You cannot apply to any colleges without any score, only on that basis you can go ahead.
As far as cracking a top Bschool is cincerned, apart from CAT there is distribution of weightage on your Work experience, Academics, Extra Curriculum Achievement as well as your scores in GDPI rounds which all accounts for final score and the cumulative score will be counted for counseling.
Despite not knowing your CAT score you need to be well versed with above-mentioned paramters and you would require fair knowledge of what all you have achieved so far plus good basic management and technical knowledge and current affairs to crack any top 25 Bschool.
Nevertheless, you need to apply for entrance exams like CAT, XAT, CMAT, etc to be eligible for MBA admissions.

All The Best..!!!!

You must be giving online mock tests for preparations of CAT exam. So with your score you must be having a good idea how much percentile you can score. If you give online mock test so with your score it also shows the predicted percentile. There is no guarantee that it needs to be true because percentile is a relative phenomenon which depends on your performance along with the performance of other students appearing for exam.

But with this predicted percentile you can check out whether you can pass the few last year's cut off or not. If you can pass last 3 year's cut off very easily then you can definitely apply for that college. If you are close to the cut off then also you should go for it. If you lack behind the cut off then you need to think whether you want to take risk or not. If you have confidence that this is not your best and you can still do better and you don't want to miss this one of the top college then you can still apply for it.

As very less time is left for CAT exam so you need to brush up on your basics and give up lots of online mock test and analyse their solutions which will help you in overcoming your mistakes and come up with a strategy to attempt your paper which will definitely help you in improving your marks and percentile.

All the best for your preparations and exams!!

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