TNPSC Combined Statistical Subordinate Service (CSSSE) Exam Syllabus
Organisation : Tamil Nadu Public Service Commission (TNPSC)
Exam Name : TNPSC Combined Statistical Subordinate Service Exam
Announcement : TNPSC Combined Statistical Subordinate Service (CSSSE) Exam Syllabus
Website : https://www.tnpsc.gov.in/English/Notification.aspx
What is TNPSC CSSS Exam?
Tamil Nadu Public Service Commission (TNPSC) conduct Combined Statistical Subordinate Service Examination. The Paper-I of the Combined Statistical Subordinate Service exam is a subject paper of graduation standard and to be chosen from any one of the following – Statistics, Mathematics, or Economics. While TNPSC CSSS Paper-II is based on General Studies, General English, Numerical Aptitude, and Mental Ability Test. Also check the given pdf link.
Related / Similar Syllabus : TNPSC Assistant Public Prosecutor Grade II Exam Syllabus
Syllabus For TNPSC CSSS Exam
The Syllabus For TNPSC CSSS Exam are given below,
PAPER-I
Mathematics / Mathematics With Statistics
UNIT I : Algebra & Trigonometry:
Theory of Equations: Polynomial equations; Imaginary and irrational roots; Symmetric functions of roots in terms of
coefficient; Sum of rth 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
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.
Symmetric; Skew Symmetric; Hermitian; Skew Hermitian; Orthogonal and Unitary Matrices; Rank of a matrix;
Consistency and solutions of Linear Equations; Cayley Hamilton Theorem; Eigen values; Eigen Vectors; Similar
matrices; Diagonalization of a matrix.
Equivalence relations; Groups; subgroups – cyclic groups and properties of cyclic groups – simple problems;
Lagrange’s theorem; Prime number; Composite number;. decomposition of a composite number as a product of
primes uniquely (without proof); divisors of a positive integer n; congurence modulo n; Euler function; highest power
of a prime number p contained in n!; Fermat’s and Wilson’s theroems – simple problems.
Sums of sines and cosines of n angles which are in A.P.; Summation of trigonometric series using telescopic method, C + i S method.
UNIT II : 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; radius of curvature in Cartesian coordinates; polar coordinates; equation of a straight line, circle and
conic; 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; applications to
area, surface are volume.
UNIT III : 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.
UNIT IV : 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 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.
UNIT V : 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 maximum 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.
UNIT VI : 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 I2.
Limits and metric spaces: Limit of a function on a real line; metric spaces; limits in metric spaces.
Continuous functions on Metric Spaces: Functions continuous at a point on the real line, reformulation, functions
continuous on a metric space, open sets, closed sets, discontinuous functions on the real line
UNIT VII : 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.
Series: convergence of sequences and series,Taylor’s series, Laurent’s series, zero’s of analytic functions.
Residues and poles: residues, the residue theorem, the principal part of functions, poles, evaluation of improper
real integrals, improper integrals, integrals involving trigonometric functions, definite integrals of trigonometric
functions
UNIT VIII : Dynamics & 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 plane curve, p-r equation of a central orbit, finding 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, moment of
inertia of triangular lamina, circular lamina, circular ring, right circular cone, sphere (hollow and solid).
STATICS: Types of forces, Magnitude and direction of the resultant of the forces acting on a particle, Lami’s
Theorem, equilibrium of a particle under several coplanar forces, parallel forces, moments, couples-simple problems.
Friction: Laws of friction, angle of friction, equilibrium of a body on a rough inclined plane acted on by several
forces, centre of gravity of simple uniform bodies, triangular lamina, rods forming a triangle, trapezium, centre of
gravity of a circular arc, elliptic quadrant, solid and hollow hemisphere, solid and hollow cone, catenary-simple problems.
UNIT IX : 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.
Queuing theory – Basic concepts – Steady state analysis of M/M/1 and M/M/systems with infinite and finite capacities.
Inventory models : Basic concepts – EOQ models : (a) Uniform demand rate infinite production rate with no
shortages (b) Uniform demand rate Finite production rate with no shortages – Classical newspaper boy problem
with discrete demand – purchase inventory model with one price break.
Game theory : Two-person Zero-sum game with saddle point – without saddle point – dominance – solving 2 x n or
m x 2 game by graphical method. Integer programming : Branch and bound method.
PAPER-I
Statistics (UG Standard)
UNIT I :
Uses, Scope and limitation of Statistics, Collection, Classification and Tabulation of data, Diagramatic and
Graphical representation, Measures of location, dispersion, Skewness and Kurtosis – Correlation and regression –
Curve Fitting – Linear and Quadratic equation by the method of least squares.
