The number of real solutions of the equation $e ^{4 x }+4 e ^{3 x }-58 e ^{2 x }+4 e ^{ x }+1=0$ is..........

Let $a, b, c, d$ be real numbers between $-5$ and $5$ such that  $|a|=\sqrt{4-\sqrt{5-a}},|b|=\sqrt{4+\sqrt{5-b}},|c|=\sqrt{4-\sqrt{5+c}}$ $|d|=\sqrt{4+\sqrt{5+d}}$ Then, the product $a b c d$ is

A man standing on a railway platform noticed that a train took $21\, s$ to cross the platform (this means the time elapsed from the moment the engine enters the platform till the last compartment leaves the platform) which is $88\,m$ long, and that it took $9 s$ to pass him. Assuming that the train was moving with uniform speed, what is the length of the train in meters?

The solutions of the quadratic equation ${(3|x| - 3)^2} = |x| + 7$ which belongs to the domain of definition of the function $y = \sqrt {x(x - 3)} $ are given by

If $x$ is real, the function $\frac{{(x - a)(x - b)}}{{(x - c)}}$ will assume all real values, provided

The sum of all the solutions of the equation $(8)^{2 x}-16 \cdot(8)^x+48=0$ is :