$6.$ For a given $20$ m simply supported beam, concentrated load with values of $\backslash (5\backslash$mathrm$\{$KN$\},10\backslash$mathrm$\{$KN$\}\backslash ),$ and $15$ KN was placed at every quarter point starting from left to right. Together with it a uniform load with a value of $\backslash (20\backslash$mathrm$\{$KN$\}/\backslash$mathrm$\{$m$\}\backslash )$ 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