Is it permissible to give a sum of money to a person whose trustworthiness is unknown, for the purpose of building a mosque in India?

Money should not be given to someone who claims to be collecting funds for a charitable cause, as such claims are often unfounded. It is better to ask him for a letter from a trustworthy charitable organization in your country that confirms the validity of his claim. Then, present this document to the charitable institutions in your area. If they are trustworthy, you can hand over the amount to them for them to send to the said organization.