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Engineering Core Papers

Circuit Theory

  1. Concept of Network and Circuit
  2. Types of elements
  3. Types of sources
  4. Source transformation.
  5. R-L-C Parameters
  6. Voltage-Current relationship for Passive Elements (for different input signals -Square, Ramp, Saw tooth and Triangular)
  7. Kirchhoff's Laws
  1. Network Reduction Techniques-Resistive networks
  2. Inductive networks and capacitive networks- Series, Parallel, Series-Parallel combinations
  3. Star-to-Delta and Delta-to-Star Transformation
  4. Mesh Analysis and Super mesh
  5. Nodal Analysis and Super node for DC Excitation
  6. Network topology-Definitions
  7. Graph
  8. Tree
  9. Basic Cut set and Basic Tie set Matrices for Planar Networks
  1. Average value, R.M.S. value, form factor and peak factor for different periodic wave forms
  2. J-notation, Complex and Polar forms of representation
  3. Steady State Analysis of series R-L-C circuits
  4. Concept of Reactance, Impedance, Susceptance, Admittance, Phase and Phase difference
  5. Concept of Power Factor, Real, Reactive and Complex power
  1. Thevenin's
  2. Norton's
  3. Maximum Power Transfer
  4. Superposition
  5. Reciprocity
  6. Tellegen's
  7. Substitution
  8. Compensation and Milliman's theorems
  1. Faraday's laws of electromagnetic induction
  2. concept of self and mutual inductance
  3. dot convention
  4. coefficient of coupling
  5. composite magnetic circuit
  6. analysis of series and parallel magnetic circuits.

Control system

  1. Open and closed loop control system Transfer function of a system Need for mathematical modelling
  2. Representation of mechanical translational and rotational systems using differential equation and determination
    of transfer function
  3. Conversions of Mechanical system to Electrical system f-V and f- I electrical analogies
  4. Block diagram reduction rules and methodology
  5. Evaluation of transfer function using block diagram
    reduction
  6. Signal flowgraphs and evaluation of transfer function
  7. Block diagram to signal flow conversion
  1. Standard test signals and their expression
  2. Type number and order of a system
  3. Transfer function of First order system for Step, ramp, Impulse and parabolic signalĀ 
  4. General transfer function of second order
    system for different damping factor based on step response
  5. Time domain specifications and their significance
  6. Transient and Steady state error analysis
  7. Static and dynamic Error coefficients
  8. Analytical design for PD, PI and PID control systems
  1. Poles and zeros of a system - Pole zero plot and concept of s planeĀ 
  2. Concept of stabilityĀ 
  3. Significance of Routh Hurwitz Technique with different cases
  4. Root locus techniques
  5. Root locus plot of typical systems
  6. Design of Compensator using root locus
  7. Lead Compensation
  1. Frequency domain specifications
  2. Bode plot approach and stability analysis
  3. Rules for sketching Bode plot of typical systems
  4. Design of Compensator using Bode Plot
  5. Lag Compensation
  6. Polar plot and
    significance
  7. Sketching the Polar plot of typical systems
  8. Nyquist stability criterion
  1. State variable representation-Conversion of state variable models to transfer function
  2. Conversion of transfer functions to state variable models
  3. Solution of state equations
  4. Concepts of Controllability and
    Observability
  5. Fuzzy logic
  6. based control system
  7. Adaptive Controller

