Is it possible to get admission in the 2nd-year of engineering after passing the 1st year of B.Sc?

No, it is not possible. For admission in 2nd-year of engineering you must have a B.Sc degree.

Eligibility criteria to seek admission in 2nd year Lateral entry admission in B.Tech is that candidate should have passed B.Sc Degree from a recognised University and passed Xll standard with Mathematics as a subject. Different Universities have different cut off marks requirements which varies from