phd interview questions pdf

Skip to primary navigation
Skip to main content
Skip to primary sidebar
Skip to secondary sidebar
Skip to footer

career-advice.jobs.ac.uk

What to do before the interview.

It is important to treat the PhD interview like a job interview. Dress smartly and bring two printed copies of your application form. It is also useful to bring your research proposal or your notes on how you will fit into the existing research project. Organise materials neatly so that you can quickly access any information requested, but also commit crucial details to memory—and rehearse.

Do background research on the university, the department, and the academics who will interview you. Prepare several informed questions about their current research and the overall research culture in the department.

Make sure you know where and when the interview will occur and arrive ahead of time. If possible, visit the building in advance. You will feel more at ease if the surroundings are a little familiar.

To avoid embarrassment, try to find out how to pronounce the names of staff members you will meet.

Tell us about yourself.

Include not only your academic background, but your personal motivation—and particularly what motivates you to do in-depth research in this specific field of study.

Why have you applied to do a PhD here?

This is where research can give you an edge. Show that you have chosen this programme/department/university for strong and valid reasons, such as your high regard for named researchers’ work, the availability of specific collections, equipment, or lab resources, and overall reputation. Give concrete examples, not banal generalities.

What can you do for us?

Academics will have to give up a great deal of time to supervise you, most of which they will receive no scheduled hours or recognition for. So, what research skills, personal attributes, connections, theoretical ideas and so on do you have that will make it worth their while? Again, give specific and concrete examples.

What do you think pursuing a PhD will do for you?

If you plan to become an academic, say so, but not in terms of just getting a job—talk about your long-term research plans . If applying to a professional doctorate programme, show that you understand the realistic career impact. Applicants pursuing a PhD towards the end of their career may want to talk about gaining recognition for innovative practice or solving complex issues through research. It is important to showcase your knowledge, motivation, background and commitment at this point.

What skills do you have that make you a good fit for the PhD place you have applied for or for the department?

Tailor your response specifically: Play up your strengths, including any prior research training and experience. Discuss project management skills, leadership skills, interpersonal skills, collaborative working, critical thinking and international experience or understanding.

Tell us about your research project.

If proposing your own topic, over-prepare. Refer to current scholarship and explain how your cutting-edge work will break new ground. If applying to join a project, show that you understand its value and demonstrate that you are the right person to make it happen. Be enthusiastic!

What would you say are your greatest strengths and weaknesses?

Yes, that tired job-interview question will appear here as well. Make sure the strengths you list include examples, and your “weaknesses” are also “strengths”—for example, “sometimes I’m a terrible perfectionist.” It is important to mention and demonstrate how your determination reaps project succession. The panel will want to know that you will persist in completing the PhD. Demonstrate this!

Tell us about a challenge you have overcome in the past.

It’s best to choose a research challenge as your answer: for example, how you handled an issue during your Master’s dissertation such as a disagreement with a supervisor or an issue with ethical approval. If you use a career or personal challenge, show how you used research or project-management skills to solve it.

What do you see as the most important issue/problem in this field today?

This question gives you space to show your knowledge of current research, theory and practice. Use this as an opportunity to showcase your knowledge.

Is there anything you would like to ask us?

This is your chance to show how informed you are and position yourself as an intellectual equal. Be prepared . Be ready.

We hope you found our Top Ten PhD Interview Questions and Answers article useful.

Find your PhD here

More phd tips:.

How To Write PhD Proposals

How to do a Distance Learning PhD at a UK university

Become a Researcher – 5 Skills You Need

PhD Funding – A Checklist of Possible Sources

Share this article

Dr Denise White FRSA

Dr Denise White FRSA is a multi-award-winning intellectual disability and music expert. Having over 25 years’ experience in the field of early years, primary, post-primary, special educational needs, further and higher education, Denise is known for her innovative and creative teaching methods that transforms lives. She is an advocate for inclusive and community-based ethical learning and teaching models.

She is a passionate education advocate with the talent to develop inspiring hands-on lessons that will capture a student’s imagination and breed success.

Known as ‘The Music Doctor’, Denise is an Author at Bookhub Publishing. Her Music Doctor Series will launch in March 2019. Denise is also a Speaker, Trainer, Consultant, Mentor and Researcher.

Web: www.themusicdoctor.co.uk

Twitter: @_TheMusicDoctor

Reader Interactions

Introduce yourself in a PhD interview (4 simple steps + examples)

The opening of an application interview for a PhD position usually starts with short introductions of everyone participating in the conversation. Many applicants wonder how to best introduce themselves in a PhD interview. Four simple steps (including examples) help you to develop a powerful self-introduction .

What to do in a PhD interview introduction

What not to do in a phd interview introduction, introductions in a phd interview.

Interviewing for a PhD position can be nerve-wrecking.

On the one hand, the interview is an advanced stage in the PhD application process and a reason to celebrate having come so far.

On the other hand, you may feel much more vulnerable during an interview than when sending a carefully crafted application letter.

A PhD application interview requires you to react quickly to questions, and you will never know what exactly the admissions committee will ask. Nonetheless, you can properly prepare for a PhD interview. One of the elements is preparing a powerful introduction of yourself.

A self-introduction summarises who you are and why you want the PhD position. A powerful self-introduction can set the tone for the whole interview.

If you are unprepared, there is a risk of going in all directions when it is your turn to introduce yourself. It may throw you off and make you extra nervous for the remainder of the interview.

