Question 1 :
$$f(x)=\left\{\begin{matrix} 2x-1& if &x>2 \\ k & if &x=2 \\  x^{2}-1& if & x<2\end{matrix}\right.$$is continuous at $$x= 2$$ then $$k =$$

Question 2 :
Function $$f(x) = \left\{\begin{matrix}(\log_{2}2x)^{\log_{x} 8};&amp; x\neq 1\\(k - 1)^{3};&amp; x = 1\end{matrix}\right.$$ is continuous at $$x = 1$$, then $$k =$$ _______.<br>

Question 3 :
If $$f(x) = \begin{cases}\dfrac{x^2-(a+2)x+a}{x-2} &amp; x\ne 2\\ 2 &amp; x = 2 \end{cases}$$ is continuous at $$x = 2$$, then the value of $$a$$ is

Question 4 :
<br/>The function $$f(x)=\begin{cases}(1+x)^{\frac{5}{x}}&amp; for \ {x}\neq 0,\\ e^{5} &amp;&#160;for \&#160; {x}=0\end{cases}$$ is ........&#160;at $${x}=0$$<br/>

Question 5 :
If as continuous function 'f' satisfies the realation&#160;<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 :
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 7 :
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 8 :
The function $$f\left( x \right)=\left[ x \right] ,$$ &#160;at $${ x }=5$$ is:<br/>

Question 9 :
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 10 :
Following function is continous at the point $$x=2$$&#160;<br/>&#160; &#160; &#160; &#160; &#160; $$f\left( x \right) = \left\{ \begin{array}{l}1 + x,\,\,\,\,when\,\,x &lt; 2\\5 - x,\,\,\,\,when\,\,x \ge 2\end{array} \right.$$

Question 11 :
If $$ f\left( x \right) =\begin{cases} 1 &amp; x&lt;0 \\ { x }^{ 2 } &amp; x\ge 0 \end{cases}$$ then at $$x=0$$

Question 12 :
If $$f(x)=\displaystyle \frac{\sin x}{x},x\neq 0$$ is to be continuous at $${x}=0$$&#160;then $$\mathrm{f}({0})=$$<br/>

Question 14 :
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 15 :
If the function $$\displaystyle f(x)=\begin{cases} 2x^{2}-3 &amp; \text{ if } 0&lt;x\leq 1 \\ x^{2}+bx-1 &amp; \text{ if } 1&lt;x&lt;2&#160;\end{cases}$$&#160;is continuous at every point of its domain then the value of $$b$$ is&#160;

Question 16 :
The function $$\cfrac { \left| x \right| }{ { x }^{ 2 }+2x } , x\ne 0$$ and $$f(0)=0$$ is not continuous at $$x=0$$ because-

Question 17 :
If $$f(x) =&#160;\begin{cases}\dfrac{(1-\sin^3x)}{3\cos^2x},&amp;x&lt;\dfrac{\pi}{2}\\\quad a, &amp; x = \dfrac{\pi}{2}&#160;\\\dfrac{b(1-\sin x)}{(\pi-2x)^2},&amp; x &gt; \dfrac{\pi}{2} \end{cases}$$ is continuous at $$x=\dfrac{\pi}{2}$$, then the value of $$\left(\dfrac{b}{a}\right)^{5/3}$$ is

Question 18 :
If&#160;$$ \displaystyle&#160;f(x)=\left\{\begin{array}{ll}\dfrac{\sqrt{1+kx}-\sqrt{1-x}}{x} &amp; \mathrm{f}\mathrm{o}\mathrm{r}-\mathrm{l} \leq x&lt;0\\2x^{2}+3x-2 &amp; \mathrm{f}\mathrm{o}\mathrm{r} 0\leq x\leq 1\end{array}\right.$$ is continuous at $$x = 0$$ then $$k$$ is:<br/>

Question 19 :
Assertion: If $$f(x)=sgn(x)$$ and $$g(x)=x(1-x^2),$$ then $$fog(x)$$ and $$gof(x)$$ are continuous everywhere Reason: $$\displaystyle&#160;fog=\begin{cases} \begin{matrix} -1, &amp; x\in \left( -1,0 \right) \cup \left( 1,\infty &#160;\right) &#160;\end{matrix} \\ \begin{matrix} 0, &amp; x\in \left\{ -1,0,1 \right\} &#160;\end{matrix} \\ \begin{matrix} 1, &amp; x\in \left( -\infty ,-1 \right) \cup \left( 0,1 \right) &#160;\end{matrix} \end{cases}$$ and $$gof\left( x \right) =0,\quad \forall \quad x\in R$$

Question 20 :
$$Lt_{x \rightarrow 0}\,f(\dfrac{1-cos\,3x}{x^2})$$ where $$f(x)$$ is a continuous function satisfying the condition $$f(\dfrac{9}{2})=\dfrac{2}{9}$$ is equal to: