Correct Option (2)

To ascertain the city of the lecturer specialized in Economics, a systematic deduction from the provided statements is required:

Statement 3 establishes: Lecturer C from Delhi is specialized in Sociology.
Statement 6 establishes: Lecturer F, specialized in Commerce, belongs to Srinagar.
Statement 7 establishes: Lecturer G, specialized in Statistics, belongs to Chennai.
Statement 2 establishes: Lecturer D is from Shillong.

At this stage, the remaining lecturers are A, B, and E. The remaining cities are Hyderabad, Kanpur, and Mumbai. The remaining subjects are Economics, History, Geography, and Mathematics.

Statement 1 indicates: The Lecturer from Kanpur is specialized in Geography.
Statement 4 states: Lecturer B is specialized in neither History nor Mathematics. Considering the remaining subjects, B's specialization must be either Geography or Economics. If B is specialized in Geography, then according to statement 1, B must be from Kanpur. This assignment (B - Geography - Kanpur) is consistent with all prior information.

Now, the remaining lecturers are A and E. The remaining cities are Hyderabad and Mumbai. The remaining subjects are Economics, History, and Mathematics.

Statement 5 specifies: Lecturer A, who is specialized in Economics, does not belong to Hyderabad. Given that Hyderabad and Mumbai are the only remaining cities, Lecturer A, specialized in Economics, must therefore belong to Mumbai.

Thus, the lecturer specialized in Economics belongs to Mumbai.

Incorrect Options:

Option 1 (Hyderabad): Hyderabad is the city assigned to Lecturer E, whose specialization is either History or Mathematics, not Economics.
Option 3 (Neither Hyderabad nor Mumbai): This option is incorrect because the analysis clearly identifies Mumbai as the city for the lecturer specialized in Economics.
Option 4 (Cannot be determined as data is inadequate): The provided information is sufficient to definitively determine the city of the lecturer specialized in Economics through logical deduction.