TNPSC Combined Statistical Subordinate Service Syllabus and Exam Pattern 2022 PDF Here!

Subject

Topics Included

Algebra and Trigonometry

• Theory of Equations: Polynomial equations; Imaginary and irrational roots; Symmetric functions of roots in terms of coefficient; Sum of nth powers of roots; Reciprocal equations; Transformations of equations.

• Descrates’ rule of signs: Approximate solutions of roots of polynomials by Newton – Raphson Method – Horner’s method; Cardan’s method of solution of a cubic polynomial.

• Summation of Series: Binomial, Exponential and Logarithmic series theorems; Summation of finite series using the method of differences – simple problems.

• Expansions of sin x, cos x, tan x in terms of x; sin nx, cos nx, tan nx, sin nx, cos nx, tan nx, hyperbolic and inverse hyperbolic functions – simple problems.

Calculus, Coordinate Geometry Of 2-Dimensions And Differential Geometry

• nth derivative; Leibnitz’s theorem and its applications; Partial differentiation. Total differentials; Jacobians; Maxima and Minima of functions of 2 and 3 independent variables – necessary and sufficient conditions; Lagrange’s method – simple problems on these concepts.

• Methods of integration; Properties of definite integrals; Reduction formulae – Simple problems.

• Conics – Parabola, ellipse, hyperbola and rectangular hyperbola – pole, polar, co-normal points, con-cyclic points, conjugate diameters, asymptotes and conjugate hyperbola.

• Curvature; the radius of curvature in Cartesian coordinates; polar coordinates; equation of a straight line, circle and conic; the radius of curvature in polar coordinates; p-r equations; evolutes; envelopes.

• Methods of finding asymptotes of rational algebraic curves with special cases. Beta and Gamma functions, properties and simple problems. Double Integrals; change of order of integration; triple integrals; area applications, surface area volume.

Differential Equations and Laplace Transforms

• First order but of higher degree equations – solvable for p, solvable for x, solvable for y, clairaut’s form – simple problems.

• Second-order differential equations with constant coefficients with particular integrals for eax, xm, eax sin mx, eax cos mx

• Method of variation of parameters; Total differential equations, simple problems.

Vector Calculus, Fourier Series and Fourier Transforms

• Vector Differentiation: Gradient, divergence, curl, directional derivative, unit normal to a surface.

• Vector integration: line, surface and volume integrals; theorems of Gauss, Stokes and Green – simple problems.

• Fourier Series: Expansions of a periodic function of period 2π; expansion of even and odd functions; half range series.

• Fourier Transform: Infinite Fourier transform (Complex form, no derivation); sine and cosine transforms; simple properties of Fourier Transforms; Convolution theorem; Parseval’s identity.

Algebraic Structures

• Groups: Subgroups, cyclic groups and properties of cyclic groups – simple problems; Lagrange’s Theorem; Normal subgroups; Homomorphism; Automorphism; Cayley’s Theorem, Permutation groups.

• Rings: Definition and examples, Integral domain, homomorphism of rings, Ideals and quotient Rings, Prime ideal and maximal ideal; the field and quotients of an integral domain, Euclidean Rings.

• Vector Spaces: Definition and examples, linear dependence and independence, dual spaces, inner product spaces.

• Linear Transformations: Algebra of linear transformations, characteristic roots, matrices, canonical forms, triangular forms.

Real Analysis

• Sets and Functions: Sets and elements; Operations on sets; functions; real-valued functions; equivalence; countability; real numbers; least upper bounds.

• Sequences of Real Numbers: Definition of a sequence and subsequence; limit of a sequence; convergent sequences; divergent sequences; bounded sequences; monotone sequences; operations on convergent sequences; operations on divergent sequences; limit superior and limit inferior; Cauchy sequences.

• Series of Real Numbers: Convergence and divergence; series with non-negative numbers; alternating series; conditional convergence and absolute convergence; tests for absolute convergence; series whose terms form a non-increasing sequence; the class I 2

• Limits and metric spaces: Limit of a function on a real line; metric spaces; limits in metric spaces.

Complex Analysis

• Complex numbers: Point at infinity, Stereographic projection

• Analytic functions: Functions of a complex variable, mappings, limits, theorems of limits, continuity, derivatives, differentiation formula, Cauchy-Riemann equations, sufficient conditions Cauchy-Riemann equations in polar form, analytic functions, harmonic functions.

• Mappings by elementary functions: linear functions, the function 1/z, linear fractional transformations, the functions w=zn, w=ez, special linear fractional transformations.

• Integrals: definite integrals, contours, line integrals, Cauchy-Goursat theorem, Cauchy integral formula, derivatives of analytic functions, maximum moduli of functions.

