Which of the following is not a private university?

The correct option is Guru Nanak Dev University.

To understand why this is the correct choice, let us evaluate the status of each university listed in the options:
1. BITS Pilani (Birla Institute of Technology and Science, Pilani): This is a well-known, private deemed university established under Section 3 of the UGC Act, 1956.
2. Techno India University: This is a private university located in Kolkata, West Bengal, established under a state private university act.
3. Guru Nanak Dev University (GNDU): This university was established in Amritsar, Punjab, on November 24, 1969, to mark the 500th birth anniversary of Sri Guru Nanak Dev Ji. It is a public state university funded and managed by the State Government of Punjab. Therefore, it is a public (government) university, not a private university.
4. Jaipur National University: This is a private university located in Jaipur, Rajasthan, established through an act of the Government of Rajasthan.

Thus, among the given choices, Guru Nanak Dev University is the only one that is not a private university.