Electro Magnetic Field / Theory

  1. Introduction to electrostatics
  2. rectangular co-ordinate
  3. Cylindrical & Spherical Co-ordinate
  4. Review of vector calculus
  5. Coulombā€™s Law and field intensity
  6. Problem based on coulombā€™s law
  7. Electric field due to
    continuous charge distribution
  8. Concept
  9. Derivation of E due Infinite Line charge
  1. Energy density in electrostatic field- Problem discussion.Ā 
  2. Biot savart law
  3. Magnetic field intensity due to Infinite line charge
  4. H- due finite and semi finite line charge
  5. Ampereā€™s circuital law and application: Infinite
    line current
  6. Infinite Sheet current
  7. Infinitely long coaxial Transmission line
  8. Problem based on ACL
  1. Introduction to EM waves
  2. Waves in general
  3. Plane wave in lossless dielectric
  4. Plane wave in free space
  5. Plane wave in good conductor
  6. Problems based on plane waves in lossless, free space and good conductor rectangular
    waveguide
  7. rectangular waveguide
  8. Problems
  1. Transmission line parameters
  2. Transmission line equivalent circuit
  3. Explanation
  4. Transmission line equation derivation
  5. Problem discussion.Ā 
  6. Transmission line characteristics: lossless Line
  7. Distortion lesslineĀ 

  8. EMI/EMC- Types of EMI/EMC - SE, CEĀ 
  9. Susceptibility
  1. Introduction to impedance matching
  2. Smith chart Introduction
  3. Reflection coefficient, Standing wave ratio Input impedance calculation in smith chart
  4. Practice problems.Ā 
  5. Single stub matching Introduction
  6. Procedure
    for single stub matching
  7. Problems solving in smith chart

Mathematics (M-Series) Papers

ENGINEERING MATHEMATICS ā€“ M1

Calculus & Linear Algebra - M1

  1. Representation of functions
  2. Limit of a function
  3. Continuity
  4. Derivatives
  5. Differentiation rules
  6. Maxima and Minima of functions of one variable
  1. Partial differentiationĀ 
  2. Homogeneous functions and Eulerā€™s theoremĀ 
  3. Total derivative
  4. Change
    of variablesĀ 
  5. JacobiansĀ 
  6. Partial differentiation of implicit functions
  7. Taylorā€™s series for functions
    of two variablesĀ 
  8. Maxima and minima of functions of two variablesĀ 
  9. Lagrangeā€™s method of
    undetermined multipliers
  1. Definite and Indefinite integralsĀ 
  2. Substitution ruleĀ 
  3. Techniques of IntegrationĀ 
  4. Integration by
    parts
  5. Trigonometric integrals
  6. Trigonometric substitutions
  7. Integration of rational functions by
    partial fraction
  8. Integration of irrational functionsĀ 
  9. Improper integrals
  1. Double integralsĀ 
  2. Change of order of integrationĀ 
  3. Double integrals in polar coordinatesĀ 
  4. Area
    enclosed by plane curvesĀ 
  5. Triple integralsĀ 
  6. Volume of solidsĀ 
  7. Change of variables in double
    and triple integrals
  1. Higher order linear differential equations with constant coefficientsĀ 
  2. Method of variation of
    parametersĀ 
  3. Homogenous equation of Eulerā€™s and Legendreā€™s typeĀ 
  4. System of simultaneous
    linear differential equations with constant coefficientsĀ 
  5. Method of undetermined coefficients

ENGINEERING MATHEMATICS - M2

Advanced Calculus & Complex Analysis - M2

  1. Eigenvalues and Eigenvectors of a real matrix
  2. Characteristic equation
  3. Properties of Eigenvalues and Eigenvectors
  4. Cayley-Hamilton theorem
  5. Diagonalization of matrices
  6. Reduction of a quadratic form to canonical form by orthogonal transformation
  7. Nature of quadratic forms
  1. Gradient and directional derivative
  2. Divergence and curl
  3. Vector identities
  4. Irrotational and Solenoidal vector fields
  5. Line integral over a plane curve
  6. Surface integralĀ 
  7. Area of a curved surfaceĀ 
  8. Volume integral - Green's, Gauss divergence and Stoke's theoremsĀ 
  9. Verification and application in evaluating line, surface and volume integrals
  1. Analytic functions
  2. Necessary and sufficient conditions for analyticity in Cartesian and polar coordomates
  3. Properties
  4. Harmonic Conjugates
  5. Construction of analytic function
  6. Conformal
    MappingĀ 
  7. Mapping by functions w = Z+C, CZ,-1/Z,Z^2
  8. Bilinear Transformation
  1. Line integralĀ 
  2. Cauchy's integral theorem
  3. Cauchy's integral formulaĀ 
  4. Taylor's and Laurent's series
  5. Singularities
  6. Residues
  7. Residue Theorem
  8. Application of residue theorem for evaluation of real integrals
  9. Use of circular contour & semicircular contour
  1. Existence conditions
  2. Transforms of elementary functions
  3. Transform of unit step function and unit impulse functionĀ 
  4. Basic properties
  5. Shifting theorems
  6. Transforms of derivatives and integrals
  7. Initial and final value theorems
  8. Inverse transforms
  9. Convolution theorem
  10. Transform of periodic functions
  11. Application to solution of linear second order ordinary differential equations with constant coefficients

