Science

No, integrated MCA is not taken with B.Sc Computer Science.
Integrated MCA is a 5-year single course combining BCA and MCA, not B.Sc.
If you do B.Sc Computer Science, you can apply for a regular 2-year MCA afterward.
So, integrated MCA and B.Sc are two different paths.

During the final year of BSc in Zoology. After that, I received an invitation to apply for M.Tech in IIT-Delhi. But, unfortunately, to pursue M.Tech degree, one should have B.Tech or MSc degree in relevant subjects. Thus, even after qualifying GATE during my bachelor's, I couldn't join or at least apply for M.Tech in any of the IITs.

Basically it depends on your category also. If you are from unreserved/ews/obc then you can go for BBAU LUCKNOW, ALLAHABAD UNIVERSITY and those central universities which are not it top 10.

Because in BHU, DU, HCU, JNU the cut offs are high and it may go to more than 160.

Hence you can see some low ranked universities. 

If you belong to sc/st category then admission in BBAU LUCKNOW, Allahabad UNIVERSITY is confirmed. 

You can also go for BHU. 

The eligibility requirements for admission to the BSc in Physics course at Sanjay Ghodawat University are that candidates must complete their Class 12 from Science stream from a recognised board of education. Moreover, the admission is based on merit; the university releases the merit after assessing candidates' achieved scores in their Class 12/HSC or equivalent.