Option 1: Delhi-Amritsar - This option is incorrect because National Highway number 2 does not join Delhi and Amritsar.
Option 2: Delhi-Mumbai - This option is incorrect because National Highway number 2 does not join Delhi and Mumbai.
Option 3: Delhi-Kolkata - This is the correct answer. National Highway number 2 joins Delhi and Kolkata.
Option 4: Delhi-Ahmedabad - This option is incorrect because National Highway number 2 does not join Delhi and Ahmedabad.
Therefore, the correct pair of places that National Highway number 2 joins is Delhi and Kolkata.