Pondicherry University

Yes, you can get B.Sc(Hons.) maths if you have filled PCM.

As per University eligibility criteria a Bachelors degree in any discipline in Science/ B.A. Geography/ B.E. Civil Engineering / Electrical and Electronics Engineering with a minimum of 55% of marks. + Entrance test.
So, graduate with ECE are not eligible for this program.

Click on the link for previous year question paper:-https://www.current-affairs.org/2606/pu-cet-pg-2016-previous-year-question-papers-pdf.

You can refer to the following books for a firm understanding of the syllabus and get proper preparation for PU LL.B:
1. CLAT and LL.B. Entrance Examination Study Package, A. P. Bhardwaj.
2. The Ultimate Guide to the LL.B. Entrance Examination 2012, M.A. Rashid.
3. Guide to LL.B. Entrance Examination 2012-13, 22nd Edn.
4. Model Test Papers for CLAT & LL.B.A. P. Bhardwaj

Hello Mohan,
It's indeed great to hear from you that you are not interested in going to either medical or engineering. To tell you frankly there are plenty of options for a student after 12th. It's as if the whole world has opened up. I am attaching a link that will give you all the required information about different possibilities after 12th. https://www-shiksha-com.cdn.ampproject.org/v/s/www.shiksha.com/courses-after-12th/amp?amp_js_v=a2&_gsa=1&usqp=mq331AQCCAE=#aoh=15546895394758&_ct=1554689557058&referrer=https://www.google.com&_tf=From %1$s&share=https://www.shiksha.com/courses-after-12th
Best wishes to you.

Integrated Ph.D. is not offered in Pondicherry University.

No, it is not possible to get admission directly into the final year of B.Sc.

Please specify what you have done till now your qualifications and your bachelors details.