Part A

English

The question paper in English will be designed to test the candidate’s understanding of English and workmanlike use of words. The syllabus covers various aspects like: Grammar and usage, vocabulary, comprehension, and cohesion in extended text to test the candidate’s proficiency in English.

200

Part B

General Knowledge

The question paper on General Knowledge will broadly cover Physics, Chemistry, General Science, Social Studies, Geography, and Current Events. The syllabus given below is designed to indicate the scope of these subjects included in this paper. The topics mentioned are not to be regarded as exhaustive and questions on topics of similar nature not specifically mentioned in the syllabus may also be asked. Candidate’s answers are expected to show their knowledge and intelligent understanding of the subject.

400

Section A (Physics)

1. Physical Properties and States of Matter

2. Mass, Weight, Volume, Density, and Specific Gravity

3. Principle of Archimedes

4. Pressure Barometer

5. Motion of objects, Velocity and Acceleration

6. Newton’s Laws of Motion

7. Force and Momentum

8. Parallelogram of Forces

9. Stability and Equilibrium of bodies

10. Gravitation

11. Elementary ideas of work, Power and Energy

12. Effects of Heat, Measurement of Temperature and Heat, change of State and Latent Heat

13. Modes of transference of Heat

14. Sound waves and their properties

15. Simple musical instruments

16. Rectilinear propagation of Light, Reflection and refraction

17. Spherical mirrors and Lenses

18. Human Eye

19. Natural and Artificial Magnets

20. Properties of a Magnet

21. Earth as a Magnet2

2. Static and Current Electricity

23. Conductors and Non-conductors

24. Ohm’s Law

25. Simple Electrical Circuits

26. Heating, Lighting and Magnetic effects of Current

27. Measurement of Electrical Power

28. Primary and Secondary Cells

29. Use of X-Rays

30. General Principles in the working of Simple Pendulum, Simple Pulleys, Siphon, Levers, Balloon, Pumps, Hydrometer, Pressure Cooker, Thermos Flask, Gramophone, Telegraphs, Telephone, Periscope, Telescope, Microscope, Mariner’s Compass; Lightning Conductors, Safety Fuses.

Section B (Chemistry)

1. Physical and Chemical changes

2. Elements, Mixtures and Compounds

3. Symbols, Formulae and simple Chemical Equations

4. Law of Chemical Combination (excluding problems)

5. Properties of Air and Water

6. Preparation and Properties of Hydrogen, Oxygen, Nitrogen, and Carbon dioxide, Oxidation and Reduction

7. Acids, bases and salts

8. Carbon—different forms

9. Fertilizers—Natural and Artificial

10. Material used in the preparation of substances like Soap, Glass, Ink, Paper, Cement, Paints, Safety Matches, and Gunpowder

11. Elementary ideas about the structure of Atom

12. Atomic Equivalent and Molecular Weights

13. Valency

Section C (General Science)

1. Difference between the living and non-living

2. Basis of Life—Cells, Protoplasms, and Tissues

3. Growth and Reproduction in Plants and Animals

4. Elementary knowledge of Human Body and its important organs

5. Common Epidemics, their causes and prevention

6. Food—Source of Energy for man

7. Constituents of food

8. Balanced Diet

9. The Solar System—Meteors and Comets, Eclipses

10. Achievements of Eminent Scientists

Section D (History, Freedom Movement, etc.)

1. A broad survey of Indian History, with emphasis on Culture and Civilization

2. Freedom Movement in India

3. Elementary study of Indian Constitution and Administration

4. Elementary knowledge of Five Year Plans of India

5. Panchayati Raj, Co-operatives and Community Development

6. Bhoodan, Sarvodaya, National Integration and Welfare State

7. Basic Teachings of Mahatma Gandhi

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

9. War of American Independence

10. French Revolution, Industrial Revolution and Russian Revolution

11. Impact of Science and Technology on Society

12. Concept of one World

13. United Nations

14. Panchsheel, Democracy, Socialism, and Communism

15. Role of India in the present world

Section E (Geography)

