Question Statement:
Match the Vector Theorems in Group-I with their Mathematical Representations in Group-II:
$\begin{array}{|ll|ll|}\hline \textbf{Group-I (Theorem)} & & \textbf{Group-II (Expression)} & \\ \hline \text{P. Green's Theorem in a plane} & & \text{1. } \iint_S (\nabla \times \vec{F}) \cdot \hat{n}\, dS = \oint_C \vec{F} \cdot d\vec{r} \\ \text{Q. Gauss Divergence Theorem} & & \text{2. } \iiint_V (\nabla \cdot \vec{F})\, dV = \iint_S \vec{F} \cdot \hat{n}\, dS \\ \text{R. Stokes' Theorem} & & \text{3. } \oint_C (M\, dx + N\, dy) = \iint_R \left(\frac{\partial N}{\partial x} - \frac{\partial M}{\partial y}\right) dx\, dy \\ \hline \end{array}$
Select the CORRECT matching combination:
Options:
- (A) P-3, Q-2, R-1
- (B) P-1, Q-2, R-3
- (C) P-2, Q-3, R-1
- (D) P-3, Q-1, R-2