National Defence Academy (NDA)

1. Selection Process for NDA

The Selection Process for NDA are :-

1. Written Examination
2. SSB Interview

2. Educational Qualification for NDA

1. Passed or appearing in Class 12.
2. For Air Force and Naval Wings: Passed or appearing in Class 12.
3. Candidates must have studied Physics, Chemistry and Mathematics in Class 12

3. Age Limit for NDA

The Age limit for NDA are

1. Minimum – 16.5
2. Maximum – 19

4. Physical Efficiency Test for NDA

In NDA physical test, the eligibility of candidates is measured as per height, weight and medical standards.

• 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 a decimal system to a binary system and vice-versa.
• Arithmetic, geometric and harmonic progressions.
• Quadratic equations with real coefficients.
• The solution of linear inequations of two variables by graphs.
• Permutation and combination.
• Binomial theorem and its applications.
• Logarithms and their applications.

• Types of matrices
• Operations on matrices
• Determinant of a matrix
• Basic properties of determinants
• Adjoint and inverse of a square matrix
• Applications of matrices

1. Solution of a system of linear equations in two or three unknowns using Cramer’s rule
2. Solution of a system of linear equations in two or three unknowns using Matrix Method

• Angles and their measures in degrees and radians
• Trigonometric ratios
• Trigonometric identities including sum and difference formulae
• Multiple and sub-multiple angles
• Inverse trigonometric functions
• Applications such as height and distance and properties of triangles.

• Rectangular Cartesian Coordinate system
• Distance formula
• Equation of a line in various forms
• The angle between two lines
• The distance of a point from a line
• Equation of a circle in standard and general form
• Standard forms of parabola, ellipse, and hyperbola
• Eccentricity and axis of a conic
• A point in three-dimensional space and the distance between two points
• Direction cosines and direction ratios
• Equation of a plane and a line in various forms
• The angle between two lines and the angle between two planes
• Equation of a sphere

• Concept of a real-valued function including domain, range, and graph of a function.
• Composite functions and their properties including one-to-one, onto, and inverse functions.
• Understanding of the notion of limit and examples of standard limits.
• Continuity of functions and examples, including algebraic operations on continuous functions.
• Derivative of a function at a point, with geometrical and physical interpretation, and applications.
• Derivatives of sum, product, and quotient of functions, a derivative of a function with respect to another function, a derivative of a composite function, and second-order derivatives.
• Understanding increasing and decreasing functions.
• Application of derivatives in problems of maxima and minima.

• Integration as the inverse of differentiation.
• Methods of integration: substitution and by parts.
• Standard integrals involving algebraic expressions, trigonometric, exponential, and hyperbolic functions.
• Evaluation of definite integrals.
• Determination of areas of plane regions bounded by curves.
• Applications of integrals.
• Definition of order and degree of a differential equation.
• Formation of a differential equation by examples.
• General and particular solutions of differential equations.
• Solutions of the first-order and first-degree differential equations of various types.
• Applications in problems of growth and decay.

• Vectors in two and three dimensions
• Magnitude and direction of a vector
• Unit and null vectors
• Addition of vectors
• Scalar multiplication of a vector
• Scalar product or dot product of two vectors
• Vector product or cross product of two vectors
• Applications in work done by a force and moment of a force and in geometrical problems

• Statistics
• Classification of data
• Frequency distribution
• Cumulative frequency distribution—examples
• Graphical representation—Histogram, Pie Chart, frequency polygon— examples
• Measures of Central tendency—Mean, median and mode
• Variance and standard deviation—determination and comparison
• Correlation and regression
• Probability
• Random experiment, outcomes and associated sample space, events
• Mutually exclusive and exhaustive events, impossible and certain events
• Union and Intersection of events
• Complementary, elementary and composite events
• Definition of probability—classical and statistical—examples
• Elementary theorems on probability—simple problems
• Conditional probability, Bayes’ theorem—simple problems
• Random variable as function on a sample space
• Binomial distribution, examples of random experiments giving rise to Binomial distribution.

• Grammar & usage
• Comprehension & cohesion
• Spotting errors
• Para Jumbling
• Fill in the blanks
• Synonyms & Antonyms
• Vocabulary
• Cloze Test
• Idioms & Proverbs
• Completion of Sentence & Para
• Sentence Correction & Improvement

Physical Measurement Test

Written Examination Pattern