ENGINEERING MATHEMATICS - M3

Transforms & Boundary Value Problems - M3

  1. Formation of partial differential equations by eliminating arbitrary constants & arbitrary functions
  2. Solutions of standard types of first order partial differential equationsĀ 
  3. Lagrangeā€™s linear equationĀ 
  4. Linear partial
    differential equations of second and higher order with constant coefficients of homogeneous types
  1. Dirichletā€™s conditionsĀ 
  2. General Fourier seriesĀ 
  3. Odd and even functionsĀ 
  4. Half range sine and cosine seriesĀ 
  5. Parsevalā€™s identityĀ 
  6. Harmonic Analysis
  1. Classification of second order partial differential equationsĀ 
  2. Method of separation of variablesĀ 
  3. Solutions of one dimensional wave equation - One dimensional equation of heat conduction (Insulated edges excluded)
  4. Steady state condition with zero boundaryĀ 
  5. Steady state condition with non-zero boundary conditions
    1. Fourier transform pairĀ 
    2. PropertiesĀ  - Fourier sine and cosine transformsĀ 
    3. Propertiesā€“ Transforms of simple functionsĀ 
    4. Convolution theorem (without proof)Ā 
    5. Parsevalā€™s identity.
  1. Z - transformsĀ 
  2. Properties of Z transformsĀ 
  3. Inverse Z transformsĀ 
  4. Convolution theorem (without Proof)Ā 
  5. Solution of linear difference equations with constant coefficients using Z-transform

Other Mathematics Papers

Numerical Methods

  1. Solution of nonlinear equations
  2. False position method
  3. Fixed point iteration methodĀ 
  4. Newton Raphson method - Solution of linear system of equations: Gaussian elimination method
  5. Gauss Jacobi methodĀ 

  6. Gauss Seidel methodĀ 
  7. Eigenvalues of a matrix by power method
  1. Curve fittingĀ 
  2. Method of least squaresĀ 
  3. Interpolation: Newtonā€™s forward and backward differenceĀ 
  4. Divided differencesĀ 
  5. Newtonā€™s divided difference
  6. Lagrangeā€™s interpolationĀ 
  7. Inverse interpolation
  1. Numerical differentiation by using Newtonā€™s forward, backward and divided differencesĀ 
  2. Numerical integration by trapezoidal and Simpsonā€™s 1/3rd and 3/8th rules
    1. Single step methods: Taylorā€™s series method, Euler and Improved Euler methods, fourth order RungeĀ 
    2. Kutta methodĀ 
    3. Multistep methods: Milneā€™s predictorĀ 
    4. corrector method
  1. Finite difference techniques: Solution of two dimensional Laplaceā€™s equations by Liebmannā€™s iterative process and Poissonā€™s equationsĀ 
  2. Solution of one dimensional heat equation using Bender Schmidt and Crank
    Nicholson difference schemes
  3. Solution of one dimensional wave equation by explicit scheme.

