National Defence Academy & Naval Academy · UPSC · Mathematics 2016-II to 2026-I · GAT 2017-I and 2022-I to 2026-I

Where the
marks actually
live

Every question from the NDA papers, broken down to sub-topic level and weighted towards what the recent sittings are actually doing rather than what the syllabus says. The GAT carries twice the marks of Mathematics, and half of its General Knowledge section is school science. Read the cut lines, then build the timetable.

Questions analysed
Sittings covered
900Marks on the table
Sub-topics
0.83 / 1.33Cost of a wrong answer
01

What you sit

Two papers, both compulsory, 900 marks between them. The General Ability Test is a single 2½-hour sitting that contains English and General Knowledge back to back — they are separated below because their contents have nothing in common, but you write them as one paper against one clock.

Paper I

Mathematics

Questions
120
Marks
300 — 2.5 per question, −0.83 per wrong
Time
2½ hours — 1.25 min per question
Shape
Class 11–12 syllabus. Algebra and Calculus are 58 of the 120 questions between them.
Verdict
The most predictable paper in the exam. Sixteen of its 49 sub-topics have appeared in all eighteen sittings.
Paper II · Part A

English

Questions
50
Marks
200 — 4 per question, −1.33 per wrong
Time
Shared with Part B — about 1 min per question
Shape
Vocabulary is over half of it. In 2026-I, 26 of the 50 questions were synonyms, antonyms and idioms.
Verdict
The volatile one. Not one format has appeared in all ten sittings.
Paper II · Part B

General Knowledge

Questions
100
Marks
400 — 4 per question, −1.33 per wrong
Time
Shared with Part A
Shape
Half of it is Physics, Chemistry and Biology — 198 marks of school science.
Verdict
The largest block of marks anywhere in the exam, and the most stable. Start here.
02

What the papers are doing

Frequency tables average away the two most useful things here: the blocks that never move, and the question formats that arrived, ran for two sittings and disappeared. Practising a dead format is the most expensive mistake available to you.

General KnowledgeHalf the paper

General Knowledge is a science paper

Physics, Chemistry and Biology account for 496 of the 1,000 General Knowledge questions and 49.5 a paper on current form — 198 marks of school-level science before you open a newspaper.

Physics alone runs 26, 25, 24, 24, 21, 25, 25, 27, 25, 25. It has never dropped below 21 in ten sittings. At 100 marks a paper it is worth more than any single topic in Mathematics, and it does not go stale between attempts.

MathematicsBankable

Algebra is a third of the paper and it never moves

Algebra runs at 33.7 questions a sitting and has never fallen below 27 in eighteen papers — 84 marks, more than the whole of Trigonometry and Probability combined.

It is not one topic but seven finishable ones: sets and relations, functions, sequences and series, quadratics and polynomials, permutations and combinations, complex numbers, binomial theorem. Each is worth 3–5 questions a paper and each appears in nearly every sitting.

EnglishNothing is safe

No English format has survived all ten sittings

The most dependable thing in the paper is synonyms, and it has still missed a sitting. Comprehension passages went to zero in 2026-I after five straight appearances. Ordering of jumbled sentence parts ran at 10 a paper through 2023-I and was zero in 2026-I.

Compare Mathematics, where sixteen sub-topics have appeared in all eighteen sittings. Every hour you spend on an English format is a bet; every hour on Mathematics or science is not.

EnglishTwo sittings and gone

Four formats that ran twice and vanished

Cloze passages appeared at 10 a paper in both 2024 sittings and have not been seen since. Discourse markers did exactly the same in 2025 — 10, 10, then zero. S1–S6 sentence ordering ran at 5 in both 2025 papers and nowhere else. Word pairs and confusables appeared in 2023-II and 2025, never twice running in the same shape.

That is a paper being reshuffled, not a syllabus changing. Recognise each format so it cannot cost you time on the day, but do not build a study block around any of them.

EnglishBack to 26

Vocabulary halved, then came back

Synonyms, antonyms and idioms ran at 10, 10, 10 in 2022-I, were cut to 5, 5, 5 across 2024, fell to 5, 0, 0 in 2025-I, and returned in 2026-I at 10, 10, 6.

That is 26 of 50 questions104 marks — from a word list. Nothing else in this exam converts rote memory into marks at that rate. A daily list is the single highest-return English habit available to you.

MathematicsRising

Probability up, statistics down

Probability has gone from 9.3 a paper before 2024-II to 12.5 across the last four. Statistics has moved the other way over the same window, from 9.4 to 6.3.

The pair together is flat at about 19 questions, so this is a reallocation, not growth. Correlation and regression is where it is coming from: 3, 2, 3, 3, 4 in the older papers, 0, 0, 1 across the last three sittings.

