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NDA & NA Syllabus

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NDA Syllabus Details:

The Union Public Service Commission (UPSC) conducts the National Defence Academy (NDA) & Naval Academy (NA) exam twice a year, offering admission to the Indian Navy, Army, and Air Force Wings. The minimum educational qualification required is the completion of the 12th class in the 10+2 pattern. The examination comprises two stages: a written examination and an interview. The detailed syllabus is as follows:

PAPER-I: MATHEMATICS (Maximum Marks – 300)

  1. ALGEBRA:
    • Concept of set, 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 system of numbers, conversion of a number in the decimal system to the binary system and vice versa.
    • Arithmetic, geometric, and harmonic progressions.
    • Quadratic equations with real coefficients, solution of linear inequalities of two variables by graphs.
    • Permutation and combination, binomial theorem, logarithms, and their applications.
  2. MATRICES AND DETERMINANTS:
    • Types of matrices, operations on matrices.
    • Determinant of a matrix, basic properties of determinants.
    • Adjoint and inverse of a square matrix, applications – solution of a system of linear equations.
  3. TRIGONOMETRY:
    • Angles and their measures in degrees and radians.
    • Trigonometrical ratios, identities, sum and difference formulae.
    • Multiple and sub-multiple angles, inverse trigonometric functions.
    • Applications – height and distance, properties of triangles.
  4. ANALYTICAL GEOMETRY OF TWO AND THREE DIMENSIONS:
    • Rectangular Cartesian coordinate system.
    • Distance formula, equation of a line in various forms.
    • Angle between two lines, distance of a point from a line.
    • Equation of a circle, standard forms of parabola, ellipse, and hyperbola.
    • Point in three-dimensional space, direction cosines, and ratios.
    • Equation of a plane and a line in various forms, angle between two lines and planes.
    • Equation of a sphere.
  5. DIFFERENTIAL CALCULUS:
    • Concept of a real-valued function, composite functions, limits.
    • Continuity of functions, derivatives, second-order derivatives.
    • Increasing and decreasing functions, applications in problems of maxima and minima.
  6. INTEGRAL CALCULUS AND DIFFERENTIAL EQUATIONS:
    • Integration as the inverse of differentiation.
    • Integration by substitution and by parts, standard integrals.
    • Definite integrals, determination of areas of plane regions.
    • Definition of order and degree of a differential equation, general and particular solutions.
  7. VECTOR ALGEBRA:
    • Vectors in two and three dimensions, magnitude, direction, and operations.
    • Scalar and vector products, applications in work done and moments of a force.
  8. STATISTICS AND PROBABILITY:
    • Classification of data, frequency distribution, graphical representation.
    • Measures of central tendency, correlation, regression.
    • Probability, random experiment, sample space, events, and probability distribution.

PAPER-II: GENERAL ABILITY TEST (Maximum Marks – 600)

Part ‘A’ – ENGLISH (Maximum Marks 200):

  • Grammar and usage, vocabulary, comprehension, and cohesion in extended text.

Part ‘B’ – GENERAL KNOWLEDGE (Maximum Marks 400):

  • Section ‘A’ (Physics): Physical properties, laws of motion, gravitation, thermodynamics, electricity, magnetism.
  • Section ‘B’ (Chemistry): Elements, compounds, acids, bases, salts, metals, non-metals, organic chemistry.
  • Section ‘C’ (General Science): Living and non-living, cell biology, human anatomy, epidemics, food constituents, solar system, achievements in science.
  • Section ‘D’ (History, Freedom Movement, etc.): Indian history, freedom movement, Indian constitution, world history, social and economic topics.
  • Section ‘E’ (Geography): Earth, rocks, weathering, ocean currents, atmosphere, climate, natural resources, regional geography of India.
  • Section ‘F’ (Current Events): Important events in India and the world, prominent personalities, current affairs.

Note: Out of the maximum marks assigned to Part ‘B,’ questions on Sections ‘A,’ ‘B,’ ‘C,’ ‘D,’ ‘E,’ and ‘F’ will carry approximately 25%, 15%, 10%, 20%, 20%, and 10% weightages, respectively.

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