Master of Operational Research:
Syllabus for the Common Entrance Test
PART-I
This part is intended to test the candidate’s vocabulary and analytical skills at a level
essential for accurate comprehension and presentation of material appropriate for this
degree. The language background expected will be of the level of English at Senior
Secondary Examination. The paper will include passages for comprehension, test of
vocabulary (synonyms and antonyms), elementary grammar and syntax.
The section on Analytical Ability and Reasoning will include standard questions on
pattern recognition, logic, Venn diagrams etc. It is not intended to be subject-specific.
PART-II
Mathematics :Vector Space, subspace and its properties, linear independence and
dependence of vectors, matrices, rank of a matrix, reduction to normal forms, linear
homogenous and non-homogenous equations, Cayley-Hamilton theorem, characteristic
roots and vectors. De Moivre’s theorem, relation between roots and coefficient of nth
degree equation, solution to cubic and biquadratic equation, transformation of equations.
Calculus : Limit and continuity, differentiability of functions, successive differentiation,
Leibnitz’s theorem, partial differentiation, Euler’s theorem on homogenous functions,
tangents and normals, asymptotes, singular points, curve tracing, reduction formulae,
integration and properties of definite integrals, quadrature, rectification of curves,
volumes and surfaces of solids of revolution.
Differential Equations: Linear, homogenous, separable equations, first order higher
degree equations, algebraic properties of solutions, linear homogenous equations with
constant coefficients, solution of second order differential equations. Linear nonhomogenous differential equations.
Real Analysis : Neighbourhoods, open and closed sets, limit points and Bolzano
Weiestrass theorem, continuous functions, sequences and their properties, limit superior
and limit inferior of a sequence, infinite series and their convergence. Rolle’s theorem,
mean value theorem, Taylor’s theorem, Taylor’s series, Maclaurin’s series, maxima amd
minima, indeterminate forms.
Statistics
Measures of central tendency and dispersion and their properties, skewness and kurtosis,
introduction to probability, theorems of total and compound probability, Bayes theorem,
random variables, probability mass and density functions, mathematical expectation,
moment generating functions, Binomial, Poisson, Geometric, Exponential and Normal
distributions and their properties, method of least squares, correlation and regression,
introduction to sampling, sampling distributions and tests of significance based on t, Chisquare and F-distributions.
Operational Research
Definition & scope of Operational Research, Formulation of simple Linear Programming
Problems, Simplex method and basics of Duality.
Characteristics of Inventory System, Simple Economic Lot Size Inventory models,
Reorder Level, Simple single period Stochastic Inventory Model.
Definition of Queues and their characteristics, Queueing Models with Markovian Input
and Markovian Service, M/M/1 & M/M/C Queueing Models.
Definitions of Reliability, Availability, Reliability of multicomponents systems, failure
time distributions: exponential and Weibull.
Computer Science
Flowcharts and algorithms, Number system : binary, octal, hexadecimal; Truth values,
Logical operations, Logic functions and their evaluation.
Computer basics, Computer generations and classifications, Fundamentals of high level
languages, Fundamentals of Operating System, C Programming Language.