MathematicsFalling

Differential equations has halved

Differential equations ran at 3–5 a paper through 2021 and reads 0, 1, 2 across the last three sittings — 3.7 a paper before 2024-II against 1.25 since. Maxima and minima has slid the same way, from 3.6 to 2.0.

Neither is gone, and both are cheap to hold once learnt. But if you are choosing what to drill in the last month, they are no longer where the marks are.

General KnowledgeBarely tested

Polity, economics and defence are almost absent

Economics has produced 13 questions in ten sittings and defence 14 — about one each per paper. Polity averaged 3.5 and then jumped to 8 in 2026-I, its highest reading in the record.

One spike is not a trend. Know the Constitution's basic structure and the current office-holders; do not read a constitutional commentary for four marks a paper.

03

Priority ladder

Tick a row when you have finished it — the bar tracks the share of expected marks you have covered, and it is remembered on this device. Every sub-topic is ranked by expected questions in your next paper — a blend weighted 60% to the last four sittings and 40% to the full record, so recent shifts move the ranking without one odd paper dominating it. The brass rule is the cut line: everything above it accounts for 80% of the marks.

#
Sub-topic
Expected share of paper
Q/paper
By sitting
Trend
04

Rising & falling

Change in questions per paper, last four sittings against everything before them. Positive means the recent papers want more of it than the older papers did.

05

Session grid

Topic weights sitting by sitting. Darker means more questions. Read across a row to see whether a topic is dependable or bursty — a row that alternates between 0 and 10 is telling you not to bet a week of study on it.

06

Study order

Built from the ladder above, in the order that converts hours into marks fastest. General Knowledge leads, and this is the opposite of the advice most aspirants are given. A GAT question is worth 4 marks against 2.5 in Mathematics; General Knowledge alone is 400 marks against Mathematics's 300; and half of General Knowledge is fixed school science that stays learnt. Mathematics is second because it is the most predictable paper, not because it pays best.

What you actually need to attempt

A wrong answer costs a third of the question's marks — 0.83 in Mathematics, 1.33 in the GAT — so an attempt only pays if you are right more than 25% of the time. Set your realistic attempt count and strike rate for each paper — they are rarely the same — and see what the sitting is actually worth.

Total

First third

Bank the certainties

  • GK science: Physics is 25 questions and 100 marks a paper on its own — mechanics, electricity and magnetism, light and optics, heat and matter first. Then Chemistry at 15 and Biology at 10. About 198 marks that do not change between attempts.
  • Maths algebra: sets and relations, functions, sequences and series, quadratics and polynomials. Roughly 20 questions and 50 marks, and every one of them has appeared in nearly every sitting.
  • English word list: synonyms, antonyms and idioms were 26 of 50 questions in 2026-I. Start the list on day one and keep it running to the exam.
Second third

Widen the base

  • Maths calculus: differentiation, definite integrals, limits, continuity and differentiability — about 13 questions a paper. Then matrices and determinants (10) and analytical geometry in the plane (10).
  • GK geography: 20 a paper, 81 marks. Geomorphology and Indian economic geography are the two densest seams; the solar system and climatology follow.
  • English structure: spotting errors, sentence completion, parts of speech, fill in the blanks. Cover the format once so it costs you nothing on the day, and move on.
Final third

Top up and time yourself

  • History and current affairs: 24 questions and 96 marks between them. The freedom struggle and international affairs are the reliable parts; current affairs has the shortest shelf life in the exam, so cover about twelve months back and do it last.
  • Maths long tail: trigonometric identities, probability of events and vectors are already covered; add heights and distances, spheres and planes only if the core is finished.
  • Full papers under clock: 1.25 minutes a question in Mathematics, 1 minute in the GAT. With 1.33 marks at stake on a wrong GAT answer, a question you cannot narrow to two options is worth leaving.

Every sub-topic in the ladder links through to real questions from these papers on SquadPrep, where you can drill them topic by topic with answers and explanations.

07

Method

Source. The NDA question papers themselves. Mathematics covers eighteen sittings, 2016-II to 2026-I. The General Ability Test covers ten, 2017-I and 2022-I to 2026-I. Per-paper averages are computed against each paper's own sitting count, never a common denominator.

Expected questions per paper = 0.6 × the last-four-sitting average + 0.4 × the all-sitting average. The recency weight is set to let a genuine format change surface within two sittings while stopping a single unusual paper from rewriting the ranking.

Trend = last-four-sitting average minus the average of everything before it.

Reliability = the share of sittings in which the sub-topic appeared at all. High expected value with low reliability means a bursty topic — know it, but do not build a week around it.

Marks. Mathematics questions are worth 2.5 and the General Ability Test 4, with a third of the question's own marks deducted for a wrong answer. Every marks figure in this file is computed from those weights, not from question counts.