(Paper -2)

• Operations On Sets
• Venn Diagrams De Morgan Laws
• Cartesian Product Relation
• Equivalence Relation
• Representation Of Real Numbers 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 And Harmonic Progressions
• Quadratic Equations With Real Coefficients
• Solution Of Linear Inequations Of Two Variables By Graphs
• Permutation And Combination
• Binomial Theorem And Its Application
• Logarithms and Their Applications
• Concept Of A Set

• Types Of Matrices
• Operations On Matrices Determinant Of A Matrix
• Basic Properties of Determinant.
• Adjoint And Inverse Of A Square Matrix
• Applications – Solution of a System of Linear Equations in Two or Three Unknowns by Cramer’s Rule and By Matrix Method.

• 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 In Standard And In General, Form
• Standard Forms Of Parabola
• Ellipse And Hyperbola
• Eccentricity And Axis Of A Conic
• 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 and Angle between Two Planes.
• The equation of a Sphere.

• 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.

• 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.

• Integration As Inverse Differentiation
• Integration By Parts And Substitution
• Standard Integrals Involving Expression Of Algebraic,
• Trigonometric,
• Evaluation of Definite Integrals – Determination of Areas of Plane Regions
• Bounded By Curves – Applications.

• 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

• Classification Of Data
• Frequency Distribution
• Cumulative Frequency Distribution – Examples
• Graphical Representation – Histogram
• Pie Chart
• Frequency Polygon – Examples
• Measures Of Central Tendency – Mean Median And Mode
• Variance And Standard Deviation – Determination And Comparison
• Correlation And Regression

• 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.

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

• Grammar And Usage
• Vocabulary
• Comprehension And Cohesion In Extended Text
• Use Of Words

• Physical Properties And States Of Matter
• Mass
• Weight
• Volume
• Density
• Specific Gravity
• Principle Of Archimedes
• Pressure Barometer.
• Motion Of Objects
• Velocity And Acceleration
• Newton’s Laws Of Motion
• Force And Momentum
• Parallelogram Of Forces
• Stability And Equilibrium Of Bodies
• Gravitation
• Elementary Ideas Of Work
• Power and Energy.
• Effects Of Heat
• Measurement Of Temperature And Heat
• Change Of State And Latent Heat
• Modes of Transference of Heat.
• Sound Waves And Their Properties
• Simple Musical Instruments.
• Rectilinear Propagation Of Light
• Reflection and Refraction.

• Spherical Mirrors and Lenses.
• Human Eye.
• Natural And Artificial Magnets
• Properties Of A Magnet
• Earth as a Magnet.
• Static And Current Electricity
• 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.
• 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; Lightening Conductors, Safety Fuses.

• Physical and Chemical Changes.
• Elements Mixtures And Compounds Symbols Formulae
• Simple Chemical Equations Law Of Chemical Combination (Excluding Problems).
• Properties Of Air And Water.
• Preparation And Properties Of    Hydrogen, Oxygen, Nitrogen, Carbon Dioxide, Oxidation, And Reduction.
• Acids Bases And Salts.
• Carbon – Different Forms.
• Fertilizers – Natural And Artificial
• Material Used In The Preparation Of Substances Like Soap Glass Ink Paper Cement Paints Safety Matches And Gun-Powder.
• Elementary Ideas About The Structure Of Atom Atomic Equivalent And Molecular Weights Valency.

• Difference Between The Living And Non-Living
• Basis Of Life – Cells, Protoplasm’s And Tissues
• Growth And Reproduction In Plants And Animals
• Elementary Knowledge Of Human Body And Its Important Organs
• Common Epidemics, Their Causes And Prevention
• Food – Source Of Energy For Man. Constituents Of Food, Balanced Diet
• The Solar System – Meteors And Comets, Eclipses.
• Achievements Of Eminent(Important) Scientists

• A Broad Survey Of Indian History, With Emphasis On Culture And Civilization
• Freedom Movement In India
• Elementary Study Of Indian Constitution And Administration
• Elementary Knowledge Of Five Year Plans Of India
• Panchayati Raj, Co-Operatives AndCommunity Development
• Bhoodan, Sarvodaya, National Integration And Welfare State, Basic Teachings Of Mahatma Gandhi
• Forces Shaping The Modern World; Renaissance, Exploration, And Discovery; War Of American Independence. French Revolution, Industrial Revolution and Russian
• Impact of Science and Technology on Society.
• Concept of One World, United Nations, Panchsheel, Democracy.
• Socialism and Communism.
• Role of India in the Present World.

• Earth Its Shape and Size.
• Latitudes and Longitudes Concept of Time.
• International Date Line.
• Movements of Earth and Their Effects.
• Origin of Earth.
• Rocks And Their Classification
• Weathering
• Mechanical and Chemical Earthquakes and Volcanoes.
• Ocean Currents And Tides
• Atmosphere And Its Composition;
• Temperature And Atmospheric Pressure Planetary Winds Cyclones And Anti-Cyclones;
• Humidity
• Condensation And Precipitation
• Types of Climate.
• Major Natural Regions of the World.
• Regional Geography Of India
• Climate Natural Vegetation.
• Mineral And Power Resources
• Location and Distribution of Agricultural and Industrial Activities.
• Important Sea Ports and Main Sea Land and Air Routes of India.
• Main Items of Imports and Exports of India.

• Knowledge Of Important Events That Have happened In India In The Recent Years
• Current Important World Events
• Famous Personalities – Both Indian And International Including Those Connected With Cultural Activities And Sports.