B.A

Yes a graduate degree from distance programme is fully valid for admission to LL.B. According to BCI bar council of India only student with open university graduate system are not allowed to admission in LL.B. Yes, you can go for LL.B. After your B.A. From YCMOU. The eligibility criteria for pursuing LL.B. In most of the top universities is that you have to get minimum of 50% marks in your graduation degree and you might have to clear some entrance test with it, ( it may vary with the university you want to take admission in)
After LL.B. You can appear for Civil and Judicial services in your respective States. IAS Services, JAGS, services in Army, Corporate Lawyer, Legal Advisors in MNC and Company, Legal Processing outsourcing, Practice in Criminal, Civil or Income Tax as an Advocate. It will be advisable if you do your degree from a well known university that provides prime placement opportunity, outstanding exposure and professional enhancement training. I can enlist some university for your help -
Lovely Professional University, Modi Law College-Laxmangarh, Rajasthan
Navrachna University-Baroda
School of Law, Gujarat University-Ahmedabad
South Calcutta Law College - Kolkata etc. I hope it helps. Good luck.