$($a$)$ Design a doubly reinforced beam $300$ mm wide and $500$ mm deep to resist factored moment of $280$ kN$-$m$.$ Take effective cover of $50$ mm on both side. Take M$-20$ concrete and Fe$-415$ steel

$($b$)$ Design a continuous one$-$way slab having three equal span of $3\mathrm{.}5$ m effective each with imposed load $3$ kN$/$m$2$ and floor finishing load $1$ kN$/$m$2.$ Take concrete M$-20$ and Fe$-250$ steel.