Is it possible to get HR or Marketing without taking CAT...??

Yes it is possible as different Institutes use different qualifying exams. Also various institutes used CAT/CMAT/MAT score for admissions into the same course.

Some good colleges accepting MAT score are TA Pai Management Institute, Manipal, Birla Institute of Technology, Mesra, Xavier Institute of Management and Entrepreneurship, Bangalore, National Institute of Technology, Warangal, Christ College, Alliance Business Academy, New Delhi Institute of Management

Some top colleges through CMAT are KJ Somaiya Institute Management and research, Xavier Institute of Social ServiceRanchi, Goa Institute of Management
Kirloskar Institute of Advanced Management Studies harihar, BIM TECHNOLOGY Greater NOIDA etc.

You should give both the exams to maximise your chances of selection into a good institute.

Hello,
Are you are an MBA aspirant and planning for admission? If yes, the first step for you is to know about themust take Top MBA entrance exams. Once you know all about the exam such as its eligibility, paper pattern, and all exam related dates, you will be able to proceed towards preparations.

You can give state universities exam in order to get that domain.
You can give other exams like mat, snap,nmat,xat,iift,others
Check this link for more information.

https://www.google.co.in/amp/s/bschool.careers360.com/articles/top-12-mba-entrance-tests%3famp

Cheers !!