You may also like: How to strategically prepare for a PhD application

Several things are pivotal in PhD interview introductions:

Keep it short: A good self-introduction is not too long. Of course, it should be longer than simply stating “ My name is … and I would like this position because I love doing research .” However, when introducing yourself, you should avoid speaking for longer than 3-4 minutes.
Don’t take away all answers to potential questions: Some applicants try to predict all possible interview questions in advance. Then they try to answer all of them as part of their self-introduction. Don’t! There will be plenty of time in the interview to go into details. In a self-introduction, stick to a handful of key points that you want to bring across.
Take non-verbal cues into account: Non-verbal cues include facial expressions, gestures and body language. During a self-introduction, you should make sure to come across excited about the interview instead of scared and defensive. Smile. Pause. You should also try to read the body language of the interviewer/s: Leaning forward, moving, or hand gestures are cues to wrap up your self-introduction.

Several things are best to be avoided when you introduce yourself in a PhD interview:

Don’t start babbling: Many PhD applicants start babbling when they are nervous. Babbling means they talk rapidly and incomprehensively. They may repeat information and go in all directions. The easiest way to prevent babbling is by preparing the self-introduction in advance. The four steps explained below can help you with this preparation.
Don’t provide too detailed information: A self-introduction in a PhD interview serves one purpose: introducing yourself at the start of the interview. Nothing more and nothing less. Hence, there is no need to go into detail about every single aspect. For instance, it is enough to explain what bachelor’s degree you earned. No need to list all individual courses that you followed.
Don’t already ask questions: It is advisable not to end your self-introduction with several questions that you have. Rest assured that there will likely be a time when the interviewers ask whether you have any questions about the PhD programme that you applied to. However, most interviews will begin with questions to the applicant and not the other way around. So be mindful of this general structure of PhD interviews, and don’t create an awkward situation by immediately bombarding your interviewer/s with your own questions.

Step 1: State your full name

The first step is easy-peasy: State your full name. Why?

Not all names can be intuitively pronounced. So help your interviewer/s by saying out loud your whole name. In that way, they will be more comfortable addressing you by name throughout the interview.

Step 2: Give a brief overview of your educational (and professional) background

Your educational background has a lot of weight in the decision of the application committee on whether you are a good match for a PhD programme or not.

Therefore, it is useful to provide a brief summary of your educational background. Those who have work experience also benefit from including it.

Step 3: Explain why you are interested in the PhD position

The next step is to justify your interest in the PhD position. There are several powerful ways to explain why you want to do a PhD.

What is important in this next step, however, is to link your motivation to the specific PhD position that you are interviewing for. Remember to keep it relatively short!

Step 4: Thank everyone for the opportunity to be interviewed

The final step is to thank everyone for the opportunity to be interviewed. Be gracious and polite, and express your enthusiasm for the interview. This will create a comfortable atmosphere in which questions can be freely asked and answered.

Get new content delivered directly to your inbox!

Subscribe and receive Master Academia's quarterly newsletter.

10 key skills of successful master's students

Clever strategies to keep up with the latest academic research, related articles.

37 creative ways to get motivation to study

Dealing with failure as a PhD student

How to deal with a desk-rejected paper

13 great academic phrases to write your discussion (+ published examples)

Discover related jobs

Discover similar employers

Accelerate your academic career

Dutch Academic Job Titles Explained

What's the difference between a universitair docent and a hoogleraar? Wh...

How to Write a Research Proposal

When applying for a postdoc position, fellowship, or grant you will ofte...

Moving to Finland to Research or Study

Who wouldn’t want to study or work in the happiest country in the world?...

Moving to Switzerland to Research or Study

Switzerland has a long tradition of attracting international students an...

On-Campus Interview Tips

On-campus interviews are an essential step in the faculty member, PhD st...

The 7 Essential Transferable Skills All PhDs Have

During your PhD, you’re not just learning about your research topic. You...

Jobs by field

Artificial Intelligence 175
Electrical Engineering 174
Machine Learning 171
Programming Languages 144
Molecular Biology 127
Materials Engineering 104
Materials Chemistry 102
Electronics 101
Management 98
Mechanical Engineering 97

Jobs by type

Postdoc 321
Assistant / Associate Professor 221
Professor 145
Researcher 118
Research assistant 100
Lecturer / Senior Lecturer 92
Tenure Track 85
Management / Leadership 69
Engineer 61

Jobs by country

Belgium 297
Netherlands 192
Switzerland 113
Finland 111
Germany 106
Luxembourg 94

Jobs by employer

KU Leuven 95
University of Luxembourg 92
Mohammed VI Polytechnic Unive... 84
Ghent University 64
ETH Zürich 60
Eindhoven University of Techn... 60
University of Twente 54
KTH Royal Institute of Techno... 42
Wenzhou-Kean University 35

This website uses cookies

A Site for Higher Mathematics

PhD & JRF Position Interview Asked Questions & Experiences(Collections)

Here we have shared some of the Interview Questions asked in PhD Exams, the Experience of Candidates and their Suggestions. Hopefully, this page will be helpful for you in your preparation for PhD Interviews & 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.

Send your interview Que/Videos us on [email protected] . Subscribe Us On

Page Editor: P Kalika

YouTube Playlist of PhD Interview Experiences/suggestions: https://www.youtube.com/playlist?list=PLDu0JgProGz4Bnzvq7sRfEsklmGivnkay

❤️ We hearty thanks to those persons who shared their Interview Questions & Experiences for others’ help. We wish you all the best for your future.

