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# (Syllabus) Punjab PSC Prelim Examination (Mathematics)

## Preliminary Examination Syllabus -   Mathematics

1. Algebra.—Elements of Set Theory; Algebra of Real and Complex numbers including  Demovire’s Theorem; Polynomials and Polynomial Equations, Relation between Co-efficients and  Roots, Symmetric functions of roots;

Elements of Group Theory; Sub-groups, Cyclic groups, Permutation groups and their  elementary properties.

Rings, Integral Domains and Fields and their elementary properties.

2. Vector Spaces and Matrices : Vector Space, Linear Dependence and Independence,  Sub-spaces, Basis and Dimensions, Finite Dimensional Vector Spaces. Linear Transformation of a  Finite Dimensional Vector Space, Matrix Representation. Singular and Non-singular  Transformations. Rank and Nullity.

Matrices.—Addition, Multiplication, Determinants of a Matrix, Properties of  Determinants of order ‘n’ Inverse of a Matrix, Cramer’s rule.

3. Geometry and Vectors.—Analytic Geometry of straight lines and conics in Cartesian  and Polar coordinates; Three Dimensional geometry for planes, straight lines, sphere, cone and  cylinder. Addition, Subtraction and Products of Vectors and Simple applications to Geometry.

4. Calculus.—Functions, Sequences, Series, Limits, Continuity, Derivatives. Application  of Derivatives.—Rates of change, Tangents, Normals, Maxima, Minima, Rolle’s Theorem, Mean  Value Theorems of Lagrange and Cauchy, Asymptotes, Curvature, methods of finding indefinite  integrals, Definite Integrals, Fundamental Theorem of Integral Calculus. Application of definite  integrals to area, length of a plane curve, Volume and Surfaces of revolution.

5. Ordinary Differential Equations.—Order and Degree of a Differential Equation, First  Order Differential Equations, Singular solution, Geometrical interpretation, Second order  equations with constant co-efficients.

6. Mechanics.—Concepts of particles-Lamina; Rigid Body; Displacements; Force; Mass;  Weight; Motion; Velocity; Speed; Acceleration; Parallelogram of forces; Parallelogram of  velocity, acceleration; resultant; equilibrium of coplanar forces; Moments; Couple; Friction;  Centre of mass, Gravity; Laws of Motion; Motion of a particle in a straight line; Simple Harmonic  Motion; Motion under conservative forces; Motion under gravity; Projectile; Escape velocity;  Motion of artificial satellites.

7. Elements of Computer Programming.—Binary system, Octal and Hexadecimal  systems. Conversion to and from Decimal systems. Codes, Bits, Bytes and Words. Memory of a  computer, Arithmetic and Logical operations on numbers. Precisions. AND ; OR, XOR, NOT and  Shift/Rotate operators, Algorithms and Flow Charts.

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Courtesy : ppsc.gov.in