Discrete Mathematics

  1. Sets - Operations on sets
  2. Laws of set theoryĀ 
  3. Partition of a setĀ 
  4. Cartesian product of setsĀ 
  5. RelationsĀ 
  6. PropertiesĀ 
  7. Equivalence relation and partial order relationĀ 
  8. PosetĀ 
  9. Graphs of relationsĀ 
  10. DigraphsĀ 
  11. Hasse
    diagramĀ 
  12. Closures of relationsĀ 
  13. Transitive closure and Warshallā€™s algorithmĀ 
  14. Functions - Types of functions
  15. Composition of functionsĀ 
  16. PropertiesĀ 
  17. Inverse of functionsĀ 
  18. Necessary and sufficient condition for
    existence of inverse functionĀ 
  19. Uniqueness of identity
  20. Inverse of composition
  1. Permutation and combinationĀ 
  2. Addition and product rulesĀ 
  3. Principle of inclusion and exclusionĀ 
  4. Pigeon-hole principle and generalized pigeon-hole principleĀ 
  5. Divisibility and prime numbersĀ 
  6. Fundamental theorem
    of arithmeticĀ 
  7. Prime factorizationĀ 
  8. Division algorithm
  9. Greatest common divisor - PropertiesĀ 
  10. Euclidā€™s algorithmĀ 
  11. Least common multiple
  1. Propositions and logical operators
  2. Truth tablesĀ 
  3. Converse, inverse and contrapositiveĀ 
  4. Tautology and contradictionĀ 
  5. EquivalencesĀ 
  6. ImplicationsĀ 
  7. Laws of logicĀ 
  8. Inference theory
  9. Rules of inferenceĀ 
  10. Direct
    method
  11. CP ruleĀ 
  12. InconsistencyĀ 
  13. Indirect methodĀ 
  14. Principle of mathematical induction
  1. GroupsĀ 
  2. Permutation group
  3. Cyclic groupĀ 
  4. PropertiesĀ 
  5. Subgroup
  6. Group homomorphismĀ 
  7. PropertiesĀ 
  8. RingĀ 
  9. Zero divisorĀ 
  10. Integral domain- Field
  11. Coding theory - Group codeĀ 
  12. Hamming codesĀ 
  13. Error correction
    using matricesĀ 
  14. Error correction - Decoding group codes
  1. DefinitionsĀ 
  2. Handshaking theorem
  3. Some special graphsĀ 
  4. Isomorphism of graphs - Paths, cycles and circuitsĀ 
  5. Connectivity in undirected graphsĀ 
  6. Eulerian and Hamiltonian graphs
  7. Matrix representation of graphs

  8. Isomorphism using adjacencyĀ 
  9. DigraphsĀ 
  10. TreesĀ 
  11. PropertiesĀ 
  12. Spanning treeĀ 
  13. Kruskalā€™s algorithm
  14. Graph coloringĀ 
  15. Chromatic number
  16. Four color theorem (statement only)

Transforms and Computational Techniques

  1. Dirichletā€™s conditionsĀ 
  2. Fourier SeriesĀ 
  3. Functions having arbitrary periodsĀ 
  4. Odd and even functionĀ 
  5. Half range sine and cosine Fourier seriesĀ 
  6. Parsevalā€™s identityĀ 
  7. Harmonic Analysis
  1. Fourier transform pair
  2. Fourier sine and cosine transformsĀ 
  3. Transforms of simple functionsĀ 
  4. Convolution theorem (without proof)Ā 
  5. Parsevalā€™s identity
  6. Z ā€“ transforms: Properties of Z transformsĀ 
  7. Inverse Z
    transformsĀ 
  8. Convolution theorem (without Proof)Ā 
  9. Solution of linear difference equations with constant coefficients using Z-transform
  1. Classification of second-order partial differential equationsĀ 
  2. Linear Partial differential equations of second and higher order with constant coefficients of homogeneous type
  3. Solutions of one dimensional wave
    equationĀ 
  4. One dimensional equation of heat conductionĀ 
  5. Steady state conditions with zero boundary
  1. Solutions of first order simultaneous differential equations by Taylorā€™s series methodĀ 
  2. Eulerā€™s method and its applicationsĀ 
  3. Runge-Kutta method of fourth order (No proof)Ā 
  4. Trapezoidal rule
  5. Simpsonā€™s one third
    and Simpsonā€™s 3/8th rule
  1. Classification of Second order PDE
  2. Solutions of Elliptic Equations
  3. Solutions of Laplace Equations by Liebmannā€™s iterative process
  4. Solutions of Poisson Equations
  5. Solutions of Parabolic equations by Bender