🎯 ISI Phd Math Jrf Interview Ques (Anonymously shared, October 2023) .

(Added on March 31, 2024)

Show that in an odd order group every element has a unique square root.
What can you say about a group with a trivial automorphism group?
Identify Z[i]/(1+3i).
X be a subset of the sequence space,l^1 such that the nth term of each x:=(x_n) in X is bounded above by 1/n^2. Then show that X is compact.
Types of singularities.
If a function is continuous on C and analytic on C\{0}, is it entire ?

🎯 Ques asked at IIT Delhi PhD Interview (Shared by Jasveen Kaur , August 2023) .

What is the property regarding eigen values of real symmetric matrix proof?
If A is a real matrix of order 2 one eigenvalue is 2+i what is its trace?
What is eigen value Caley Hamilton them?
General characteristic pol eqn of order 2?
A matrix of order n has char polynomial monic poly of degree n
Can a3+2a +1 be char eqn of any matrix of order 3 why or why not
Diagonlizable matrix defn
Can ques 2 matrix be diagnolsble why
Why distinct eigen value is necessary condition
What if eigenvalues are not distinct
Differentiability at point xo
Diff implies continuity proof
Converse true or not give an example
Local minima in fnc of one variable
Diff of a function of two variables
Local minima of func of two variable
What about global minima
If f is linear fnc local minima at xo
Is it global minima or not?

🎯 Interview Experience of ISI M.Math at ISI Bangalore (Shared by Anonymously , July 2023) .

(Added on March 31, 2024 )

I was asked my preference and I replied with Basic Analysis and Algebra. They asked me two questions, one from Analysis and the other from Algebra.

They sufficiently helped me by providing hints along the way. I’m attaching the asked questions.

🎯 Interview questions in NBHM, TIFR-CAM, IISER TVM (through NBHM channel), and NISER (Shared by Drishti Sunder Phukon , June 2023) .

Sir, I would like to submit interview questions in NBHM, TIFR-CAM, IISER TVM (through NBHM channel), and NISER so that it would help others. Please find attached the pdf of the same.

I got selected for NBHM masters scholarship, and waiting for results from IISER TVM and NISER.

🎯 IIT Kanpur Phd-Interview Question (Shared by Surajit Pal, May 2023 ) .

🎯 PhD Interview questions asked at IIT Ropar (Shared by Bikky Gupta) .

(Added on May 06, 2023)

“Last I got a mail from IIT Ropar I selected in Phd program, your collection of question give me idea how to prepare for interview, Thank you so much from bottom of my heart. I have question that they ask during my interview. I am attaching here.

🎯 PhD Interview questions asked at IIT Bombay, Kanpur, Jodhpur, Hyderabad, Madras & IISER Pune (Shared by Anik Bhowmick) .

‘I am Anik Bhowmick, I have appeared in several PhD interviews this year. I have attached a pdf so that you can share it and help students around the world.’

(Added on May 05, 2023)

🎯Interview questions asked at IIT Bombay, Kanpur and NBHM PhD (Anonymously received) .

(Added on 18-12-2022)

🎯Interview questions at IISER Pune and IIT Guwahati (Anonymously received) .

I had given an interview at IIT Guwahati and IISER Pune in the June session. In IISER Pune, they asked questions from linear algebra, ordinary differential equations, real analysis. They are as follows.

What is the minimal polynomial. What is the characteristic polynomial.
What are the relationship between minimal polynomial and charactestic polynomial. Can you proof those relationships between minimal polynomial and charactestic polynomial. In ordinary differential equations, they asked questions from uniqueness and existence theorem. Statement and example of uniqueness theorem.
What is the reimann integration. They asked some examples of reimann integration.
What is the uniform convergence in sequence of functions.
Is continuity implement the uniform convergence of sequence and series of functions. Can you proof it .

During IIT Guwahati, they asked questions from partial differential equations.

Write down the general equations of second order pde.
What is the heat equations. In heat equations,.what are the parameters.
Can you proof the heat equations, from where it is derived .

(Added on 30-07-2022)

🎯 NBHM PhD 2022 Interview Questions shared by Bittu Singh .

🎯 CMI PhD Interview experience (Anonymously Shared)

🎯 IISER Pune PhD 2022 July Interview questions shared by Umesh

(Added on 04-07-2022)

🎯 PhD Interview/Admission Questions IITB, IITK & IITM (04-07-2022)

(Anonymously Shared)

IIT Madras Que.

🎯 Hello, Sir, Sending PhD interview questions of IISER Bhopal, IIT Indore and IIT Hydrabad.

(Added on 28-05-2022)

🎯Hello ! I attended the PhD interview at IIT Dharwad this year. I’m sharing the questions below.

(Anonymous Shared)

What is the order of A_n ? Prove your claim.
What group is the quotient Gl_n(R)/Sl_n(R) isomorphic to? What about Gl_n(C)/Sl_n(C) ?
What group is the quotient M_n(R)/H isomorphic to ? (H is the set of matrices in M_n(R) with trace 0.)
Let H be the group of all 10th roots of unity under multiplication. What group is the quotient (C*,•)/H isomorphic to?
G is a finite group such that all its non-identity elements are of order 2. What can you say about G?
Prove that the additive group of a field of order p^n is isomorphic to Zp × Zp × … × Zp (n times).
What is the order of Sl_n(Zp) ? Prove it.
V is a real vector space. f & g are linear functionals on V such that ker(f) ⊂ ker(g). How are f and g related?

