To determine who lives in Flat-Q of Floor 2, we can systematically construct the floor and flat arrangement based on the given clues.

There are 3 floors (1, 2, 3) and 2 flats (Flat-P in the west, Flat-Q in the east) on each floor.

Let's analyze the clues step-by-step:
1. E lives two floors above the person who belongs from Delhi.
Since there are only 3 floors, the person from Delhi must live on Floor 1, and E must live on Floor 3.
2. The one who belongs from Jaipur lives to the east of the one who belongs from Delhi.
Since Flat-P is to the west of Flat-Q, the person from Delhi must live in Flat-P of Floor 1, and the person from Jaipur must live in Flat-Q of Floor 1.
3. E and D live in different named flats.
4. F lives below E and belongs from Kolkata.
Since E is on Floor 3, F (from Kolkata) must be on Floor 2 or Floor 1. But since Floor 1 has Delhi and Jaipur, F must live on Floor 2.
5. The one who belongs from Chennai lives to the north-east of the one who belongs from Kolkata (F).
Since F lives on Floor 2, the one from Chennai must live to the north-east, which means on Floor 3 in Flat-Q. Thus, F must live in Flat-P of Floor 2 (Kolkata). Therefore, the Chennai person lives in Flat-Q of Floor 3.
6. Let's find E's flat. Since Chennai is on Floor 3, Flat-Q, E must live in Floor 3, Flat-P.
Since E is in Flat-P, and "E and D live in different named flats", D must live in Flat-Q (either Floor 2 or Floor 1). Since Jaipur is at Floor 1, Flat-Q, D must live on Floor 2, Flat-Q.
7. The one who belongs from Pune lives immediately above the person who lives to the west of D.
D is in Floor 2, Flat-Q. The person to the west of D is F (Floor 2, Flat-P). The person immediately above F is E (Floor 3, Flat-P). Therefore, E belongs to Pune.
8. A and C live in the same named flat.
Currently, the filled positions are:
Floor 3: Flat-P = E (Pune), Flat-Q = _ (Chennai)
Floor 2: Flat-P = F (Kolkata), Flat-Q = D (_)
Floor 1: Flat-P = _ (Delhi), Flat-Q = _ (Jaipur)
The remaining people are A, B, and C.
A and C must be in the same named flat. The only flats with two open spaces of the same name are Flat-P (Floor 1 is empty) and Flat-Q (Floor 3 and Floor 1 are empty). Since Floor 1 Flat-P is the only empty spot in Flat-P, A and C cannot both be in Flat-P. Thus, A and C must be in Flat-Q.
This means A and C occupy Flat-Q of Floor 3 and Floor 1. Specifically:
- A and C are at Floor 3, Flat-Q (Chennai) and Floor 1, Flat-Q (Jaipur).
9. A doesn't belong from Chennai.
Therefore, C must belong to Chennai (Floor 3, Flat-Q), and A must belong to Jaipur (Floor 1, Flat-Q).
10. This leaves the remaining positions for B:
- Floor 1, Flat-P (Delhi) must be occupied by B.
- Floor 2, Flat-Q (occupied by D) is the only slot left without a designated city. The remaining cities are Mumbai and others. The remaining person for Floor 2, Flat-Q is D.
11. C and the one who belongs from Mumbai do not live on the same floor.
C lives on Floor 3. The person from Mumbai cannot live on Floor 3. The city of D (Floor 2, Flat-Q) must therefore be Mumbai.
Thus, the person living in Flat-Q of Floor 2 is D, who belongs to Mumbai.

Therefore, the correct answer is The one who belongs to Mumbai.