If $f(x) = \begin{cases} \frac{x^2 - (a+2)x + a}{x-2} & x \neq 2 \\ 2 & x = 2 \end{cases}$ is continuous at $x = 2$,then the value of $a$ is

Let $f:[0, \infty) \rightarrow [0, \infty)$ be defined as $f(x) = \int_{0}^{x} [y] \, dy$,where $[x]$ is the greatest integer less than or equal to $x$. Which of the following is true?

Let $f(x) = [x]\sin \left( \frac{\pi}{[x + 1]} \right)$,where $[.]$ denotes the greatest integer function. The domain of $f$ is and the points of discontinuity of $f$ in the domain are

Let $f(x) = \begin{cases} \frac{(1 + \tan x)^{\frac{1}{x}} - e}{x} & x \neq 0 \\ k & x = 0 \end{cases}$ be continuous at $x = 0$,then the value of $k$ is:

If $f(x) = \begin{cases} \frac{\sqrt{1+kx}-\sqrt{1-kx}}{x}, & -1 \leq x < 0 \\ 2x^2+3x-2, & 0 \leq x \leq 1 \end{cases}$ is continuous at $x = 0$, then $k$ is equal to

If the function $f(x) = \begin{cases} \frac{\log_{e}(1-x+x^{2}) + \log_{e}(1+x+x^{2})}{\sec x - \cos x}, & x \in (-\frac{\pi}{2}, \frac{\pi}{2}) - \{0\} \\ k, & x = 0 \end{cases}$ is continuous at $x = 0$,then $k$ is equal to.