Can the police in India ask someone to give their mobile and search into them without any warrant?
Yes, as per my knowledge.
At Private Place : Yes. As per CrPC and IT Act, a written order with reasons plus independent witnesses.
At Public Place : Yes. As per IT Act, if an officer can prove that a mobile phone falls under a Public Place through effect jurisdiction due to its activity by proving the effect test.
In any case, an officer should be an inspector or above the rank of office. On the other hand, without a warrant scenario, a search may be restricted by the public if they suspect any illegality.