UPSC NDA II 2025 Syllabus (National Defence Academy & Naval Academy Exam)

1. Mathematics (300 Marks)

Algebra:

• Concept of set, operations on sets, Venn diagrams

• De Morgan laws

• Cartesian product, relation, functions

• Complex numbers: basic properties, modulus, argument

• Quadratic equations

• Arithmetic, geometric, and harmonic progressions

• Permutation and combination

• Binomial theorem

• Logarithms and their applications

Matrices and Determinants:

• Types of matrices, operations on matrices

• Determinant of a matrix, properties

• Adjoint and inverse of a matrix

• Applications – solution of simultaneous equations (up to three variables)

Trigonometry:

• Angles and their measures (degrees and radians)

• Trigonometric ratios and identities

• Inverse trigonometric functions

• Height and distance applications

Analytical Geometry of Two and Three Dimensions:

• Cartesian coordinate system

• Distance formula, section formula

• Straight lines, angle between two lines

• Circle, parabola, ellipse, and hyperbola

• Three-dimensional space: distance, direction cosines and ratios

• Equation of a line and a plane

Differential Calculus:

• Concept of limit, continuity, and differentiability

• Derivatives of standard functions

• Application of derivatives – maxima and minima

Integral Calculus and Differential Equations:

• Integration as inverse of differentiation

• Definite integrals and their properties

• Applications of integrals – area under curves

• Differential equations – order and degree

• Solution of first-order and first-degree differential equations

Vector Algebra:

• Magnitude and direction of vectors

• Addition of vectors, scalar and vector product

• Applications to geometry and physics

Statistics and Probability:

• Statistics: mean, median, mode, variance, and standard deviation

• Probability: basic concepts, simple problems on conditional probability and Bayes theorem

2. General Ability Test (600 Marks)

Part A: English (200 Marks)

• Grammar and usage

• Vocabulary

• Comprehension and cohesion

• Spotting errors

• Fill in the blanks

• Synonyms and antonyms

• Idioms and phrases

• Sentence improvement and arrangement

Part B: General Knowledge (400 Marks)

Section A – Physics:

• Physical properties and states of matter

• Motion, force, and laws of motion

• Work, energy, and power

• Heat, temperature, and thermodynamics

• Sound and light (reflection, refraction, etc.)

• Electricity and magnetism

• Nuclear physics and radioactivity

• Basic instruments and measurements

Section B – Chemistry:

• Elements, compounds, and mixtures

• Atomic structure

• Chemical equations and reactions

• Acids, bases, and salts

• Carbon and its compounds

• Properties of air and water

• Preparation and uses of hydrogen, oxygen, nitrogen, and carbon dioxide

• Natural and synthetic materials

Section C – General Science:

• Basic biology – cells, tissues, human body systems

• Food, nutrition, and health

• Disease and prevention

• Reproduction and genetics

• Environmental science and pollution

Section D – History, Freedom Movement:

• Ancient, Medieval and Modern Indian History

• Indian freedom struggle and national movement

• Key personalities and movements (Gandhi, Nehru, etc.)

• Constitution and its development

Section E – Geography:

• Earth structure and formation

• Latitude, longitude, time zones

• Atmosphere, climate, and weather

• Ocean currents and tides

• Indian and world geography

• Natural resources and agriculture

Section F – Current Events:

• Recent national and international events

• Sports and culture

• Scientific developments

• Important political and economic affairs

SSB Interview (900 Marks)

• Stage I: Officer Intelligence Rating (OIR) tests and Picture Perception & Description Test (PPDT)

• Stage II: Group Testing Officer Tasks, Psychology Tests, Interview, and Conference