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Saturday, 28 April 2012

Delhi University DU CET-2012 Syllabus for Common Entrance Test


Delhi University (DU) 

DU CET-2012 

M.Sc. Operational Research and M.A. / M.Sc.  Applied Operational Research

M.Sc. Operational Research at University of Delhi, North Campus 
M.A. / M.Sc.  Applied Operational Research at University of Delhi, South Campus
M.Phil and Doctor of Philosophy (Ph.D) Programmes

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.  


For complete details visit website http://du.ac.in/