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 relative directions of Gandhinagar and Patna with respect to Delhi, let us analyze their geographical positions on the map of India:

1. Location of Delhi:
Delhi is located in Northern India (approximately 28.6° N latitude, 77.2° E longitude).

2. Direction of Gandhinagar (Capital of Gujarat) relative to Delhi:
Gandhinagar is located in Western India, situated south and west of Delhi (approximately 23.2° N latitude, 72.6° E longitude). Therefore, looking from Delhi towards Gandhinagar, the direction is south-west.

3. Direction of Patna (Capital of Bihar) relative to Delhi:
Patna is located in Eastern India, situated south and east of Delhi (approximately 25.6° N latitude, 85.1° E longitude). Therefore, looking from Delhi towards Patna, the direction is south-east.

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