Syllabus & Syllabus weightage

NDA Paper I – Mathematics Syllabus

Total Marks: 300
Duration: 2.5 Hours
Type: Objective (MCQs)
Standard: Class 11 & 12 level

1. Algebra

• Concept of set, operations on sets, Venn diagrams
• De Morgan laws
• Cartesian product, relation, equivalence relation
• Real numbers, complex numbers (modulus, argument, square roots)
• Binary numbers
• Quadratic equations with real coefficients
• Arithmetic, geometric and harmonic progressions
• Permutations and combinations
• Binomial theorem and its applications
• Logarithms and their applications

 2. Matrices and Determinants

• Types of matrices
• Operations on matrices
• Determinants
• Properties of determinants
• Applications – solving systems of linear equations using Cramer's Rule

 3. Trigonometry

• Angles and their measures (in degrees and radians)
• Trigonometric identities and equations
• Inverse trigonometric functions
• Height and distance problems
• Properties of triangles
• Use of trigonometric tables

 4. Analytical Geometry (2D and 3D)

• 2D Geometry:
• Cartesian coordinate system
• Straight lines, distance formula
• Equation of a line in various forms
• Angle between two lines
• Circles, parabola, ellipse, hyperbola – standard forms and properties
• 3D Geometry:
• Direction cosines and direction ratios
• Equation of a line and a plane
• Angle between two lines, between line and plane

 5. Differential Calculus

• Concept of a function
• Domain, range, composite functions, inverse functions
• Limits and continuity
• Derivatives of standard functions
• Rules of differentiation (product, quotient, chain rule)
• Derivatives of implicit functions
• Geometrical interpretation – tangent and normal
• Maxima and minima (basic problems)

 6. Integral Calculus and Differential Equations

• Integration as inverse of differentiation
• Standard integrals and their applications
• Methods: substitution, partial fractions, integration by parts
• Definite integrals – properties, applications (area under curve)
• Differential equations (first order, first degree)
• General and particular solutions

 7. Vector Algebra

• Vectors in 2D and 3D
• Magnitude and direction
• Unit vector, position vector
• Addition, subtraction, scalar multiplication
• Dot product and cross product
• Applications in geometry and physics

 8. Statistics and Probability

• Statistics:
• Mean, median, mode
• Variance and standard deviation
• Probability:
• Basic probability theory
• Independent and dependent events
• Addition and multiplication rules
• Bayes' Theorem (basic understanding)

NDA Paper II – General Ability Test (GAT) Syllabus

Total Marks: 600
Duration: 2.5 Hours
Type: Objective (MCQs)
Sections:

• Section A – English: 200 Marks
• Section B – General Knowledge: 400 Marks

 Section A: English (200 Marks)

Focus: Testing the candidate’s understanding of English and basic grammar.

Topics Covered:

• Vocabulary (synonyms, antonyms, one-word substitutions)
• Grammar and usage
• Spotting errors
• Sentence structure
• Tenses, verbs, articles, prepositions, conjunctions
• Comprehension and passage reading
• Para jumbles and rearrangement
• Fill in the blanks
• Idioms and phrases
• Active & Passive voice
• Direct and Indirect speech

 Section B: General Knowledge (400 Marks)

The General Knowledge section is further divided into 6 subjects:

1. Physics (Class 11 & 12 level)

• Physical properties and states of matter
• Motion, Newton’s laws, force, gravity
• Work, energy, and power
• Heat, temperature, pressure
• Sound, waves, reflection and refraction
• Light (basic optics), mirrors and lenses
• Electricity and magnetism
• Simple electrical circuits, Ohm's law
• Conductors and insulators
• Modern physics (Atoms and nuclei), basic electronics

2. Chemistry

• Physical and chemical changes
• Elements, compounds, mixtures
• Atomic structure, molecules and chemical equations
• Laws of chemical combination
• Acids, bases and salts
• Metals and non-metals
• Chemical bonding
• Carbon and its compounds (basic organic chemistry)
• Periodic table and classification of elements

3. General Science

• Basics of biology – cells, tissues, human body systems
• Nutrition, health and diseases
• Growth and reproduction in plants and animals
• Environment and ecology
• Biotechnology and its applications
• Latest scientific developments

4. History, Freedom Movement

• Ancient, Medieval and Modern Indian History
• Indian Freedom Struggle and important leaders/events
• Indian Constitution and administration
• Nationalism and social reform movements
• French, Russian and Industrial Revolutions
• World Wars and their effects

5. Geography

• Earth’s structure and origin
• Latitudes, longitudes, time zones
• Rocks and minerals
• Atmosphere and its layers
• Climate and weather
• Indian physical geography – rivers, mountains, plateaus, coasts
• Natural vegetation and wildlife
• Agriculture and industries
• Maps and map reading

6. Current Events

• National and international current affairs
• Important government schemes
• Sports and awards
• Science and technology updates
• Cultural and political events
• Defence-related news and military exercises

Syllabus weightage

Mathematics – Topic-Wise Weightage (Out of 120 Questions)

 Focus Areas: Calculus, Algebra, Trigonometry, and Matrices consistently dominate the paper.

GAT Paper – Section A: English (50 Questions)

Focus Areas: Vocabulary, Grammar, and Comprehension form the backbone of the English section.

 GAT Paper – Section B: General Knowledge (100 Questions)

Focus Areas: Physics is the most asked, followed by History and Geography. Current Affairs is increasing in importance.

Summary: What to Prioritize

 For Maths:

• Focus more on Calculus, Trigonometry, Algebra, and Matrices.
• Don't ignore Probability and Coordinate Geometry.

 For GAT English:

• Build strong vocabulary and grammar basics.
• Practice comprehension regularly.

 For GAT GK:

• Revise Class 9–12 NCERT Physics, History, and Geography.
• Stay updated with monthly current affairs.