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Here is the Syllabus for NDA

Mathematics

• Differential Calculus

1. Concept of a real valued function–domain, range and graph of a function.

2. Increasing and decreasing functions.

3. Derivative of function at a point, geometrical and physical interpretation of a derivative - applications.

4. Derivatives of sum, product and quotient of functions, derivative of a function with respect to another function, derivative of a composite function.

5. Continuity of functions—examples, algebraic operations on continuous functions.

6. Composite functions, one to one, onto and inverse functions. Notion of limit, Standard limits - examples.

7. Second order derivatives.

8. Application of derivatives in problems of maxima and minima.

• Statistics and Probability

1. Statistics

2. Variance and standard deviation

3. Union and Intersection of events.

4. Conditional probability, Bayes’ theorem - simple problems.

5. Complementary, elementary and composite events.

6. Probability: Random experiment, outcomes and associated sample space, events, mutually exclusive and exhaustive events, impossible and certain events.

7. Random variable as function on a sample space.

8. Graphical representation

9. Measures of Central tendency - Mean, median and mode.

10. Binomial distribution, examples of random experiments giving rise to Binomial distribution.

11. Definition of probability - classical and statistical - examples. Elementary theorems on probability - simple problems.

• Vector Algebra

1. Vector product or cross product of two vectors.

2. Applications—work done by a force and moment of a force and in geometrical problems.

3. Addition of vectors, scalar multiplication of a vector

4. Vectors in two and three dimensions,

5. Unit and null vectors

6. Scalar product or dot product of two vectors.

• Analytical Geometry Of Two And Three Dimensions

1. Equation of a circle in standard and in general form. Standard forms of parabola, ellipse and hyperbola.

2. Equation of a sphere.

3. Angle between two lines.

4. Rectangular Cartesian Coordinate system. Distance formula. Equation of a line in various forms.

5. Distance of a point from a line.

6. Equation two points.

7. Equation of a plane and a line in various forms.

8. dimensional space, distance between two points.

9. Direction Cosines and direction ratios.

10. Angle between two lines and angle between two planes.

11. Eccentricity and axis of a conic. Point in a three

• Trigonometry

1. Angles and their measures in degrees and in radians. Trigonometric ratios.

2. Inverse trigonometric functions.

3. Applications-Height and distance, properties of triangles.

4. Trigonometric identities Sum and difference formulae. Multiple and Sub-multiple angles.

• Matrices And Determinants

1. Basic Properties

2. Adjoint and inverse of a square matrix,

3. Applications- Solution of a system of linear equations in two or three unknowns

4. Determinant

5. Types of matrices, operations on matrices.

• Algebra

1. Sets and Venn diagrams.

2. Representation of real numbers on a line.

3. Arithmetic, Geometric and Harmonic progressions.

4. De Morgan laws, Cartesian product, relation, equivalence relation.

5. Complex numbers—basic

6. properties, modulus, argument, cube roots of unity. Binary system of numbers.

7. Conversion of a number in the decimal system to binary system and vice-versa.

8. Logarithms and their applications.

9. Quadratic equations with

10. real coefficients. Solution of linear in equations of two variables by graphs.

11. Permutation and Combination. Binomial theorem and its applications.

• Integral Calculus And Differential Equations

1. General and particular solution of differential equations, solution of first order and first-degree differential equations of various types - examples

2. Application in problems of growth and decay.

3. Integration as inverse of differentiation, integration by substitution and by parts, standard integrals involving algebraic expressions, trigonometric, exponential and hyperbolic functions.

4. Definition of order and degree of a differential equation, formation of a differential equation by examples.

5. Evaluation of definite integrals— determination of areas of plane regions bounded by curves—applications.

ENGLISH

1. Comprehension

2. Fill in the blanks

3. Complete the sentences

4. Idioms and phrases

5. Synonym and antonym

6. Active and passive voice

7. Finding errors

HISTORY

1. Indian history: Culture and civilization

2. Bhoodan, Sarvodaya, National Integration and Welfare State, Basic Teachings of Mahatma Gandhi

3. India freedom struggle

4. Panchayati Raj, Co-operatives and Community Development

5. French Revolution, Industrial Revolution and Russian Revolution.

6. Impact of Science and Technology on Society.

7. Concept of one World, United Nations, Panchsheel, Democracy, Socialism and Communism

8. Forces shaping the modern world; Renaissance, Exploration and Discovery

GEOGRAPHY

1. Land forms of india

2. Movements of Earth and their effects.

3. Layers of earth

4. Type of soils

5. Climate and Atmosphere

6. Rivers

7. Cyclones and Anticyclones

8. Solar system and universe

9. Rocks and their classification

Natural and Artificial Magnets, Properties of a Magnet, Earth as a Magnet.

1. Spherical mirrors and Lenses, Human Eye.

2. Density and Specific Gravity, Principle of Archimedes, Pressure Barometer.

3. Rectilinear propagation of Light, Reflection and refraction.

4. Static and Current Electricity, conductors and Non-conductors,

5. Physical Properties and States of Matter, Mass, Weight, Volume,

6. Heat, Measurement of Temperature and Heat, change of State and Latent Heat, Modes of transference of Heat

7. Ohm’s Law, Simple Electrical Circuits, Heating, Lighting and Magnetic effects of Current, Measurement of Electrical Power, Primary and Secondary Cells, Use of X-Rays.

8. Equilibrium of objects

9. Laws of motion

10. Gravitation

11. Work, power and energy

CHEMISTRY

1. Elements, Mixtures and Compounds, Symbols, Formulae and simple Chemical Equations, Law of Chemical Combination

2. Properties of Air and Water

3. Fertilizers— Natural and Artificial

4. Material used in the preparation of substances like Soap, Glass, Ink, Paper, Cement, Paints, Safety Matches and Gun-Powder

5. Elementary ideas about the structure of Atom, Atomic Equivalent and Molecular Weights, Valency

6. Preparation and Properties of Hydrogen

Rest of the syllabus and Exam Pattern is in the comment box.