NDA (National Defence Academy)

Every topic matched to the official PDF Official notice, upsc.gov.in

48 topics, each explained 8 units

NDA & NA is UPSC's exam for entry into the Army, Navy and Air Force wings of the National Defence Academy, held twice a year for unmarried candidates who have passed Class 12 (Physics, Chemistry and Mathematics are compulsory for the Air Force, Navy and the Naval Academy's 10+2 Cadet Entry Scheme). Selection has two stages — a written examination on Mathematics and General Ability, followed by an SSB Interview with psychological tests, group tasks and a personal interview spread over several days — so preparation must cover both the written papers and interview readiness. Since the General Ability paper alone spans English plus Physics, Chemistry, General Science, History, Geography and Current Events, steady daily revision across school-level subjects matters more than last-minute cramming.

Exam Pattern

Conducting body: Union Public Service Commission (UPSC). Exam name: National Defence Academy & Naval Academy Examination (NDA & NA), held twice every year — NDA (I) and NDA (II). Eligibility: unmarried candidates only; for the Army wing a pass in Class 12 / equivalent is enough, while for the Air Force, Navy and the 10+2 Cadet Entry Scheme of the Indian Naval Academy, Class 12 with Physics, Chemistry and Mathematics is required. Age: roughly 16½ to 19½ years — confirm the exact date window in each year's notice.

Selection has two stages: (1) a written examination of 900 marks, and (2) an SSB Interview of 900 marks — total 1800 marks.

WRITTEN EXAMINATION (objective / MCQ, set in both English and Hindi except the English portion):

Paper I — Mathematics: 300 marks, 120 questions, duration 2 hours 30 minutes.
Paper II — General Ability Test (GAT): 600 marks, 150 questions, duration 2 hours 30 minutes. GAT has two parts — Part A English (200 marks) and Part B General Knowledge (400 marks) covering Physics, Chemistry, General Science, History & Freedom Movement, Geography and Current Events.
Negative marking: one-third (1/3) of the marks assigned to a question is deducted for each wrong answer.

SSB INTERVIEW (900 marks): Stage I is a screening (Officer Intelligence Rating + Picture Perception & Description Test). Only those who clear Stage I go to Stage II — psychological tests, Group Testing Officer (GTO) tasks and the personal interview, spread over about 4–5 days.

This is the long-stable NDA pattern; always confirm marks, age and eligibility against the specific NDA (I) / (II) notification for the year you are applying in.

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Full Syllabus

1 Mathematics (Paper I)

What the syllabus lists	What it means and how to prepare
Algebra	Algebra — equations, inequalities and progressions build speed by practising quadratic, log and AP/GP problems from an NCERT-level book first.
Matrices & Determinants	Matrices & Determinants — arranging numbers in rows and columns and finding their determinant value learn the standard operations (addition, multiplication, inverse) step by step, they follow fixed rules.
Trigonometry	Trigonometry — angles, ratios and identities of triangles memorise the standard identities and practise height-and-distance type problems until the steps feel automatic.
Analytical Geometry (2D & 3D)	Analytical Geometry (2D & 3D) — locating points, lines, circles and planes using coordinates draw a rough sketch for every problem before applying the formula, it prevents sign mistakes.
Differential Calculus	Differential Calculus — the rate at which a quantity changes start with basic limits and derivative rules, then move to problems on maxima-minima and tangents.
Integral Calculus & Differential Equations	Integral Calculus & Differential Equations — finding area under a curve, and equations that describe how something changes learn the standard integration formulas by heart and practise substitution-method problems.
Vector Algebra	Vector Algebra — quantities that have both magnitude and direction, like force or velocity practise addition, dot product and cross product with simple diagrams so the direction stays clear.
Statistics & Probability	Statistics & Probability — organising data (mean, median, mode) and estimating the chance of an event practise with everyday examples like coins and dice to build intuition.

2 GAT — English (Part A)

What the syllabus lists	What it means and how to prepare
grammar and usage	Grammar and usage — the correct rules for forming sentences (tense, subject-verb agreement, prepositions) revise one grammar rule a day and mark your own mistakes to fix the pattern, not just the single sentence.
vocabulary	Vocabulary — the stock of words you recognise and can use correctly read short English passages daily and note down new words with their meaning in a small notebook.
comprehension and cohesion — testing understanding of English and workmanlike use of words	Comprehension and cohesion — understanding a passage's meaning and how its sentences link together logically practise by reading a paragraph and summarising it in your own words in one or two lines.

