Initially for MINDS(IITD) or CMINDS(IITB) there was a written test, if you qualify then you will proceed to the interview round.
You can follow the link given below for the syllabus. As both the written tests (no ve marks) was more or less the same:
https://bit.ly/3Or8Nrw (IITB CMINDS)
In IITD there were 3 coding questions in addition to MCQs & MSQs and the test was conducted on HackerEarth platform.
IITD Interview Questions and Resources:
Around 40 people were shortlisted for the interview.The interview was conducted on 3rd June 2022(Till that time 3 coap rounds were over).My interview was scheduled at 4pm on Microsoft Teams.In my panel there were 3 professors.Each professor asked me questions from different subjects(given below).And the interview lasted for around 4050 mins.
General Questions:

Give a brief academic introduction about yourself.

Currently what offers do you have?If you get M.Tech will you consider it or stick to MS(R) program and Why?

What are your favorite subjects? (Best answer, Linear Algebra & Probability for AI and Data science profile interviews.)
Also go through basic AI/ML stuff. Resource: https://bit.ly/3xy4tzO
Linear Algebra:
Take an equation Ax=B

Explain the solution of the system of linear equations w.r.t column space?

When will the system have a solution?

If matrix A has full rank, then for what B vectors does the system have a solution?

If the B vector doesn’t lie on the column space of A then how to get an approximate solution(projection concept)?
Resources:
https://bit.ly/3Qza41C (Must read upto 23rd video)
https://bit.ly/3xIokMP (Alternative to above resource)
Calculus:

What is a convex function?(Read thoroughly about concave & convex functions).

What is gradient?Give its geometrical significance.

What's a directional derivative?
Resources:
https://bit.ly/3OdsK5h (Must read Gradient section thoroughly)
https://bit.ly/3zOvvpc
Probability & Statistics:

What is covariance for 2 random variables x & y?

Proof that for independent random variables covariance is 0.

Prove E(x+y)=E(x)+(y) for both independent & dependent cases.

Prove E(xy)=E(x)E(y) for an independent case.

A coin is tossed n times we define a random variable as follows,where xi is ith coin toss, prob. of head in each toss is p(success):
Find E(x(bar)) and Var(x(bar)).(Use linearity of expectation concept)
Also do read thoroughly joint pdf,pmf, conditional expectation,total expectation,CDF etc.
Resources & Tips:
Keep handy all the distributions equations and graphs,specially normal distribution and approximation of poisson & binomial distributions using normal distribution.
Also go through proof of the memoryless property of geometrical & exponential distribution.
Recommended videos:
https://bit.ly/3OtYFhK (Must read upto 98th video)
https://bit.ly/3OoqmbC (Sampling distribution concept)
https://bit.ly/3n1d499
https://bit.ly/3OaaZ6O
https://bit.ly/3HBPE3G (Just go through week 3 important set of problems)
Algorithm:

Suppose you need to climb a stair of n steps and you can take at a time 1 step or extend your leg and take 2 steps or 3 steps at a time.Finds number of ways you can climb n steps.
(Hint: Take sol. as T(n).For T(n) we have 3 tree branches T(n1)(taking 1 step at a time)/T(n2) (taking 2 steps at a time)/T(n3) (taking 3 steps at time) then again solve the subproblems of size (n1)/(n2)/(n3) )
Verdict: Selected (IITD)
Note:

If you have a 650+ Gate score(Gen) you should definitely prepare well ahead as you will most probably get a call.Applicable for all branches.

IITB focuses more on LA & Prob.(specially joint distribution which was not part of the GATE syllabus).You have to study beyond the GATE syllabus.

You should never go out of studies after GATE for a long time else it will be difficult for you to crack the interviews.

Must be prepared with the B.Tech final year project.
Best of Luck for your selection :)