Step 1: Concept
pH is the negative logarithm of the $H^{+}$ ion concentration.
Step 2: Meaning
Calculate total millimoles of $H^{+}$ ions:
From $HCl$: $100 \times 0.1 = 10$ mmol.
From $H_{2}SO_{4}$: $100 \times 0.05 \times 2 = 10$ mmol.
Total $H^{+}$ = $20$ mmol = $0.02$ moles.
Step 3: Analysis
Final concentration $[H^{+}]$ = Moles Volume (L) = $0.02 / 2.0 = 0.01$ M = $10^{-2}$ M.
pH = $-\log[10^{-2}] = 2$.
Step 4: Conclusion
The pH of the resulting solution is 2.
Final Answer: (C)