ALGEBRA:

• Concept Of A Set
• Operations on Set
• Venn Diagrams De Morgan Laws
• Cartesian Product Relation
• Equivalence Relation
• Representation of Real Number on a Line
• Complex Numbers – Basic Properties
• Modulus Argument
• Cube Roots of Unity
• Binary System of Numbers
• Conversion of a number in Decimal
• System to binary system and vice-versa
• Arithmetic
• Geometric & Harmonic Progression
• Quadratic Equations with Real Coefficients
• The solution of Linear Inequations of two variables by Graph
• Permutation and combination
• Binomial theorem and its application
• Logarithms and their applications

Matrices and Determinant:

• Types of Matrices
• Operations on Matrices Determinant of a Matrix
• Basic Properties of Determinant
• Adjoint & Inverse of a Square Matrix
• Applications—Solutions of a System of Linear Equations in two or three unknowns by Cramer’s Rule and by Matrix Method.

Analytics Geometry Of Two and Three Dimension:

• Rectangular Cartesian Coordinate System
• Diatance Formula
• Equation of a line in various forms
• The angle between two lines
• Equations of a circle in standard and in general form
• Ellipse & Hyperbola
• Eccentricity ad Axis of a Conic
• The point in a three Dimensional space, Distance between two points
• Direction Cosines and Direction Ratios
• The equation of a plane and a Line in various forms
• The angle between two lines & the angle between two planes
• The equation of a sphere

Trigonometry:

• Angles And Their Measures In Degrees And In Radians
• Trigonometrical Ratios
• Trigonometric Identities Sum And Difference Formulae
• Multiple And Sub-Multiple Angles
• Inverse Trigonometric Functions
• Applications – Height And Distance
• Properties of Triangles.

Differential Calculus:

• Concept Of A Real-Valued Function – Domain
• Range And Graph Of A Function
• Composite Functions
• Derivative Of Function At A Point
• Derivatives Of Sum
• Product And Quotient Of Functions
• Derivative Of A Function With Respect Of Another Function
• Derivative Of A Composite Function
• Second-Order Derivatives
• Increasing And Decreasing Functions
• Application of Derivatives in Problems of Maxima and Minima.

Syllabus for Integral Calculus:

• Integration as Inverse Differentiation
• Integration by parts and Substitution
• Standard Integrals Involving Expression of Algebric
• Hyperbolic and Exponential Function
• Trigonometric
• Evaluation of definite Integrals—Determination of areas of plane regions bounded by curves.

Syllabus for Differential Equation:

• Definition Of Order And Degree Of A Differential Equation
• Formation Of A Differential Equation
• General And Particular Solution Of A Differential Equation
• Solution Of First Order And First Degree Differential Equations Of Various Types
• Application In Problems Of Growth And Decay

Statistics:

• Classification of data
• Frequency distribution
• Cumulative Frequency Distribution—examples
• Graphical Representation – Histogram
• Pie chart
• Frequency Polygon – examples
• Measures of Central Tendency – Mean Median & Mode
• Variance & Standard Deviation Determination & Comparision
• Correlation and Regression

Syllabus for Probability:

• Random Experiment
• Outcomes And Associated Sample Space
• Events
• Mutually Exclusive And Exhaustive Events
• Impossible And Certain Events
• Union And Intersection Of Events
• Complementary
• Elementary And Composite Events
• Conditional Probability
• Bayes’ Theorem – Simple Problems
• Random Variable As Function On A Sample Space
• Binomial Distribution
• Examples of Random Experiments Giving Rise to Binominal Distribution.

Syllabus for Vector Algebra:

• Vectors In Two And Three Dimensions
• Magnitude And Direction Of A Vector
• Unit And Null Vectors Addition Of Vectors
• Scalar Multiplication Of Vector

PHYSICS:

• Newton’s Laws of Motion,
• Force and Momentum,
• The motion of objects,
• Parallelogram of Forces,
• Stability and Equilibrium of bodies,
• Gravitation, elementary ideas of work,
• Velocity and Acceleration,
• Power and Energy,
• Properties of a Magnet,
• Earth as a Magnet
• Siphon, Levers,
• Balloon, Pumps,
• Hydrometer, Pressure Cooker
• Sound waves and their properties,
• Simple musical instruments,
• Natural and Artificial Magnets
• Thermos Flask, Gramophone
• Telegraphs, Telephone, Periscope
• Telescope, Microscope
• Mariner’s Compass
• Lightening Conductors
• Safety Fuses
• Simple Pendulum.
• Simple Pulleys
• Physical Properties and States of Matter
• Mass, Weight, Volume, Density, and Specific Gravity
• Principle of Archimedes
• Pressure Barometer
• Effects of Heat
• change of State and Latent Heat
• Modes of transference of Heat
• Rectilinear propagation of Light
• Reflection and refraction
• Spherical mirrors and Lenses
• Human Eye, Static and Current Electricity
• Measurement of temperature and heat
• conductors and Non-conductors
• 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.

CHEMISTRY:

• Preparation and Properties of Nitrogen
• Hydrogen, Oxygen & Carbon Dioxide
• Oxidation & Reduction
• The material used in the preparation of substances like Glass, Soap, Paper, Ink, Cement, Paints, Safety Matches, Gunpowder
• Carbon – different forms
• Physical & Chemical changes
• Symbols, Formulas, and simple Chemical Equations
• Law of Chemical Combination (excluding problems)
• Properties of Air and Water
• Acids, bases and salts, Elements, Mixtures and Compounds
• Fertilizers – Natural and Artificial
• Elementary ideas about the Structure of Atom
• Atomic, Equivalent and Molecular Weights, Valency.

GENERAL SCIENCE:

• Basis of Life – Cells, Protoplasms, and Tissues
• Constituents of food, Balanced Diet
• Achievements of Eminent Scientists
• Difference between the living and non-living
• Elementary knowledge of the human body and its important organs
• Food – Source of Energy for man
• Growth and Reproduction in Plants and Animals
• Common Epidemics, their causes, and prevention
• The Solar System – Meteors and Comets, Eclipses.

HISTORY:

• Freedom Movement in India
• Bhoodan, Sarvodaya
• National Integration and Welfare State
• Basic Teachings of Mahatma Gandhi
• A broad survey of Indian History, with emphasis on Culture and Civilisation
• Elementary knowledge of Five Year Plans of India
• Elementary study of Indian Constitution and Administration
• Panchayati Raj, Forces shaping the modern world
• Renaissance, Exploration, and Discovery
• War of American Independence
• French Revolution
• Industrial Revolution and Russian Revolution
• Impact of Science and Technology on Society
• Concept of one World
• United Nations, Panchsheel
• Democracy, Socialism, and Communism
• Co-operatives and Community Development
• Role of India in the present world.

GEOGRAPHY:

• Origin of Earth, Weathering – Mechanical and Chemical
• Earthquakes and volcanoes
• The atmosphere and its composition
• Temperature and Atmospheric Pressure
• Rocks and their classification
• Planetary Winds, cyclones, and Anti-cyclones
• Humidity, Condensation, and Precipitation
• Major Natural Regions of the World
• Important Sea ports and main sea
• land and air routes of India
• Main items of Imports and Exports of India
• Types of Climate
• The Earth, its shape and size, Lattitudes and Longitudes
• Concept of time, International Date Line
• Movements of Earth and their effects
• Ocean Currents and Tides
• Regional Geography of India
• Climate, Natural vegetation
• Mineral and Power resources
• location and distribution of agricultural and industrial activities.