The Bihar Public Service Commission will be releasing the recruitment notification soon on the official website for various posts under BPSC. Like every year, a good number of vacancies are expected. Candidates preparing for the examination need to know all the details of the examination like the syllabus, exam pattern, and all other processes related to the examination. The BPSC Examination is conducted in three different stages that include the Prelims, Mains Exam, and the Interview. The Main examination will have 4 sections that include General Hindi, General Studies in two parts, and also an optional paper. There are 34 optional subjects that the candidates can choose from as per their choice. Candidates who are interested in choosing Mathematics as their optional paper can check out the BPSC Math Optional Syllabus in the article below.

Download BPSC Mathematics Optional Syllabus as PDF

BPSC Mathematics Optional Syllabus

Section- I

1. Linear Algebra
2. Vector space bases, dimension of finitely generated space. Linear transformations, Rank, and nullity of a linear transformation, Cayley Hamilton theorem. Eigenvalues and Eigenvectors.
3. Matrix of a linear transformation. Row and Column reduction. Echelon form. Equivalence. Congruence and similarity. Reduction to canonical forms.
4. Orthogonal, symmetrical, skew-symmetrical, unitary, Hermitian, and Skew-Hermitian matrices – their eigenvalues, orthogonal and unitary reduction of quadric and Hermitian forms, positive definite quadratic forms. Simultaneous reduction.
5. Calculus. Real numbers, limits, continuity, differentiability, Mean-Value theorem, Taylor’s theorem, indeterminate forms, Maxima and Minima, Curve Tracing, Asymptotes, Functions of several variables, partial derivatives. Maxima and Minima, Jacobian. Definite and indefinite integrals, double and triple integrals (techniques only). Application to Beta and Gamma functions. Areas, Volumes, Centre of gravity.
6. Analytic Geometry of two and three dimensions: First and second-degree equations in two dimensions in Cartesian and polar coordinates. Plane, Sphere Paraboloid, Ellipsoid. Hyperboloid of one and two sheets and their elementary properties. Curves in space, curvature, and torsion. Frenet’s formula.
7. Differential Equations. Order and Degree and a differential equation, differential equation of first order and degree, variables separable. Homogeneous, Linear, and exact differential equations. Differential equations with constant coefficients. The complementary function and the particular integral of eax, cosax, sinax, xm, eax, cosbx, eax, sin bx.
8. Vector, Tensor, Statics, Dynamics and Hydrostatics:

• • Vector Analysis – Vector Algebra, Differential of Vector function of a scalar variable, Gradient, Divergence and Curl in Cartesian Cylindrical and spherical coordinates and their physical interpretation. Higher order derivatives. Vector identities and vector equations, Gauss and Stocks theorems.
  • Tensor Analysis – – Definition of Tensor, the transformation of coordinates, contravariant and covariant tensor, Addition and multiplication of tensors, contraction of tensors, Inner product, fundamental tensor, Christoffel symbols, covariant differentiation. gradient, Curl, and divergence in tensor notation.
  • Statics – Equilibrium of a system of particles, work, and potential energy. Friction, Common catenary. Principle of Virtual Work stability of equilibrium, equilibrium of forces in three dimensions.
  • Dynamics – Degree of freedom and constraints. Rectilinear motion. Simple harmonic motion. Motion in a plane. Projectiles. Constrained motion. Work and energy motion under impulsive forces. Kepler’s laws. Orbits under central forces. The motion of varying mass. A motion under resistance.
  • Hydrostatics – Pressure of heavy fluids. Equilibrium of fluids under a given system of forces Centre of pressure. Thrust on curved surfaces, Equilibrium, and pressure of gases problems relating to the atmosphere.

Join BPSC Online Course For Exam Preparation!

