Any private person may arrest any person who in his presence commits following offence :

Cognizable offence
Non-bailable offence
Cognizable and Non-bailable offence
Non-cognizable and Non-bailable offence

The correct answer is (c), Cognizable and Non-bailable offence.

A cognizable offence is an offence that can be registered by a police officer without a warrant. A non-bailable offence is an offence for which bail is not granted as a matter of right.

Any private person may arrest any person who in his presence commits a cognizable and non-bailable offence. This is because such an offence is considered to be a serious offence that poses a threat to the public.

The other options are incorrect because they do not accurately reflect the law. A non-cognizable offence is an offence that cannot be registered by a police officer without a warrant. A bailable offence is an offence for which bail is granted as a matter of right.

Here is a table that summarizes the key differences between cognizable and non-cognizable offences, and bailable and non-bailable offences:

| Offence | Cognizable | Non-cognizable |
|—|—|—|
| Registration | Can be registered by a police officer without a warrant | Cannot be registered by a police officer without a warrant |
| Bail | Bail is not granted as a matter of right | Bail is granted as a matter of right |

I hope this helps! Let me know if you have any other questions.