🎯 PhD test and interview questions collection shared by Nidhi Shukla, Download the PDF file (17Pages).

SNU PhD test

The least value of n for which Sn has abelian subgroup of order 30?
Co-Variance of two random variable lies between 0 and 1?
How to find connected set if set contains element in the form of matrix?
A Set containing (x ,y) such that X square + y square is equal to 1 and xy is not equal zero_ compact?
T is a mapping from V1to V2 where v1 and V2 are finite dimensional vector spaces let S be a subset of V1 then the relationship between dimension of T(S1) and dimension of S1?
AA’=A’A=I
=>0for all x
If a function is given in terms of series then how to find its continuity & Differentiability?

PhD Interview at IITs, IISc, IIPE, etc. Download PDF File: Click here

🎯 TIFR Mumbai PhD Interview April 2022 Questions Shared by Dhiman Das.

(Added on 07-04-2022)

🎯 Hello Sir, I am selected for PhD at Aligarh Muslim University. I thank you for all the updates and notes and videos. Sharing my interview questions. Pls keep anonymous. Thank you again for running the kalika community.

(Added on 30-12-2021)

🎯 PhD Interview 2021 Questions asked at VIT Bhopal

Sir, I have appeared for an Interview for VIT Bhopal on 8th december and also got selected. I am attaching the file of questions here. Also big thanks to you sir as the collections of interview questions is very helpful for me. and also I am following your study material of many topics for preparing for CSIR & GATE. Regards Suneel Kumar

🎯 PhD Interview 2021 Questions asked at UNIVERSITY OF DELHI

Hey, I have given Interview at UNIVERSITY OF DELHI. The interview questions are follows: First we have to make a presentation on any of our favourite topic in not more than 8 minutes. My topic was “Fundamental Theorem of Finite Abelian Groups” The questions asked are as follows: 1) What are elementary divisors? Give an example. 2) Given two finite Abelian Groups G and H. How can we check whether they are isomorphic or not with the help of elementary divisors? 3) What are the future plans that you would like to work with the theorem that you presented? 4) What is the partial converse of Lagrange theorem for Non-Abelian groups that we have from “Fundamental Theorem of Finite Abelian Groups”? 5) How many groups upto isomorphism are there of order 15? 6) What is Cauchy theorem? 7) With the help of Sylow theorem, show that the group of order 15 is Cyclic? 8) Do you know Free Abelian group? 9) What is Commutator group? 10) What are the derived series? 11) With the help of derived series can we define Solvable group? 12) What is Characteristic subgroup? 13) Relation between Characteristic subgroup and Normal subgroup? 14) Why is every characteristic subgroup normal? 15) What is the Commutator subgroup of GL_n(R). Why?

🎯 PhD Interview 2021 Questions asked at IISER MOHALI

Hey, I have given an interview at IISER MOHALI. The questions are as follows: 1) What is the unit group of Z_n? (in terms of n) 2) What are the maximal ideals of Z? (I said of type pZ where p is prime) 3) Prove that Maximal ideals of Z are only of type pZ where p is prime? 4) Consider the complex polynomial ring C[x]. What are its irreducible elements? What are its maximal ideals? 5) Consider C[x,y], what are its maximal ideals? 6) Are the ideals <x-a> and <x-b> in the ring C[x] same? For what condition on ‘a’ and ‘b’ will they be same? 7) Is the space L²[a,b] a Hilbert space? 8) Consider [0,1]. As every point in [0,1] can be written in decimal expansion. Consider the set of all points in [0,1] whose decimal expansion do not include the number 5. What is its measure?

(Added on 17-12-2021)

🎯 VIT VELLORE PhD Interview 2021 Questions

Me Nowshad Ali Mir from Jammu and Kashmir. I have appeared for interview on 20th of Oct, 2021 at VIT VELLORE. INTERVIEWERS asked me simple questions:

What is Differential Equation?
what is Order of D.E?
General Solution
particular Solution
Singular Solution
Complementary function
Particular Integral
Can C.F alone can be a solution of D.E?
Can P.I alone can be a solution of D.E?
How many arbitrary constants are in General Solution of D.E?
and some questions about my Research Proposal.

🎯 IIT Kanpur, Madrash, BHU & IISER Berhampur PhD Interview Dec 2021 Questions (Anonymous Share)

(Added on 10-12-2021)

My Name is ———— and I got selected in PhD at IIT Madras for 2022 January session, Here I am attached the following interview questions of mine. Click on the link to read.

🎯 IIT Kanpur PhD Interview December 2021 Questions (Anonymous Share)

What can we say about group G if its order is 27?
How many non-abelian groups are up to isomorphism of order 27? What about its center?
If |G| = p^3(p is prime), show that G has a subgroup of order p^2?
Let V be a vector space over C and T: V to V is a linear operator such that for v in V there exists n in N(naturals) satisfying T^n (v) = v. What can be said about the linear operator T? [Hint: Show that T is diagonalizable]

🎯 IIT Bombay PhD Interview Dec 2021 Questions (Anonymous Share)

Consider the polynomial f(x) with rational coefficients, then how many homomorphisms are there from Q[x]/<f(x)> to C which maps 1 to 1?
Is (Q,+) finitely generated? Explain.
Consider the function f(z) = 1/(z^2+1). Is the function entire? Why/Why not. Are there any singularities? Classify them.
Consider f(z) = 1/(z^2+1). What is the radius of convergence for the power series about z=100?
Give the entire function f such that Re(f(z)) tends to 0 and z tends to infinity.
What is a Lipschitz function? Is it continuous?
Is the set of all Lipschitz continuous function on [0,1] dense in C[0,1]?
Can C[0,1] be approximated by polynomials?

