GATE 1996 CSE & IT PYQ

Question

Let $$G$$ be a context free grammar where $$G = \left( {\left\{ {S,A,.B,C} ight\},\left\{ {a,b,d} ight\},P,S} ight)$$ with productions $$P$$ given below
$$\eqalign{ & S o ABAC\,\,\,\,\,\,\,\,\,S o aA{\mkern 1mu} \left| \varepsilon ight. \cr & S o bB{\mkern 1mu} \left| \varepsilon ight.\,\,\,\,\,\,\,\,\,\,\,\,\,\,C o d \cr} $$

($$\varepsilon $$ denotes the null string). Transform the given grammar $$G$$ to an equivalent context- free grammar $${G^1}$$ that has no $$\varepsilon $$ productions ($$A$$ unit production is of the from $$x o y,\,x$$ and $$y$$ are non terminals).