does JNU provide BA programme course?

Yes, JNU Jaipur provides BA programme course.

B. A. (HONS.) ENGLISH

Duration: 3 years

Eligibility: 10+2 (any stream). Preference to those who have passed in II Division

Selection Procedure: Merit and Interview

B.A. HONS. + M.A. ENGLISH

Duration: 5 years

Eligibility: 10+2 (any stream) for BA(Hons) and II Div. for MA programme

Selection Procedure: Merit and Interview

The School of Languages, Literature and Society was set up in 2008. The programmes of the school are designed to provide knowledge and competence in the fields of literature, language, culture and society for a wide range of professions in such sectors as teaching, civil services, media or public relations. The main objective of the School is to offer training in theories and methods of literary/critical thinking as well as their application in practical contexts. By focusing on specific genres and texts, we encourage students to engage in critical practices that make them aware of the effects of social, political, cultural, historical and ideological formulations. The School also prepares and trains the students to avail the opportunities in the spheres that need language competence. The teaching is supplemented with seminar presentations, projects and guest lectures by subject experts/specialists. The students are provided opportunities to attend literary fests / cultural events to enhance their literary/artistic sensibilities and enhance their skills in literary appreciation.(https://www.jnujaipur.ac.in)

Hello Deepanshu,
If you are asking about JNU Delhi, then-
JNU Delhi provide B.A. hons in Language such as Japanese, Chainese, Parsian, Korean language etc. Other than this, No core BA course available here.
If you are asking about JNU, Jaipur then-
There is no BA course available in this university.
BA LLB is available here. In dept of social Science, only PG Course available here.
Good Luck