## PAPER I - Part i (Geographical, Historical, Cultural and General Knowledge of Rajasthan)

Location, extent, relief features, climate, drainage, vegetation, agriculture, livestock, dairy development, population distribution, growth, literacy, sex ratio, religious composition, industries, planning, budgetary trends, major tourist centres.

Ancient Culture & Civilisation of Rajasthan, Kalibangan, Ahar, Ganeshwar, Bairath.

History of Rajasthan from 8^{th} to 18^{th} Century

❶ Gurjar Pratihars

❷ Chauhans of Ajmer

❸ Relations with Delhi Sultanate - Mewar, Ranthambore and Jalore.

❹ Rajasthan and Mughals - Sanga, Pratap, Mansingh of Amer, Chandrasen, Rai Singh of Bikaner, Raj singh of Mewar.

History of freedom struggle in Rajasthan

❶Peasants and Tribal Movements.

❷Prajamandal Movement.

Integration of Rajasthan

Role of women during Medieval and Modern period.

Society and Religion

❶ Lok Devata and Devian.

❷ Saints of Rajasthan.

❸ Architecture - Temples, Forts and Palaces.

❹ Paintings - Various Schools.

❺ Fairs and Festivals.

❻ Customs, Dresses and Ornaments.

❼ Folk Music and Dance.

❽ Language and Literature

Office of Governor; Role and Functions of Chief Minister and Cabinet; State Secretariat and Chief Secretary; Organisation and role of the Rajasthan Public Service Commission and State Human Rights Commission, Panchayati Raj in Rajasthan.

## PAPER I - Part ii (Current Affairs of Rajasthan)

Major current issues and happenings at state level related to socio-economic, political, games and sports aspects.

## PAPER I - Part iii(General Knowledge of World & India)

Continents, Oceans and their characteristics, global wind system, environmental problems, global strategies, globalization and its impacts, population trend and distribution, India and U.N.O., Major trends in International policies with special reference to Globalization and Nuclear nonproliferation.

Location and its advantages, Monsoonal system, drainage characteristics, changing patterns of agriculture and industries, national income-concept & trends, poverty, reduction schemes, Features of India's foreign policy, Nehru's contribution in its making.

Major Landmarks in the Constitutional History of India with special reference to Government of India Acts of 1919 and 1935

Gandhi's contribution to National Movement; Ambedkar and Constitution; Making; Salient features of Indian Constitution, Fundamental Rights, Duties and Directive Principles of State Policy; offices of the Indian President and Prime Minister; India's federal system; Major Political Parties.

## PAPER I - Part iv (Educational Psychology)

Educational Psychology - its meaning, scope and implications for teacher in classroom situations. Various psychologists and their contributions in education.

Learning - its meaning and types, different theories of learning and implications for a teacher, transfer of learning, factors affecting learning, constructivist learning.

Development of learner - Physical, emotional and social development, development of child as an individual- concept development.

Personality - meaning, theories and assessment, adjustment and its mechanism, maladjustment.

Intelligence and creativity - meaning, theories and measurement, role in learning, emotional intelligence- concept and practices, human cognition.

Motivation - meaning and role in the process of learning, achievement motivation.

Individual differences - meaning and sources, Education of children with special needs - Gifted and talented students, slow learners, delinquency.

Development and implications in education of - Self concept, attitudes, interest, habits, aptitude and social skills.

# PAPER II : Part - i (Secondary and Senior Secondary standard)

## Number system

Irrational numbers

real numbers and their decimal expansions

operation on real numbers,

Laws of exponents for real number

Fundamental theorem of Arithmetic.

Plane Geometry : Angles and lines at a point, Angles made by a transversal with two lines

classification of triangles on the basis of sides and angles, Rectilinear figures

congruence of triangles

inequalities of triangles,

similar triangles

Area of plane figures, Circles, Arcs and Angles subtended by them

Tangents to a circle.

## Algebra

Linear Equations (in two variables)

Polynomials in one variable

zeroes of a polynomial,

Remainder theorem

Factorization of polynomials

algebraic identifies

Mathematical induction

Binomial theorem

Quadratic equations

nature of roots

linear inequalities

finite and infinite sequences

Arithmetic progression

Geometric Progression

Harmonic Progression

Permutations, Combinations, Matrix

Determinants of order two and three

Inverse matrix

solution of simultaneous linear equations of two and three unknowns, Sets, Relations and Functions

Complex numbers, its elementary properties

Argand plane and polar representation of complex numbers

square root of a complex number.

## Surface Area and Volume

Cube, Cuboids, Cone, Cylinder and Sphere

Conversion of solid from one shape to another

frustum of a Cone.

Trigonometry : Angles and their measurements

Trigonometric ratios of acute angles

Angles and lengths of arc

trigonometric functions

compound multiple angles

solutions of trigonometric equations

inverse trigonometric functions

properties of triangles.