  6. Schmidt formula
  7. Solutions of Parabolic equations by Crank
  8. Nicolson formula
  9. Solutions of Hyperbolic equations by Explicit formula

Probability & Queuing Theory

  1. Probability conceptsĀ 
  2. Discrete and continuous random variablesĀ 
  3. Probability distribution function, Cumulative distribution functionĀ 
  4. MomentsĀ 
  5. Central and raw moments, Expectation and varianceĀ 
  6. Moment
    generating function (MGF)
  7. Tchebycheffā€™s inequalityĀ 
  8. Function of a random variable
  1. Discrete distributionĀ 
  2. Binomial distribution, Poisson distributionĀ 
  3. MGF, Mean, Variance, Theoretical frequencies and applicationsĀ 
  4. Continuous distributionĀ 
  5. Exponential and normal distributionsĀ 
  6. MGF, Mean,
    Variance and applications
  1. Joint distributionsĀ 
  2. Marginal and conditional distributionsĀ 
  3. CovarianceĀ 
  4. Correlation and linear regression
  5. Central limit theorem (for independent and identically distributed random variables)
  1. Queueing theoryĀ 
  2. Characteristics of a queueing ModelĀ 
  3. Kendalā€™s notationĀ 
  4. Poisson queues - (M/M/1): (āˆž/FIFO) ModelĀ 
  5. System characteristicsĀ 
  6. ApplicationsĀ  (M/M/s):
  7. (āˆž/FIFO) Model
  8. System characteristics
  9. Applications - (M/M/1): (ō€‡/FIFO) Model
  10. System characteristicsĀ 
  11. Applications.
  1. Markov process
  2. Markov chainĀ 
  3. One step transition probability matrix
  4. Chapman Kolmogorov theoremĀ 
  5. Limiting probabilitiesĀ 
  6. Classification of states of a Markov chain

