If the domain of the function $f(x) = \log_{(10x^{2}-17x+7)}(18x^{2}-11x+1)$ is $(-\infty, a) \cup (b, c) \cup (d, \infty) - \{e\}$, then $90(a+b+c+d+e)$ equals:

Let $[x]$ denote the greatest integer not more than $x$. If $A$ and $B$ are the domains of the functions $f(x)=\frac{x-[x]}{\sqrt{|x|-x}}$ and $g(x)=\frac{x-[x]}{\sqrt{|x|+x}}$ respectively, then

The mid-point of the domain of the function $f(x) = \sqrt{4 - \sqrt{2x + 5}}$ for real $x$ is

If the domain of the function $f(x) = \log_e \left( \frac{2x+3}{4x^2+x-3} \right) + \cos^{-1} \left( \frac{2x-1}{x+2} \right)$ is $(\alpha, \beta]$,then the value of $5\beta - 4\alpha$ is equal to

If the range of $f(x) = \frac{2x^4-14x^2-8x+49}{x^4-7x^2-4x+23}$ is $(a, b]$,then $(a + b)$ is

Let $f(x) = \sqrt{\frac{x+1}{x+3}}$ and $g(x) = \sqrt{\frac{2-x}{x+3}}$ be two real-valued functions. Then the domain of $f/g$ is