## Calculus

1 Differential Calculus - Limits, differentiability, continuity, derivative of Sum and Difference, derivative of product of functions, Composite functions, implicit functions, trigonometric functions, parametric functions, Second order derivative, Rolle's and Lagrange's mean value theorem, applications of derivatives, Increasing/decreasing function, tangents and normals, maxima and minima of one variable.

2 Integral Calculus - Indefinite integrals, definite integrals, definite integral as a limit of sum, Applications of definite integral in finding the area under simple curves, arc of circles, lines/parabola/ellipse, area between the two above said curves.

## Co-ordinate Geometry

1 Two Dimensional Geometry - Distance between two points, Sections formula, area of triangle, locus, equations of straight line, pair of straight lines, circles, parabola, ellipse, hyperbola, their equations, general properties, tangent, normal, chord of contact, pair of tangents.

2 Co-ordinate Geometry in 3 - dimensions - Co-ordinate axes and co-ordinate planes in three dimensions, co-ordinates of a point, distance between two points and section formula, direction cosines/ratios of a line joining two points, Cartesian and vector equation of a line, coplaner and skew lines, shortest distance between two lines, cartesian and vector equation of a plane, Angle between (i) two lines, (ii) two planes (iii) a line and a plane, distance of a point from a plane.

## Statistics

Mean, Mode, Median

Quartiles, Deciles, Percentiles

Measure of dispersion

Probability - Laws of probability

addition and multiplications law

conditional probability

Random variable and probability distributions

repeated independent (Bernoulli) trials and Bionomial distribution.

## Vector

Dot product, Cross product, their properties

Scalar triple product

Vector triple product and related problems.

# PAPER II : Part ii (Graduation Standard)

## 1 Abstract Algebra

Group, Normal subgroup, permutation group, Quotient group

Homomorphism & groups

Isomorphism theorems

Calay and Lagrange's theorems

Automorphism.

## 2 Calculus

Partial derivatives

Maxima and Minima of functions of two variables

Asymptotes, double and triple integrals

Beta and Gamma functions. Mean Value Theorems.

## 3 Real Analysis

Real numbers as a complete ordered field

linear sets, lower and upper bounds

limit points, closed and open sets

Real sequence, limit and convergence of a sequence

Riemann integration

convergence of series

absolute convergence

uniform convergence of sequence and series of functions.

## 4 Vector Analysis

Differentiation of a vector functions of scalar variable

Gradient, divergence and curl (rectangular co-ordinates)

vector identities

Gauss's Stoke's and Green's theorems.

## 5 Differential Equations

Ordinary differential equations of first order and first degree

differential equations of first order but not of first degree

Clairaut's equations

general and singular solutions,

linear differential equations with constant coefficients

homogeneous differential equation

second order linear differential equations

simultaneous linear differential equations of first order.

## 6 Statics and Dynamics

Composition and resolution of co-planer forces

component of a force in two given directions

equilibrium of concurrent forces

parallel forces and moment

velocity and acceleration

simple linear motion under constant acceleration

Laws of motion, projectile.

## 7 Linear Programming

Graphical method of solution of linear programming in two variables

convex sets and their properties

simplex method

Assignment problems

Transportation problems.

## 8 Numerical Analysis and Difference Equation

Polynomial interpolation with equal or unequal stepsize

Lagrange's interpolation formula

Truncation error

Numerical differentiation

Numerical integration

Newton-Cotes quadrature formula

Gauss's quadrature formulae

convergence, Estimation of errors

Transcendental and polynomical equations

bisection method, Regula-falsi method

method of interation Newton - Raphson method, Convergence

First and higher order homogeneous linear difference equations

non homogenous linear difference equations

Complementary functions,

Particular integral.

# PAPER II : Part - iii (Teaching Methods)

Meaning and Nature of Mathematics.

Aims & Objectives of Mathematics Teaching.

Methods of Mathematics Teaching (analytic, synthetic, inductive, deductive, heuristic, Project & Laboratory).

Using various techniques of teaching mathematics viz - Oral, written, drill, assignment, supervised - study & programmed Learning.

Arousing and maintaining interest in learning of Mathematics.

Importance & meaning of planning, Preparing Lesson Plan, Unit Plan, Yearly Plan, Short Lesson Plan.

Preparing low cost improvised teaching aids, Audio-Visual aids in Mathematics.

Transfer of mathematics learning to various subjects and actual life situation.

Planning & equipments of Mathematics laboratory.

The mathematics teacher academic & professional - preparation.

Principle of curriculum & qualities of a good text book.

Process of obtaining feed-back and evaluation in Mathematics in terms of Cognitive, Affective and Psycho-motor Development.

Preparation and use of tests for evaluation such as achievement test & diagnostic test.

Diagnostic, Remedial and enrichment programmes with respect to syllabus at Secondary and Senior Secondary stages.

Mathematics for gifted and retarded children.