Probability and Stochastic Processes

  1. One-dimensional random variable: Discrete Case
  2. Probability function, Cumulative Distribution Function, continuous random variable
  3. Probability density function, Cumulative distribution function
  4. properties, Problems
    on one
  5. dimensional random variable, Expectation, variance, MomentsĀ 
  6. raw and central moments, Binomial distribution
  7. moments, Binomial distribution-Applications, Poisson distribution
  8. moments, Poisson
    distribution -Applications
  9. Exponential distribution
  10. moments, Exponential distribution -Applications
  11. Normal Distribution
  12. moments, Normal Distribution-Applications
  13. Uniform Distribution-moments, Uniform
    Distribution-Applications
  14. Function of a random variable
  15. Applications of random variables in engineering
  1. Two-dimensional random variables
  2. Discrete cases, Probability function of (X, Y)
  3. Marginal probability distribution, Conditional probability distribution of (X, Y),
  4. Problems on discrete random variables, Continuous
    random variables
  5. Joint PDF, Marginal Probability distributions, Conditional probability distribution of (X, Y),
  6. Problems on continuous two-dimensional random variables, Independent random variables, Cumulative
    distribution function
  7. properties of F(x, y), Expected values of two-dimensional random variables, Covariance and correlation, Conditional expected values
  8. Problems on uncorrelated random variables
  9. Functions of
    two-dimensional random variables
  10. Probability density functions of the type Z=XY
  11. Probability density functions of the type Z=X-Y, Probability density functions of the type Z=X/Y
  12. Application of two-dimensional
    random variables in engineering
  1. Limit theorems--Markov's inequality, Chebyshev's inequality without proof,
  2. Chebyshev's inequality - Applications, Chebyshev's inequalityĀ 
  3. Applications using Binomial distribution
  4. Chebyshev's inequalityā€“
    Applications using Exponential distribution,
  5. The weak law of large numbers, Central limit theorem without proof,
  6. Central limit theorem - Applications,
  7. Central limit theorem- Applications using Poisson random
    variables,
  8. Central limit theorem- Applications using Exponential random variables,
  9. The strong law of large numbers, The strong law of large numbers, One-sided Chebychev's inequality,
  10. Cauchy Schwartz inequality,
    Chernoff bounds, Chernoff bounds for the standard normal variate, Chernoff bounds for the Poisson random variate, Jenson's inequality
  11. Applications of Central Limit Theorem in engineering
  1. Random Processes
  2. Introduction, Classification of random processes, Distribution of the process
  3. Averages of the process, Stationary, SSS, WSS processes
  4. Problems on stationary and SSS processes, Problem
  5. Problems on WSS process, Problems on WSS process,
  6. Autocorrelation function
  7. properties, Proof of properties, Problems on autocorrelation function,
  8. Application of autocorrelation function, Cross-correlation properties,
  9. Proof of properties, Problems on Cross-correlation function, Ergodicity, Mean ergodic process, Mean ergodic theorem,
  10. Applications of random process in engineering.
  1. Power spectral density function- properties,
  2. Proof of properties,
  3. Problems on power spectral density function,
  4. Problems on power spectral density function,
  5. Power density spectrum,
  6. Problems based on power
    density spectrum,
  7. Linear systems with random inputs,
  8. Representation of system in the form of convolution,
  9. Unit impulse response of the system, Properties, Applications of unit impulse function,
  10. Einstein Weiner-
    Khinchine Relationship,
  11. Cross-power density spectrum-problems,
  12. Cross-power density spectrum Cross-power density spectrum,
  13. Applications of power spectral density functions in engineering, Applications of power
    spectral density functions in engineering

Probability & Random Variables

  1. Probability
  2. Axioms of probabilityĀ 
  3. Conditional Probility
  4. Baye's TheoremĀ 
  5. Discrete and Continuous Random Variables
  6. Moments - Moment Generating Functions
  7. Binomial, Poisson, Geometric, Uniform, Exponential & Normal Distributions
  8. Ā 
  1. Ā Joint Distributions
  2. Marginal and Conditional Distributions
  3. Covariance
  4. Correlation and Linear Regression
  5. Transformation of Random VariablesĀ 
  6. Central Limit Theorem(for Independent & Identically Distributed Random Variables).
  1. Ā Classification
  2. Stationary Process
  3. Markov Process
  4. Poisson Process
  5. Discrete Parameter Markov Chain
  6. Chapman Kolmogorov EquationsĀ 
  7. Limiting Distributions
  1. Ā Markovian Queues
  2. Birth & Death Processes
  3. Single & Multiple Server Queueing Models
  4. Little's Formula
  5. Queues with Finite Waiting Rooms
  6. Queues with Impatient Customers : Balking & Renegining
  1. Ā Finite Source Models
  2. M/G/1 Queue
  3. Pollaczek Khinchin Formula
  4. M/D/1 as Special Cases
  5. Series Queues
  6. Open Jackson Networks

