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BCSWritten
BCS written syllabus
General and technical cadres · 235 pages
Compulsory subjects and post-related subjects for professional and technical cadres. Confirm the applicable subject code in the recruitment notice.
Published by BPSC. Collected 2026-11-14. Confirm the edition and subject against your recruitment notice before studying.
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SYLLABUS FOR BCS (WRITTEN) EXAMINATION
115/235
MATHEMATICS
(POST RELATED)
Subject Code: 551
Total Marks-200
Part-I
Marks: 100
Group-A: Algebra, Analytical Geometry, Linear Algebra.
1. Order properties of real numbers. Inequalities involving different types of means, Chebyshev‘s
inequality.
2. Complex numbers, DeMoivre‘s theorem and its applications.
3. Summation of finite algebraic and trigonometric series.
4. Polynomials and their roots, Honer‘s scheme (synthetic division), Descartes rule of signs.
5. Relation between roots and coefficients. Symmetric functions of roots.
Analytical Geometry
1. Pairs of straight lines. Transformation of coordinates.
2. General equation of the second degree, Reduction to standard forms, Conics in general.
3. Planes and straight lines in three dimensions, shortest distance between two straight lines.
4. Vector algebra with applications to geometry.
Linear Algebra
1. Algebra of Matrices. Systems of linear equations and their solutions.
2. Vector spaces over the field of real numbers, Subspaces, Linear dependence and independence of
vectors, Basis and dimension.
3. Linear transformations, Rank and nullity.
4. Eigenvectors and eigenvalues.
Group-B. Differential and Integral Calculus (including Elementary Real Analysis)
1. Sets of real numbers, Supremum and infimum, the completeness axiom Dedekind‘s theorem, The
Archimendian property.
2. Convergence of infinite sequences and series of real numbers, Standard theorems and tests of
convergence. Absolute convergence.
3. Continuous functions. Intermediate value theorem. Uniform continuity.
4. The derivative. Rolle‘s Theorem, Mean value theorems, Toylor‘s theorem with remainder, Taylor‘s
series, indeterminate forms.
5. Maxima, minima, tangents and normals.
6. Indefinite integrals, Techniques of integration, Recurrence Relations.
7. The Riemann integral, The fundamental theorem of calculus.
8. Improper integrals. Tests of convergence.
9. Determination of areas and volumes.