Algebra constitutes nearly 30% of the NDA Mathematics paper, making it the most critical section for candidates. Our quick revision notes focus on Set Theory, Complex Numbers, Quadratic Equations, and Binomial Theorem. Mastering these high-weightage topics through consistent practice is the definitive pathway to securing a qualifying score in 2026.
What is the Exam?
The National Defence Academy (NDA) examination is a prestigious national-level entrance test conducted by the Union Public Service Commission (UPSC) twice a year. It serves as the gateway for young aspirants to join the Indian Army, Navy, and Air Force wings of the NDA. The selection process is a rigorous two-stage journey: a written examination followed by the Service Selection Board (SSB) interview, which evaluates the candidate's intelligence, personality, and physical fitness.
Key Highlights 2026
- Conducting Body: UPSC
- Exam Mode: Offline (Pen and Paper)
- Paper Level: Higher Secondary (10+2) level
- Total Marks (Mathematics): 300
- Total Questions: 120
- Negative Marking: 0.83 marks deducted per incorrect answer
- Algebra Weightage: Approximately 35–40 questions
Syllabus 2026
Algebra is the backbone of the NDA Maths paper. Below is the breakdown of the essential chapters you must prioritize for your quick revision notes.
| Topic | Key Concepts for Revision |
|---|---|
| Sets and Relations | Power sets, Venn diagrams, Cartesian product, equivalence relations |
| Complex Numbers | Modulus, argument, cube roots of unity, polar form |
| Quadratic Equations | Roots relations, nature of roots, complex roots |
| Sequences & Series | AP, GP, HP, sum of $n$ terms, arithmetic-geometric series |
| Logarithms | Properties of logs, base change formula, expansion |
| Binomial Theorem | General term, middle term, coefficients |
| Permutations & Combinations | Fundamental counting principle, circular permutation |
Exam Pattern
The Mathematics paper is a specialized test that requires speed and accuracy. To excel, you must practice free mock tests for Defence on Exam Bhai to simulate the high-pressure environment of the examination hall.
| Paper | Subject | Duration | Total Marks |
|---|---|---|---|
| Paper I | Mathematics | 2.5 Hours | 300 |
| Paper II | General Ability Test | 2.5 Hours | 600 |
Eligibility Criteria
As per the official notifications published on upsc.gov.in, candidates must adhere to the following:
- Nationality: Citizen of India, subject of Nepal/Bhutan, or Tibetan refugee who settled in India before January 1, 1962.
- Age Limit: Must be between 16.5 and 19.5 years at the time of commencement of the course.
- Educational Qualification:
- For Army Wing: 12th class pass of the 10+2 pattern of School Education or equivalent examination conducted by a State Education Board or a University.
- For Air Force and Naval Wings: 12th class pass with Physics, Chemistry, and Mathematics.
Application Process
- Visit the official UPSC website at upsc.gov.in.
- Fill in the One-Time Registration (OTR) profile.
- Navigate to the 'Active Examinations' tab and select 'NDA & NA Examination'.
- Pay the requisite fee (exempted for SC/ST/Sons of JCOs/NCOs/ORs).
- Select your exam centre and submit the application. Ensure you keep a printout of the confirmation page.
Preparation Strategy
We at Exam Bhai recommend a structured approach. Algebra is formula-heavy and requires conceptual clarity rather than rote learning.
- Formula Sheets: Maintain a dedicated notebook for algebraic identities.
- Strategic Practice: You should attempt previous year paper analysis for Defence on Exam Bhai to identify repetitive patterns in questions regarding Complex Numbers and Quadratic Equations.
- Time Management: Since you have 150 minutes for 120 questions, you must learn to skip lengthy calculations. If you find a question taking more than 90 seconds, mark it for review and move on.
- Consistency: Regularly access curated revision study materials for Defence on Exam Bhai to stay updated with the latest trends.
Cut-Off Trends
Historical data sourced from upsc.gov.in suggests that the qualifying mark per subject typically hovers around 25% to 30%. However, the final recommended cut-off is significantly higher. For the written examination, scoring above 350 out of 900 is generally considered a safe threshold for interview calls, but for Mathematics specifically, aiming for a score of 120+ provides a significant competitive advantage.
Frequently Asked Questions
Q1: How many questions are asked from Algebra in the NDA exam? Ans: Algebra typically accounts for 35 to 40 questions out of the 120 questions in the Mathematics paper, making it the highest weightage segment.
Q2: Is NCERT sufficient for NDA Algebra? Ans: NCERT is excellent for building foundational concepts. However, for the competitive edge required for NDA, you must supplement it with advanced practice sets and previous year questions.
Q3: What are the most important chapters in Algebra? Ans: Focus heavily on Complex Numbers, Quadratic Equations, and Permutations & Combinations as these appear frequently.
Q4: Should I use a calculator for Algebra problems? Ans: No. Calculators are strictly prohibited in the NDA examination. You must practice mental calculation and shortcuts.
Q5: How can I improve my speed in Mathematics? Ans: Speed comes from identifying the nature of the question within seconds. Regular mock tests and memorizing standard algebraic results are key.
Q6: What if I am not from a PCM background? Ans: While you can still apply for the Army wing, you will still face the same Mathematics paper as the PCM students. You must dedicate extra time to mastering the basics of algebra to cross the subject cut-off.
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