Question 1 :
$\displaystyle \underset{x\rightarrow 0}{\lim}\dfrac{(1 - \cos 2x)^2}{2x \tan x - x \tan 2x}$ is equals to:
Question 2 :
If $f\left( x \right) = \left\{ \begin{gathered}  \frac{{{x^2}}}{a}\, - a,\,\,\,\,if\,0 < x < a \\  \,\,\,\,\\ 0,\,\,\,\,if\,x = 0\\ \\ a - \frac{{{a^2}}}{{{x^2}}},\,\,if\,x > a \\ \end{gathered}  \right. $<br/>then $\mathop {\lim }\limits_{x \to a} f\left( x \right)$ is equal to :
Question 3 :
Let a function $f(x)=\left\{\begin{array}{l}bx+c \quad \mathrm{f}\mathrm{o}\mathrm{r}\quad x>1\\3cx-2b+1\quad \mathrm{f}\mathrm{o}\mathrm{r}\quad x<1\end{array}\right.$. Then a relation between $b$ and $c$ such that $\underset { x\rightarrow 1 }{ \lim } f(x)$ exists is<br>
Question 4 :
Let $\alpha$ and $\beta$ be the distinct roots of $ax^{2}+bx+c=0$ then $\displaystyle \lim_{x\rightarrow a}$ $\displaystyle \frac{1-\cos(ax^{2}+bx+c)}{(x-\alpha)^{2}}$ is equal to-
Question 5 :
The value of $\lim {x\rightarrow \infty}x^2 sin \left ( \iota n \sqrt {cos\dfrac {\pi}{x}}\right)$ is
Question 6 :
$\displaystyle\quad \lim _{ x\rightarrow \infty  }{ \cfrac { \sqrt { { x }^{ 2 }+1 } -\sqrt [ 3 ]{ { x }^{ 3 }+1 }  }{ \sqrt [ 4 ]{ { x }^{ 4 }+1 } -\sqrt [ 5 ]{ { x }^{ 4 }+1 }  }  } $ is equals to
Question 8 :
$\mathop {\lim }\limits_{x \to \pi } \dfrac{{{x^\pi } - {\pi ^x}}}{{{x^x} - {\pi ^\pi }}}$ is equal to 
Question 14 :
$\underset { x\rightarrow 0 }{ \lim } \dfrac { { 3 }^{ 2x }-{ 2 }^{ 3x } }{ x } $ is equal to
Question 15 :
$\underset { x\rightarrow a }{ \lim } \dfrac { \sqrt { a+2x } -\sqrt { 3x }  }{ \sqrt { 3a+x } -2\sqrt { x }  } $ is equal to