1. The Earth, its shape and size

2. Latitudes and Longitudes, Concept of time

3. International Date Line

4. Movements of Earth and their effects

5. Origin of Earth

6. Rocks and their classification

7. Weathering—Mechanical and Chemical, Earthquakes, and Volcanoes

8. Ocean Currents and Tides<br>9. Atmosphere and its composition

10. Temperature and Atmospheric Pressure, Planetary Winds, Cyclones and Anti-cyclones

11. Humidity; Condensation and Precipitation; Types of Climate

12. Major Natural regions of the World

13. Regional Geography of India—Climate, Natural vegetation, Mineral and Power resources

14. Location and distribution of agricultural and Industrial activities

15. Important Sea ports and main sea, land, and air routes of India

16. Main items of Imports and Exports of India

Section F (Current Events)

1. Knowledge of Important events that have happened in India in the recent years

2. Current important world events

3. Prominent personalities—both Indian and International including those connected with cultural activities and sports

Unit I: Relations and Functions

Relations and Functions

Types of relations: reflexive, symmetric, transitive, and equivalence relations. One to one and onto functions.

Inverse Trigonometric Functions

Definition, range, domain, principal value branch. Graphs of inverse trigonometric functions.

Unit II: Algebra

Matrices

Concept, notation, order, equality, types of matrices, zero and identity matrix, transpose of a matrix, symmetric and skew-symmetric matrices. Operations on matrices: Addition and multiplication, scalar multiplication. Non-commutativity of multiplication of matrices and existence of non-zero matrices whose product is the zero matrix (restrict to square matrices of order 2). Invertible matrices and proof of the uniqueness of inverse (real entries only).

Determinants

Determinant of a square matrix (up to 3 x 3 matrices), minors, co-factors, applications of determinants in finding the area of a triangle. Adjoint and inverse of a square matrix. Consistency, inconsistency, number of solutions of system of linear equations by examples, solving system of linear equations in two or three variables (having unique solution) using the inverse of a matrix.

Unit III: Calculus

Continuity and Differentiability

Continuity and differentiability, chain rule, derivative of inverse trigonometric functions like sin⁡−1(x),cos⁡−1(x),tan⁡−1(x)\text{like } \sin^{-1}(x), \cos^{-1}(x), \tan^{-1}(x). Derivative of implicit functions. Concept of exponential and logarithmic functions. Derivatives of logarithmic and exponential functions. Logarithmic differentiation, derivative of functions expressed in parametric forms. Second order derivatives.

Applications of Derivatives

Rate of change of quantities, increasing/decreasing functions, maxima and minima (first derivative test motivated geometrically, second derivative test as a provable tool). Simple problems illustrating basic principles and real-life situations.

Integrals

Integration as an inverse process of differentiation. Integration of functions by substitution, partial fractions, and parts. Evaluation of simple integrals and problems based on them. Fundamental Theorem of Calculus (without proof). Basic properties of definite integrals and evaluation of definite integrals.

Applications of the Integrals

Finding the area under simple curves, especially lines, circles/parabolas/ellipses (in standard form only).

Differential Equations

Definition, order and degree, general and particular solutions of a differential equation. Solution by the method of separation of variables, solutions of homogeneous differential equations of first order and first degree. Solutions of linear differential equations of the type dydx+py=q\frac{dy}{dx} + py = q and dxdy+px=q\frac{dx}{dy} + px = q, where p and q are functions of x or constants.

Unit IV: Vectors and Three-Dimensional Geometry

Vectors

Vectors and scalars, magnitude and direction of a vector. Direction cosines and direction ratios of a vector. Types of vectors (equal, unit, zero, parallel, collinear vectors), position vector of a point, negative of a vector, components, addition, multiplication by a scalar, position vector of a point dividing a line segment in a given ratio. Definition, geometrical interpretation, properties and application of scalar (dot) product, vector (cross) product.

Three-Dimensional Geometry

Direction cosines and direction ratios of a line joining two points. Cartesian and vector equations of a line, skew lines, shortest distance between two lines. Angle between two lines.

Unit V: Linear Programming

Linear Programming

Introduction, related terminology (constraints, objective function, optimization), graphical method for problems in two variables, feasible and infeasible regions (bounded/unbounded), feasible and infeasible solutions, optimal feasible solutions (up to three non-trivial constraints).

Unit VI: Probability

Probability

Conditional probability, multiplication theorem on probability, independent events, total probability, Bayes’ theorem, Random variable and its probability distribution, mean of random variable.