3 GAT — General Knowledge (Part B) Physics

What the syllabus lists	What it means and how to prepare
motion	Motion — how position, speed and acceleration are described and measured go through the basic definitions and formulas (speed = distance/time) with simple daily-life examples like a moving vehicle.
force	Force — a push or pull that can change an object's motion or shape learn Newton's basic laws in plain language and connect each one to a real example you already know.
work-power-energy	Work-power-energy — how much work is done, how fast it's done, and the capacity to do work understand the plain-word meaning of each term before touching any formula.
heat & temperature	Heat & temperature — the difference between the energy that flows (heat) and how hot or cold something is (temperature) note the everyday units and instruments, like a thermometer, used to measure them.
light	Light — how light travels, reflects and bends revise the basics of a mirror and a lens with simple ray diagrams rather than memorising formulas alone.
sound	Sound — how sound travels as a wave and its everyday properties like pitch and loudness connect each property to something you hear daily, like a loud horn versus a soft whisper.
magnetism	Magnetism — how magnets attract or repel and create a field around them learn the basic properties of a magnet through simple diagrams of field lines.
electricity	Electricity — the basics of electric current, circuits and common devices that use them understand a simple circuit diagram (battery, wire, switch, bulb) before moving to formulas.
simple machines	Simple machines — basic devices like the lever, pulley and inclined plane that make work easier learn how each one is used around you, for example a see-saw as a lever.
everyday physics	Everyday physics — how physics ideas show up in ordinary things you see and use daily keep a habit of asking 'why does this happen' about small daily observations and connect it to what you've studied.

4 GAT — Chemistry

What the syllabus lists	What it means and how to prepare
physical & chemical changes	Physical & chemical changes — telling apart a change where the substance stays the same (like ice melting) from one where a new substance forms (like burning paper) practise by classifying everyday examples into the two types.
elements-mixtures-compounds	Elements-mixtures-compounds — the three basic ways matter is classified in chemistry go through simple everyday examples of each (iron as an element, air as a mixture, water as a compound) to fix the difference.
acids-bases-salts	Acids-bases-salts — the three groups of common chemical substances and the general idea used to identify them link each to a familiar household item, like lemon for acid.
oxidation & reduction	Oxidation & reduction — reactions where a substance gains or loses oxygen (or electrons) the simplest way to start is with the everyday example of iron rusting, which is an oxidation reaction.
common gases	Common gases — the everyday properties and uses of gases like oxygen, nitrogen and carbon dioxide make a simple table for each gas noting where it's found and what it's used for.
carbon and its compounds	Carbon and its compounds — the basics of carbon's properties and the common substances it forms start with the simplest compounds you already know, like carbon dioxide, and build up from there.
fertilisers	Fertilisers — substances added to soil to help crops grow better remember a few common examples and, in plain terms, what each mainly provides to the plant.
preparation of common substances	Preparation of common substances — the basic idea of how everyday chemical substances are made focus on understanding the general process in simple words rather than memorising exact equations.

5 GAT — General Science

What the syllabus lists	What it means and how to prepare
living vs non-living	Living vs non-living — the basic features that separate a living thing from a non-living one, like growth and reproduction list these features and test them against a few everyday objects and organisms.
cells & tissues	Cells & tissues — the basic unit of life (cell) and groups of similar cells working together (tissue) a simple diagram of a cell with its main parts labelled helps more than reading paragraphs.
the human body & food	The human body & food — the basic organ systems of the body and the role food plays in keeping them working a simple chart connecting each major organ system to its function is an efficient way to revise.
common diseases	Common diseases — familiar illnesses, how they spread and basic prevention learn them in small groups by cause (like water-borne or air-borne) rather than as one long unconnected list.
the basic science of everyday life	The basic science of everyday life — simple scientific reasoning behind common daily observations keep noting down 'why' questions from your surroundings and try to answer them using what you've read.

6 GAT — History & Freedom Movement

What the syllabus lists	What it means and how to prepare
highlights of Indian history	Highlights of Indian history — the major periods and turning points of India's past build a simple timeline of key events so you can place any name or date in its correct period.
the freedom movement	The freedom movement — the events, leaders and movements that led to India's independence group them by decade and remember one or two key facts about each rather than every detail.
the Constitution & Panchayati Raj	The Constitution & Panchayati Raj — the basic structure of India's Constitution and its system of local self-government learn the broad framework first (main organs, three tiers of Panchayati Raj) before the finer details.
broad world history / social reform	Broad world history / social reform — major world events and India's own social reform movements keep this at a general-awareness level, focusing on well-known names and movements rather than obscure detail.

