Pakistanis can only go by air or overland by bus or train, no personal vehicles. We only get visas to visit blood relatives or for business. I have heard of exceptions, but never met any of them.
Generally, someone going to meet the relatives with a purchased ticket to New Delhi with Air India has a higher chance of getting a visa soon. Its reciprocal, Indians with a ticket with PIA get preference by Pakistani Consulate in India.
Group visits from institutions are possible, educational Institutions have regular visits to India.