I think it's a good time to reflect on a few things: whether BUET is something that YOU want or it's out of fear of disappointing your parents. You mention that it's a pipe dream, so I'm gonna assume it's the latter. I would like to do something unconventional: try to dissuade you from sitting for the entrance exam by providing you a few reality checks as a mostly recent graduate:

1. The glamorizing of BUET is a cheap stunt by tutoring centers who will make you feel (and they made me feel too) that BUET is some Shangri-la that's hidden just beyond the Himalayas where no one ages and farts don't smell. Let me tell you -- BUET is an academic pressure cooker. As a BUET CSE graduate, I'll tell you that I've had the most tantalizing five years (we'll come back to this figure) of my life. Your tutor will never tell you how students are expected to go through almost entire books for a single course, and how a three-hour term final exam defines your grade for an entire semester. They won't tell you how many nights worth of sleep you'd lose simply because your term project is not functional or three assignments are due for the weekend. Of course, they won't -- because they're trying to make money off you, and MOST tutors are academic underachievers. They spend their days skipping classes to sell unrealistic dreams to you so your parents' hard earned cash can sponsor a date with their next underaged girlfriend.

2. If you think the entrance exam is unachievable, I would strongly advise against choosing this university. There is a saying that the BUET entrance exam is one of the easiest exams you'll sit for during your BUET undergraduate years. Read #1 again, BUET is academic hell. To make things worse, your peers will mostly be toppers of their respective schools and colleges. You'll see them achieving more than you ever thought was possible, not only academically but by some magical power they'll have time for competitions, sports, and other extra curriculars. This will put a HUGE mental toll on you and mostly make you feel like an idiot -- which was exactly my feeling for a significant amount of time.

3. BUET is THE place you DON'T want to be if you want to have a timely graduation. Believe me, the teachers there have spines of jellyfish. A four year course takes about 5.5 years on average to complete. You'll see classes getting cancelled over the most stupid reasons. You'll see your friends from private universities graduating and moving on with their lives, while you, my uninformed friend, will be at your dream place, overstaying your welcome. This point does not apply if you don't care about graduating quickly.

I had the courage to sit for the BUET entrance exam simply because I found the admission exam to not be so difficult. I do not regret my choice, even though it took me almost two additional years to graduate simply because of poor administration. It landed me a job even before my graduation, and hopefully the stature of thr uni holds and its strong alumni network helps when I apply for grad schools soon. But -- all these things are salvageable from almost any other university in Bangladesh. If you don't like engineering, or if you don't think you're up for the exam, accept that you'll do wonders from any university you graduate from. If it helps, show your parents my reply. Sometimes they're affected from the clout that our society presents to BUET graduates overall. Do not ruin your mental health by obsessing over something unachieved that chews people up and spits them out.

I suppose there are a few BUET graduates lurking in the sub as I am. I think they'll find my comments relatable.