Lateral entry

I don't think so that this is conducted through distance mode.

Get all the Eligibility related information on the following link provided below: https://www.shiksha.com/b-tech/course/b-e-in-mechatronics-engineering-kamaraj-college-of-engineering-and-technology-virudhunagar-240382

Robotics is a good to be choose.

Here is the list of colleges for B.Tech in metallurgy:
https://www.shiksha.com/b-tech/colleges/b-tech-in-metallurgical-engineering-colleges-india

Check the below link to see colleges providing lateral entry in Civil Engineering. You can choose the college based on ranking, fee structure, placements and student reviews of the college. https://www.google.com/url?sa=t&source=web&rct=j&url=https://www.shiksha.com/b-tech/colleges/b-tech-in-civil-e

Lateral entry engineering is nothing, but after completing your Diploma you get admission for direct 2nd year entry your 1st year is waived off. This is known as lateral entry, you can get lateral entry only after completing your Diploma. Hope this might help you.

To get admission for B.Tech colleges, you will need minimum of 75%, because the competition is too high.