NDA Maths Previous Year Questions Topic Wise

Let me be honest with you.

When students join us at Alpha NDA Academy, most of them have already spent weeks collecting notes, watching YouTube videos, and downloading PDFs. But when we sit with them on Day 1 and ask  “Have you gone through the previous year papers topicwise?”  almost nobody has.

That’s the gap. And it costs students months of wasted effort.

We’ve been coaching NDA aspirants from Sikar, Rajasthan for years now. Students come to us from Jhunjhunu, Churu, Jaipur, Haryana, Gujarat, even from Madhya Pradesh. Different states, different schools, different backgrounds. But one thing that works for every single one of them  without exception  is understanding the NDA Maths PYQ pattern before touching any textbook.

So that’s what this article is. A real, honest breakdown of NDA Maths previous year questions topicwise  not a copy/paste from the UPSC website, but what we’ve actually seen after studying 10 papers from 2020 to 2025.

First, Understand What You’re Dealing With

The NDA Maths paper is not like your board exam. Let’s get that straight.

In board exams, you have time. You can write steps, reattempt, and think slowly. NDA gives you 120 questions in 150 minutes. That’s 75 seconds per question  and if you get one wrong, you don’t just lose 2.5 marks, you lose 3.33 marks total because of negative marking.

Here’s the official breakdown from the UPSC NDA notification:

Detail	Numbers
Total Questions	120
Total Marks	300
Marks Per Correct Answer	+2.5
Deduction Per Wrong Answer	?0.83
Time Allowed	2.5 hours
Minimum to Qualify	25% (approx. 75 marks)

That minimum 25% sounds easy. But here’s the catch: the cutoff for written selection usually goes much higher once SSB marks come into the picture. So your real target should be 150+ in Maths, not 75.

To understand how this scoring works in full detail, go through our article on the NDA Marking Scheme.  We’ve explained it with real examples of how marks get lost unnecessarily.

NDA Maths Topic Wise Questions: What 10 Papers Tell Us

Since UPSC conducts NDA twice a year, 2020 to 2025 gives us 10 papers to study. We’ve mapped every chapter, counted the questions, and noted the difficulty. Here’s what the data actually looks like:

Topic	Approx. Questions Per Paper	Approx. Marks	Difficulty Level
Algebra	25–30	62–75	Easy to Moderate
Trigonometry	20–25	50–62	Easy to Moderate
Differential Calculus	10–15	25–37	Moderate
Integral Calculus	10–15	25–37	Moderate to Hard
Matrices & Determinants	10–15	25–37	Moderate
Analytical Geometry (2D)	10–12	25–30	Moderate
Statistics & Probability	10–15	25–37	Easy to Moderate
Vector Algebra	5–7	12–17	Moderate to Hard
3D Geometry	4–6	10–15	Hard
Binary, Harmonic & Others	3–5	7–12	Varies

Look at this table carefully. Algebra alone is almost one-fourth of the paper. Algebra + Trigonometry + Calculus together cover nearly 60 to 65% of the entire 300 marks.

That means if a student just gets these three areas right, they’re already scoring somewhere between 180–195 marks  more than enough to clear the written stage comfortably.

 

ChapterbyChapter: What’s Actually Coming in the Paper

Algebra  25 to 30 Questions (Don’t Skip a Single Subtopic)

 

This is the backbone of the NDA Maths paper. Every year. Every paper.

What surprises most students when they sit with us is how predictable Algebra actually is. The question types repeat. The approach repeats. Even the numbers sometimes feel familiar if you’ve practiced enough PYQs.

Here’s what shows up most often:

Quadratic Equations  Nature of roots, sum and product of roots, discriminant. This is probably the single most repeated concept in the entire NDA Maths syllabus. We’ve seen 3 to 5 questions from this alone in almost every paper.

Sequences and Series (AP & GP)  Finding the nth term, sum of n terms, finding which term equals a given value. Questions repeat almost in the same format, just with different numbers. If you’ve solved 50 previous year questions from this topic, you’ll immediately recognize the pattern in the exam.

Permutations and Combinations  Arrangements, selections, word arrangements. Usually 3 to 5 questions. And here’s something important  if your P&C is weak, Probability will also suffer because the two are directly connected. Fix P&C and you fix both.

Complex Numbers  Modulus, argument, polar form, De Moivre’s theorem. Around 2 to 3 questions. Direct formula application mostly.

Sets, Relations, and Functions  Venn diagrams, union, intersection. 2 to 4 questions. Very scoring if practiced once properly.

Binomial Theorem, Logarithms  Usually 2 to 3 questions each. Don’t ignore them.

One thing we do at Alpha with every new batch: we collect all Quadratic Equation questions from the last 10 NDA papers and give them together to students. It takes about 2 hours. But after that, students understand  these questions are not random. They follow a structure. And once you see that, your confidence in the exam hall is completely different.

