phd maths entrance question paper

Sample Qualifying Exams

Some old departmental qualifying exams are available here (all links are PDF’s)

Some old qualifications questions from 1990-2002 [PDF] Some PDF files of questions arranged by topics.

• PDE’s
• C* algebras
• probability
• algebraic geometry
• differential topology
• representation theory
• algebraic topology

Collected by Danny Calegari and Tom Coates.

• banach spaces
• fluid mechanics
• combinatorics
• foundations
• measure theory
• commutative algebra
• galois theory
• noncommutative rings
• universal algebra
• complex analysis
• game theory
• numerical analysis

IIT Bombay Department of Mathematics

The m.sc mathematics programme, ph.d admissions.

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Admission to Ph.D programme in Mathematics and Statistics

2016 ). With state-of-the art infrastructural facilities and a sound research base, IITB Mathematics offers a Ph.D. programme in a wide variety of areas. The program leading to the Ph.D. degree involves a course credit requirement and a research project leading to thesis submission. All that you need to know about admissions to our PhD program can be found in the information brochure for PhD admissions, which can be found at the following link. ----- A special welcome to all who wish to pursue a career in Mathematics and Statistics research. The Department of Mathematics, IITB offers a Ph.D. program in a wide variety of areas. To know more about the research interests of faculty members, please visit the page here . The program leading to the Ph.D. degree involves a course credit requirement, clearing of qualifier examinations and a research project leading to thesis submission. For more details, follow one of the links below

A special welcome to all who wish to pursue a career in Mathematics and Statistics research. The Department of Mathematics, IITB offers Ph.D. program in the areas of Mathematics and Statistics. Admission to the PhD program is based on a written test and interview. There are separate written tests and interviews for students in Mathematics and Statistics. The syllabus is given below. Students are required to choose one option specifying either Mathematics or Statistics.

To know more about the research interests of faculty members, please visit the page here . The program leading to the Ph.D. degree involves a course credit requirement, clearing of qualifier examinations and a research project leading to thesis submission. For more details, follow one of the links below

Syllabus for Entrance exam can be found here Past question papers can be found here

Syllabus for Mathematics Entrance Exam

Syllabus for Statistics Entrance Exam

Past Question Papers

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Access phd entrance exam model question paper for effective preparation.

Access and download sample question papers for PhD-related exams to familiarize yourself with the format, content, and level of difficulty, helping you prepare effectively for your upcoming examinations. We provide entrance exam sample papers for individual subjects as wel as university-specific. To keep them relevant for you, we also include questions based on the PhD previous year question paper.

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Abstract Algebra

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Linear Algebra

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Vector Calculus

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Multivariable Calculus

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Integral Calculus

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DUET MPhil Phd in Mathematics Question Paper with Answer Keys 2019-20 Download PDF

DUET MPhil Phd in Mathematics Question Paper with Answer Keys 2019-20

DUET MPhil Phd in Mathematics Question Paper with Answer Keys 2019

Delhi University Entrance Test (DUET) 2019-20 MPhil Phd in Mathematics Question Paper with Answer Keys Free Download PDF is available in www.oldquestionpapers.net which has been provided by many students this DUET 2019-20 paper is available for all the students in FREE and also DUET MPhil Phd in Mathematics Question Paper 2019-20 fully solved DUET with answer keys and solution.

You can get daily updates on DUET 2019-20 from www. oldquestionpapers .net here  you can also check similar links for other related study materials on DUET MPhil Phd in Mathematics Question Paper question bank 2019-20 is also available in English and Hindi Language.

EXAMPLE QUESTIONS

Q1. The mathematician who was awarded Abel’s prize for a proof of Fermat’s Last Theorem is

• 1. Andrew Wiles.
• 2. Johan F. Nash.
• 3. S. R. Srinivasa Varadhan.
• 4. Lennart Carleson.

Q2. Founder of Indian Mathematical Society(IMS) was

• 1. Asutosh Mukherjee.
• 2. S. Narayana Aiyer.
• 3. M.T. Narayaniyengar.
• 4. V. Ramaswamy Aiyer.

Q3. Let R be a commutative ring with identity. If R is an Artinian domain, then the total number of prime ideals in R is

• 2. infinite.

Q4. The famous Indian mathematician Srinivas Ramanujan passed away in the year

Q5. Let F be a finite field with 9 elements. How many elements of F have order 8?

Q6. Which of the following statements is not true

• 1. An uncountable discrete space is not separable.
• 2. Every closed subspace of a separable space is separable.
• 3. Every compact metric space is Lindelof.
• 4. Every second countable space is separable.

Q7. Which of the following websites is of Mathematical Reviews

• 1. https://mathscinet.ams.org
• 2. https://mathscinet.ac.in
• 3. https://math.ac.au
• 4. https://www.mathjournal.org.

