Engineering Entrance Exam

The marks you have scored in your JEE examination is a quite decent one and as you are looking for the colleges in Uttar Pradesh, I would recommend you to get your rank by following link :

https://www.shiksha.com/college-predictor 

You can get admission in any renown private college or colleges such as Invertis University in Bareilly, Mangalmay group of institutions in greater noida, ABES engineering college in Ghaziabad. 

No, in order to be admitted to NITs, candidates in the General Category must achieve at least 95 percentile. To be admitted to NITs, candidates from the Reserved category must have an 80+ percentile score. So unfortunately with 70-75 percentile, you can not get into any NIT. The candidates are advised to visit: JEE Main Rank Predictor 2024: Calculate JEE Rank From Percentile/Score  to check for the college in which they are eligible.

With your rank, to get computer Science engineering in any college in Delhi is very tough. Top engineering colleges in Delhi will have cutoffs much higher than your rank for the CSE branch. Admission to these institutions with such rank is generally not possible.
You can go for some private colleges. 

Admission in Harcourt Butler Technical University, (HBTU) Kanpur will be done on basis of merit of JEE Main examination result. A Candidate who is domicile of Uttar Pradesh i.e. he / she has passed the 10+2 qualifying examination from Institution located in U.P. is eligible for counselling . Defence quota is applicable and it has 5% seats reserved. The cutoff for chemical engineering for OBC category was 63232 last year and probably will not consider such a lower rank .

You can get admission in any government college through UPTAC counseling as per data of opening-closing rank on the website I can check that you can get top government AKTU colleges like  Kamla Nehru Institute of Technical Sultanpur, Bundelkhand Institute of Engineering and Technical College Jhansi, all Rajkiya Engineering colleges like Banda Pratapgadh, Mirjapur Bijnor and many more.

If you want to take only Lucknow University yes also you can get the desired branch at Lucknow University at this rank.

Yes, 6820 rank is a good rank as it falls between (5000-7000) and admission to B.Tech Computer Science and Engineering at  SRM Ghaziabad. SRMJEEE rank within 20000 is considered a good rank for admission. So, you have an advantage and can easily get admission to SRM Ghaziabad. 

Yes, definitely you can easily get a seat at Amrita School of Engineering Bengaluru in CSE as your marks are better than the criteria. Amrita School of Engineering Bengaluru application forms are available on the official website of the university. Eligible candidates can fill out the application forms online.

It is true that some colleges and universities accept applications from home state quota students as well as members of other backward classes (OBCs). A youngster who received a 98.99 percentile score in the JEE Mains 2024 exam is one such instance. With an OBC NCL certificate from Patna, he is a Delhi student doing his 12th year of schooling.
Finding out if a particular institute accepts both quotas requires looking through their admissions policies. For this reason, use the official phone number or email address listed on the official page to get in direct contact with the institute you want to enroll in.

If it is a general rank then you can not get in it, especially CSE branch You can't get admission only if you use the home quota other branch you can get at this rank. If it is your category rank you can definitely get an NIT college CSE branch with home state quota that offers. To check for the college in which you are eligible, visit: JEE Main Rank Predictor 2024: Calculate JEE Rank From Percentile/Score.