Section II

1. Algebra– Groups, sub-groups, normal subgroups, homomorphism of groups, quotient groups. Basic isomorphism theorems. Sylow theorems. Permutation Groups, Cayley’s theorem. Rings and Ideals, Principal Ideal Domains, unique factorçation domains, and Euclidean domains. Field Extensions. Finite fields.
2. Real Analysis- Metric spaces, their topology with special reference to Rn sequence in a metric space, Cauchy sequence, Completeness, Completion Continuous functions, Uniform Continuity, Properties of Continous function on Compact sets. Riemann Stieltjes integral, Improper integrals and their conditions of existence. Differentiation of functions of several variables, Implicit function theorem, maxima and minima, Absolute and conditional convergence series of real and complex terms, Re-arrangement of series. Uniform convergence, Infinite products, Continuity, differentiability, and integrability for series, Multiple integrals.
3. Complex Analysis- Analytic functions, Cauchy’s theorem, Cauchy’s integral formula, Power series, Taylor’s, Singularities, Cauchy’s Residue theorem, and Contour integration.
4. Partial Differential Equations- Formations of partial differential equations. Types of integrals of partial differential equations of first order Charpits method. Partial differential equation with constant coefficient.
5. Mechanics- Generalised coordinates, Constraints, Holonomic and Non-holonomic systems, D’ Alembert’s principle, and Lagrange’s equations. Moment of Inertia, Motion of rigid bodies in two dimensions.
6. Hydrodynamics- Equation of continuity, Momentum, and energy. Inviscid Flow Theory – Two-dimensional motion, streaming motion, Sources, and Sinks.
7. Numerical Analysis- Transcendental and Polynomial Equations – Methods of tabulation, bisection, regula-talsi, secant, and Newton-Raphson and order of its convergence.
8. Interpolation and Numerical differentiation – Polynomial interpolation with equal or unequal step sçe.
9. Spline interpolation – Cubic splines. Numerical differentiation formulae with error terms.
10. Numerical integration – Problems of approximate guardrative quadrature formulae with equispaced arguments. Caussina quardrature convergence.
11. Ordinary differential equations – Euler’s method, Multistep-predictor corrector methods – Adam’s and Milne’s method, convergence and stability, Runge – Kutta methods.
12. Probability and Statistics:
    • Statistical methods – Concept of statistical population and random sample. Collection and presentation of data. The measure of location and dispersion. Moments and shepherd’s correction cumulants. Measures of Skewness and Kurtosis.
    • Curve fitting by least-squares regression, correlation, and correlation ratio. Rank correlation, Partial correlation co-efficient, and Multiple correlation co-efficient.
    • Probability – Discrete sample space, Events, their union and intersection, etc., Probability – Classical relative frequency and axiomatic approaches. Probability in continuum probability space conditional probability and independence, Basic laws of probability, Probability of combination of events, Bayes theorem, Random variable probability function, Probability density function. Distributions function, Mathematical expectation. Marginal and conditional distributions, Conditional expectation.
    • Probability distributions – Binomial, Poisson Normal Gamma, Beata. Cauchy, Multinomial, Hypergeometric, Negative Binomial, Chebychey’s Lemma. (Weak) law of large numbers, Central limit theorem for independent and identical varieties, standard errors, Sampling distribution of T.F and Chi-square and their uses in tests of significance large sample tests for mean and proportion.
13. Mathematical Programming – Definition and some elementary properties of convex sets, simplex methods, degeneracy, duality, sensitivity analysis rectangular games, and their solutions. Transportation and assignment problems. Kuha Tucker condition for non-linear programming Bellman’s optimality principle and some elementary applications of dynamic programming.
14. Theory of Queues – Analysis of steady-state and transient solution for queueing system with Poisson arrivals and exponential service time.
15. Deterministic replacement models, sequencing problems with two machines, n jobs, 3 machines, n jobs (special case), and n machines, 2 jobs.

Check out the BPSC Previous Year Papers and download them now!

BPSC Mains Exam Pattern 2023

The BPSC Main Examination consists of 4 sections that include General Hindi, 2 parts of General Studies, and a section on the optional paper. The total marks of the main exam are 900 marks and each section or paper is conducted with a time duration of 3 hours.

Check the BPSC Syllabus and Exam Pattern here!

We hope that this article could help you have a better understanding of the BPSC Maths Optional Syllabus. If you want to know about all the Government examinations and get the latest notifications about the same, download the Testbook App. You can also prepare for the Government Examinations here.