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

Let $[x]$ be the greatest integer $\leq x$. Then the number of points in the interval $(-2, 1)$,where the function $f(x) = |[x]| + \sqrt{x - [x]}$ is discontinuous,is $........$.

If a real valued function $f(x) = \begin{cases} \frac{x^2+(a+3)x+(a+1)}{x+3} & x \neq -3 \\ -\frac{5}{2} & x = -3 \end{cases}$ is continuous at $x = -3$,then $\lim_{x \rightarrow a} (x^2+x+1) = $

If $f(x) = \begin{cases} 1+6x-3x^2, & x \leq 1 \\ x+\log_2(b^2+7), & x > 1 \end{cases}$ is continuous at all real $x$,then $b=$

Let a function $f: R \rightarrow R$ be defined as
$f(x) = \begin{cases} \sin x - e^x & \text{if } x \leq 0 \\ a + [-x] & \text{if } 0 < x < 1 \\ 2x - b & \text{if } x \geq 1 \end{cases}$
where $[x]$ is the greatest integer less than or equal to $x$. If $f$ is continuous on $R$,then $(a + b)$ is equal to:

The function $f(x) = p[x + 1] + q[x - 1],$ where $[x]$ is the greatest integer function,is continuous at $x = 1$ if: