Syllabus for NDA Written Exam

The National Defence Academy (NDA) written exam consists of two papers: Mathematics and General Ability Test (GAT). Let's take a closer look at the syllabus for each of these papers.

Mathematics:
1. Algebra:
- Sets, relations, and functions
- Complex numbers and quadratic equations
- Matrices and determinants
- Permutations and combinations
- Mathematical induction
- Binomial theorem and its simple applications
- Sequences and series
- Limit, continuity, and differentiability
- Integral calculus
- Differential equations
- Coordinate geometry
- Three-dimensional geometry
- Vector algebra
- Statistics and probability

2. Trigonometry:
- Trigonometric ratios and identities
- Trigonometric equations
- Inverse trigonometric functions
- Heights and distances

3. Analytical Geometry of Two and Three Dimensions:
- Rectangular Cartesian Coordinate System
- Distance formula
- Equation of a line and a plane
- Locus and its equation
- Translation of axes
- Rotation of axes
- Slope of a line
- Equation of a line in different forms
- Angle between two lines
- Distance of a point from a line
- Distance between two parallel lines
- Condition of perpendicularity and parallelism of two lines
- Equation of a circle
- Equation of a sphere
- Intersection of a line and a sphere
- Equation of a parabola, ellipse, and hyperbola

4. Differential Calculus:
- Concept of a real-valued function
- Limits, continuity, and differentiability
- Derivatives of standard functions
- Derivatives of sums, differences, products, and quotients of functions
- Chain rule
- Concept of a derivative
- Derivative of a function at a point
- Second-order derivatives
- Mean value theorem
- Maxima and minima
- Application of derivatives in problems of maxima and minima

5. Integral Calculus and Differential Equations:
- Integration as the inverse process of differentiation
- Integration of a variety of functions by substitution, by partial fractions, and by parts
- Definite and indefinite integrals
- Formation of ordinary differential equations
- Solution of homogeneous and linear differential equations
- Applications of integrals in finding areas under simple curves, etc.

General Ability Test (GAT):
1. English:
- Grammar and usage
- Vocabulary
- Comprehension and cohesion in extended text to test the candidate's proficiency in English

2. General Knowledge:
- Physics
- Chemistry
- General Science
- Social Studies
- Geography
- Current Events

3. Current Affairs:
- Questions related to current events in various fields like sports, politics, awards, etc.

4. History:
- Ancient, Medieval, and Modern History

5. Geography:
- Physical, Economic, and Human Geography

6. Physics:
- Laws of motion, energy, and power
- Work, force, and energy
- Motion and time
- Grav