Dynamics and Statics

• DYNAMICS: kinematics of a particle, velocity, acceleration, relative velocity, angular velocity, Newton’s laws of motion, equation of motion, rectilinear motion under constant acceleration, simple harmonic motion.

• Projectiles: Time of flight, horizontal range, range in an inclined plane. Impulse and impulsive motion, collision of two smooth spheres, direct and oblique impact-simple problems.

• Central forces: Central orbit as a plane curve, p-r equation of a central orbit, finding the law of force and speed for a given central orbit, finding the central orbit for a given law of force.

• Moment of inertia: Moment of inertia of simple bodies, theorems of parallel and perpendicular axes, the moment of inertia of triangular lamina, circular lamina, circular ring, right circular cone, sphere (hollow and solid).

Operations Research

• Linear programming – formulation – graphical solution – simplex method

• Big-M method – Two-phase method-duality- primal-dual relation – dual simplex method – revised simplex method – Sensitivity analysis. Transportation problem – assignment problem.

• Sequencing problem – n jobs through 2 machines – n jobs through 3 machines – two jobs through m machines – n jobs through m machines.

• PERT and CPM: project network diagram – Critical path (crashing excluded) – PERT computations.

Mathematical Statistics

• Statistics – Definition – functions – applications – complete enumeration – sampling methods – measures of central tendency – measures of dispersion – skewness- kurtosis.

• Sample space – Events, Definition of probability (Classical, Statistical & Axiomatic ) – Addition and multiplication laws of probability – Independence – Conditional probability ty– Bayes theorem – simple problems.

• Random Variables (Discrete and continuous), Distribution function – Expected values & moments – Moment generating function – probability generating function – Examples. Characteristic function – Uniqueness and inversion theorems – Cumulants, Chebychev’s inequality – Sample problems.

• Random Variables (Discrete and continuous), Distribution function – Expected values & moments – Moment generating function – probability generating function – Examples. Characteristic function – Uniqueness and inversion theorems – Cumulants, Chebychev’s inequality – Sample problems.

• Concepts of bivariate distribution – Correlation : Rank correlation coefficient – Concepts of partial and multiple correlation coefficients – Regression : Method of Least squares for fitting Linear, Quadratic and exponential curves - simple problems.

• Standard distributions – Binomial, Hyper geometric, Poisson, Normal and Uniform distributions – Geometric, Exponential, Gamma and Beta distributions, Inter-relationship among distributions.

• Sampling Theory – sampling distributions – concept of standard error-sampling distribution based on Normal distribution : t, chi-square and F distribution.

• Point estimation-concepts of unbiasedness, consistency, efficiency and sufficiency- Cramer Rao inequality-methods of estimation : Maximum likelihood, moments and minimum chi-square and their properties.

• Test of Significance-standard error-large sample tests. Exact tests based on Normal, t, chi-square and F distributions with respect to population mean/means, proportion/proportions variances and correlation coefficient. 

• Theory of attributes – tests of independence of attributes based on contingency tables – goodness of fit tests based on Chi-square.

• Analysis of variance : One way, two-way classification – Concepts and problems, interval estimation – confidence intervals for population mean/means, proportion/proportions and variances based on Normal, t, chi-square and F.

• Tests of hypothesis : Type I and Type II errors – power of test-Neyman Pearson Lemma – Likelihood ratio tests – concepts of most powerful test –simple problems

General Science

• Scientific Knowledge and Scientific temper - Power of Reasoning- Rote Learning Vs Conceptual Learning - Science as a tool to understand the past, present and future.

• Nature of Universe - General Scientific Laws – Mechanics - Properties of Matter, Force, Motion and Energy - Everyday application of the basic principles of Mechanics, Electricity and Magnetism, Light, Sound, Heat, Nuclear Physics, Laser, Electronics and Communications.

• Elements and Compounds, Acids, Bases, Salts, Petroleum Products, Fertilizers, Pesticides.

• Main concepts of Life Science, Classification of Living Organisms, Evolution, Genetics, Physiology, Nutrition, Health and Hygiene, Human diseases.

• Environment and Ecology.

Current Events 

• History - Latest diary of events - National symbols - Profile of States - Eminent personalities and places in the news-Sports-Books and authors.

• Polity - Political parties and political system in India - Public awareness and General administration - Welfare oriented Government schemes and their utility, Problems in Public Delivery Systems.

• Geography - Geographical landmarks.

• Economics - Current socio-economic issues.

• Science - Latest inventions in Science and Technology.

Geography in India

• Location – Physical features - Monsoon, rainfall, weather and climate - Water resources - Rivers in India - Soil, minerals and natural resources - Forest and wildlife - Agricultural pattern.

• Transport - Communication.

• Social geography – Population density and distribution - Racial, linguistic groups and major tribes.

