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Complex Numbers

Complex numbers as an ordered pair of real numbers and fundamental operations, Representation of complex numbers in the form a+ib, Modulus and Amplitude of complex numbers, illustrations, geometrical and polar representation of complex numbers in the Argand plane, Argand diagram.

De Moivre's Theorem

De Moivre's theorem, integral and rational indices, nth roots of unity, geometrical interpretations, and illustrations.

Quadratic Expressions

Quadratic expressions, equations in one variable, sign of quadratic expressions, change in signs, maximum and minimum values, quadratic inequalities.

Theory Of Equations

Relation between the roots and coefficients in an equation, solving equations when two or more roots of it are connected by certain relations, equation with real coefficients, occurrence of complex roots in conjugate pairs and its consequences, transformation of equations, and reciprocal equations.

Permutations And Combinations

The fundamental principle of counting - linear and circular permutations, permutations of 'n' dissimilar things taken 'r' at a time, permutations when repetitions allowed, circular permutations, permutations with constraint repetitions, combinations-definitions and certain theorems.

Binomial Theorem

Binomial theorem for positive integral index, binomial theorem for rational index (without proof), approximations using binomial theorem.

Partial Fractions

Partial fractions of f(x) / g(x) when g(x) contains non-repeated linear factors, partial fractions of f(x)/g(x) when g(x) contains repeated and/or non-repeated linear factors, partial fractions of f(x)/g(x) when g(x) contains irreducible factors.

Measures Of Dispersion

Mean deviation, variance and standard deviation of ungrouped/grouped data, coefficient of variation, analysis of frequency distributions with equal means but different variances.

Probability

Random experiments and events, the classical definition of probability, axiomatic approach and addition theorem of probability, independent and dependent events, conditional probability, multiplication theorem, Bayes ' theorem, random variables and probability distributions, random variables, theoretical discrete distributions, binomial and Poisson distributions.

Circle

Circle in standard form

centre and radius of a circle

length of a tangent,

conditions for a line to be tangent,

chord joining two points on a circle, equation of the tangent at a point on the circle,

point of contact, etc

System Of Circles

The angle between two intersecting circles, the radical axis of two circles, properties of common chord and common tangent of two circles, the radical centre, and the intersection of a line and a circle.

Parabola

Conic sections, parabola, equation of the parabola in standard form, different forms of parabola, parametric equations, equations of tangent and normal at a point on the parabola ( cartesian and parametric), conditions for a straight line to be a tangent.

Ellipse

Equation of ellipse in standard form, parametric equations, equation of tangent and normal at a point on the ellipse (cartesian and parametric), condition for a straight line to be a tangent.

Hyperbola

Equation of hyperbola in standard form, parametric equations, equations of tangent and normal at a point on the hyperbola (cartesian and parametric), conditions for a straight line to be a tangent, asymptotes.

Integration

Integration as the inverse process of differentiation, standard forms, properties of integrals, method of substitution, integration of algebraic expressions, exponential, logarithmic, trigonometric and inverse trigonometric functions, integration by parts, integration by partial fractions method, reduction formulae.

Definite Integrals

Definite integral as the limit of a sum, interpretation of the definite integral as an area, fundamental theorem of integral calculus, reduction formulae, application of the definite integral to areas.

Differential Equations

Formation of a differential equation, degree and order of an ordinary differential equation, solving differential equations by various methods.

Chapters

Topics

Waves

Transverse and longitudinal waves, Displacement relation in a progressive wave,

The speed of a travelling wave, the principle of superposition of waves, the Reflection of waves, Beats, Doppler effect.

Ray Optics and Optical Instruments

Reflection of Light by Spherical Mirrors, Refraction, Total Internal Reflection, Refraction at Spherical Surfaces and Lenses, Refraction through a Prism, Dispersion by a Prism, Some Natural Phenomena due to Sunlight, Optical Instruments.

Wave Optics

Huygens Principle, Refraction and reflection of plane waves using Huygens Principle, Coherent and Incoherent Addition of Waves, Interference of Light Waves and Young's Experiment, Diffraction, Polarisation.

Electric Charges and Fields

Electric Charges, Conductors and Insulators, Charging by Induction, Basic Properties of Electric Charge, Coulomb's Law, Forces between Multiple Charges, Electric Field, Electric Field Lines, Electric Flux, Electric Dipole, Dipole in a Uniform External Field, Continuous Charge Distribution, Gauss's Law, Application of Gauss's Law.

Electrostatic Potential and Capacitance

Electrostatic Potential, Potential due to a Point Charge, Potential due to an Electric Dipole, Potential due to a System of Charges, Equipotential Surfaces, Potential Energy of a System of Charges, Potential Energy in an External Field, Electrostatics of Conductors, Dielectrics and Polarisation, Capacitors and Capacitance, The Parallel Plate Capacitor, Effect of Dielectric on Capacitance, Combination of Capacitors, Energy Stored in a Capacitor, Van de Graaff Generator.