🎯 IIT BHU PhD Interview Dec 2021 Questions (Anonymous Share)

Consider the 2×2 matrix that rotates each vector by an angle alpha, then what can be said about its eigenvectors?
Can there be a continuous function f:[a,b] to Q(rationals) ?

(Added on 01-12-2021)

🎯 IIT Kharagpur PhD Interview 2021 Questions (Anonymous Share)

“ Thank you sir for your effort for making us available such questions!”

The interview was for 30 mins. Area of interest: graph theory.

1st 10 mins, they show the 1st 5 questions which I had to solve in 10mins. Next few questions they asked verbally.

Note: These are the memory based questions. Some small differences may be there.

K_4 is planar?
What is spanning tree?
Every graph is tree?
How can one represent graph in a computer?

🎯 IISc Banglore PhD Interview 2021 Questions (Anonymous Share)

Let G be a finite group and G/Z(G) is cyclic then show that G is Abelian.
Is the series (n=1 to infinity) [2+sin(n)]/n converge?
If f:[0,1] to R is continuous function and Integral from 0 to 1 f(x) dx = 0. Then, does there exists x in [0,1] such that f(x) = 0 ?

(Added on 24-11-2021)

🎯 NBHM PhD Interview 2021 Questions (Anonymous Share) (This Student got selected in NBHM ).

I am very thankful to Mr. P kalika sir. Your videos helped me a lot.

🎯 Interview Questions for PhD Admission at IIT Hyderabad (Anonymous Share).

1) Tell us about your favorite theorem in Linear Algebra. Prove it. Why do you like it? 2) What is the Characteristic Polynomial of a matrix? 3) What is the Rank of the matrix? How do we find it?

(Added on 19-11-2021)

🎯 Interview Questions for PhD at IIT Jodhpur dated 18-11-2021 (Anonymous Share).

🎯 NBHM PhD Scholarship 2021 Interview Questions (Anonymous Share) (This Student got selected).

(Added on 07-11-2021)

🎯 NBHM Phd Scholarship 2021 Interview & IMSc Phd Admission 2021 Interview Questions (Anonymous Share) (This Student got selected in NBHM ).

(Added on 22-10-2021)

I have appeared for BITS Pilani Interview and have been selected in it as well. I don’t remember the questions, but they were just 3-4 and one of them was what is the Nilpotent Group? Interview was very easy.

I have also appeared for the NBHM Phd Scholarship Interview and have been selected.

The questions are as follows:

If the order of a group G is >3, then find two automorphisms of G.
Can we always find a real polynomial f(x) such that f(1) =2 and f(4) =7? What if f(a) = b and f(c) =d (a,b,c,d are all real)? [Hint: Vandermonde Matrix]
Can we always find a real polynomial f(x,y) such that f(1,2) =2 and f(4,7) =9? What if f(a,b) = c and f(d,e) =f (a,b,c,d,e,f are all real)? [Hint: Chinese Remainder Theorem]
Given a continuous function f:R to R satisfying f(x+y)=f(x)+f(y). Find f(x). Justify.

I have also appeared for IMSc Phd Interview . The questions are as follows:

Given a group G, H is an index 3 subgroup of G. Then either H is a normal subgroup or there exists a subgroup N in H which is normal in G and has index 2 in H.
Suppose {a_n} is a sequence of real numbers, fix L in R(real numbers). Assume that for every subsequence {a_n_k} there exists a further subsequence {a_n_k_p} which converges to L. Show that {a_n} is convergent to L.
Show that Image of a non-constant entire function is dense in C(complex numbers)?

🎯 Some memory based ques from today’s DUET Mphil/PhD exam. (Shared by Kirandeep Kaur )

(Added on 04-10-2021)

Download PDF

🎯 Hello sir recently I experienced NBHM PhD interview and sending my interview questions here. (Shared by Parna Saha)

(Added on 22-09-2021)

First they asked my preference and I said abstract algebra. Then they asked two questions from the nbhm phd written test. One is prove the formula ” number of idempotent elements in Zn = 2^d” And another one from linear algebra and I answered the question in written exam wrong but still they said to try there… Then they ask

What is class equation?
What is the cardinality of center of a group of order 27? Explain it by the help of class equation.
Number of Homomorphism from S3 to Z6? Explain.
Let A,B are closed sets in R. Consider the set dist(A,B) defined by {|x-y|:x in A,y in B} = 0 then what can you say about the intersection of the sets A and B.
One question from topology which I didn’t remember.

Suggestions: If you are appearing nbhm interview try to read the proofs of the formula we generally use and prepare your nbhm exam questions..all of them And whatever your preference can be…they ask question from real analysis and topology.

🎯 I am attaching here pdf of questions asked in PhD interviews at IIT, IIIT, and IISER. These are collection of questions based on my experience of one year (Shared by Divya ).

