Most favorable answer would be Hindi, but this is not right. Actually, India has NO national language. India has national flower (Lotus), national animal (tiger), national bird (Peacock), but in Indian constitution, there is no provision of having national language, so, there is no national language for India by law.
Article 343 (1) talks about official languages of India. According to article 343 (1), Hindi and English are official languages of India.
Suresh Kachhadia has filed PIL about national language of India. Gujarat High Court has clarified that, Hindi is not the national language of India.