Concept:
Vaccination and public awareness programs have been highly effective in controlling certain infectious diseases.
Step 1: Diseases controlled by vaccines.
- Smallpox $\rightarrow$ Eradicated globally through vaccination
- Polio $\rightarrow$ Controlled through mass immunization programs
- Diphtheria and Tetanus $\rightarrow$ Controlled through routine vaccination
Step 2: Evaluate other options.
- Amoebiasis $\rightarrow$ Not controlled by vaccines (incorrect)
- AIDS $\rightarrow$ No effective vaccine available (incorrect)
- Common cold $\rightarrow$ No vaccine due to many viral strains (incorrect)
Step 3: Conclusion.
Thus, the correct group is smallpox, polio, diphtheria, and tetanus.