(Added on 21-09-2021)\

Download PDF shared by Divya: Click Here

🎯 Hello here is the question of PhD interview University of Calcutta (Ballygunge Science College) pure Mathematics (Shared by Amitabha Bhattacharya )

(Added on 21-09-2021)

🎯 IISER Mohali PhD Interview 2021 Questions (Anonymous Share)

(Added on 08-08-2021)

Give some examples of non- commutative rings.
What are the ideals in the ring M_2(R)?
Consider a ring R and an ideal I, and if it contains some invertible element. What is special about this ideal?
Let f: C to C is an analytic function. Let P(z) = a_0 + a_1 z + … + a_n z^n is a n degree polynomial. Also P(f) = 0. What can we say about this function?
A function function in real is always continuous? If yes then prove. If not then give a counter-example.
Which type of discontinuities does an increasing function have?
Do we have any homomorphisms from S_3 to Z_6? Justify.
Is there a continuous map from [0,1] to (0,1)? Why/Why-not?
Construct a surjective map from (0,1) to [0,1].
Construct a bijective map from (0,1) to [0,1].

🎯 IIIT Delhi PhD Interview 2021 Questions (Anonymous Share)

What is Quotient group? How to define it. What is the equivalence relation here?
What is a Factor ring?
Let G/H be a factor group. Why do we require H to be a normal subgroup.
Give an example of a group G and its non-normal subgroup H such that G/H is not a group.
What is a Field Extension?
When do we say a field extension is finite?
Is every finite field extension algebraic?
What about the converse? Give a counter-example. Prove it.
What is an Algebraically Closed Field?
What is the difference between Algebraic Closure and Algebraically Closed Field?
Give an example of an Algebraically Closed Field?
Give an example of a non-Algebraically Closed Field?
Let p be prime and consider the polynomial 1+x+x^2+…+x^(p-1) over Q. Is it reducible or irreducible. Why
What is the splitting field of the above polynomial?
What is a general linear group?
What is the order of GL(2,Z_p)? How.

🎯 NIT Patna PhD Interview 2021 Questions (Shared by Soubhik Paramanik )

(Added on 31-07-2021)

🎯 NIT Allahabad PhD Interview 2021 Questions (Anonymously Shared )

(Added on 26-07-2021)

State existence and uniqueness theorem
Define Leibnitz condition
y’=siny is linear or non linear? Why?
y’=√y what is it’s degree
Define regular singular points.
Is it possible to find series solution using regular singular point.
Define indical equation
Value of integration of exp(x²) , limit is from 0 to infinity
f(x)=x|x| differentiable at x=0 or not , if yes what is the value of f'(0)
How to find tangent plane of f(x,y,z)=0
What is equation of plane

🎯 IIT INDORE PhD Interview 2021 Questions (Anonymously Shared )

(Added on 23-06-2021)

What is dim of R(Q)?
Why dimension is infinite?
Any n dimension vector space over Q is countable or not
f(x) = x sin(1/x) for x≠0, f(x)=0 for x=0Is f(x) continuous ?
Why limit of sin(1/x) does not exist at x=0 ?
The given function in que 4 is differentiable or not?
If the function is continuous then its derivative is continuous?
f(x) = x² sin(1/x) for x≠0, = 0 for x=0 is continuous. Then it is differentiable. What if we replace x² by x³?
In general f(x) = x^alpha sin(1/x^beta) for x≠0, = 0 for x=0 Condition on alpha beta for differentiability
sin(1/x) as x tends to zero range of limit
What is Sturm Separation Theorem?
y1=x & y2= sinx then can you form second order differential equation
V=P5(x) (R) Let set {1,x}Prove it is LI
v1 & v2 are any two vector in 2 dim plane the line joining point v1 & v2 passing through origin is LI or LD

🎯 IIT Bhubneswar PhD Interview 2021 Questions (Shared by Radhanandan Mandal ).

🎯 IIT Jodhpur PhD Interview 2021 Questions (Anony mously Shared )

(Added on 16-06-2021)

What is Chinese Remainder Theorem
Application of Chinese Remainder Theorem
What is Prime Number
Chinese remainder theorem in Ring Theory
What is an Irreducible Element
What you know about set of Integers
What is relation in Prime element & Irreducible element

🎯 IISc Bangalore PhD Interview 2021 Questions (Thanks to Lalbahadur Sahu )

🎯 IIT Mandi PhD Interview 2021 Questions (Anonymously Shared )

(Added on 15-06-2021)

State and explain existence and uniqueness theorem of ODE.
What is ODE ? What is PDE ?
What is order and degree ?
What is characteristics equations ?

Email Address

Subscribe Us

🎯 IIT Delhi PhD Stage-1 Interview 2021 Questions (Anonymously Shared )

🎯 Anonymously Shared – 1

Definition of Differentiability
f(x) = x sin(1/x) for x≠0, = 0 for x=0 is diff. or not. Prove it.
Definition of continuous function. Give an example of Discontinuous function.
If A & B are 2×2 matrices such that AB =0 then BA=0 ?
In above question, if (AB)²=0 what about BA² ?
In group G if every non identity element has order 2 then is it Abelian group? If yes, Prove it.
Let G be a group of odd order, F: G to G defined as F(x) = x². Is it a homomorphism? If yes, prove it.

