Hello,

First of all the eligibility criteria for Air Force Wing of NDA is passed or appearing 10+2 from a recognized board with physics, chemistry, and mathematics, only unmarried males are allowed for this exam, and their age should be between 16.5 and 19.5 years.

Coming to the exam, it is conducted in offline mode having Mathematics(120 questions) and GAT(150 questions), each for a duration of 2 hours and 30 minutes, total marks is 900. the paper is set in English/Hindi.

Paper I for Mathematics has the following subjects and their respective topics;

Differential Calculus

• Concept of a real valued function–domain, range and graph of a function.
• Increasing and decreasing functions.
• Derivative of function at a point, geometrical and physical interpretation of a derivative - applications.
• Derivatives of sum, product and quotient of functions, derivative of a function with respect to another function, derivative of a composite function.
• Continuity of functions—examples, algebraic operations on continuous functions.
• Composite functions, one to one, onto and inverse functions. Notion of limit, Standard limits - examples.
• Second order derivatives.
• Application of derivatives in problems of maxima and minima.

Statistics and Probability

• Statistics
• Variance and standard deviation
• Union and Intersection of events.
• Conditional probability, Bayes’ theorem - simple problems.
• Complementary, elementary and composite events.
• Probability: Random experiment, outcomes and associated sample space, events, mutually exclusive and exhaustive events, impossible and certain events.
• Random variable as function on a sample space.
• Graphical representation
• Measures of Central tendency - Mean, median and mode.
• Binomial distribution, examples of random experiments giving rise to Binomial distribution.
• Definition of probability - classical and statistical - examples. Elementary theorems on probability - simple problems.

Vector Algebra

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

Analytical Geometry Of Two And Three Dimensions

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

Trigonometry

• Angles and their measures in degrees and in radians. Trigonometric ratios.
• Inverse trigonometric functions.
• Applications-Height and distance, properties of triangles.
• Trigonometric identities Sum and difference formulae. Multiple and Sub-multiple angles.

Matrices And Determinants

• Basic Properties
• Adjoint and inverse of a square matrix,
• Applications- Solution of a system of linear equations in two or three unknowns
• Determinant
• Types of matrices, operations on matrices.
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Algebra

• Sets and Venn diagrams.
• Representation of real numbers on a line.
• Arithmetic, Geometric and Harmonic progressions.
• De Morgan laws, Cartesian product, relation, equivalence relation.
• Complex numbers—basic properties, modulus, argument, cube roots of unity. Binary system of numbers.
• Conversion of a number in the decimal system to binary system and vice-versa.
• Logarithms and their applications.
• Quadratic equations with real coefficients. Solution of linear in equations of two variables by graphs.
• Permutation and Combination. Binomial theorem and its applications.

Integral Calculus And Differential Equations

• General and particular solution of differential equations, solution of first order and first-degree differential equations of various types - examples
• Application in problems of growth and decay.
• Integration as inverse of differentiation, integration by substitution and by parts, standard integrals involving algebraic expressions, trigonometric, exponential and hyperbolic functions.
• Definition of order and degree of a differential equation, formation of a differential equation by examples.
• Evaluation of definite integrals— determination of areas of plane regions bounded by curves—applications.

GAT consists of English/History/Geography/Physics/Chemistry.

you can check out the official notification of 2022 at https://www.upsc.gov.in/sites/default/files/Notif-NDANA-I-2022-engl-221221.pdf to know more details regarding this,