is it permissible in islam to pray salat ul janaza of a women who marry hindu men and continue salat and roza whole life

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.

The funeral prayer over a dead Muslim even if he is dissolute is a communal obligation.

There is no doubt that the marriage of a Muslim woman with a non-Muslim man is void and this is dissoluteness and a grave major sin, and it is pure Zina (fornication or adultery) and not marriage. Nonetheless, this is not a sound reason for the Muslim community to abandon the funeral prayer over her. Ibn ‘Abdul Barr said: “All the Muslims agreed as a matter of consensus that it is not permissible to abandon the funeral prayer over disobedient Muslims because of their sins even if they have committed great major sins.”

However, a group of Muslims must perform the funeral prayer over her while the scholars and virtuous people whom people follow should not perform the funeral prayer over her publicly so that the people would be deterred from what she did.

Ibn Taymiyyah said: “As regards the people who show dissoluteness while they are still believers like the Muslims who commit grave major sins, then some Muslims must perform the funeral prayer over such people, and whoever refrains from praying (the funeral prayer) over one of them as a way of deterring the people who are like them from their act, in the same way as the Prophet refrained from performing the funeral prayer over someone who committed suicide, the one who takes from the booty of war before its division (according to the Sharee’ah) and an indebted person who did not pay back his debt, and in the same way as many righteous predecessors used to refrain from performing the funeral prayer over innovators; then whoever acts according to this Sunnah, he has done well….”

Allaah Knows best.