🎯 Anonymously Shared – 2

Def. Of open ball.
Def. Of closed ball.
Def. Of boundary point.
[0,1] Union [7,9] center 8 and radius 1 boundary point Or isse related kya puch rahe samajh nhi aaya
Complex se fundamental theorem ka proof.
Difference between differential function and analytic function.
Analytic function, singular point, CR equation, types of singularity, examples of isolated singularity.
df/dzbaar = 0 wala result proof kro

🎯 Anonymously Shared – 3

If a subring of a ring is integral domain, does it imply Ring is also an integral domain?
Definition of Integral domain.
A given n×n non invertible matrix will be a zero divisor or not?
Is S a subgroup of G?
Is S a normal subgroup of G
Def of similar matrices
does there exist some infinite group having only finite no. Of subgroups?
There are infinitely many prime numbers. Proof.
If f is non negative continuous function such that [integral (0to1) fdx]=0
Then what can u conclude about f?
√x is Uc. Why so?

🎯 Anonymously Shared – 4

🎯 Interview Questions for PhD Admission 2021 at IISc Bangalore ( Shared By Sayan Roy )

(Added on 12-06-2021)

🎯 Interview Questions for PhD Admission 2021 at IIT Hyderabad (Anonymously Shared )

(Added on 11-06-2021)

I have given an online PhD Interview for IIT Hyderabad. The questions are as follows:

Is the collection of all polynomials of degree at most 2 over the field of reals a vector space?
Now the function that p(x) goes to its derivative, is it a Linear Transformation?
Give its Matrix Representation.
Is the matrix diagonalizable? Why/Why not?
Prove that a Nilpotent matrix is diagonalizable if and only if it is a zero matrix.
Give examples of 2000 (or infinitely) rings.
Give infinite examples of fields of characteristic 0.
Give infinite examples of Galois extensions.
What is the degree of a field extension?
What is the degree of the extension Q(w_n) over Q, where w_n is n-th root of unity.

🎯 Interview Questions for PhD Admission 2021 at IISER Kolkat a (Anonymously Shared )

(Added on 10-06-2021)

🎯 PhD Admission 2021 IIT Delhi interview quest ion… ( Shared by Sandeep )

(Added on 09-06-2021)

🎯 PhD Admission 2021 IISER Kolkata telephonic interview questio n… (Anonymously Shared )

(Added on 08-06-2021)

How many finite algebraically closed fields are there upto isomorphism?
how many fields of order 12 are there upto isomorphism?
what is caley hamilton theorem?
how can we represent all those primes which are of the form -sum of 2 integer.
series (n^1/n -1) is convergent or divergent.
series (n/(n+1))^(1/n) convergent or divergent. ?

🎯 PhD Admission 2021 Interview Que. Asked at IIT Mandi ( Shared by Dhiman Das )

(Added on 28-05-2021)

● sir maine linear algebra and pde mai interview diya

◆ linear algebra se eigen vector defination

◆ null vector eigen vector ho sakta hai kiya ??

◆ diagonalisibility se and A*A’ diagonalisble or not ase question kiyaa

◆ pde se classifiacation se kuch question kiya

◆ and heat wave de almbert se question kiya sir

🎯 PhD Admission 2021 interview Que. Asked at IIT Kharagpur (Anonymously Shared )

Expand f(z)=1/z(z-2) by Laurent series expansion in the domain 0<|z|<2 and 2<|z|<infinity.
How do these two series differ?
What are different iterative methods for solving system of equations?
How is Gauss Jacobi method different from Gauss Seidel method?
Which of the above has better convergence?
When does the Gauss Jacobi method converges?
What is meaning of diagonally dominant matrix?
Is a diagonally dominant matrix invertibe?
Is the function f(x)=x^2-y^2 harmonic?

📚 (Suggestion) 👉🏻 Questions asked are easy so one has to be clear about all fundamentals while preparing for interview.

🎯 PhD Admission 2021 interview Que. Asked at IISc Banglore ( Shared By Sandip )

One of my friends give interview(today) in iisc bangalore for integrated phd..

🎯 PhD interview questions Asked at IIT Mandi ( Shared by Manisha Agarwal)

(Added on 25-05-2021)

Definitions of field, ring, vector space, field extension, linear transformation
Application of field and field extension
Collection of all polynomial form a vector space or not?
Collection of all polynomial of degree greater than or equal to n is subspace or not?
Collection of all polynomial of deg less than or equal to n form subspace or not?
If subspace then give any linear transformation on this.

📚 Their Suggestions…

Sir please try to cover latex and mtlab computer applications which we require in phd interview…try to cover as soon as possible.

As they ask that do u know any computer applications like latex and matlab I think it is also one of the factor so that anyone got selection or not

🎯 PhD interview questions Asked at IIT Guwahati (Topic: Real Analysis) ( Shared by Harinand Singh)

Sequence of function x^n [0, 1] uniform cgt Or not.
Above question on [0, 1)
Examples of continus function
Range of polynomial
Example of a nonconstant poly which
Rang is bdd.

📚 Their Suggestions …

This was my first interview, According to me, jisme intersted h us topic ko ache se taiyar kre aur basic bhi. Maine unhe ode bola but O bole kisi aur me interested h to maine real bola O bs real se hi Sare question puche aur thodi bahut help bhi krte h

🎯 PhD Interview Questions Asked at IIT Mandi (Topic: PDE ,& ODE ) ( Shared by Shadhank )

I have appeared in IIT Mandi PhD interview.

