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Match the problem type in Group-$1$ with the numerical method in Group-$2$.

$\begin{array}{cc}\

&\text{Group-$1$} & \text{Group-$2$} \\

&\text{P. System of linear algebraic equations} & \text{ I. Newton-Raphson} \\

&\text{Q. Non-linear algebraic equations} & \text{II. Gauss-Seidel} \\

&\text{R. Ordinary differential equations} & \text{III. Simpsonâ€™s rule} \\

&\text{S. Numerical integration} & \text{IV. Runge-Kutta}\\ \end{array}$

Choose the correct set of combination.

- $P-II,\:Q-I,\:R-III,\:S-IV$
- $P-I,\:Q-II,\:R-IV,\:S-III$
- $P-IV,\:Q-III,\:R-II,\:S-I$
- $P-II,\:Q-I,\:R-IV,\:S-III$