First of all, there is no fixed GATE score that makes you eligible to do a Ph.D. at IIT Madras as the selection process comprises a number is criteria with the GATE score being just one of them. The students applying for a PhD program at IIT Madras, go through a rigorous admission process. To become eligible one needs to fulfill the following criteria

• Master's or a dual degree in the relevant disciplines with a CGPA of 6.5 or above.
• Candidates with BE/BTech degrees can apply directly for a Ph.D. (MS+PhD) in Engineering or Sciences after their Bachelor’s degree. 
• M.S scholars with CGPA>8.0 are eligible to upgrade to the Ph.D. program in the same department and receive a dual degree i.e. (MS+PhD) 

I hope I made it clear!

To get into IIT Madras, you need to clear JEE Advanced exam. Your All India Rank (AIR) in JEE Advanced is crucial for admission to IIT Madras, as the institute considers only candidates who clear the JEE Advanced exam and meet the institute's cutoff criteria.

The minimum AIR required for admission to IIT Madras varies from year to year and depends on several factors such as the number of applicants, the difficulty level of the exam, and the number of available seats. In general, you should aim to secure an AIR in the top 500-1000 to have a good chance of getting admission to IIT Madras.

To achieve this rank, you need to prepare well for the JEE Advanced exam, which tests your understanding of concepts in physics, chemistry, and mathematics. You should practice solving problems and take mock tests to improve your speed and accuracy.

Apart from your AIR, IIT Madras also considers other factors such as your performance in Class 12 exams, your academic background, and your performance in other co-curricular activities. So, focus on your overall development and maintain a good academic record to increase your chances of getting admission to IIT Madras.

The cut-off score for CAT for the Department of Management Studies (DOMS) at IIT Madras varies from year to year and is subject to change. However, for the 2022-2024 batch, the CAT cut off for General category candidates was 95, while the cut-off for OBC category was 85.

It's important to note that the CAT score is only one of the criteria for admission to the MBA program at DOMS IIT Madras. The institute also considers academic performance, work experience, and performance in group discussions and personal interview rounds while making admission decisions.

Unlike MTech, admission to MS or Ph.D. is based more on their interview and aptitude test than on GATE score.

• For some of the master's programs, like MS candidates are shortlisted after a round of technical interviews. IIT Madras prefer students with GATE scores of at least 90 percentile or more.
• For Ph.D. too, candidates will be considered if they score between 1000-2000. Here, a rank less than 800 is considered excellent and such candidates will be considered for Ph.D. courses through GATE scores.

Thus we can say that the cut-off required for joining MS and Ph.D. programs at IIT Madras, for example, is lesser compared with the cut-off required for admission into the MTech program

Admissions into IIT Madras are possible through ranks ranging from 1-10000 depending on the category, branch, number of seats available, etc.

To make the most out of IIT resources make sure you have clarity of goals and know what and why you are doing.

IIT Madras JEE Advanced Cutoff 2022 for General Category for various branches is listed below. The overall cutoff for JEE-Advanced is 167 - 10837 rank.