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A particle is moved along the different \( y_{\uparrow} \) paths \( O A C, O B C \) and \( O D C \) as shown in the figure. Path \( O D C \) is a parabola, \( y=4 x^{2} \). Find the work done by a force \( \vec{F}=x y \hat{i}+x^{2} y \hat{j} \) on the particle along these paths.
\begin{tabular}{|c|l|l|}
\hline \multicolumn{2}{|c|}{ Column I } & \multicolumn{2}{c|}{ Column II } \\
\hline i. & \( W_{O A C} \) & a. \( 15 / 3 \mathrm{~J} \) \\
\hline ii. & \( W_{O B C} \) & b. \( 19 / 3 \mathrm{~J} \) \\
\hline iii. & \( W_{O D C} \) & c. \( 2 \mathrm{~J} \) \\
\hline & & d. \( 8 \mathrm{~J} \) \\
\hline
\end{tabular}
Now match the given columns and select the correct option from the codes given below.
Codes:
(2) \( \begin{array}{lll}\mathrm{a} & \mathrm{b} & \mathrm{c}\end{array} \)
(4) c \( \quad \) d \( \quad \) a
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