Question 1 :
If $ f\left( x \right) =\begin{cases} 1 & x<0 \\ { x }^{ 2 } & x\ge 0 \end{cases}$ then at $x=0$
Question 3 :
The function $f(x) = \dfrac{1 - \sin \, x +\cos \, x}{1 + \sin \, x + \cos \, x} $ is not defined at $x = \pi$. If $f(x)$ is continuous at $x = \pi$, then  the value of $f(\pi)$ is 
Question 4 :
The function  $\displaystyle f(x)=\begin{cases}\displaystyle \frac{x^{2}}{a} & 0\leq x< 1 \\ a & 1\leq x< \sqrt{2} \\ (2b^{2}-4b)/x^{2} & \sqrt{2}\leq x< \infty  \end{cases}$ is continuous for $0\leq x< \infty $, then the most suitable values of $a$ and $b$ are
Question 5 :
If$\displaystyle f\left ( x \right )=\frac{\sin 3x+A\sin 2x+B\sin x}{x^{5}},x\neq 0$, iscontinous at $x = 0$ then<br>
Question 6 :
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 7 :
If $f(x)=\begin{cases} \cfrac { 1-\cos { 4x } }{ { x }^{ 2 } } \quad ,\quad \quad \quad x<0 \\ a\quad \quad \quad \quad \quad ,\quad \quad \quad x=0 \\ \cfrac { \sqrt { x } }{ \sqrt { 16+\sqrt { x } } -4 } \quad \quad \quad ,\quad x>0 \end{cases}$, then the correct statement is-
Question 8 :
If $f(x)=\left\{\begin{matrix} \displaystyle\frac{1-\cos 4x}{x^2}, & when x < 0\\ a, & when x=0 \\ \displaystyle\frac{\sqrt{x}}{\sqrt{(16+\sqrt{x})}-4}, & when x> 0\end{matrix}\right.$ is continuous at $x=0$, then the value of a will be.<br>
Question 9 :
Let $f(x)$ be a continuous function whose range is $[2, 6.5]$. If $\displaystyle h\left ( x \right )= \left [ \dfrac{\cos x+f\left ( x \right )}{\lambda } \right ], \lambda \in N $, be continuous, where $[ \cdot  ]$ denotes the greatest integer function, then the least value of $ \lambda$ is 
Question 10 :
If $f(x)=\begin{cases} mx-1,\quad x\le 5 \\ 3x-5,\quad x>5 \end{cases} $ is continuous then value of m is:
Question 11 :
If $f(x)=\begin{cases} \cfrac { x(1+a\cos { x } )-b\sin { x } }{ { x }^{ 3 } } ,\quad x\neq 0 \\ 1,\quad \quad \quad \quad x=0 \end{cases}$ then $f$ is continuous for values of $a$ and $b$ given by-
Question 12 :
The value of $k$ for which the function$\displaystyle f\left ( x \right )=\frac{\left ( e^{x} -1\right )^{4}}{\sin \left ( \frac{x^{2}}{k^{2}} \right )\log \left \{ 1+\left ( \frac{x^{2}}{2} \right ) \right \}},x\neq 0;f\left ( 0 \right )=8$may be continuous function is<br>
Question 13 :
The function $f(x) = x - |x - x^2|, -1 \leq x \leq 1$ is continuous on the interval<br>
Question 14 :
At $x = \dfrac {3}{2}$, the function $f(x) = \dfrac {|2x - 3|}{2x - 3}$ is
Question 15 :
If $f(x)=\displaystyle \lim_{p\to\infty }\dfrac{x^{p}g(x)+h(x)+7}{7x^{p}+3x+1};x\neq 1$ and $f(1)=7, f(x),g(x)$ and $h(x)$ are all continuous functions at $x=1$ . Then which of the following statement(s) is/are correct