Current Electricity

Electric Current, Electric Currents in Conductors, Ohm's law, Drift of Electrons and the Origin of Resistivity, Limitations of Ohm's Law, Resistivity of various Materials, Temperature Dependence of Resistivity, Electrical Energy, Power, Combination of Resistors, Cells, emf, Internal Resistance, Cells in Series and in Parallel, Kirchhoff's Laws, Wheatstone Bridge, Meter Bridge.

Moving Charges and Magnetism

Magnetic Force, Motion in a Magnetic Field, Motion in Combined Electric and Magnetic Field, Magnetic Field due to a Current Element, Biot-Savart Law, Magnetic Field on the Axis of a Circular Current Loop, Ampere's Circuital Law, The Solenoid and the Toroid, Force between Two Parallel Currents, the Ampere, Torque on Current Loop, Magnetic Dipole, The Moving Coil Galvanometer.

Magnetism and Matter

The Bar Magnet, Magnetism and Gauss's Law, The Earth's Magnetism, Magnetisation and Magnetic Intensity, Magnetic Properties of Materials, Permanent Magnets and Electromagnets.

Electromagnetic Induction

The Experiments of Faraday and Henry, Magnetic Flux, Faraday's Law of Induction, Lenz's Law and Conservation of Energy, Motional Electromotive Force, Energy Consideration: A Quantitative Study, Eddy Currents, Inductance, AC Generator.

Alternating Current

AC Voltage Applied to a Resistor, Representation of AC Current and Voltage by Rotating Vectors, AC Voltage Applied to an Inductor, AC Voltage Applied to a Capacitor, AC Voltage Applied to a Series LCR Circuit, Power in AC Circuit: The Power Factor, LC Oscillations, Transformers.

Electromagnetic Wave

Displacement Current, Electromagnetic Waves, Electromagnetic Spectrum.

Dual Nature of Radiation and Matter

Electron Emission, Photoelectric Effect, Experimental Study of Photoelectric Effect, Photoelectric Effect and Wave Theory of Light, Einstein's Photoelectric Equation: Energy Quantum of Radiation, Particle Nature of Light: The Photon, Wave Nature of Matter.

Atoms

Alpha-particle Scattering, Rutherford's Nuclear Model of Atom, Atomic Spectra and Bohr Model of the Hydrogen Atom, The Line Spectra of the Hydrogen Atom.

Nuclei

Atomic Masses and Composition of Nucleus, Size of the Nucleus, Mass-Energy and Nuclear Binding Energy, Nuclear Force, Radioactivity, Nuclear Energy.

Semiconductor Electronics: Materials, Devices And Simple Circuit

Classification of Metals, Conductors and Semiconductors, Intrinsic Semiconductor, Extrinsic Semiconductor, p-n Junction, Semiconductor diode, Application of Junction Diode as a Rectifier.

Communication System

Elements of a Communication System, Basic Terminology Used in Electronic Communication Systems, Bandwidth of Signals, Bandwidth of Transmission Medium, Propagation of Electromagnetic Waves, Modulation and its Necessity, Amplitude Modulation, Production of Amplitude Modulated Wave, Detection of Amplitude Modulated Waves.

Chapters

Topics

Human Geography

Meaning, Nature, scope and relevance of Human Geography; Man - Environment relationships ;

Branches of Human Geography - their general characteristics

World Population

Distribution, density of population, Growth of population in the world.

Composition of population: Age and Sex.

Factors affecting/influencing the distribution of population

Migration: Internal and international; Causes and consequences

Human Development: concepts, Indicators and world patterns

Economic Geography

Economic Geography: Definition, Scope and Significance ;

Sectors of Economic activity: Concepts, changing trends.

Primary Activities: Concepts, changing trends. Food gathering, pastoral, mining and subsistence agriculture. In modern agriculture, people engage in agricultural and allied activities. Fisheries - factors and important fishing grounds; agricultural regions of the world.

Secondary Activities: Concepts. Manufacturing industries: Locational factors, types - distribution and production - Agro-based: Textile (cotton), forest-based (paper), Mineral-based (Iron and steel): Petrochemical. Small-scale manufacturing industries: locational factors, distribution and production. People engaged in secondary activities: examples

Tertiary Economic activities: Concepts, Trade, Transport and tourism; services, people engaged in the tertiary activities with some examples

Quaternary economic activities: Concepts, people engaged in the quaternary with some examples.

World Transport and Trade

Relative significance of different means of transport - Land transport, Railways - transcontinental

railways, Airways and Waterways.

Factors affecting land, water and air transport ;

World oceanic routes; important inland waterways and important canals ;

International trade - Impact of globalisation and economic development.

