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NDA Written Exam Syllabus & Question Weightage

Analyze every minute details of the UPSC NDA syllabus for Mathematics and GAT. Review topic distributions, marking weights, and sectional cutoff guidelines.

NDA Exam Pattern & Marking Scheme

The UPSC NDA written exam consists of two papers. Both papers feature multiple-choice questions (MCQs) and are conducted on the same day in offline mode. Candidates must clear the individual sectional cutoff (typically 25%) in both papers to be eligible for SSB evaluation.

Parameter Paper 1: Mathematics Paper 2: General Ability Test (GAT)
Total Questions 120 Questions 150 Questions
Maximum Marks 300 Marks 600 Marks
Correct Answer Weight +2.5 Marks +4.0 Marks
Negative Marking (1/3rd) -0.83 Marks -1.33 Marks
Duration 2.5 Hours (150 Mins) 2.5 Hours (150 Mins)
Sectional Cutoff 25% (75 Marks) 25% (150 Marks)

Detailed Topic-wise NDA Syllabus

Select a subject tab below to explore the minute, official UPSC syllabus guidelines. All subtopics listed here are fully covered in SenaPrep's study material modules and practice quizzes.

1. Algebra

  • Sets & Operations: Venn diagrams, set operations (union, intersection, difference), De Morgan laws, Cartesian product, relation, equivalence relations.
  • Real & Complex Numbers: Representation of real numbers on a line. Complex numbers—basic properties, modulus, argument, polar form, cube roots of unity.
  • Sequences & Series: Binary system of numbers (decimal to binary conversion & vice versa). Arithmetic Progression (AP), Geometric Progression (GP), and Harmonic Progression (HP).
  • Quadratic Equations & Inequalities: Solutions of quadratic equations with real coefficients, relations between roots and coefficients. Graphical solution of linear inequations in two variables.
  • Permutations, Combinations & Theorem: Permutations and Combinations. Binomial theorem and its applications. Logarithms and their algebraic properties.

2. Matrices and Determinants

  • Matrix Types & Operations: Transpose, symmetric and skew-symmetric matrices, orthogonal matrices. Addition, scalar multiplication, and multiplication of matrices.
  • Determinants & Inverses: Determinants of a square matrix, properties of determinants. Adjoint and inverse of a square matrix.
  • Linear Equation Systems: Solving linear equations in 2 or 3 variables using Cramer's Rule and Matrix Inverse Method.

3. Trigonometry

  • Trigonometric Ratios & Identities: Radian and degree measurements. Trigonometric functions, standard identities, sum and difference formulas.
  • Multiple Angles & Inverse functions: Multiple and sub-multiple angle values. Inverse trigonometric functions (domain, range, principal value branch).
  • Applications: Heights and distances, properties of triangles (sine formula, cosine formula, area of triangles).

4. Analytical Geometry (2D and 3D)

  • 2D Coordinate Geometry: Distance formula, section formula, midpoint. Equations of a straight line in intercept, slope-intercept, normal, and parametric forms. Angle between two lines. Distance of a point from a line.
  • Conic Sections: Circles in standard and general form. Standard equations of Parabola, Ellipse, and Hyperbola, including eccentricity, directrix, and latus rectum.
  • 3D Geometry: Coordinate axes in 3D space, distance between two points. Direction cosines and direction ratios. Equation of a plane and a straight line in vector and Cartesian forms. Angle between two planes and lines. Sphere equations.

5. Differential Calculus

  • Functions: Real-valued functions, domain, range, graphs. Composite functions, one-to-one, onto, and inverse functions.
  • Limits, Continuity & Derivatives: Standard limits, continuity, algebraic operations on continuous functions. Derivative of a function, geometrical and physical interpretations. Derivatives of sum, product, quotient, composite functions (Chain Rule).
  • Applications: Second-order derivatives. Increasing and decreasing functions. Maxima and minima of single variable functions.

6. Integral Calculus & Differential Equations

  • Integration: Integration as the inverse of differentiation. Integration by parts, substitution, and partial fractions. Standard integrals. Definite integrals and area under simple curves.
  • Differential Equations: Definition of order and degree. Formation of differential equations. Solution of first-order, first-degree differential equations (variable separable, homogeneous, and linear forms).

7. Vector Algebra

  • Vector Operations: Vectors in 2D and 3D space, magnitude and direction. Unit and null vectors. Addition, scalar multiplication.
  • Dot & Cross Products: Scalar (dot) product and vector (cross) product of two vectors. Applications in geometry, work done, and moment of a force.

8. Statistics and Probability

  • Statistics: Graphical representation of data (Histogram, Pie Chart, frequency polygon). Measures of central tendency (Mean, Median, Mode). Variance and standard deviation. Correlation and regression lines.
  • Probability: Sample space, mutually exclusive and exhaustive events. Probability theorems (union, intersection). Conditional probability, Bayes' Theorem. Random variables, binomial distributions.

Practice Syllabus Chapter-by-Chapter

Ensure you are thoroughly prepared for every topic in the UPSC syllabus. Click on any of the chapters below from SenaPrep's interactive database to test your knowledge with free live questions.

Frequently Asked Questions

What is the syllabus level for the NDA exam?

Paper 1 (Maths) matches Class 11 and 12 CBSE curriculum, while GAT covers basic high school science and social studies up to Class 10/12 level.

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