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The displacement \( (x) \) of a particle depends on time \( (t) \) as \( \mathrm{x}=\alpha t^{2}-\beta t^{3} \)
\( \mathrm{P} \)
\begin{tabular}{|l|l|l|l|}
\hline \multicolumn{2}{|c|}{ Column-I } & \multicolumn{2}{c|}{ Column-II } \\
\hline (A) & \begin{tabular}{l}
The particle will be at \\
its starting point after \\
time
\end{tabular} & (P) & \( \frac{\alpha}{\beta} \) \\
\hline (B) & \begin{tabular}{l}
The particle will be at \\
rest at time
\end{tabular} & (Q) & \( \frac{2 \alpha}{3 \beta} \) \\
\hline (C) & \begin{tabular}{l}
The average velocity \\
of particle from \( t=0 \) to \\
\( t=t_{0} \) is equal to its \\
instantaneous velocity \\
at time \( t=t_{0} \). The value \\
of \( t_{0} \) is equal to
\end{tabular} & (R) & \( \frac{\alpha}{3 \beta} \) \\
\hline (D) & \begin{tabular}{l}
No net force will act on \\
the particle at time t is \\
equal to
\end{tabular} & (S) & \( \frac{\alpha}{2 \beta} \) \\
\hline
\end{tabular}

Now match the given columns and select the correct option from the codes given below.
Codes:
\begin{tabular}{lllll}
& A & B & C & D \\
(1) & \( \mathrm{Q} \) & \( \mathrm{S} \) & \( \mathrm{R} \) & \( \mathrm{P} \) \\
(2) & \( \mathrm{P} \) & \( \mathrm{Q} \) & \( \mathrm{S} \) & \( \mathrm{R} \) \\
(3) & \( \mathrm{S} \) & \( \mathrm{R} \) & \( \mathrm{P} \) & \( \mathrm{Q} \) \\
(4) & \( \mathrm{R} \) & \( \mathrm{Q} \) & \( \mathrm{S} \) & \( \mathrm{P} \)
\end{tabular}


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