Question 1 :
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 2 :
The function $f\left( x \right)=\left[ x \right] ,$  at ${ x }=5$ is:<br/>
Question 3 :
If $f(x) = (1 + 2x)^{\frac{1}{x}}$, for $x \neq 0$ is continuous at $x = 0$, then $f(0) = $_______.
Question 4 :
If $ f\left( x \right) =\begin{cases} 1 & x<0 \\ { x }^{ 2 } & x\ge 0 \end{cases}$ then at $x=0$
Question 5 :
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 6 :
If $f(x)=\displaystyle \frac{\sin x}{x},x\neq 0$ is to be continuous at ${x}=0$ then $\mathrm{f}({0})=$<br/>
Question 7 :
$f(x)=\left\{\begin{matrix} 2x-1& if &x>2 \\ k & if &x=2 \\  x^{2}-1& if & x<2\end{matrix}\right.$is continuous at $x= 2$ then $k =$
Question 8 :
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 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 11 :
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 12 :
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 13 :
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 14 :
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 15 :
<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 16 :
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 17 :
Let $f(x) = \left\{\begin{matrix} -2,& -3 \leq x \leq 0\\ x - 2,  & x < x \leq 3\end{matrix}\right.$ and $g(x) = f(|x|) + |f(x)|$<br/>Which of the following statements are correct?<br/>1. $g(x)$ is continuous at $x = 0$.<br/>2. $g(x)$ is continuous at $x = 2$.<br/>3. $g(x)$ is continuous at $x = -1$.<br/>Select the correct answer using the code given below
Question 18 :
If $f(x)=\begin{cases} \cfrac { { x }^{ 2 }-(a+2)x+2a }{ x-2 } ,\quad \quad x\neq 2 \\ 2,\quad \quad \quad \quad \quad \quad \quad x=2 \end{cases}$ is continuous at $x=2$, then $a$ is equal to-
Question 19 :
The function $f(x) = [x]$, where $[x]$ denotes greatest integer function is continuous at ___
Question 20 :
If $f(x)=\begin{cases} \sin { x } \quad if\quad x\le 0 \\ { x }^{ 2 }+{ a }^{ 2 }\quad if\quad 0<x<1 \\ bx+2\quad if\quad 1\le x\le 2 \\ 0\quad if\quad x>2 \end{cases}$ is continuous on $R$, then $a+b+ab=$
Question 21 :
If the function $\displaystyle f\left( x \right)=\begin{cases} \begin{matrix} 1+\sin { \dfrac { \pi }{ 2 } x } , for & -\infty <x\le 1 \end{matrix} \\ \begin{matrix} ax+b, for & 1<x<3 \end{matrix} \\ \begin{matrix} 6\tan { \dfrac { \pi x }{ 12 } } ,for & 3\le x<6 \end{matrix} \end{cases}$ is continous in the interval $(-\infty,6)$ then the value of $a$ and $b$ are?
Question 22 :
If $f(x) = \left\{\begin{matrix}\dfrac {1 - \cos x}{x},& x\neq 0\\ k,& x = 0\end{matrix}\right.$ is continuous at $x = 0$, then the value of $k$ is<br>
Question 23 :
If $\displaystyle f\left( x \right)=\frac { 1 }{ 2 } x-1$, then on the interval $[0,\pi]$
Question 24 :
The function $f(x)=\begin{cases} 0,&  \text{x  is irrational }\\  1,& \text{x is rational }\end{cases}$ is
Question 25 :
Consider the function $f\left( x \right) =2\sqrt { 6-[x] } $ at $2<x\le 3$ , where $[x]$ denotes step up function, then at $x=2$ the function <br/>
Question 26 :
Let $\displaystyle f(x)=\begin{cases} 1 & \text{ if } x\   is\    rational \\  0 & \text{ if } x\     is\    irrational \end{cases}$.Then,
Question 27 :
The function $f(x) = x - |x - x^2|, -1 \leq x \leq 1$ is continuous on the interval<br>