The questions were from topic PDE & ODE. The questions were as follows:

Classify second order PDE with examples of each one? Which type of PDE is classified in these categories (Hyperbolic, Parabolic & Elliptic)?
From where the Characteristic Equation comes in such PDE and on the basis of roots of which how we decide the above classification?
Classify the homogeneous Laplace Equation in two dimension. (which is also a second order PDE)
What is degree and order of a differential equation?
What is Initial Value Problem? Why it is called as IVP? Is IVP holds for the differential equation having order greater than one? (Discuss)
What is Boundary Value Problem?
What are the boundary conditions and how many types of boundary conditions are there? How it it different from Initial Condition?
What is Sturm-Liouville’s Problem? Is it regular or not?
How many types of BVP? What is regular BVP?
Is Heat equation in one dimension an IVP or BVP?

🎯 Some of the PhD Interview Questions that were asked to me in the academic year 2020-2021. The interviews were held online ( Anonymously Shared )

(Added on 10-05-2021)

Interview Questions in IIT Delhi.(Round 1)

Give an example of an ode such that f(x,y) does not satisfy the Lipschitz’ condition, but still a solution exists.
What is the most important theorem on finite groups? State and sketch the proof.
State Sylow’s Second Theorem.
If the Correspondence (aH)(bH)=(abH) defines the binary operation on the Set of distinct left cosets of H in G. Is H a normal subgroup in G?
What was the need of an orthonormal basis, when we already had a standard ordered basis?

Interview Questions in IISER Kolkata.(Round 1: Telephonic)

Prove that R is a field if and only if R[x] is a P.I.D.
Does R/p become an integral domain if we have only R as a commutative ring without unity and p a prime ideal in R.?
Give an explicit form of the prime ideals in the ring Z*Z.
If R is a ring such that every subring in R is an ideal in R, prove that R is either isomorphic to Z or isomorphic to Z/nZ.
Does there exist a non-commutative ring of order 15?

Interview Questions in IISER Kolkata.(Round 2: Google Meet)

Is every complex matrix diagonalizable?
Prove that rank(A*A)=rank(A).
Relation between the minimal and characteristic polynomial of similar matrices.
If G and H are Abelian groups, M and N are their subgroups respectively, such that G is isomorphic to H, M is isomorphic to N, then is G/M isomorphic to G/N?
Let f be an onto ring homomorphism from a PID R to an Integral domain S, such that f is not injective, prove that S is a field.
what is the dimension of R[x,y]/<x^3,y^2> as a vector space over R?
How many irreducible polynomials are there in Z_2[x]?
Show that in a finite group of odd order every element has a unique square root.
Prove that the image of a non constant entire function is dense in C.

🎯 This Interview Experience is Shared by Gautam Kaushik (PhD Aspirant 2021 ).

🔢 PhD Interview Questions Shared by ‘Ritika Das’ (PhD Aspirant 2021 ).

Interview Questions Asked at Visva Bharati University , Kolkata .

🎯 PhD Interview Questions & Suggestions Shared by ‘Prince Bharti’ (PhD Aspirant 2021 ).

I admitted PhD in January 2021 session at Hyderabad Central University.

I selected subjects for interview namely Differential equations and Fuzzy Theory. Because I do project in MPhil on Fuzzy Theory so it’s beneficial for me. They ask some questions about my project.

And from Differential equations they ask from SLP and BVP , what is the difference between them, and example of these, and knowledge about boundary conditions that’s it.

Thank you sir 🙏

📚 (Our Question) Any Suggestions from your Side…

Yes sir according to me , interview k liye apna ek subject tyyar kr ke jana chahiye, or uske main main topics per command ho and given conditions , related examples ko dhyan se smajhna kafi halpful rhega. Jiska nhi pta use dheere se sorry bol de or apni pasand ka topic unhe bta do bss , ab aap tyyar rhe sb kuch usi me se poocha jane wala h😊😊 that’s it. Thank you sir.

Ye bhi add kr lena, aapke notes kafi useful rhe mere addmission m , thank you very much sir 🙏 , isi tarah se hmari help krte rhiye …

🎯 PhD Interview Questions & Suggestions Shared by ‘Sanket’ (PhD Aspirant 2021 ).

Recently I’ve appeared for VIT Vellore and BITS Pilani interview. Here I’m providing my Interview Questions in handwritten format…

” Just prepare some basics … Means whatever you are going to tell about research interests. Prepare basics nicely. Prepare one favourite theorem. Lots of example and counter examples”

🎯 PhD Interview Questions & Suggestions Shared by ‘Sanjeev ‘ (PhD Aspirant 2021 ).

Hello sir I was asked few questions in Tezpur Univ phd interview

Shift operators
Formula for Sequence of rationals that converges to a given irrational c
Difference between hamel and schauder bases and benefits or need of schauder basis
Idea of Cantor’s set and its prop and proof sketch of some of the prop
Basic on group theory

Thank you very much for providing useful tips and updating us on events happening in Mathematical world.

Hello Sir…my suggestions are One may clear the competitive exams but clearing interview is completely different. We need to have good knowledge of topics. Must read standard books (including proofs) like Bartle for Analysis, Gallian for Algebra, etc. Avoid random guess because one wrong answer would expose all your weaknesses. If you don’t know the answer them simply say I can try try and after try if could not get answer then say that you don’t know the answer… Logical implications must be sound.

Note: This page is under construction…