7 GAT — Geography

What the syllabus lists	What it means and how to prepare
the Earth	The Earth — its shape, motion and basic structure start with the simple facts (rotation, revolution, main layers) before layering on more detail.
latitudes & longitudes	Latitudes & longitudes — the imaginary lines used to locate any place on Earth practise reading a world map and identifying a few well-known lines like the Equator and the Tropic of Cancer.
atmosphere & climate	Atmosphere & climate — the layers of air around the Earth and the general weather pattern of a region connect the basic layers and climate types to a map so they're easier to recall.
oceans & winds	Oceans & winds — the major water bodies and wind patterns that shape climate and trade a labelled world map showing the main oceans and wind belts is worth more here than plain text notes.
India's regions	India's regions — the country's major physical regions like the Himalayas, the plains and the plateaus a simple outline map with each region marked is the fastest way to fix this in memory.
agriculture	Agriculture — the major crops grown in India and the conditions they need a simple table of crop, region and season together is easier to revise than separate notes.
natural resources	Natural resources — India's key minerals, forests and water resources and where they're mainly found link each resource to its main region on a map rather than memorising a plain list.

8 GAT — Current Events

What the syllabus lists	What it means and how to prepare
important national and international events	Important national and international events — significant happenings in India and around the world build a habit of reading one reliable news source daily and jotting down the day's two or three most important headlines.
prominent personalities	Prominent personalities — well-known individuals currently in the news across fields like public life, sports and science keep a simple running list with just their name and why they're in the news.
sports and cultural activities of the recent period	Sports and cultural activities of the recent period — recent sporting results and cultural happenings worth knowing about a short weekly note of major sports results and cultural events keeps this fresh without needing to reread old news.

Not covered in this pack — where to find it

Vacancy count	Not stated in this pack — check the year's official notification.
Exact exam date for NDA (I) / NDA (II)	Not stated — the pack only says the exam is held twice a year.
Application fee	Not stated in this pack.
Qualifying or cut-off marks	Not stated — only the total marks per paper and stage are given.
Exact age-limit dates	Not stated precisely — the pack gives only an approximate 16½–19½ year range and says to confirm each year's window.

Free practice — 22 questions

Work out the answer yourself first, then tap “Show answer”. Every answer shows the method, not just the letter.

What is the total marks for the NDA written examination (Paper I + Paper II combined)?
- A 900
- B 600
- C 1200
- D 1800
Show answer

A — 900

Paper I (Mathematics) is 300 marks and Paper II (GAT) is 600 marks; 300 + 600 = 900 marks for the written examination.

Exam Pattern — Written Examination
How many marks are allotted to the SSB Interview stage in NDA selection?
- A 600
- B 900
- C 1200
- D 1500
Show answer

B — 900

The official notification states the SSB Interview carries 900 marks, equal to the written examination's 900 marks.

Exam Pattern — SSB Interview
What is the total combined marks of the written examination and the SSB Interview in NDA selection?
- A 1500
- B 1650
- C 1800
- D 2100
Show answer

C — 1800

900 (written) + 900 (SSB Interview) = 1800 total marks.

Exam Pattern — Total Selection Marks
How many questions are there in Paper I (Mathematics) of the NDA written exam?
- A 90
- B 100
- C 150
- D 120
Show answer

D — 120

Paper I (Mathematics) has 120 questions for 300 marks.

Exam Pattern — Paper I (Mathematics)
How many questions are there in Paper II (General Ability Test) of the NDA written exam?
- A 150
- B 120
- C 135
- D 160
Show answer

A — 150

Paper II (GAT) has 150 questions for 600 marks.

Exam Pattern — Paper II (GAT)
What is the duration given for Paper I (Mathematics) in the NDA written exam?
- A 2 hours
- B 2 hours 30 minutes
- C 3 hours
- D 1 hour 30 minutes
Show answer

B — 2 hours 30 minutes

The official notification states Paper I (Mathematics) has a duration of 2 hours 30 minutes.

Exam Pattern — Paper I (Mathematics)
How many marks are deducted for each wrong answer in the NDA written exam?
- A One-fourth of the marks assigned
- B Half of the marks assigned
- C One-third of the marks assigned
- D No marks are deducted
Show answer

C — One-third of the marks assigned

The official notification states one-third (1/3) of the marks assigned to a question is deducted for each wrong answer.

Exam Pattern — Negative Marking
How many marks does Part A (English) of GAT (Paper II) carry?
- A 150
- B 250
- C 300
- D 200
Show answer

D — 200

GAT Part A (English) carries 200 marks out of the paper's 600.

Exam Pattern — GAT Part A (English)
How many marks does Part B (General Knowledge) of GAT (Paper II) carry?
- A 400
- B 300
- C 350
- D 450
Show answer

A — 400

GAT Part B (General Knowledge) carries 400 marks out of the paper's 600 (200 + 400 = 600).

