Persons: A, B, C, D, E, F, and G.
Cities: Indore, Agra, Cuttack, Gwalior, Mumbai, Pune, Jaipur.
Days: Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, and Sunday.
1. Three people go between E and the one who belongs to Cuttack.
2. E goes just before F but after Thursday.
| CASE 1 | CASE 2 | | |
|---|
| DAYS | PERSONS | CITIES | PERSONS | CITIES |
| Monday | | Cuttack | | |
| Tuesday | | | | Cuttack |
| Wednesday | | | | |
| Thursday | | | | |
| Friday | E | | | |
| Saturday | F | | E | |
| Sunday | | | F | |
3. Number of people going before F is same as after A.
4. Two people go between A and the one, who belongs to Agra.
5. G belongs to Indore and goes before the one, who belongs to Agra.
| CASE 1 | CASE 1A | CASE 2 | | | |
|---|
| DAYS | PERSONS | CITIES | PERSONS | CITIES | PERSONS | CITIES |
| Monday | | Cuttack | | Cuttack | A | |
| Tuesday | A | | A | | | Cuttack |
| Wednesday | | | G | Indore | G | Indore |
| Thursday | G | Indore | | | | Agra |
| Friday | E | Agra | E | Agra | | |
| Saturday | F | | F | | E | |
| Sunday | | | | | F | |
6. Two people go between G and the one, who belongs to Gwalior.
7. F does not belong to Gwalior. So, Case 1A is eliminated.
| CASE 1 | CASE 2 | | |
|---|
| DAYS | PERSONS | CITIES | PERSONS | CITIES |
| Monday | | Cuttack | A | |
| Tuesday | A | | | Cuttack |
| Wednesday | | | G | Indore |
| Thursday | G | Indore | | Agra |
| Friday | E | Agra | | |
| Saturday | F | | E | Gwalior |
| Sunday | | Gwalior | F | |
8. F neither belongs to Jaipur nor Pune. So, F belongs to Mumbai.
| CASE 1 | CASE 2 | | |
|---|
| DAYS | PERSONS | CITIES | PERSONS | CITIES |
| Monday | | Cuttack | A | |
| Tuesday | A | | | Cuttack |
| Wednesday | | | G | Indore |
| Thursday | G | Indore | | Agra |
| Friday | E | Agra | | |
| Saturday | F | Mumbai | E | Gwalior |
| Sunday | | Gwalior | F | Mumbai |
9. B goes before the one, who belongs to Pune but after C. So, Case 1 is eliminated.
So, A belongs to Jaipur. D belongs to Pune. C belongs to Cuttack.
The final arrangement is,
| DAYS | PERSONS | CITIES |
|---|
| Monday | A | Jaipur |
| Tuesday | C | Cuttack |
| Wednesday | G | Indore |
| Thursday | B | Agra |
| Friday | D | Pune |
| Saturday | E | Gwalior |
| Sunday | F | Mumbai |
I. The one, who go immediately before E goes to Pune.
II. Four people go to party between E and A.
III. F is the last person to attend the party.
Hence, every sentence except III is true about E.