Step 1: Identifying the elements and their common ores.
Begin by recognizing the chemical elements listed in Column I and their naturally occurring ores in Column II. The elements are Aluminum (Al), Iron (Fe), Titanium (Ti), and Copper (Cu). Their respective ores are Bauxite (Al), Hematite (Fe), Rutile (Ti), and Chalcopyrite (Cu). This step involves recalling basic metallurgy knowledge to establish the correct associations.
Step 2: Matching each element to its ore.
- Aluminum (Al) is primarily extracted from Bauxite, which is option 4.
- Iron (Fe) is commonly derived from Hematite, which is option 2.
- Titanium (Ti) is obtained from Rutile, which is option 1.
- Copper (Cu) is sourced from Chalcopyrite, which is option 3.
Thus, the correct mapping is P (Al) $\to$ 4, Q (Fe) $\to$ 2, R (Ti) $\to$ 1, S (Cu) $\to$ 3.
Step 3: Evaluating the provided options.
- (A) P $\to$ 4, Q $\to$ 2, R $\to$ 3, S $\to$ 1: Incorrect, as R (Ti) should map to 1 (Rutile), not 3 (Chalcopyrite), and S (Cu) should map to 3, not 1.
- (B) P $\to$ 2, Q $\to$ 4, R $\to$ 1, S $\to$ 3: Incorrect, as P (Al) should map to 4 (Bauxite), not 2 (Hematite), and Q (Fe) should map to 2, not 4.
- (C) P $\to$ 3, Q $\to$ 1, R $\to$ 4, S $\to$ 2: Incorrect, as P (Al) should map to 4, not 3, and the other mappings do not align with the correct ores.
- (D) P $\to$ 4, Q $\to$ 2, R $\to$ 1, S $\to$ 3: Correct, as it matches Al $\to$ Bauxite, Fe $\to$ Hematite, Ti $\to$ Rutile, and Cu $\to$ Chalcopyrite.
Step 4: Concluding the correct match.
The correct answer is determined by aligning each element with its primary ore based on metallurgical knowledge. Option (D) accurately reflects this relationship: P (Al) $\to$ 4 (Bauxite), Q (Fe) $\to$ 2 (Hematite), R (Ti) $\to$ 1 (Rutile), S (Cu) $\to$ 3 (Chalcopyrite).
\[
\boxed{\text{P $\to$ 4, Q $\to$ 2, R $\to$ 1, S $\to$ 3 (D)}}
\]