { 2 }{ 3 } \right) } \right] } $ is
Question 10 :
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 11 :
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 12 :
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 13 :
The value of $sin^{-1} x + cos^{-1} x (|x| \geq 1)$ is
Question 14 :
<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 15 :
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