NBHM EXAM National Board for Higher Mathematics FOR MSC & PHD 2025 2026 PAST YEAR COMPLETE SOLUTION SUGGESTION MOCK TESTS SPECIAL TRICKS
NBHM Exam 2025–2026: Complete Guide for MSc & PhD Aspirants
Past Year Solutions, Suggestions, Mock Tests & Special Tricks
Introduction to NBHM Exam
The National Board for Higher Mathematics (NBHM) conducts a competitive exam every year to provide scholarships for MSc and PhD students in mathematics. If you're aiming for NBHM 2025–2026, this article will give you a complete roadmap, including past year solutions, suggestions, mock tests, and expert tips to help you ace the exam.
Why NBHM Exam Matters?
Scholarship Opportunity: Top-performing students receive NBHM scholarships for MSc and PhD programs.
Gateway to Research & IITs: Many students use this as a stepping stone for research opportunities in prestigious institutes like TIFR, ISI, IITs, IISc, and CMI.
Challenging Yet Rewarding: The exam tests deep mathematical understanding rather than rote learning.
NBHM Exam 2025–2026: Important Details
Exam Details | Information |
Conducting Body | National Board for Higher Mathematics (NBHM) |
Exam Level | National |
Eligibility | MSc & PhD Mathematics aspirants |
Mode of Exam | Offline |
Subjects Covered | Algebra, Analysis, Linear Algebra, Number Theory, Combinatorics, Calculus, and more |
Scholarship Offered | ₹6,000 to ₹35,000 per month (varies by level) |
Official Website |
NBHM Exam Pattern & Syllabus (Updated for 2025–2026)
The NBHM Exam focuses on conceptual understanding rather than memorization. Here’s a breakdown of the pattern:
NBHM Exam Pattern
Duration: 150 minutes (2.5 hours)
Number of Questions: ~30 (Varies)
Types of Questions:
Multiple Choice Questions (MCQs) – 10 Questions
Short Answer Type Questions – 10 Questions
Long-form Descriptive Questions – 10 Questions
NBHM Exam Syllabus
Real Analysis (Sequences, Series, Limits, Continuity, Differentiability)
Linear Algebra (Vector Spaces, Matrices, Determinants, Eigenvalues)
Abstract Algebra (Groups, Rings, Fields, Homomorphisms)
Number Theory (Divisibility, Modular Arithmetic, Prime Numbers)
Combinatorics & Probability
Calculus & Differential Equations
📌 Tip: While the syllabus is similar to MSc entrance exams, NBHM focuses more on problem-solving and proofs rather than direct applications.
Past Year NBHM Question Papers & Solutions (2015–2024)
One of the best ways to prepare is by solving past year papers. Here are some key insights from previous years:
Year | Exam Difficulty Level | Most Asked Topics |
2024 | Moderate | Linear Algebra, Number Theory |
2023 | Tough | Real Analysis, Abstract Algebra |
2022 | Easy-Moderate | Probability, Combinatorics |
2021 | Moderate | Differential Equations, Algebra |
2020 | Hard | Metric Spaces, Group Theory |
💡 Where to Get Past Papers?
Visit NBHM Official Website
Join Telegram Groups & Online Forums for solutions
NBHM Preparation Books (TIFR, IIT JAM Books are also useful)
NBHM Ph.D. 2025 Eligibility Criteria
Candidates for NBHM Ph.D. Qualifications include a strong interest in mathematics and a master’s degree in mathematics or statistics (pure or applied). Alternatively, they may be final-year students in these degree courses. A consistently good academic record with a first-class or equivalent grade from the Plus Two level is required.
Educational Qualification:
Candidates who have completed a B.Sc. (Honours) course with a second class are eligible to apply, provided they either hold a master's degree or are in the final year of the program.
Those holding a four-year B.S. (or equivalent) degree, or in the final year of such a program, can also apply. However, eligibility for the NBHM scholarship is contingent upon securing admission to a recognized Ph.D. program by August 2025.
Students applying for Ph.D./Integrated Ph.D. programs at HRI, IISER Pune, IMSc, or NISER must participate in the written test. Apart from the previously mentioned students, those with a B.Sc./B. Stat/B.S./B.Tech/B.E degree or in the final year of such courses can apply, provided they maintain a consistently good academic record from the Plus Two level.
Age Limit:
There is no upper age limit for NBHM, with the focus primarily on educational qualifications. Eligibility is determined by the completion of B.S./M.A/M.Sc (or equivalent) degree and securing admission to a recognized Ph.D. program on or before August 2025.
