The NDA exam consists of two papers:

📌 Paper-I: Mathematics (300 Marks)
📌 Paper-II: General Ability Test (600 Marks)

Paper-I: Mathematics (Code No. 01, Maximum Marks: 300)

1. Algebra

• Concept of sets, operations on sets, Venn diagrams, De Morgan laws.
• Cartesian product, relation, equivalence relation.
• Representation of real numbers on a line.
• Complex numbers – basic properties, modulus, argument, cube roots of unity.
• Binary number system: Conversion between decimal and binary.
• Arithmetic, Geometric, and Harmonic progressions.
• Quadratic equations with real coefficients.
• Linear inequalities with two variables (graphical solutions).
• Permutations and Combinations.
• Binomial theorem and its applications.
• Logarithms and their applications.

2. Matrices and Determinants

• Types of matrices, operations on matrices.
• Determinant of a matrix and its properties.
• Adjoint and inverse of a square matrix.
• Solving a system of linear equations using Cramer’s Rule and Matrix Method.

3. Trigonometry

• Angles (degrees & radians), trigonometric ratios & identities.
• Sum and difference formulas, multiple and sub-multiple angles.
• Inverse trigonometric functions.
• Applications: Heights & distances, properties of triangles.

4. Analytical Geometry (2D & 3D)

• Cartesian coordinate system, distance formula.
• Equations of lines, angle between two lines, distance of a point from a line.
• Equation of a circle, parabola, ellipse, and hyperbola.
• Eccentricity and axes of conic sections.
• 3D Geometry: Distance between two points, direction cosines & ratios.
• Equations of planes and lines, angles between planes and lines.
• Equation of a sphere.

5. Differential Calculus

• Functions: Domain, range, graphs, composite functions, inverse functions.
• Limits and continuity.
• Differentiation: Basic rules, product/quotient rule, second-order derivatives.
• Increasing & decreasing functions, maxima & minima applications.

6. Integral Calculus & Differential Equations

• Integration as an inverse of differentiation.
• Standard integrals, integration by substitution & by parts.
• Definite integrals & applications (area under curves).
• Differential Equations: Order & degree, general & particular solutions.
• Applications in growth & decay problems.

7. Vector Algebra

• Vectors in 2D and 3D, magnitude & direction, unit and null vectors.
• Addition, scalar multiplication, dot & cross products.
• Applications in work, force, and geometry.

8. Statistics & Probability

• Data classification, frequency distribution, graphical representation (Histogram, Pie Chart, etc.).
• Measures of central tendency (Mean, Median, Mode), variance & standard deviation.
• Probability: Random experiments, sample space, events, classical & statistical probability.
• Bayes’ Theorem, Binomial distribution.

Paper-II: General Ability Test (Code No. 02, Maximum Marks: 600)

📝 Part A: English (200 Marks)

• Grammar and usage
• Vocabulary
• Comprehension
• Cohesion in extended texts

📝 Part B: General Knowledge (400 Marks)

Section A: Physics

• Physical Properties of Matter: Mass, Weight, Volume, Density, Specific Gravity.
• Motion: Velocity, Acceleration, Newton’s Laws, Force, Momentum.
• Heat & Thermodynamics: Measurement of heat, latent heat, heat transfer.
• Sound Waves & their properties, musical instruments.
• Optics: Reflection, Refraction, Spherical mirrors, Lenses, Human Eye.
• Electricity & Magnetism: Ohm’s Law, circuits, X-rays.
• General Principles: Pendulums, Pulleys, Hydrometers, Pressure Cookers, Telescopes.

Section B: Chemistry

• Elements, Mixtures & Compounds.
• Properties of Air & Water, Hydrogen, Oxygen, Nitrogen, Carbon Dioxide.
• Acids, Bases, and Salts.
• Different Forms of Carbon.
• Everyday Chemistry: Fertilizers, Soap, Glass, Cement, Gunpowder.
• Atomic Structure, Molecular Weights, Valency.

Section C: General Science

• Living & Non-Living Things.
• Basis of Life: Cells, Protoplasm, Tissues.
• Human Body & Important Organs.
• Common Epidemics, Causes & Prevention.
• Food & Nutrition: Balanced Diet.
• Solar System, Meteors, Comets, Eclipses.
• Achievements of Eminent Scientists.

Section D: History & Freedom Movement

• Indian History: Culture & Civilization.
• Freedom Movement in India.
• Indian Constitution & Administration.
• Five-Year Plans, Panchayati Raj, Co-operatives.
• Concepts: Bhoodan, Sarvodaya, National Integration, Gandhi’s Teachings.
• World History: Renaissance, Industrial Revolution, Russian Revolution.
• United Nations, Democracy, Socialism, India’s Role in the World.

Section E: Geography

• Earth’s Shape & Size, Latitudes & Longitudes, Time Zones.
• Earth’s Movements & Effects, Origin of Earth.
• Rocks & Weathering, Earthquakes & Volcanoes.
• Ocean Currents, Tides, Atmosphere & Weather.
• Regional Geography of India: Climate, Natural Vegetation, Minerals, Industries.
• Major Sea Ports, Trade Routes, Exports & Imports.

Section F: Current Events

• Important National & International Events.
• Prominent Personalities (Indian & Global).
• Cultural, Sports, and Political Events.

Weightage of General Ability Test Sections

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