Question 1 :
Function $f(x) = \left\{\begin{matrix}(\log_{2}2x)^{\log_{x} 8};& x\neq 1\\(k - 1)^{3};& x = 1\end{matrix}\right.$ is continuous at $x = 1$, then $k =$ _______.<br>
Question 2 :
If $f(x)=\displaystyle \frac{\sin x}{x},x\neq 0$ is to be continuous at ${x}=0$ then $\mathrm{f}({0})=$<br/>
Question 3 :
If the function $\displaystyle f(x)=\begin{cases} 2x^{2}-3 & \text{ if } 0<x\leq 1 \\ x^{2}+bx-1 & \text{ if } 1<x<2 \end{cases}$ is continuous at every point of its domain then the value of $b$ is 
Question 4 :
$f(x)=\left\{\begin{matrix} 2x-1& if &x>2 \\ k & if &x=2 \\  x^{2}-1& if & x<2\end{matrix}\right.$is continuous at $x= 2$ then $k =$
Question 5 :
If as continuous function 'f' satisfies the realation <br/>$\int_{0}^{t}(f(x) \, - \, \sqrt{f^1(x)})dx \, = \, 0 \, and \, f(0) \, = \, {-1}$<br/>the f(x) is equal to
Question 6 :
If $ f\left( x \right) =\begin{cases} 1 & x<0 \\ { x }^{ 2 } & x\ge 0 \end{cases}$ then at $x=0$
Question 7 :
If $f(x) = \begin{cases}\dfrac{x^2-(a+2)x+a}{x-2} & x\ne 2\\ 2 & x = 2 \end{cases}$ is continuous at $x = 2$, then the value of $a$ is
Question 8 :
Following function is continous at the point $x=2$ <br/>          $f\left( x \right) = \left\{ \begin{array}{l}1 + x,\,\,\,\,when\,\,x < 2\\5 - x,\,\,\,\,when\,\,x \ge 2\end{array} \right.$
Question 9 :
The integer $'n'$ for which $\mathop {\lim }\limits_{x \to 0} \dfrac{{\cos 2x - 1}}{{{x^n}}}$ is a finite non-zero number is
Question 10 :
If $f\left( x \right) =\dfrac { 3sinx-sin\left( 3x \right) }{ { 2x }^{ 3 } } ,x\neq 0,f\left( 0 \right) =2,$ at $x=0,f$ is
Question 11 :
<br/>The function $f(x)=\begin{cases}(1+x)^{\frac{5}{x}}& for \ {x}\neq 0,\\ e^{5} & for \  {x}=0\end{cases}$ is ........ at ${x}=0$<br/>
Question 12 :
If $f(x) = (1 + 2x)^{\frac{1}{x}}$, for $x \neq 0$ is continuous at $x = 0$, then $f(0) = $_______.
Question 13 :
The function $f(x)=\dfrac{1-\sin x+\cos x}{1+\sin x+\cos x}$ is not defined at $x=\pi$. The value of $f(\pi)$ so that $f(x)$ is continuous at $x=\pi$ is
Question 14 :
The function $f\left( x \right)=\left[ x \right] ,$  at ${ x }=5$ is:<br/>
Question 16 :
If $f(x)=\displaystyle\frac{\log(1+ax)-log(1-bx)}{x}$ for $x\neq 0$ and $f(0)=k$ and $f(x)$ is continuous at $x=0$, then $k$ is equal to:<br>
Question 17 :
Let $[x]$ denotes the greatest integer less than or equal to $x$. Then, the value of $\alpha$ for which the function $f(x)=\begin{cases}\dfrac{\sin[-x^2]}{[-x^2]} &x\neq 0 \\ \alpha&x=0 \end{cases}$ is continuous at $x = 0$, is
Question 18 :
Assertion: The function $y=f(x)$, defined parametrically as $y=t^2+t|t|,x=2t-|t|,t\in R,$ is continuous for all real $x.$
Reason: $f\left( x \right)=\begin{cases} \begin{matrix} 2{ x }^{ 2 }, & x\ge 0 \end{matrix} \\ \begin{matrix} 0, & x<0 \end{matrix} \end{cases}$
Question 19 :
If the function $f(x)=\begin{cases} { \left( \cos { x } \right) }^{ 1/x } \\ k,\quad \quad x=0 \end{cases},\quad x\neq 0$ is continuous at $x=0$ then the value of $k$ is-
Question 20 :
If $f(x) =\begin{cases} \dfrac{\sin(p+1)x + \sin x}{x}& , &x < 0\\\quad \quad \quad q&,& x = 0\\ \dfrac{\sqrt{x^2 + x}- \sqrt{x}}{x^{3/2}}&,& x > 0\end{cases}$ is continuous at $x = 0$ the $(p, q)$ is
Question 21 :
If $f(x) = \left\{\begin{matrix} ax + 3, & x \leq 2\\ a^2 x - 1, & x > 2\end{matrix}\right.$, then the values of $a$ for which $f$ is continuous for all $x$ are
Question 22 :
If $\displaystyle f\left( x \right)=\frac { 1 }{ 2 } x-1$, then on the interval $[0,\pi]$
Question 23 :
If $f(x)=\begin{cases} \cfrac { \log { \left( 1+ax \right) } -\log { \left( 1-bx \right) } }{ x } ,\quad \quad x\neq 0 \\ k,\quad \quad \quad \quad \quad \quad \quad x=0 \end{cases}$, is contiuous at $x=0$, then $k$ is equal to-
Question 24 :
If $f(x) = \begin{cases}\dfrac{(1-\sin^3x)}{3\cos^2x},&x<\dfrac{\pi}{2}\\\quad a, & x = \dfrac{\pi}{2} \\\dfrac{b(1-\sin x)}{(\pi-2x)^2},& x > \dfrac{\pi}{2} \end{cases}$ is continuous at $x=\dfrac{\pi}{2}$, then the value of $\left(\dfrac{b}{a}\right)^{5/3}$ is
Question 25 :
Let $\displaystyle f(x)=\begin{cases} 1 & \text{ if } x\   is\    rational \\  0 & \text{ if } x\     is\    irrational \end{cases}$.Then,
