Hi

Yes you can give one subject privately in National Institute of Open School (NIOS) , which allows students to appear for upto four subjects in "ondemand" examination. You can also give only one subject in senior secondary examination

among the following subjects

Hindi (301), English (302),Sanskrit (309), Mathematics (311), Physics (312), Chemistry (313), Biology (314), History (315),Geography (316), Political Science (317), Economics (318), Business Studies (319), Accountancy(320), Home Science (321), Psychology (328), Sociology (331), Painting

(332), EnvironmentalScience (333), Mass Communication (335), Data Entry Operations (336). and Introduction to Law (338).

Stream for On-line admission is open throughout the year for those learners who have already passed the Secondary Examination from the recognised Board and wish to take part admission in one subject or up to 4 subjects for updating their qualification, or learners who had appeared but could not clear, or who were eligible but could not appear in the Public Examination of the Secondary level from any recognised Board.

For Secondary and Sr.Secondary
(Rs. 500/- per subject + Rs. 200/- for subject involving practical.)

For more on this refer the below links

https://sdmis.nios.ac.in/

https://www.nios.ac.in/on-demand-examination/on-demand-examination-system-registration.aspx

Hope this answers your query!