Exam Pattern — GAT Part B (General Knowledge)
Which paper carries more marks in the NDA written exam — Paper I (Mathematics) or Paper II (GAT)?
- A Paper I (Mathematics), 300 marks vs 600
- B Paper II (GAT), 600 marks vs 300
- C Both carry equal marks
- D Paper I, 400 marks vs 500
Show answer

B — Paper II (GAT), 600 marks vs 300

Paper I (Mathematics) is worth 300 marks while Paper II (GAT) is worth 600 marks, so GAT carries more.

Exam Pattern — Marks Comparison
Solve for the roots of the quadratic equation x² − 5x + 6 = 0.
- A x = 1, 6
- B x = -2, -3
- C x = 2, 3
- D x = 2, -3
Show answer

C — x = 2, 3

Factor as (x-2)(x-3)=0, so x=2 or x=3. Check: sum of roots = 5 (=-b/a) and product = 6 (=c/a), both matching the equation.

Algebra
Find the 10th term of the arithmetic progression 3, 7, 11, 15, ...
- A 35
- B 37
- C 41
- D 39
Show answer

D — 39

nth term = a + (n-1)d = 3 + (10-1)×4 = 3 + 36 = 39.

Algebra
Find the 5th term of the geometric progression 2, 6, 18, 54, ...
- A 162
- B 150
- C 108
- D 180
Show answer

A — 162

nth term = a×r^(n-1) = 2×3⁴ = 2×81 = 162 (common ratio r = 3).

Algebra
What is the determinant of the matrix [[3, 4], [1, 2]]?
- A 1
- B 2
- C 5
- D 10
Show answer

B — 2

For a 2×2 matrix [[a,b],[c,d]], determinant = ad − bc = (3×2) − (4×1) = 6 − 4 = 2.

Matrices & Determinants
A vertical tower casts a shadow of 20 m when the sun's angle of elevation is 45°. What is the height of the tower?
- A 10 m
- B 20√2 m
- C 20 m
- D 40 m
Show answer

C — 20 m

tan(45°) = height / shadow length = 1, so height = shadow length = 20 m.

Trigonometry
What is the distance between the points (0, 0) and (3, 4) on the coordinate plane?
- A 4
- B 6
- C 7
- D 5
Show answer

D — 5

Distance = √((3−0)² + (4−0)²) = √(9+16) = √25 = 5.

Analytical Geometry (2D & 3D)
What is the derivative of f(x) = x³ at x = 2?
- A 12
- B 6
- C 8
- D 18
Show answer

A — 12

f'(x) = 3x²; at x = 2, f'(2) = 3×4 = 12.

Differential Calculus
Evaluate the definite integral ∫ from 0 to 3 of 2x dx.
- A 6
- B 9
- C 12
- D 3
Show answer

B — 9

∫2x dx = x²; evaluated from 0 to 3 gives 3² − 0² = 9.

Integral Calculus & Differential Equations
What is the magnitude of the vector with components (3, 4)?
- A 3
- B 4
- C 5
- D 7
Show answer

C — 5

Magnitude = √(3² + 4²) = √25 = 5.

Vector Algebra
What is the mean of the numbers 2, 4, 6, 8, 10?
- A 5
- B 7
- C 8
- D 6
Show answer

D — 6

Mean = sum of values ÷ count = 30 ÷ 5 = 6.

Statistics & Probability
What is the probability of rolling a 4 on a single fair six-sided die?
- A 1/6
- B 1/2
- C 1/3
- D 1/4
Show answer

A — 1/6

There is exactly one favourable outcome (rolling a 4) out of 6 equally likely outcomes, so probability = 1/6.

Statistics & Probability
What are the coordinates of the midpoint of the line segment joining points (2, 3) and (4, 7)?
- A (2, 4)
- B (3, 5)
- C (6, 10)
- D (1, 2)
Show answer

B — (3, 5)

Midpoint = ((x1+x2)/2, (y1+y2)/2) = ((2+4)/2, (3+7)/2) = (3, 5).

Analytical Geometry (2D & 3D)

These questions are built from the official pattern and syllabus on this page. Every answer was independently re-solved before it was published.

This exam recruits at these levels: 12th Pass

Note — Always confirm the syllabus and pattern against that year's official notification — changes are possible.

Start PractisingPlay a free quiz in Meri Taiyari

NDA (National Defence Academy) — related updates

No new NDA (National Defence Academy) vacancy is open right now. It'll show up here the moment a notification lands.

Get Free Alerts

Official source: https://upsc.gov.in/examinations/active-examinations