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

## NDA Syllabus – National Defence Academy Syllabus

**Paper 1 Maths**

The Mathematics paper in the NDA exam covers a wide range of topics, typically 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 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)

**UPSC NDA Exam Pattern – National Defence Academy**

The UPSC NDA (National Defence Academy) exam follows a specific pattern that consists of a written examination and an interview process. Here’s a detailed exam pattern for the NDA exam:

**Written Examination**

**Paper-I: Mathematics**- Duration: 2.5 hours
- Maximum Marks: 300
- Questions: Objective-type multiple-choice questions
- Syllabus: Mathematics topics up to the 10+2 (12th) level, as described in the NDA syllabus.

**Paper-II: General Ability Test (GAT)**- Duration: 2.5 hours
- Maximum Marks: 600
- Questions: Objective-type multiple-choice questions
- Divided into two parts:
**Part A – English:**This section assesses the candidate’s proficiency in the English language.**Part B – General Knowledge:**This section evaluates the candidate’s knowledge in various subjects, including Physics, Chemistry, General Science, Social Studies (History, Geography, Civics), and Current Events (National and International Importance).

**Interview/Personality Test (SSB Interview)**

Candidates who qualify in the written examination are called for the Services Selection Board (SSB) interview, which is conducted in two stages:

**Stage I – Officer Intelligence Rating (OIR) Test and Picture Perception & Description Test (PP&DT):**- OIR Test: This includes reasoning and intelligence-related questions.
- PP&DT: Candidates are shown a picture and are required to write a story based on it.

**Stage II – Interview, Group Testing Officer Tasks, Psychology Tests, and Conference:**- Interview: Candidates are interviewed by SSB officials to assess their personality, communication skills, and suitability for the armed forces.
- Group Testing Officer Tasks: This includes group discussions, group planning exercises, and outdoor tasks.
- Psychology Tests: These include various psychological assessments to evaluate the candidate’s cognitive and behavioral traits.
- Conference: The final selection conference is held to decide the candidate’s suitability for commissioning.

**Medical Examination**

Candidates who clear the SSB interview undergo a medical examination to ensure they meet the prescribed medical standards. This examination is conducted by the Armed Forces Medical Services (AFMS) and includes a thorough physical examination and medical tests.

**Final Selection**

The final selection of candidates is based on their performance in the written examination, SSB interview, and medical examination. Successful candidates are then admitted to the NDA for training, and upon successful completion of the training program, they are commissioned as officers in their respective service branches.