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I am sharing someone else experience. I am quoting him. I graduated now from IIM B. I prepared for CAT while I was working. I used to leave from home by 9.30 - 10 times in morning and be back in home by 9 - 10 after dinner from work. Some days, I had to stay in office late. My work comes under the category of hectic ( mentally, not physically ). This is what I did for the written CAT exam. Spend one hour every day in the morning, going through the chapters (Apti, DI, LR). I had materials, and I went chapter by chapter some day and random questions some day. Ensured I solved 20 problems in the beginning and as I progressed the speed increased tremendously. In office, open a browser tab and go to Arts & Letters Daily. Ensured I read three articles each day before I leave office. I'm generally curious, so I would read some random things without any background. Helped a lot in RC. The Hindu, Business standard in browser tab in office. Read in between meetings, when I was distracted etc. But, utilize time in office. Along with wordweb. Everyday, walk for 20 minutes or so in the night leisurely and recite to myself
all multiplication tables ( 1 to 20 )
Squares of numbers, cubes of numbers
Calculate % components for 1/2, 1/3. 1/15
Take 5 random numbers and compute their squares and cubes ( short cut ways )
I know the set of people who are preparing for CAT we especially had a guy who is very motivated and he would provide us the problems that are challenging & we would spend time discussing quickly. Mostly casual chat types. In our office, it was appreciated to prepare for exams and hence this was easy. Weekends, I gave one mock test, either from home or test center. I would try to solve the problem after the exams ( the ones I was not able to find quick solutions for ) & see if there are options. This would be complete in the weekend itself. Overall, CAT is about being in touch with the basics. You can solve the paper if you are given twice the time. It is all about speed and accuracy. These will not come unless you are in regular touch. Allot small amounts of time every day and you will surely crack it. All the best for your CAT.

As far as I know, LPU has criteria of a minimum of 85 percentile in the JEE Mains exam to get admission. But JEE Mains is not considered for the 2022 session as of now. but still, last year LPU was considered 85 percentile in Jee Mains. apart from this , you should have a minimum of 60% marks in the 12th class with mandatory subjects English Maths and Physics. LPU offers B.Tech in various fields such as CSE, EE, ECE, ME, CE, Automobile, Chemical, Aerospace, Biotechnology, etc. You can also apply for scholarships and gain the opportunity of fee concession. They conduct LPU NEST exams for students for both eligibility and scholarships. You can give that exam. You never know you may get a scholarship. So give it a try. That's all from my side I hope this helps :) for more, you can check the LPU website.

JEE Mains and JEE Advanced are two different engineering entrance exams. JEE Mains is conducted just after 12th Boards in the month of April. Clearing Mains, you can get a rank and admission into the NITs (National Institute of Technology), IIITs, and various other colleges like Amity. Many private colleges admit students through the Mains score too. JEE Mains paper 1 has 90 MCQ Single Correct Option questions. 30 each from Maths, Physics and Chemistry. Marking Scheme is +4, -1. And full marks in 360. JEE Mains paper 2 is only for those interested in Architecture and is not for B.Tech admission, but B.Arch admissions. Clearing the cutoff in Mains paper 1 will make you eligible for JEE Advanced exam. Clearing JEE Advanced and getting a decent rank will land you in IITs. It is conducted in the month of May. JEE Advanced has 2 papers of 3 hours each. The full marks, marking scheme, question pattern everything varies every year (in 2016 full marks was 372 while in 2015 it was 504). The level of questions in JEE Advanced is higher than that of Mains and it has Multiple correct option type, integers, matrix and paragraph questions. JEE Mains tests your memory and basic concepts while Advanced tests your core concepts. Every year 12+ lac students appear for Mains and only 1.52 lac students qualify for Advanced. (Given that you are serious in your preparation, getting a decent rank in Mains and qualifying for Advanced is easy, so don't think that getting in top 2 lac will be difficult).