If $f(x) = \frac{x^2-10x+25}{x^2-7x+10}$ and $f$ is continuous at $x=5$,then $f(5)$ is equal to

If $f(x) = \begin{cases} \frac{1-\sqrt{2} \sin x}{\pi-4x} & \text{if } x \neq \frac{\pi}{4} \\ a & \text{if } x = \frac{\pi}{4} \end{cases}$ is continuous at $x = \frac{\pi}{4}$,then $a$ is equal to

If $f(x) = \int_{-1}^x |t| \, dt$,$x \ge -1$,then

Let $[x]$ represent the greatest integer not more than $x$. The discontinuous points of the function $f(x) = \frac{5+[x]}{\sqrt{11+[x]-6 \sqrt{2+[x]}}}$ lie in the interval

If the function $f(x) = \begin{cases} \frac{2}{x} \{\sin(k_1+1)x + \sin(k_2-1)x\} & , x < 0 \\ 4 & , x = 0 \\ \frac{2}{x} \log_e \left(\frac{2+k_1x}{2+k_2x}\right) & , x > 0 \end{cases}$ is continuous at $x = 0$,then $k_1^2 + k_2^2$ is equal to

The set of points of discontinuity of the function $f(x) = \frac{\tan x \cdot \tan^{-1}\left(\frac{1}{x-1}\right)}{x(x-3)(x-5)}$ is