Delhi University DU Syllabus for Common Entrance Test MA MSc OR AOR

UNIVERSITY OF DELHI

DEPARTMENT OF OPERATIONAL RESEARCH

ADMISSION NOTIFICATION-2011

M.Sc. Operational Research (O.R.), University of Delhi (North Campus)

M.A./ M.Sc. Applied Operational Research (A.O.R.), University of Delhi (South Campus)

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.

About DU

The University of Delhi was established in 1922 as a unitary, teaching and residential university by an Act of the Central Legislative Assembly. The first convocation of Delhi University was also held in the Assembly Hall in Old Secretariat Building which now houses the Legislative Assembly of Delhi, on 26 March 1923 with 750 invitees. Honorary Degrees were conferred on Lord Reading (Viceroy of India), Sir Md. Jahan and Sir Hari Singh Gaur, the first Vice Chancellor of the University. Only three colleges existed then in Delhi: St. Stephens College founded in 1881, Hindu College founded in 1899 and Ramjas College founded in 1917, which were affiliated to the University. The University thus had a modest beginning with just three colleges, two faculties (Arts and Science) and about 750 students. The first college to move to the campus was St Stephen's in 1942, followed by Hindu, Ramjas and Commerce (now known as Shri Ram College of Commerce). There was Zakir Husain College also, The origin of the Zakir Husain College can be traced to the closing years of the 17th Century.

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