Q8. Let G be a cyclic group of order 42. The number of distinct composition series of G is

Q9. Which of the following statements is not true

• 1. The set of all algebraic numbers is countable.
• 2. The set of rational numbers is equivalent to the set of natural numbers
• Given a Set A , there exists a function f : A → P ( A ) that is into ( P ( A ) denotes power set of A )
• There is one-one function taking (– 1, 1) into ℝ

Q10. Consider the following statement:

I x 3 – 9 is not irreducible over Z 7 II x 3 – 9 is not irreducible over Z 11 Then

• 1. II is false but I is true.
• 2. both I and II are true.
• 3. both I and II are false.
• 4. I is false but II is true.

DUET MPhil PhD in Mathematics Questio n Paper with Answer Keys 2019-20 Download PDF File:

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PhD in Mathematics

Minimum Eligibility

A minimum of 17 years of education with a Master's degree in Mathematics/Computer Science/Statistics/Operations Research/Physics or an equivalent degree with 55% marks in the aggregate or equivalent grade.

Entrance Test and Interview. A minimum of 50% marks will have to be secured separately, in both the Entrance Test and the Interview, in order to be eligible for admission. The weightage of the Entrance Test will be 50% and the weightage of the Interview will be 50%.

Format of the Entrance Test Paper

• The duration of the Entrance Test will be 2 hours.
• The question paper will consist of 70 multiple choice questions.
• There will be no negative marking.
• Candidates up to five times the number of seats available will be short-listed for interview on the basis of their performance in the Entrance Test, subject to a minimum cut off.
• A final merit list will be drawn by adding together the marks of the Entrance Test and the interview.
• Calculators are not allowed. However, Log Tables may be used.
• The questions may be asked in the Entrance Test in the following areas:

Analysis:  Real functions; limit, continuity, differentiability; sequences; series; uniform convergence; functions of complex variables; analytic functions, complex integration; singularities, power and Laurent series; metric spaces; stereographic projection; topology, compactness, connectedness; normed linear spaces, inner product spaces; dual spaces, linear operators; Lebesgue measure and integration; convergence theorems.

Algebra: Basic theory of matrices and determinants; eigenvalues and eigenvectors; Groups and their elementary properties; subgroups, normal subgroups, cyclic groups, permutation groups; Lagrange's theorem; quotient groups, homomorphism of groups; Cauchy Theorem and p-groups; the structure of groups; Sylow's theorems and their applications; rings, integral domains and fields; ring homomorphism and ideals; polynomial rings and irreducibility criteria; vector space, vector subspace, linear independence of vectors, basis and dimensions of a vector space, inner product spaces, orthonormal basis; Gram-Schmidt process, linear transformations.

Differential Equations:  First order ordinary differential equations (ODEs); solution of first order initial value problems; singular solution of first order ODEs; system of linear first order ODEs; method of solution of dx/P=dy/Q=dz/R; orthogonal trajectory; solution of Pfaffian differential equations in three variables; linear second order ODEs; Sturm-Liouville problems; Laplace transformation of ODEs; series solutions; Cauchy problem for first order partial differential equations (PDEs); method of characteristics; second order linear PDEs in two variables and their classification; separation of variables; solution of Laplace, wave and diffusion equations; Fourier transform and Laplace transform of PDEs.

Numerical Analysis:  Numerical solution of algebraic and transcendental equations; direct and iterative methods for system of linear equations; matrix eigenvalue problems; interpolation and approximations; numerical differentiation and integration; composite numerical integration; double numerical integration; numerical solution for initial value problems; finite difference and finite element methods for boundary value problems.

Probability and Statistics:  Axiomatic approach of probability; random variables; expectation, moments generating functions, density and distribution functions; conditional expectation.

Linear Programming:  Linear programming problem and its formulation; graphical method, simplex method; artificial starting solution; sensitivity analysis; duality and post-optimality analysis.

Preference will be given to those opting for the research in the following areas:

• Numerical Methods
• Computational Fluid Dynamics
• Graph Theory
• Function Spaces
• Fourier Analysis
• Parallel Algorithms
• Scientific Computing
• Optimization Techniques
• Swarm Intelligence
• Mathematical Biology
• Nonlinear Dynamical System
• Bio-informatics
• Optimization
• Graph theory
• Differential Equations
• Numerical Analysis
• Mathematical Modeling

For a sample paper, click here .

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Kumaun University Ph.D. Entrance Exam Previous Question Papers PDF

Kumaun University Ph.D. Entrance Exam Previous Question Papers PDF | RDET Old Papers : All the candidates who are going to take the Research Degree Entrance Test (RDET) for Ph.D. Course are searching for Kumaun University Ph.D. Entrance Exam Previous Papers. All those candidates can download the Kumaun University RDET Sample Papers from the links given at the end of the page. Additionally, we had also given the detailed information of the Kumaun University Ph.D. Entrance Exam Pattern in the below sections. Check all the sections to know more details of Kumaun University RDET Sample Papers in the below sections.

