Question 1 :
If $f(x)=\dfrac{1}{1-x},$ the the point of discontinuity of the function $f[f\{f(x)\}]$ is /are

Question 3 :
If $f$ : $R\rightarrow R$ is defined by $f(x)=\left\{\begin{array}{ll}\dfrac{x+2}{x^{2}+3x+2} &amp; x\in R-\{-1,-2\}\\-1 &amp; &#160;x=-2\\0 &amp; x=-1\end{array}\right.$then $f$ is continuous on the set:<br/>

Question 4 :
Let $f(x)=\cos2x.\cot\left (\displaystyle \frac{\pi }{4}-x \right )$ If $f$ is continuous at $x=\displaystyle \frac{\pi}{4}$ then the value of $f(\displaystyle \frac{\pi}{4})$is equal to

Question 5 :
If the function $f\left( x \right) $, defined as $\displaystyle&#160;f\left( x \right)=\begin{cases} \begin{matrix} \dfrac { a\left( 1-x\sin { x } &#160;\right) +b\cos { x } +5 }{ { x }^{ 2 } } , &amp; x&lt;0 \end{matrix} \\ \begin{matrix} 3, &amp; x=0 \end{matrix} \\ \begin{matrix} { \left\{ 1+\left( \dfrac { cx+d{ x }^{ 3 } }{ { x }^{ 2 } } &#160;\right) &#160;\right\} &#160;}^{\frac1x }, &amp; x&gt;0 \end{matrix} \end{cases}$ is continuous at $x=0$, then

Question 6 :
If the function $\displaystyle f\left( x \right)=\begin{cases} \begin{matrix} 1+\sin { \dfrac { \pi }{ 2 } x } , for &amp; -\infty &lt;x\le 1 \end{matrix} \\ \begin{matrix} ax+b, for &amp; 1&lt;x&lt;3 \end{matrix} \\ \begin{matrix} 6\tan { \dfrac { \pi x }{ 12 } } ,for &amp; 3\le x&lt;6 \end{matrix} \end{cases}$ is continous in the interval $(-\infty,6)$ then the value of $a$ and $b$ are?

Question 7 :
<br>lf $\mathrm{f}(\mathrm{x})=\left\{\begin{matrix}1+x &amp;x\leq 1 \\3-ax^{2}&amp; x&gt;1\end{matrix}\right.$ is continuous at ${x}=1$ then ${a}=({a}&gt;0)$<br>

Question 8 :
If $f\left( x \right) =\begin{cases} \dfrac { 1-\sin ^{ 3 } x }{ 3\cos ^{ 2 } x } ,\quad \text{if}\quad x&lt;\dfrac { \pi&#160; }{ 2 }&#160; \\ a,\quad \text{if}\quad x=\dfrac { \pi&#160; }{ 2 }&#160; \\ \dfrac { b(1-\sin&#160; x) }{ (\pi -2x)^{ 2 } } ,\quad \text{if}\quad x&gt;\dfrac { \pi&#160; }{ 2 }&#160; \end{cases}$ so that $f(x)$ is continuous at $x=\dfrac{\pi}{2}$, then

Question 9 :
The function $y = f(x)$ is defined by $x = 2t - |t|, y =t^2+t |t|, t\in R$ in the interval $x\in [-1,1]$ then<br>

Question 10 :
If $f(x)=\begin{cases} a{ x }^{ 2 }-b\quad if\quad \left| x \right| &lt;1 \\ -\cfrac { 1 }{ \left| x \right| } \quad if\quad \left| x \right| \ge 1\quad \end{cases}$ is derivable at $x=1$ then the values of $a+b$ is

Question 11 :
Let $k$ be a non-zero real number. If $f(x) = \displaystyle&#160;\left\{\begin{matrix} \dfrac{(e^x - 1)^2}{\displaystyle \sin \left ( \frac{x}{k} \right ) \log \left ( 1 + \frac{x}{4} \right )},&#160;&amp; x \neq 0\\ 12, &amp; x = 0\end{matrix}\right.$ is a continuous function, then the value of $k$ is

Question 12 :
Let $f$ be a non-zero real valued continuous function satisfying $f(x + y) = f(x). f(y)$ for all $x, y$ $\epsilon$ $R$. If $f(2) = 9$ then $f(6) =$

Question 13 :
&#160;If $\displaystyle f\left ( x \right )=\left\{\begin{matrix}\dfrac{\sin 3x+a\sin 2x+b\sin x}{x^{5}} &amp;x\neq 0 \\c,&#160;&#160;&amp;x=0&#160;\end{matrix}\right.$ is continuous at $x=0$, find the values of $a,b,c$.<br/>

Question 14 :
Let$f:\left [ 0, 1 \right ]\rightarrow \left [ 0, 1 \right ]$ be a continuous function. Then

Question 15 :
If the function $\displaystyle f(x)=\dfrac{1-\cos x\:\cos 2x\:\cos 3x}{\sin^{2}2x}$ is continuous at $x=0$, then $f(0)$must be equal to&#160;