**TNPSC CSSSE Syllabus & Exam Pattern PDF**: The Tamil Nadu Public Service Commission has released TNPSC CSSSE Syllabus on its Official Web portal @ tnpsc.gov.in. The **TNPSC Combined Statistical Subordinate Service Examination Exam Pattern** is uploaded on this page for the sake of the Candidates. Candidates who have applied for TNPSC CSSSE Jobs and preparing for Apprentice Exam 2023 should check this article for **TNPSC CSSSE Syllabus** and test pattern PDF. Here we have uploaded the Subject Wise Syllabus and Detailed Exam Pattern to help the Aspirants in their Exam Preparation. So all the Applicants are advised to read this article entirely and Download the **TNPSC Combined Statistical Subordinate Service Examination Syllabus and Exam Pattern** for the Below Section free of cost.

**TNPSC CSSSE Syllabus 2023 PDF**

Organization Name |
Tamil Nadu Public Service Commission (TNPSC) |

Post Name |
Computer–vaccine storekeeper, Block Health Statistician, Statistical Assistant |

Exam Name |
Combined Statistical Subordinate Service Examination |

Category |
Syllabus |

Selection Process |
Written Examination, Verification of Certificates |

Job Location |
Tamil Nadu |

Official Site |
tnpsc.gov.in |

**Check TNPSC CSSSE Exam Pattern 2023 PDF**

Subject |
Duration |
Maximum Marks |

Paper – I (Subject Paper)(200 Questions)
Degree Standard Any one of the following (ii) Mathematics (Code No.276) (iii) Economics (Code No. 275) |
3 hours | 300 Marks |

Paper-II(General Studies)(100 Questions)
General Studies (Degree Standard) – 75 Questions and Aptitude and Mental Ability Test (SSLC Standard) – 25 Question |
2 hours | 200 Marks |

Total |
500 |

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**Algebra and 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.
- Descartes 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.

**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; 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; 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.
- 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.

**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 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 transform; 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 I 2
- Limits and metric spaces: Limit of a function on a real line; metric spaces; limits in metric spaces.

**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.

**UNIT VIII 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).

**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.

**UNIT IX 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 – 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 – Simple problems.

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