Hello Aspirant,

See if you want to have the syllabus for NDA 2021 exam then why to spend money when you are getting it for free. I am describing down the complete syllabus for NDA 2021 :-

@Mathematics

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

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 in two or three unknowns by Cramer’s rule and by matrix method

Trigonometry

• Angles and their measures in degrees and in radians
• Trigonometrical ratios
• Trigonometric identities sum and difference formula
• Multiple and sub-multiple angles
• Inverse trigonometric functions
• Applications-height and distance, properties of triangles

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 in standard and in general form
• Standard forms of parabola, ellipse, and hyperbola
• Eccentricity and axis of a conic
• Point in a three dimensional space, distance between two points
• Direction cosines and direction ratios
• Equation two points
• Equation of a plane and a line in various forms
• Angle between two lines and angle between two planes
• Equation of a sphere

Differential calculus

• Concept of a real valued function-domain, range, and graph of a function
• Composite functions, one to one, onto, and inverse functions
• Notion of limit, standard limits-examples
• Continuity of functions-examples, algebraic operations on continuous 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
• Second order derivatives
• Increasing and decreasing functions
• Application of derivatives in problems of maxima and minima

Integral calculus and differential equations

• Integration as inverse of differentiation, integration by 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
• Definition of order and degree of a differential equation, formation of a differential equation by examples
• General and particular solution of a differential equations, solution of first order and first degree differential equations of various types-examples
• Application in problems of growth and decay

Vector algebra

• 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-work done by a force and moment of a force, and in geometrical problems

Statistics and probability

• 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
• Statistics: 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
• Probability: 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
• Probability: Examples of random experiments giving rise to binominal distribution

@English

• Grammar and usage
• Vocabulary
• Comprehension and cohesion

For complete syllabus please visit the link given below :-

https://competition.careers360.com/articles/nda-syllabus

I hope this information helps you.

Good Luck!!