Role of WTO in International trade (World Trade Organization)

Environment and Resources

Resources: Definition, Classification - Resource depletion Environment: Meaning, definition and components; Environmental conservation and management; sustainable development

Human Settlements Settlement

Settlement types - rural and urban; urbanization trends and consequences

Physiography

Locational characteristics; Physical setting; Physiographic divisions; Geology, Drainage system: The Himalayan and Peninsular System

Climate

Origin of monsoon, climatic regions in India; distribution of temperature and rainfall Soils: Types and distribution, characteristics; Soil degradation and conservation

Vegetation: Types and distribution Wildlife conservation, Biosphere reserves

Population

Population: Size, Growth, Distribution and Density from 1901-2011; demographic characteristics: literacy, sex ratio; regional variations in population growth, Trends of Urbanization, population problems. Migration: International, National, causes and consequences. Human Development: Introduction and Regional Pattern

Resources

Mineral and Energy Resource Base: distribution and production Minerals - Iron ore, Manganese and Bauxite; Power resources - Coal, Petroleum and natural gas, hydroelectric power; Non - conventional sources of energy (Solar, Wind and Biogas), Conservation of Resources.

Land Resources

Agriculture: General Land Use, Land Use Classification Distribution and production of Major Crops - wheat, rice, sugarcane, cotton, caster and ground nut, Coffee and tea - their distribution, production and trade; Impacts of Green Revolution on Indian agriculture; Problems of Indian agriculture. Land Degradation

Water Resources

Irrigation and Power: Types of Irrigation, Wells, canals and tanks; Major multipurpose projects: Bakra Nangal, Nagarjuna Sagar, Narmada and Damodar Valley Corporation. Rain Water Harvesting and Watershed Management.

Industries

Location factors, growth, distribution and trade Iron and Steel, Petro Chemicals, Pharmaceuticals and Knowledge-based industries (IT), Globalization and Economic Development, SEZs

Transport and Trade

Means of transport; roadways, railways, airways and waterways, Major ports of India’s International trade.

Telangana

Administrative regions; physiography, Geology, Drainage

Climate

Distribution of climate, temperature and rainfall. Soils: Types and distribution, characteristics; Soil degradation and conservation Vegetation: Types and distribution

Population

Size, Growth, Distribution and Density from 1961-2011; demographic characteristics: literacy, sex ratio; Rural and Urban populations.

Chapters

Topics

Indian Constitution – Historical Content

a) Indian National Movement; Phases of National Movement, b) The Government of India Acts 1909, 1919, 1935

c) Constituent Assembly and framing of Indian Constitution d) Philosophy and basic features of the Constitution

Fundamental Rights & Directive Principles of State Policy

1. Fundamental Rights

2. Directive Principles of State Policy

3. Fundamental Duties

Union Government

1. The President of India

2. The Vice-President of India

3. The Prime Minister of India d)

4. Union Council of Ministers e) Parliament of India

5. Supreme Court of India

State Government

a) Governor

b) Chief Minister

c) Council of Ministers in the state

d) Legislative: Legislative Assembly

e) Legislative Council

f) High Court

Centre-State Relations

a) Centre-State Legislative, Administrative, Financial Relations

b) Centre-State Conflicts: Sarkaria Commission, M.M.Punchhi Commission

c) Centre Finance Commission

d) Inter–State Council

e) NITI Aayog

Local Governments

a) Rural Development & Panchayat Raj Institutions

b) Grassroot democracy: 73rd Amendment

c) 74th Amendment

d) Panchayat Raj and Urban Local bodies in Telangana

Election System in India

a) Central Election Commission

b) Powers and functions of the Election Commission

c) Electoral Reforms in India

d) Political Parties in India

e) Anti-Defection Law

Contemporary Issues in Indian Politics

a) Dynamic nature of Indian Politics

b) Regionalism

c) Coalition Politics

d) Corruption

e) Terrorism

Emergence of Telangana State

a) Formation of Hyderabad State

b) Political development

c) Gentlemen's Agreement

d) Emergency of Andhra Pradesh

e) Violation of Safeguards

f) 1969 Agitation – Telangana Praja Samithi

g) Reaction of Mulki Judgment

h) Telangana Movement

i) Role of JACs in Telangana Movement

j) A.P. Reorganisation Act, formation of Telangana state

SMART Governance

1. SMART Governance

b) Good Governance

c) E-Governance

d) Right to Information Act

e) Lokpal, Lokayutha Act - 2013

f) Transparency and Accountability

India and the World

a) Determinants of Foreign Policy

b) Basic Features of India’s Foreign Policy

c) India and Non-Aligned Movement

d) India and BRICS

e) India and BIMSTEC

f) SAARC

g) UNO