UNIT II :
Probability – Addition, Multiplication and Baye’s Theorems and their application. Tchebychev’s inequality.
Random variables – Univariate and Bivariate – Probability distributions – Marginal and conditional distributions –
Expectations – Moments and cumulants generating functions.
UNIT III :
Probability distributions – Binomial, Poisson, Geometric and Hypergeometric. Continuous distributions –
Uniform, exponential and normal. Sampling distributions and standard error, student’s ‘t’, Chi-square and F statistic –
distributions and their applications.
UNIT IV :
Estimation – Point estimation – properties of estimates Neyman – Fisher Factorization theorem(without proof)
Cramer – Rao inequality, Rao – Blackwell theorem – MLE and method of Moments estimation – Interval estimation – for
population mean and variance based on small and large samples.
UNIT V :
Tests of Hypothesis – Null and Alternative – Types of errors – Power of test, Neyman – Pearson lemma, UMP
and Likelihood ratio tests, Test procedures for large and small samples – Independence of attributes, Chi-square test –Goodness of fit
UNIT VI :
Simple random sample – stratified, systematic, Cluster (Single stage) Estimation of mean and variance in SKS – Sample Survey – Organisation – CSO and NSSO – Sampling and Non-Sampling errors. Analysis of Variance – Principles of design CRD, RBD and LSD – Factorial experiments 22, 23 and 32 (Without confounding) Missing plot techniques.
Syllabus : http://www.syllabus.gen.in/uploads/pdf2022/2736-1.pdf
UNIT VII :
Concept of SQC – Control Charts – X, R, p and charts Acceptance sampling plan – single and double – OC
curves Attributes and Variables plan. OR Models – Linear Programming problems – Simplex method Dual – Primal, Assignment problems, Net work – CPM and PERT
UNIT VIII : Time series – Different components – Trend and Seasonal Variations – Determination and elimination
UNIT IX : Index Numbers – Construction and uses – Different kinds of simple and weighted index numbers – Reversal
tests – construction and use of cost of living index numbers – Birth and death rates – Crude and standard death rates,
Fertility rates – Life table construction and uses.
UNIT X : Statistical Computing using Excel – Understanding on the usage of Statistical Packages including SPSS, MINITAB and SAS
Paper-II
General Studies
UNIT-I : General Science
(i) Scientific Knowledge and Scientific temper – Power of Reasoning – Rote Learning Vs Conceptual Learning – Science as a tool to understand the past, present and future.
(ii) 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.
(iii) Elements and Compounds, Acids, Bases, Salts, Petroleum Products, Fertilizers, Pesticides.
(iv) Main concepts of Life Science, Classification of Living Organisms, Evolution, Genetics, Physiology, Nutrition, Health and Hygiene, Human diseases.
(v) Environment and Ecology.
UNIT-II: Current Events
(i) History – Latest diary of events – National symbols – Profile of States – Eminent personalities and places in news – Sports – Books and authors.
(ii) 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.
(iii) Geography – Geographical landmarks.
(iv) Economics – Current socio – economic issues.
(v) Science – Latest inventions in Science and Technology
UNIT- III: Geography Of India
(i) Location – Physical features – Monsoon, rainfall, weather and climate – Water resources – Rivers in India – Soil, minerals and natural resources – Forest and wildlife – Agricultural pattern.
(ii) Transport – Communication.
(iii) Social geography – Population density and distribution – Racial, linguistic groups and major tribes.
(iv) Natural calamity – Disaster Management – Environmental pollution: Reasons and preventive measures – Climate change – Green energy.
UNIT – IV: History And Culture Of India
(i) Indus valley civilization – Guptas, Delhi Sultans, Mughals and Marathas – Age of Vijayanagaram and Bahmani Kingdoms – South Indian history.
(ii) Change and Continuity in the Socio – Cultural History of India.
(iii) Characteristics of Indian culture, Unity in diversity – Race, language, custom.
(iv) India as a Secular State, Social Harmony.
UNIT-V: Indian Polity
(i) Constitution of India – Preamble to the Constitution – Salient features of the Constitution – Union, State and Union Territory.
(ii) Citizenship, Fundamental rights, Fundamental duties, Directive Principles of State Policy.
(iii) Union Executive, Union legislature – State Executive, State Legislature – Local governments, Panchayat Raj.
(iv) Spirit of Federalism: Centre – State Relationships.
(v) Election – Judiciary in India – Rule of law.
(vi) Corruption in public life – Anti-corruption measures – Lokpal and LokAyukta – Right to Information – Empowerment of women – Consumer protection forums, Human rights charter