• Natural calamity – Disaster Management – Environmental pollution: Reasons and preventive measures- Climate change- Green energy.

History and Culture of India

• Indus valley civilization - Guptas, Delhi Sultans, Mughals and Marathas - Age of Vijayanagar and Bahmani Kingdoms - South Indian history.

• Change and Continuity in the Socio-Cultural History of India.

• Characteristics of Indian culture, Unity in diversity – Race, language, custom.

• India as a Secular State, Social Harmony.

Indian Polity

• Constitution of India - Preamble to the Constitution - Salient features of the Constitution - Union, State and Union Territory.

• Citizenship, Fundamental Rights, Fundamental Duties, Directive Principles of State Policy.

• Union Executive, Union legislature – State Executive, State Legislature – Local governments, Panchayat Raj.

• Spirit of Federalism: Centre-State Relationships.

• Election - Judiciary in India – Rule of law.

• Corruption in public life- Anti-corruption measures – Lokpal and LokAyukta - Right to Information - Empowerment of women - Consumer protection forums, Human rights charter.

Indian Economy

• Nature of Indian economy – Five-year plan models - an assessment – Planning Commission and Niti Ayog.

• Sources of revenue – Reserve Bank of India – Fiscal Policy and Monetary Policy - Finance Commission – Resource sharing between Union and State Governments - Goods and Services Tax.

• Structure of Indian Economy and Employment Generation, Land reforms and Agriculture - Application of Science and Technology in agriculture - Industrial growth - Rural welfare oriented programmes – Social problems – Population, education, health, employment, poverty.

Indian National Movement

• National renaissance – Early uprising against British rule - Indian National Congress - Emergence of leaders – B.R.Ambedkar, Bhagat Singh, Bharathiar, V.O.Chidambaranar, Jawaharlal Nehru, Kamarajar, Mahatma Gandhi, Maulana Abul Kalam Azad, Thanthai Periyar, Rajaji, Subash Chandra Bose and others.

• Different modes of Agitation: Growth of Satyagraha and Militant movements.

• Communalism and partition.

History, Culture, Heritage and Socio-Political Movements in Tamil Nadu

• History of Tamil Society, related Archaeological discoveries, Tamil Literature from Sangam age till contemporary times.

• Thirukkural : 

(a) Significance as Secular literature

(b) Relevance to Everyday Life

(c) Impact of Thirukkural on Humanity

(d) Thirukkural and Universal Values - Equality, Humanism, etc.

(e) Relevance to Socio Politico-Economic affairs

(f ) Philosophical content in Thirukkural

• Role of Tamil Nadu in freedom struggle - Early agitations against British Rule - Role of women in the freedom struggle.

• Evolution of 19th and 20th Century Socio-Political movements in Tamil Nadu - Justice Party, Growth of Rationalism - Self Respect ]Movement, Dravidian movement and Principles underlying both these movements, Contributions of Thanthai Periyar and Perarignar Anna.

Development Administration in Tamil Nadu

• Human Development Indicators in Tamil Nadu and a comparative assessment across the Country – Impact of Social Reform movements in the Socio-Economic Development of Tamil Nadu.

• Political parties and Welfare schemes for various sections of people – Rationale behind Reservation Policy and access to Social Resources - Economic trends in Tamil Nadu – Role and impact of social welfare schemes in the Socio-economic development of Tamil Nadu.

• Social Justice and Social Harmony as the Cornerstones of Socio-Economic development.

• Education and Health systems in Tamil Nadu.

• Geography of Tamil Nadu and its impact on Economic growth.

• Achievements of Tamil Nadu in various fields.

• e-governance in Tamil Nadu.

Aptitude and Mental Ability Test

• Simplification – Percentage - Highest Common Factor (HCF) Lowest Common Multiple (LCM).

• Ratio and Proportion

• Simple interest - Compound interest - Area - Volume - Time and Work

• Logical Reasoning - Puzzles-Dice - Visual Reasoning - Alphanumeric Reasoning – Number Series.

Paper

Subject

Questions

Maximum Marks

Duration

Paper 1

Statistics or Mathematics

200

300

3 hours

Paper 2

3 hours

General Studies

75

150

Aptitude and Mental Ability Test

25

Subject

Books

Author/Publisher

Mathematics 

TNPSC Combined Statistical Subordinate Service Exam Book

V. V. K. Subburaj

Aptitude and Mental Ability Test

General Intelligence and Mental Ability Test 

R. Gupta 

Current Events 

Current Affairs Yearly 

Arihant Publication 

History, Culture, Heritage and Socio-Political Movements in Tamil Nadu

History and Culture of Tamil Nadu 

Chithra Madhavan

Development Administration in Tamil Nadu

Development Administration in Tamil Nadu

Mr Sivan Kalai