NBHM Ph.D. 2025 Application Form
NBHM applications should be submitted on plain paper following the prescribed format provided in the official notification. The completed application form for NBHM Ph.D. Admission 2025, along with a recent passport-sized photograph and a self-addressed envelope, should be sent to the official address.
Important Notes:
NBHM applications for Zone 1 will be accepted online only, and hard copies will not be entertained in Zone 1.
The application fee for applications completed on or before Dec 2025 is INR 500.
For NBHM applications completed after Dec 2025, the application fee will be INR 650.
How to Apply for NBHM Ph.D. 2025: Step 1 - Registration:
Step 1 - Application:
Register on the portal and create a profile using a valid email address.
Step 2 - Application:
Log in to the portal with the registered email address and password.
Provide details about yourself and select the preferred zone.
Confirm the accuracy of the entries and proceed to the fee payment process.
After successful payment, a generated application number will be provided.
Download the receipt-cum-pre-admission-ticket.
The receipt-cum-pre-admission-ticket will also be sent to the registered email.
Step 3 - Admit Card:
Make two photocopies of the receipt-cum-pre-admission-ticket.
Complete the postal address for correspondence, paste a recent color photograph, and enter your roll number and signature on each photocopy.
Wait until the center-wise lists of candidates are published to find your roll number.
Bring both original copies of your admission ticket to the test center.
NBHM Ph.D. 2025 Exam Centers
NBHM’s written test is going to be performed offline beneath the centers allocated as various zones. The required information on the exam center will be placed on the NBHM Admit Card. Candidates may go to the place where the test will be held once at least one day before the test so that they do not have any issues on the day of the test. Candidates must also have to bring a legitimate photo identification form to the exam-taking center.
NBHM Ph.D. 2025 Exam Pattern
NBHM candidates are required to participate in a written examination, which will have questions based on topics commonly covered in mathematics master degree programs. The duration of the NBHM exam is set at 150 minutes and will include short answer questions. The performance in NBHM Written Examination will determine the shortlisted candidates for interview, which is an important step in the final selection process. Previous question papers from previous years will be available for reference on the NBHM website as well as on the IMSc website..
NBHM Ph.D. 2025 Syllabus
As this is a Ph.D. course, the syllabus is not rigidly structured and predefined; Instead, courses are included at both the undergraduate (UG) and postgraduate (PG) levels of mathematics. The questionnaire is divided into three sections, each covering specific areas. For more information on the course design and components, please see below.
Section A: Algebra Syllabus
The NBHM Algebra syllabus encompasses various subtopics, including:
Abstract Algebra
Set Theory
Binary Operations
Matrix Theory
Groups Algebra
Rings and Fields
Polynomials (Calculus, Matrix Polynomials, Roots)
Section B: Analysis Syllabus The Mathematics
Analysis syllabus is primarily divided into three sections: Complex, Functional, and Real. Candidates are advised to thoroughly cover these extensive topics. The detailed NBHM Analysis Syllabus is as follows:
Complex Analysis Syllabus
Polar Coordinates
Poles and Residues
Real Analysis Syllabus
Sequence and Limits
Metric Spaces
Series (Infinite Series Expansion, Taylor Series Expansion)
Functional Analysis Syllabus
Continuous Function
Maxima and Minima
Differential Function
Defining Function
Section C: Geometry Syllabus
The NBHM Geometry syllabus primarily comprises two sub-topics. Please see below for more details:
Plane Algebraic Syllabus
Line
Circle
Ellipses
Elliptical Curve
Cubic Curves
Spheres (3D Shapes)
Algebraic Geometry Syllabus
Polar Coordinates
Cartesian Coordinates
NBHM Ph.D. 2025 Result
The results of the NBHM methodology are generally available on the web. Instead of publishing individual results, a full list of candidates showing the names of the nominees is published. Follow the steps below to check NBHM results
Step 1: Visit the NBHM website.
Step 2: Look for the NBHM notification and click on it.
Step 3: Navigate to the link corresponding to your Zone.
Step 4: Verify if your name is listed; if selected, take a printout for reference.
NBHM Ph.D. 2025 Counselling
The NBHM 2025 consultation process will be published on the official website soon. It is noteworthy that NBHM has a limited number of seats, leading to fierce competition. Once the results are published, the selected candidates will receive an invitation to join, which includes additional services such as verifying documents. As an NBHM applicant, it is important that you are well equipped with all the necessary documents.
IISER Pune, IISER Mohali, NISER, IMSc, etc. will publish their individual admission details considering NBHM scores for admission. NBHM itself will not provide any login details. Candidates are advised to apply to these institutions separately, as each college will have a specific counseling program. During the counseling process, candidates will be required to submit academic records along with an introduction and personal information.