 

Trigonometry  20 to 25 Questions (Free Marks if You Practice)

Every student is scared of Trigonometry. Honestly, we don’t understand why.

NDA Trigonometry is mostly formula based. If your identities are memorised and you’ve practiced Heights and Distances regularly, this section gives you marks faster than any other part of the paper. We’ve seen students finish 18 to 20 Trig questions in under 30 minutes in mock tests.

What comes in the paper:

Trigonometric Identities  sin²? + cos²? = 1 and its derivatives, compound angle formulas, double angle, half angle. 8 to 10 questions usually. Many are direct substitution.

Heights and Distances  Realworld application: angle of elevation, angle of depression, distance between two points with trig. 3 to 5 questions. These are among the most straightforward questions in the whole paper.

Inverse Trig  Principal values, basic properties. 3 to 5 questions.

Properties of Triangles  Sine rule, cosine rule, area formulas. 3 to 4 questions.

We’ve personally seen students who came to us weak in Trig. Some hadn’t even touched the topic in Class 11  and within 3 months of daily practice, they were scoring 35 to 40 marks just from this section. The fear isn’t real. The practice gap is.

If Maths in general feels overwhelming, read our article on why NDA Maths is difficult for students. We’ve addressed the root causes honestly, not with generic advice.

 

Differential Calculus  10 to 15 Questions (Class 1112 Level Only)

Students hear “Calculus” and immediately imagine JEElevel difficulty. That’s not NDA.

NDA Differential Calculus is Class 11 and 12 NCERT level. No tricks, no extreme derivations. Just concepts applied cleanly.

Limits and Continuity  L’Hôpital’s rule, basic limit evaluation. 3 to 5 questions.

Differentiation  Product rule, quotient rule, chain rule, implicit differentiation. 5 to 7 questions. If you know the rules, these are mechanical.

Applications  Maxima and minima, increasing/decreasing functions, tangents and normals. 3 to 5 questions.

Any student who has studied NCERT Class 11 and 12 Maths properly doesn’t need to do anything extra for this section. The NDA level is right there.

 

Integral Calculus  10 to 15 Questions (Practice More, Fear Less)

This is where the slight difficulty bump happens. But again  manageable.

Integration by Substitution  Most common. 3 to 5 questions.

Integration by Parts  Appears regularly. 2 to 3 questions.

Definite Integrals  Properties of definite integrals, evaluation. 3 to 5 questions.

Area Under Curves  1 to 2 questions usually.

Differential Equations  Variable separable and homogeneous types. 2 to 3 questions.

One thing we noticed specifically: from 2022 onwards, Differential Equations started appearing more regularly than before. Students who skipped this thinking it’s “too hard for NDA” lost 5 to 7 marks unnecessarily. Don’t make that mistake.

 

Matrices and Determinants  10 to 15 Questions (Your Most Reliable Section)

Honest opinion? This is the most predictable scoring section in the entire NDA Maths paper.

The question types barely change. Types of matrices, operations, determinant properties, finding the inverse using adjoint, solving linear equations using Cramer’s Rule  these come every single time.

Students at Alpha who prepare Matrices properly almost never lose marks here in the actual exam. It’s formuladriven, patterndriven, and completely learnable in 2 to 3 weeks of focused effort.

If you’re looking for a “safe zone” in NDA Maths, this is it.

 

Statistics and Probability  10 to 15 Questions (Don’t Underestimate)

This section got 11 questions in NDA 1 2023 alone, the highest any single topic got in that paper. Yet we still see students reaching us who haven’t touched Statistics because they thought it’s “less important.”

Mean, Median, Mode, Variance, Standard Deviation  these are direct formula questions. 5 minutes of reading the right formula and practicing 20 questions is often enough to score here.

Probability is slightly more thinkingbased but still follows patterns. Basic probability, addition rule, multiplication rule, Conditional Probability, Bayes’ Theorem, Binomial Distribution basics  these cover everything that comes.

We tell every student at Alpha: Statistics is the section where hardworking students gain 25 to 37 marks that careless students give away. Don’t give it away.

 

Analytical Geometry 2D  10 to 12 Questions

Straight Lines  Slope, intercept, angle between lines, perpendicular distance. 4 to 6 questions.

Circles  Standard equation, centreradius form, tangent to a circle. 3 to 4 questions.

Conic Sections  Parabola, ellipse, hyperbola in basic form. 2 to 3 questions. Only the standard forms are tested, not the advanced problem solving you’d see in JEE.

 

Vector Algebra  5 to 7 Questions

Dot product, cross product, angle between vectors, scalar triple product, projection of one vector on another  these are the standard question types. 5 to 7 questions per paper means around 12 to 17 marks on the line.

