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With 27 percentile in CAT, your chances of getting admission to the Army Institute of Management (AIM K) are quite low as the institute has a higher cutoff. AIM K generally requires a minimum percentile of 70 or higher in CAT for admission to its MBA program.
However, you may still be eligible to apply for admission to other MBA programs in various other colleges that accept CAT scores. Many B-Schools have their own eligibility criteria and weightage for the CAT score and other selection rounds. So, you may still have a chance to get admission to an MBA program with your CAT percentile.
It is recommended that you research and apply to other MBA colleges that accept CAT scores and have a lower cutoff percentile. Some of the options you can consider are:
National Institute of Technology (NIT) MBA programs
MBA programs offered by state universities and colleges
Private B-Schools offering MBA programs.
However, it is important to note that the admission process for each college may vary, and you should thoroughly research their eligibility criteria and selection process before applying. You can also consider taking other MBA entrance exams like MAT, CMAT, XAT, etc., which can expand your options for admission to MBA programs.

There are some MBA colleges in India that offer direct admission without requiring an entrance exam, but these colleges may not necessarily have the best placement records. Admission criteria for these colleges may vary, and some may require a minimum GPA or work experience. It's important to note that admission to reputable MBA programs often requires a competitive entrance exam score, such as the CAT GMAT or XAT along with a strong academic record and work experience. These programs often have a rigorous curriculum, experienced faculty, and a robust network of alumni and industry connections, which can lead to better career opportunities and higher salaries after graduation. While it may be tempting to pursue a programme that offers direct admission without an entrance exam, I recommend thoroughly researching the college and its placement record before making a decision. You may also want to consider taking an entrance exam to increase your chances of admission to a reputable MBA programme with strong placement opportunities. Ultimately, the decision on whether to pursue an MBA programme that requires an entrance exam or one that offers direct admission should be based on your personal goals, career aspirations, and individual circumstances.