How to prepare for NBHM?
The NBHM test is designed for candidates who are dedicated to or have already devoted their lives to the field of Mathematics. Those appearing for the NBHM face intense competition, as candidates from all over the nation seek the scholarship and admission through this test. Moreover, the syllabus and difficulty level of the exam are at a high proficiency level. Candidates are required to thoroughly prepare and study topics at both postgraduate and graduate levels.
NBHM Previous Year Papers:
Candidates can access NBHM's previous year question papers and mock test papers on the Institute of Mathematical Science (IMSC) website, the official body hosting the exam. Preparing through mock test papers is a wise step to secure good marks in the NBHM exam. To obtain NBHM Previous Year Question papers, candidates can visit the IMSC website, click on the NBHM Model Questions tab on the homepage, and find a list of question papers and answer keys. Clicking on the question paper link will open it in a new tab in PDF form.
NBHM Interview Preparation:
For NBHM interview preparation, candidates can refer to mock interview videos available online. Based on feedback from previous candidates, it has been observed that questions beyond the core mathematics syllabus are also asked, primarily to assess a candidate's conviction and commitment to NBHM.
NBHM Ph.D. 2025 Scholarship
Successful candidates will be awarded a scholarship of INR 25,000 per month for the first and second years, followed by INR 28,000 per month for subsequent years. Additionally, they will receive a contingency grant of INR 32,000 per year and a house rent allowance under central government norms wherever applicable.
NBHM scholarships typically cover a period of four years, sanctioned on an annual basis, and are subject to renewal at the end of each year, contingent upon satisfactory progress. The scholarship amount may be increased after evaluation by the Board after the second year. If deemed appropriate, the scholarship may be extended for a fifth year at the discretion of NBHM.
To avail themselves of the NBHM scholarship benefits, successful students must enroll in a recognized Ph.D. degree program, and the scholarship will be disbursed through the institution they join. Part-time research students are not eligible for this scholarship.
Best Books & Study Materials for NBHM 2025–2026
Top Books Recommended by Toppers
📚 Real Analysis – Principles of Mathematical Analysis by Walter Rudin📚 Linear Algebra – Linear Algebra Done Right by Sheldon Axler📚 Abstract Algebra – Topics in Algebra by Herstein📚 Number Theory – An Introduction to the Theory of Numbers by Hardy & Wright📚 Combinatorics – Discrete Mathematics by Kenneth Rosen
📌 Tip: Instead of just reading books, solve problems rigorously. NBHM tests how well you apply concepts, not just your theoretical knowledge.
NBHM 2025–2026: Special Tricks & Strategies to Score High
🔥 1. Master Proof-Writing Skills
Many NBHM questions require proof-based solutions, so practice writing structured, logical proofs.
Learn different proof techniques: Contradiction, Induction, Direct Proof, etc.
🔥 2. Focus on High-Weightage Topics
Linear Algebra, Real Analysis, and Number Theory carry significant weight.
Abstract Algebra & Probability have moderate importance.
🔥 3. Take Timed Mock Tests
Simulate real exam conditions by taking mock tests regularly.
Analyze your mistakes and focus on weak areas.
Solve at least 5–7 past papers before the actual exam.
🔥 4. Join Online Discussion Forums & Telegram Groups
Join NBHM study groups where aspirants discuss solutions, doubts, and strategies.
Engaging in discussions helps you see different approaches to solving problems.
🔥 5. Avoid Common Mistakes✔️ Don’t spend too much time on a single question.✔️ Read the question carefully—misinterpretation can lead to losing marks.✔️ Keep your solutions well-structured—examiners prefer neat, step-by-step answers.
NBHM Mock Tests 2025–2026: Where to Practice?
Mock tests help you understand your strengths and weaknesses. Here’s where you can find high-quality practice tests:
✔️ NBHM Official Website – Sample Papers & Previous Year Papers✔️ ISI, IIT JAM & TIFR Mock Tests – Many questions overlap with NBHM syllabus✔️ Dr. Sourav Sir’s Classes – Special Mock Tests & Solution Strategies
Final Words: Start Preparing Now!
NBHM is a tough but rewarding exam. With the right strategy, practice, and dedication, you can crack it and secure a scholarship for MSc or PhD studies.
🎯 Start today: Solve past papers, take mock tests, and focus on conceptual clarity.💬 Got doubts? Feel free to ask in the comments or join our NBHM Preparation Community.
🚀 Best of luck for NBHM 2025–2026! Stay focused and keep practicing!
Comments