Don’t skip this. 5 questions wrong here plus the negative marking is easily a 20mark swing.

 

3D Geometry  4 to 6 Questions (Hard, But Don’t Avoid)

Direction cosines, equation of a line in 3D, equation of a plane, angle between a line and a plane  these are the concepts tested.

The questions are genuinely harder than other sections. But 4 to 6 questions means 10 to 15 marks. Even if you can correctly attempt 3 out of 6, that’s 7.5 marks you didn’t have before. Learn the basics and the formulas. Don’t go deep, but don’t completely ignore it either.

Miscellaneous Topics  3 to 5 Questions

Binary number system (decimal to binary and back), Harmonic Progressions, second order derivatives, Bayes’ Theorem  these smaller topics together bring 3 to 5 questions. Easy to cover in a weekend. Easy marks to lose if ignored.

 

What Changed Year by Year (2020 to 2025)

Not everything stays the same. Here’s what we noticed when we sat down and compared papers side by side:

2020 and 2021  Algebra and Trigonometry dominated. Statistics was lighter. Papers felt more traditional.

2022  Matrices had heavier weightage than usual. 3D Geometry started making more appearances. NDA 2 2022 had questions from Straight Lines, Circles, Statistics, Integration, Vectors, Probability, Differentiation  quite spread out.

2023  NDA 1 2023 was eyeopening. Statistics and Data Interpretation had 11 questions  the highest for any single topic in recent memory. Integration and Trigonometry both got 9 questions. Students who had ignored Statistics paid for it.

2024 and 2025  Distribution became more balanced again. Calculus settled around 18 to 22 questions combined. Algebra held its dominant position. Matrices stayed consistent.

The big lesson from 5 years of observation: the core pattern doesn’t change drastically, but Statistics can swing significantly. Never underestimate it.

 

How We Recommend Using PYQs in Actual Preparation?

There’s a wrong way and a right way to use previous year papers. Most students do it the wrong way.

Wrong way: Open a full paper from 2019, attempt 120 questions randomly, check answers, feel bad about the score, move on.

Right way  and this is exactly what we follow at Alpha NDA Academy:

Start with the syllabus. Know what you’re supposed to study before you touch any question. Our NDA Exam Syllabus guide lays it out chapter by chapter so nothing is missed.

Then go topicwise. Take one chapter, say, Quadratic Equations. Collect all Quadratic Equation questions from 2019 to 2025. Sit down for one focused session and solve them all. By the time you’re done, you’ll have seen every type of question UPSC asks from that chapter. Do this for every topic.

Then move to accuracy tracking. After each topic session, count how many you got right. Don’t just look at the answer key and understand why you got it wrong. Was it a concept gap? Formula gap? Silly calculation error? All three need different fixes.

Only after you’ve covered all topics this way, start full mock tests. Every Saturday, our students at Alpha attempt a full 120question mock test. Not for the score  for the diagnosis. What did I attempt correctly? Where did I lose marks unnecessarily? Which topic needs more work?

And revise. This part everyone forgets. Matrices finished in October? By December it starts fading. Weekly formula revision is nonnegotiable.

For a full monthwise preparation plan, check our detailed NDA Preparation Tips guide.

 

Priority Order If You’re Short on Time

If your exam is in 3 to 6 months and you need to be smart about where to put effort:

Master these first  no excuses: Algebra (all subtopics), Trigonometry (identities + heights & distances), Matrices & Determinants, Statistics & Probability, Differential Calculus

Cover these properly after: Integral Calculus, Analytical Geometry 2D, Vector Algebra

Don’t skip, but keep brief: 3D Geometry (learn formulas, solve 10–15 past questions), Binary Numbers, Harmonic Progression

This priority list is based on marks available versus effort required. Not our personal preference for actual paper data.

 

A Quick Reality Check About NDA Maths Difficulty

“Sir, NDA Maths is very tough na?”

We get this from almost every student who walks in for counselling. And every time, our answer is the same: no, it isn’t. Not at NDA level.

NDA Maths is based on what you studied in Class 11 and 12. The topics are familiar. The NCERT books cover nearly everything. What makes it hard is the time pressure and the negative marking, not the actual content.

Students who struggle in NDA Maths usually have one of three problems: they skipped Class 11 and 12 basics because school exams didn’t test them seriously, they haven’t built a daily practice habit, or they carry a mental block from past Maths experiences.

All three are fixable. We’ve fixed all three with students from Arts backgrounds, Commerce students, students who failed Class 11 Maths in school. They cleared NDA written with decent Maths scores.

If you’re a student who didn’t study Maths in Class 12 and are wondering whether NDA is still possible, read our honest guide on joining NDA without Maths in 12th. And if you’re wondering whether one year is really enough to turn things around, we’ve answered that too  is 1 year enough for NDA preparation.

