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 8th to 18th 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.
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)
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,
Area of plane figures, Circles, Arcs and Angles subtended by them
Tangents to a circle.
Linear Equations (in two variables)
Polynomials in one variable
zeroes of a polynomial,
Factorization of polynomials
nature of roots
finite and infinite sequences
Permutations, Combinations, Matrix
Determinants of order two and three
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
compound multiple angles
solutions of trigonometric equations
inverse trigonometric functions
properties of triangles.
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.
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.
Mean, Mode, Median
Quartiles, Deciles, Percentiles
Measure of dispersion
Probability - Laws of probability
addition and multiplications law
Random variable and probability distributions
repeated independent (Bernoulli) trials and Bionomial distribution.
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
Calay and Lagrange's theorems
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
convergence of series
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)
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
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
8 Numerical Analysis and Difference Equation
Polynomial interpolation with equal or unequal stepsize
Lagrange's interpolation formula
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
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.