Here we have shared some of the Interview Questions asked in various PhD Exams, the experience of candidates, and their suggestions. Hopefully, this page will be helpful for you in your preparation for PhD Interviews and Exams. This piece of information is shared only for educational purposes.
We request all of you, if you have recently appeared in a Ph.D. interview or Assistant Prof. Interview or JRF Position Interview, please share your Interview Que. /Experience /Suggestions to us for others’ benefit, Your little contribution can help New aspirants to prepare themselves.
To publish your questions/experiences, send your interview questions/videos to us at maths.whisperer@gmail.com. Our information sharing channels
YouTube Playlist of PhD Interview Experiences/suggestions: https://www.youtube.com/playlist?list=PLDu0JgProGz4Bnzvq7sRfEsklmGivnkay
❤️ We heartily thank those persons who shared their interview questions and experiences for the others’ help. We wish you all the best for your future.
(Last updated on July 19, 2025)
🎯 Various PHD Interview Questions (Shared by Drishti Sunder Phukon)
Interview Questions for NBHM Doctoral Scholarship Interview 2025, IMSc PhD Interview 2025, IISER Pune PhD Interview 2025, HRI PhD Interview 2025, IIT Madras PhD Interview 2025, IIT Bombay PhD Interview 2025, IISc PhD Interview 2025, CMI PhD Interview 2025, TIFR-CAM Int. PhD. Interview, NBHM Masters Scholarship Interview, IISER Thiruvananthapuram Int. PhD. Interview, NISER Bhubaneswar Int. PhD. Interview.
“I appeared this year in various interviews for admission to PhD program in Mathematics. The interview questions available on your website were of great help for my preparation. Now I would like to contribute by sharing the questions asked to me, so that future aspirants can benefit from it. Please find the pdf of the questions attached with this email. Thank you for maintaining such a valuable resource. “
Yours sincerely
Drishti Sunder Phukon
🎯 PHD Interview Questions (Shared by Arka Prabha, July 2025).
Interview Questions of HRI, IITM, IISERB, IIIT Roorkee, IISERM, IIT Ropar, and IISERK.
“Thank you very much for creating such a great platform full of interview questions. It helped a lot. I wish to present to you the questions I’ve faced in my interviews. Thanking you “
Arka Prabha Roy
🎯 PHD Interview Questions asked at IIT KHARAGPUR (Shared by Soumodip Das, June 2025).
My name is Soumodip Das .
Today i got a mail from iit kharagpur that i am selected for phd . your videos and interview questions are really helpfull to me during the phd interview preparation.
So I am sharing my interview experience at IIT KHARAGPUR.My iit kharagpur interview questions :
(My research interest is Complex analysis )
1) give a example of a function which is not differentiable in Complex plane but differentiable in R^2
( I gave a example, they said how do you know it is not differentiable in C . I said about C-R Equation )
2) proof df/d(z bar) =0
( after writing 1 line they stopped me )
3) Define residue of function at a point
( I defined by laurent series )
4) can you find residue of a function without laurent series ?
( I gave a formula to find residue )
5) can you proof how we find this formula ??
( i started to proof but after writing 2 lines they said ok )
6) what is cauchy residue theorem ?? Prove it .
( i state the theorem and again when i started to prove , they stopped me )
7) define singularity
8) how a function behave at a removable singularity, pole and essential singularity .
9) can you proof all the behavior
( I said yes ,this time they don’t ask to write this proof )
10) if A^2 =0 then what can you say about the rank of A ?
11) define diagonalizable matrix
12) Given a matrix [[1, 2], [0, a]]
for what values of a, this matrix is diagonalizable ??
( I gave the answer for a not equal 1)
13) How do you know for a not equal to 1 , this matrix is not diagonalizable ??
Give me detail explanation
( i explain it by Am and Gm )
14) If Am = Gm for each eigenvalue, then prove that the matrix is diagonalizable.
(I prove it using the idea of independent eigen vectors )
15) what is the GM of eigen value ? Define it ?? If Gm is 5 and am is 8 then how many jordan blocks are there ?
(My suggestion is to make 2 or 3 topics very strong. Read all the theorems and try to prove them yourself and ask yourself questions.)
Thank you so much .
🎯 Interview Questions asked at IISER PUNE (Shared by Apurva Pujari, May 2025).
Respected Sir,
I first want to thank you for giving us this platform, where we can prepare for our interviews so effectively, without wasting our time to search different different websites. I’m sharing my interview questions, asked in IISER Pune in April 2025.
Preference – Group Theory, Ring Theory, General Topology.
- As 3 is prime in Z(√2), is it also prime in Z(√3) ?
- Is 5 prime in Z(√2)?
- Let T be a set of all diagonal matrices in GL(3,C) and N(T) be it’s normalizer. in written test you proved that N(T)/T is isometric to S3 , using group action. Will your proof also work for 4×4 matrices ? will it be isomorphic to S4?
- What is orbit stabilizer theorem? Will it also work if the set X is infinite?
- can S4 be embedded in GL4(C)? Can it be generalized for any n?
- Can any finite group be embedded into GLn(C) ?
- As S¹ is not homeomorphic to R, is S¹⁰⁰ can be homeomorphic to R²⁷⁵ ? Why
- Is SO(n,C) compact? how?
- take R¹⁰⁰, let S be the set of all lines passing through origin, is it compact?
- Is Every closed & bounded set of a metric space compact ?
- Let f be a continuous bijection between two topological spaces, is f inverse also continuous? give counter example.
After that They wanted me to ask something different from my preferences. So they asked one question from Algebraic topology and one from Complex analysis –
12. What is the fundamental group of a slipper?
13. Is |Z|² analytic ?
I hope this will help some students, as the questions on your website helped me for my preparation.
Thank You,
Apurva Pujari.
Thank you for your contributions and support.
P Kalika 