Colleges in Lucknow

No, you cannot get a government college with this rank.

Yes, you can get gov colleges and there are 50% chances for IET.

If you opt for an integrated programme you cannot pursue a similar programme from another college in the duration of the integrated programme. Only after the completion of BBA+MBA, you can go for a separate MBA course. But why do want to opt for an integrated programme and waste time and effort if you are going to opt for an individual MBA anyway? Make your choice wisely.

I'm not sure of any other government college but IET Lucknow is not possible for you with this rank. They only have 500 seats.

Here is the seat matrix for IET Lucknow. You can get admission here:
Chemical Engineering 60
Civil Engineering 60
Computer Science and Engineering 60
Electrical Engineering 60
Electronics and Communication Engineering 60
Electronics and Instrumentation Engineering 60
Information Technology 60
Mechanical Engineering 60

No. Look for other colleges like LUCKNOW UNIVERSITY or Amity or BBDU.

Amity is a good option for law but I would suggest you to go for Amity Law School, Noida. It has a better exposure and faculty.

Lucknow is not the best place for doing BCA but it's not bad too. Some good colleges for the same are:
Lucknow University
Amity
BBD
SRMU
Modern Academy

UPSEE 2018 College Predictor
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Hello Sudhanshu,
I am attaching a link that will predict college for you.
https://www.shiksha.com/b-tech/resources/upsee-college-predictor