For a given $20$ m simply supported beam, concentrated load with values of $5$ KN$,10$ KN$,$ and

$15$ KN was placed at every quarter point starting from left to right. Together with it a uniform

load with a value of $20$ KN$/$m was placed at the first quarter point up to the right support. If the

value of the moment of inertia varies such that it starts at E from left support up to the last

quarter point and begins to double to the remaining length of the beam, calculate the

$($a$)$ deflection at $3$ m from right support,

$($b$)$ deflection at $2$ m to the right of midspan,

$($c$)$ slope at $2$m from left support, and

$($d$)$ slope at first quarter point front the left support