The NDA Examination is conducted twice a year by the Union Public Service Commission to recruit candidates in Army, Navy, and Air Force. NDA Written exam consists of two papers: Mathematics and GAT. Mathematics Section in NDA exam includes 120 questions and a total of 300 marks with 2.5 marks being awarded for each correct answer and 0.83 marks deducted for each incorrect one. The paper duration is of 2 and half hours.View NDA study plan below

For Mathematics NDA Syllabus candidates are required to know maths till 12th standard. This section tests the candidates’ calculative skills. Let us know the topic-wise NDA Mathematics syllabus and distribution of questions for each topic in the exam.

Sets Theory ( Day 1-7)
Venn diagrams, De Morgan laws, Cartesian product, relation, equivalence relation. Real numbers

Complex numbers ( Day 8-12)
Modulus, Cube roots, Conversion of a number in Binary system to Decimals and vice-versa. Arithmetic, Geometric and Harmonic progressions.
Quadratic equations ( Day 13-20)
Linear inequations, Permutation and Combination

Binomial theorem and Logarithms.  (Day 21-24)

Matrices and Determinants ( Day 25-30)
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.Angles and their measures in degrees and in radians.

Trigonometric ratios( Day 31-40)
Trigonometric identities Sum and difference formulae. Multiple and Sub-multiple angles. Inverse trigonometric functions. Applications-Height and distance, properties of triangles.

Calculus ( Day 41-80)
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, Continuity of functions, algebraic operations on continuous functions. Derivative of function at a point, geometrical and physical interpretation of a derivative-application. 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.

Vector Algebra ( Day 81-90)
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.

Analytical Geometry Of Two and Three Dimension ( Day 91-110)
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. Direction Cosines and direction ratios. Equation of a plane and a line in various forms. Angle between two lines and angle between two planes. Equation of a sphere.

Statistics & Probability ( Day 111-120)
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

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