TNPSC CSSS

See the detailed recruitment program of the Combined Statistics Service of TNPSC 2022.

TNPSC CSSS Algebra and Trigonometry Program 2022:

• Equation theory: polynomial equations; Imaginary and irrational roots; Symmetric functions of the roots in terms of coefficient; Sum of the powers rth of the roots; Reciprocal equations; Transformations of equations.
• Descartes' rule of signs: Approximate solutions of the roots of Newton's polynomials - Raphson's method - Horner's method; Method of solving a cubic polynomial according to Cardan.
• Summation of series: theorems of binomial, exponential, and logarithmic series; Adding finite series with the difference method - simple problems.
• Expansion of sin x, cos x, tan x as a function of x; sin nx, cos nx, tan nx, sin nx, cos nx, tan nx, hyperbolic, and inverse hyperbolic functions - simple problems.

TNPSC CSSS Calculation, 2-dimensional coordinate geometry and differential geometry Program 2022:

• nth derivative; Partial differentiation, Leibnitz's theorem, and its applications. Total deviations; Jacobins; Maximum and Minimum of functions of 2 and 3 independent variables - necessary and sufficient conditions; Lagrange method - simple problems on these concepts.
• Integration methods; Properties of definite integrals; Reduction Formulas - Simple Problems.
• Conics - Parabola, rectangular hyperbola, and ellipse, hyperbola, - poles, polar points, concyclic points, co-normal, conjugate diameters, asymptotes, and conjugate hyperbola.
• Curvature; the radius of curvature in Cartesian coordinates; polar coordinates; equation of a line, a circle, and a conic; the radius of curvature in polar coordinates; equations pr; evolved; envelopes.
• Approaches of finding asymptotes of rational algebraic curves with unique cases. Beta & gamma functions, their properties, and some problems. Double integrals; change of order of integration; triple integrals; surface applications, surface volume.

TNPSC CSSS Laplace transform and differential equations Syllabus 2022:

• First-order equations but of higher degree - solvable for p, solvable for x, solvable for y, claimant form - simple problems.
• Second-order differential equations with steady coefficients with distinct integrals.
• Method of varying the parameters; Total differential equations, simple problems.

TNPSC CSSS Vector calculation, Fourier series, and Fourier transform Program 2022:

• Vector differentiation: gradient, divergence, curvature, directional derivative, unit normal to a surface.
• Vector integration: line, area, and volume integrals; Gauss, Stokes, and Green theorems - simple problems.
• Fourier series: Developments of a periodic function of period 2π; expansion of even and odd functions; mid-range series.
• Fourier transform: infinite Fourier transforms (complex form, no derivation); transform the sine and cosine; simple properties of Fourier transforms; Convolution theorem; The identity of Parseval.

TNPSC CSSS Algebraic Structures Course Syllabus 2022:

• Groups: Subgroups, cyclic groups, their properties, and some problems; Lagrange's theorem; Normal subgroups; automorphism; homomorphism; 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 the quotients of an integral domain, the Euclidean rings.
• Vector spaces: definition and examples, linear dependence and independence, dual spaces, internal product spaces.
• Linear transformations: Algebra of linear transformations, matrices, characteristic roots, triangular forms, canonical forms.

TNPSC CSSS Real Analysis Syllabus 2022:

• Sets and functions: Sets and elements; Operations on the sets; functions; real value functions; equivalence; accounting; real numbers; upper minimum limits.
• sequences of real numbers: definition of sequence and sort sequence; limit of a sequence; convergent sequences; divergent sequences; limited sequences; monotonic sequences; operations on convergent sequences; operations on divergent sequences; upper limit and lower limit; Cauchy sequences.
• Series of real numbers: convergence and divergence; series with non-negative numbers; alternating series; conditional convergence and absolute convergence; absolute convergence test; series whose terms form a non-increasing sequence.
• Limits and metric spaces: Limit of a function on a real line; metric spaces, and limits in metric spaces.

TNPSC CSSS Complex Analysis Syllabus 2022:

• Complex numbers: Point at infinity, Stereographic projection
• Analytical functions: Functions of a complex variable, applications, limits, limit theorems, continuity, derivatives, derivative formula, Cauchy-Riemann equations, conditions sufficient Cauchy-Riemann equations in polar form, analytical functions, harmonic functions.
• Mappings for elementary functions: linear functions, the 1 / z function, linear fractional transformations, the functions w = zn, w = ez, special linear fractional transformations.
• Integrals: definite integrals, boundaries, line integrals, Cauchy Goursat theorem, Cauchy integral formula, derivatives of analytical functions, maximum moduli of functions.

TNPSC CSSS Dynamics and Statics Syllabus 2022:

• DYNAMICS: kinematics of a particle, velocity, acceleration, relative velocity, angular velocity, Newton's laws of motion, equation of motion, rectilinear motion in constant acceleration, simple harmonic motion.
• Balls: Flight time, horizontal range, range in an inclined plane. Impulsive and impulsive movements, a collision of two smooth spheres, direct impact, and simple oblique problems.
• Central forces: central orbit in the form of a plane curve, equation for a central orbit, find the law of force and speed for a given central orbit, find the central orbit for a provided law of force.
• Moment of inertia: Moment of inertia of simple bodies, theorems of parallel and perpendicular axes, a moment of inertia of triangular plate, circular plate, circular ring, right circular cone, sphere (hollow and solid).

TNPSC CSSS Operational Research Program 2022:

• Linear programming, formulation, graphical solution, simplex method
• BigM method, two-phase method, duality primal relation, double simplex method, revised simplex method, sensitivity analysis. Transport problem - assignment problem.
• Sequence problem: n jobs on 2 machines, n jobs on 3 machines, two jobs on m machines, n jobs on m machines.
• PERT and CPM: network diagram design, critical path (excluding crash), PERT calculations.

TNPSC CSSS Mathematics Statistics Syllabus 2022:

• Statistics, complete enumeration, sampling methods, measures of central tendency, measures of dispersion, asymmetric kurtosis.
• Sampling space: Laws of addition and multiplication of probability, Independence, Conditional probability, Bayes theorem.
• Random variables, Distribution function, Expected values and moments, Moment-generating function, Probability-generating function, Uniqueness and inversion theorems - Cumulants, Chebyshev inequality.