 

Books That Actually Work for NDA Maths PYQ Practice

Based on what works for the students we’ve trained:

NCERT Class 11 and 12 Maths  Start here. Don’t skip these even if you feel they’re “basic.” NDA questions are at exactly this level.

R.S. Aggarwal – Mathematics for NDA/NA  The most practical book for NDAspecific question practice. Chapterwise, patternaligned, good difficulty level.

Pathfinder for NDA/NA (Arihant)  Has previous year papers bundled in. Good for chapter analysis.

Disha Publications – NDA Chapterwise Solved Papers  Organized properly for the topicwise approach we described above.

At Alpha, we supplement these with our own DPP sheets (Daily Practice Problems) that we update every year based on the latest paper analysis. Students who join our batches get these as part of their preparation material.

 

5 Mistakes That Cost Students Marks in NDA Maths

We watch students write mock tests every Saturday. The same mistakes show up, batch after batch.

Attempting when unsure  This is the number one score killer. Because of negative marking, a wrong answer costs you 3.33 marks total (you lose 2.5 you could have scored + 0.83 deducted). If you’re 5050 on a question, leave it. Come back if time allows.

Ignoring Statistics, Easy marks, predictable question types, and yet students skip it because it “doesn’t feel like Maths.” Those students lost 25+ marks they didn’t have to.

Never practicing under time pressure. Sitting at home solving questions with no timer is not exam preparation. The exam has 75 seconds per question. Practice that way from Month 1.

Finishing a topic and never revising it  Integration done in January, exam in April. By March, half the formulas are gone. Weekly revision isn’t optional.

Running away from 3D Geometry and Differential Equations  These look scary. They’re worth 15–20 marks combined. Even 4 correct answers from these sections can swing your rank meaningfully. Learn the basics.

 

Quick Reference: Topic Priority Table

Topic	Expected Questions	Priority
Algebra	25–30	Master First
Trigonometry	20–25	Master First
Differential Calculus	10–15	Master First
Matrices & Determinants	10–15	Master First
Statistics & Probability	10–15	Very Important
Integral Calculus	10–15	Very Important
Analytical Geometry 2D	10–12	Very Important
Vector Algebra	5–7	Cover Well
3D Geometry	4–6	Cover Basics
Miscellaneous	3–5	Brief Study

 

How We Prepare Students for Maths at Alpha NDA Academy?

At Alpha NDA Academy, Sikar, we don’t just tell students to “practice more.” There’s a system behind everything.

Maths class starts with concept clarity  never with shortcuts. A student who understands why a formula works will still get the answer even under pressure. A student who memorised it for the exam? They blank out when the question is slightly twisted.

After concept sessions, every student solves 10 to 15 questions daily from the topic being covered. Not optional. These are checked, wrong answers are discussed, and patterns are explained.

Error notebooks are a big part of how we train. Every wrong answer goes in  the question, the mistake made, the correct approach. Students revisit these notebooks before mock tests. It sounds simple. It genuinely works. The same mistakes stop repeating within a few weeks.

Every Saturday is full mock test day  120 Maths questions, 150 minutes, proper OMR sheet. After the test, we go through performance together. Accuracy rate, topicwise scores, time distribution. Parents get a detailed performance report the same day. No hiding weak areas.

This consistency is behind the 90% written selection rate we’ve maintained across batches.

Once you clear the Maths paper, what comes next matters just as much. Read our guide on what happens after the NDA written exam so you’re not caught off guard by the SSB stages.

 

Frequently Asked Questions

Which chapter has the most questions in NDA Maths?

– Algebra  consistently has 25 to 30 questions per paper. Within Algebra, Quadratic Equations and Sequences & Series are the most repeated.

Is Calculus really that important for NDA?

–  Yes. Differential Calculus and Integral Calculus together make up roughly 18 to 25% of the paper  anywhere from 22 to 30 questions combined. You can’t afford to skip either.

Can a student genuinely score 150+ in NDA Maths

– Absolutely. Students who are solid in Algebra, Trig, Matrices, Statistics, and Calculus regularly cross 150. Many of our students hit 170 to 190 in mock tests after 6 to 8 months of proper preparation.

Do NDA Maths questions repeat?

– Not word for word. But the concept, structure, and format repeat heavily. That’s exactly why topicwise PYQ practice is so effective  you start recognising the question type before you’ve even finished reading it.

How much time should I give Maths daily?

– Minimum 1.5 to 2 hours, every day without gaps. At Alpha, students are solving Maths questions from 7 AM as part of their morning academic session. Consistency over intensity  that’s the real formula.

Is NCERT enough for NDA Maths?

– NCERT is the base and you must complete it properly. After NCERT, add R.S. Aggarwal’s NDA book for practice volume and chapterwise PYQs for pattern recognition. That combination is more than enough.