Kumaun University RDET consists of Interviews for the shortlisted candidates in the Written Exam and this Interview is for 100 marks. And the duration will be of 2 hours . Kumaun University Ph.D. entrance Exam will be conducted for 100 Objective Type Questions (Multiple Choice Questions).

Table of Contents

Kumaun University Ph.D. Previous Question Papers

Kumaun university rdet sample papers pdf.

All the candidates who had applied for the Research Degree Entrance Test (RDET) have to solve the Previous Question Papers. Candidates can gain to know the type of questions that will be asked in the exam. At the end of the page, we had given direct links to download the Kumaun University Ph.D. Entrance Exam Previous Question Papers PDF . Also, candidates can gain more marks in the exams by solving the Kumaun University Question Papers. So, go through the complete page and then proceed for further preparation.

Kumaun University Ph.D. Entrance Exam Pattern

In this section, we had given the details of Kumaun University Ph.D. Entrance Exam Pattern. The officials of Kumaun University going to conduct the Written Test in a concerned subject for 100 marks and the duration will be of 2 hours . Kumaun University Ph.D. entrance Exam will be conducted for 100 Objective Type Questions (Multiple Choice Questions). Besides, each question carries one mark and there shall be no negative marking. Qualifying marks for the Kumaun University Ph.D. Entrance Exam are General – 50 % , OBC – 45 % and SC/ ST/ VH/ PH – 40% .

There will be no revaluation for the Kumaun University Ph.D. Entrance Exam answer sheet. Kumaun University RDET consists of Interviews for the shortlisted candidates in the Written Exam and this Interview is for 100 marks. Candidates who qualify for the Written Exam the final merit will be prepared as from 70% marks from Written Test and 30 % marks from the Interview/ Presentation.

Kumaun University RDET Sample Papers

All the candidates can download the Kumaun University Ph.D. Entrance Exam Previous Question Papers from the links given below. Candidates can download the Kumaun University Ph.D. Entrance Exam Previous Question Papers in PDF format.

Note: All the applicants have to remember that the above given Kumaun University RDET Sample Papers are only for reference use.

Further, keep checking our site @ Exams.Freshersnow.Com for all the latest updates of Kumaun University Question Papers.

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AMU Entrance Ph.D Question Papers

Are you preparing for the AMU Ph.D. Entrance Papers? In that case, you’ve found the right site! It can be frightening to take a university exam, but don’t worry; we’re here to make it as stress-free as we can.

Also Check: AMU Entrance Question Paper 2023

AMU Ph.D Papers are held annually to choose candidates for undergraduate and graduate programs. It is administered by AMU both online and offline. The test is divided into objective and subjective sections. The objective portion consists of multiple-choice questions, and the personal section is made up of essay-style questions. The test measures how familiar the candidate is with the topics.

Note: After Purchasing the Papers please wait for 10-20 sec it will redirect you to download the Paper.

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A thorough and organized strategy is necessary for preparing for the AMU Ph.D. Entrance Question Papers. You may improve your preparation and raise your chances of success by familiarizing yourself with the exam format, studying the curriculum, practicing previous years’ test questions, scheduling your time wisely, learning more about the topic, getting advice, and keeping up with current events. Never lose sight of the importance of being focused, keeping a good outlook, and persevering in your efforts. You may pass the AMU Ph.D. admission test with perseverance and the appropriate study techniques, and you can start a fruitful academic adventure.

IGNOU PHD Entrance Exam Question Paper

• 1.1 Download IGNOU PHD Entrance Question Papers

IGNOU PHD Entrance Question Paper

IGNOU PHD Entrance exam question paper of 2019, 2018, 2017 and 2016 are available at ignouhub.in for free downloading.

Students of Indira Gandhi National Open University who have to take admission in IGNOU Ph.D. programme may require previous year Entrance Question Papers to prepare for upcoming PHD IGNOU entrance test.

These old entrance question papers of PHD entrance can be easily downloaded from university official website.

However, candidates find it difficult to search and download IGNOU PHD previous year Entrance Question Papers from official website.

To make it easy for them, we have uploaded pdf files of all the previous year Entrance Question Papers of IGNOU PHD entrance test on our website.

They just need to just click on the year for which they want to download IGNOU PHD entrance exam question paper. Some students also call it as IGNOU PHD sample Entrance Question Papers.

Download IGNOU PHD Entrance Question Papers

The Indira Gandhi National Open University conducts the PHD entrance test once in a year i.e. in the month of October or November.

We have uploaded IGNOU Entrance Question Papers here. Here are the links to download previous entrance question papers:

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