Question 1 :
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 2 :
$f(x)=\left\{\begin{matrix} 2x-1& if &x>2 \\ k & if &x=2 \\  x^{2}-1& if & x<2\end{matrix}\right.$is continuous at $x= 2$ then $k =$
Question 3 :
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 4 :
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 5 :
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 6 :
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 7 :
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 8 :
The function $f\left( x \right)=\left[ x \right] ,$  at ${ x }=5$ is:<br/>
Question 9 :
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 10 :
If $ f\left( x \right) =\begin{cases} 1 & x<0 \\ { x }^{ 2 } & x\ge 0 \end{cases}$ then at $x=0$
Question 11 :
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 12 :
The value of $ \displaystylef(0)$, so that function, $f(x)=\cfrac { \sqrt { { a }^{ 2 }-ax+{ x }^{ 2 } } -\sqrt { { a }^{ 2 }+ax+{ x }^{ 2 } } }{ \sqrt { a+x } -\sqrt { a-x } } $ becomes continuous for all $x$, is given by-
Question 13 :
If $f(x)=\dfrac{\sin 3x+A\sin 2x+B\sin x}{x^5},x\neq 0$ then the value of $\left ( f(0)+A+B \right )$ equal to $(Considering\:  f(x)\:  to\:  be\:  continuous\:  at \: x = 0 )$<br/>
Question 14 :
Consider $f(x) = x^2 + ax +3$ and $g(x) = x + b $ and $F(x) = \displaystyle \lim_{n \rightarrow \infty} \frac{f(x) + x^{2n} g(x)}{1 + x^{2n}}$<br/><br/>If F(x) is continuous at $x = -1$, then