With respect to the location of Delhi on the map of India the directions of the locations of Gandhinagar (Capital of Gujarat) and Patna (Capital of Bihar) respective are

The correct option is south-west and south-east.

To determine the directions of Gandhinagar (Capital of Gujarat) and Patna (Capital of Bihar) relative to Delhi, let us analyze their geographical positions on the map of India:

1. Delhi is located in the northern region of India.
2. Gandhinagar (Gujarat) is located to the west and south of Delhi. Therefore, relative to Delhi, Gandhinagar lies in the south-west direction.
3. Patna (Bihar) is located to the east and south of Delhi. Therefore, relative to Delhi, Patna lies in the south-east direction.

Thus, with respect to the location of Delhi, the respective directions of Gandhinagar and Patna are south-west and south-east.