The syllabus for UPSC NDA (National Defence Academy) examination (NDA 2) consists of two papers: Mathematics and General Ability Test (GAT). Below, I’ll provide a detailed syllabus for both papers:

## UPSC NDA 2 Syllabus – National Defence Academy 2 Syllabus

**Paper 1 Maths**

The Mathematics paper in the NDA 2 exam covers various topics up to the 10+2 (12th) level. The syllabus includes:

**Algebra:**- Concepts of sets, operations on sets, Venn diagrams
- De Morgan laws
- Real numbers
- Complex numbers
- Polynomials
- Linear equations
- Quadratic equations
- Arithmetic, geometric, and harmonic progressions

**Matrices and Determinants:**- Types of matrices
- Operations on matrices
- Determinants of matrices
- Adjoint and inverse of a matrix

**Trigonometry:**- Trigonometric ratios
- Trigonometric identities
- Heights and distances

**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
- Equation of a sphere

**Differential Calculus:**- Concept of a function
- Derivative of a function
- Limits and continuity
- Differentiation of algebraic, trigonometric, exponential, and logarithmic functions
- Applications of derivatives

**Integral Calculus and Differential Equations:**- Integration as an inverse process of differentiation
- Integration by substitution and by parts
- Standard integrals involving algebraic expressions, trigonometric, exponential, and logarithmic functions
- General and particular solutions of differential equations

**Vector Algebra:**- Vectors and scalars
- Scalar and vector products
- Vector addition and subtraction
- Position vector and a vector joining two points
- Scalar and vector triple products

**Statistics and Probability:**- Statistics: Classification of data, frequency distribution, cumulative frequency distribution, graphical representation of data, and more.
- Probability: Random experiments, outcomes, and associated sample space, events, and their probability, etc.

**Paper 2 General Ability Test (GAT)**

The General Ability Test in the NDA 2 exam comprises two parts: Part A (English) and Part B (General Knowledge).

**Part A – English:** This section tests the candidate’s proficiency in English. The syllabus includes:

- Vocabulary
- Grammar
- Comprehension
- Usage of Words

**Part B – General Knowledge:** This section assesses the candidate’s knowledge in various subjects:

- Physics
- Chemistry
- General Science
- Social Studies (History, Geography, and Civics)
- Current Events (National and International Importance)

It’s important to note that the NDA 2 syllabus is extensive and covers a broad range of topics. Candidates should prepare thoroughly and refer to relevant textbooks and study materials to excel in the examination. Additionally, staying updated with current affairs is essential for success in the General Knowledge section.