Statistical Modeling

  1. Random samplingĀ 
  2. Sampling from finite and infinite populationsĀ 
  3. Estimates and standard error (sampling with replacement and sampling without replacement)Ā 
  4. Sampling distribution of sample meanĀ 
  5. stratified
    random samplingĀ 
  6. Systematic sampling and cluster sampling
  1. Definition of StatisticsĀ 
  2. Basic objectivesĀ 
  3. Applications in various branches of science with examplesĀ 
  4. Collection of Data: Internal and external data, primary and secondary dataĀ 
  5. Population and sampleĀ 
  6. Representative sampleĀ 
  7. Descriptive Statistics: Classification and tabulation of univariate dataĀ 
  8. graphical representationĀ 
  9. Frequency curvesĀ 
  10. Descriptive measures
  11. central tendency and dispersion.
  1. Point estimationĀ 
  2. criteria for good estimates (unbiasedness, consistency)Ā 
  3. Methods of estimation including maximum likelihood estimationĀ 
  4. Sufficient statistic: concept and examples, complete sufficiency and their
    application in estimation
  5. Test of hypothesis: concept and formulationĀ 
  6. Type I and Type II errorsĀ 
  7. Neyman Pearson lemma
  1. Comparison with parametric inferenceĀ 
  2. Use of order statistics
  3. Sign testĀ 
  4. Wilcoxon signed rank testĀ 
  5. Mann
  6. Whitney testĀ 
  7. Run testĀ 
  8. Kolmogorov
  9. Smirnov testĀ 
  10. Spearmanā€™s and Kendallā€™s test
  11. Tolerance region
  1. Basics of Time Series Analysis and ForecastingĀ 
  2. StationaryĀ 
  3. ARIMA Models: IdentificationĀ 
  4. Estimation and ForecastingĀ 
  5. Applications to industrial problems

Probability and Statistics

  1. Probability concepts, Types of Events, Axioms and theoremsĀ 
  2. Conditional probability, Bayeā€™s theorem (without proof)Ā 
  3. Applications of Bayeā€™s Theorem. Random variablesĀ 
  4. Discrete case and continuous case
  5. Mathematical expectation, Variance
  6. discrete case and continuous case - Raw MomentsĀ 
  7. Central MomentsĀ 
  8. Moment generating function (MGF)Ā 
  9. discrete and continuous random variable
  1. Discrete distributionsĀ 
  2. Introduction- Mean and Variance of Binomial Distribution
  3. Fitting a Binomial distribution
  4. MGF of Binomial Distribution
  5. Poisson Distribution
  6. Mean and Variance of Poisson Distribution
  7. Fitting
    a Poisson distribution
  8. MGF of Poisson distribution
  9. Geometric distribution mean and variance, Memoryless property
  10. Continuous distributionsĀ 
  11. Introduction- Uniform distributionĀ 
  12. MGF, Mean and Variance-
    Exponential distributionĀ 
  13. MGF, Mean and Variance, Memoryless property
  14. Normal distribution
  1. Sampling DistributionsĀ 
  2. Type I and Type II errors
  3. large sample test
  4. Test of significance for single proportion
  5. Test of significance for difference of proportions
  6. Test of significance for single mean
  7. Test of significance
    for difference of means
  8. Small sample tests
  9. Studentā€™s t- test for single mean- t- test for the difference of means- Fisherā€™s F-test
  10. Test of significance for two sample variances- Chi -square tes for the goodness of
    fit- Chi-square test for the independence of attributes.
  1. Correlation and its Properties
  2. Karl Pearsonā€™s coefficient of correlation
  3. Spearmanā€™s rank correlation coefficient for repeated and non-repeated ranks
  4. Linear Regression lines and Properties
  5. Relation between
    correlation and regression coefficient
  6. Introduction to Analysis of Variance (ANOVA)
  7. One-way ClassificationĀ 
  8. two-way classification
  1. Introduction ā€“ Process controlĀ 
  2. control charts for variables - X & R, X
    and S charts
  3. control charts for attributes: p-chart, np-chart, c- chart and their applications in process control

ELEMENTS OF OPERATIONS RESEARCH

Mathematics Paper (MBA)

  1. Operations Research
  2. Meaning
  3. DefinitionĀ 
  4. Origin and History
  5. Characteristic Features
  6. Need
  7. Scope
  8. Steps
  9. Techniques
  10. Application
  11. Limitations
  1. Meaning
  2. Requirements
  3. Assumptions
  4. Applications
  5. Formulating Lpp ā€“Advantages
  6. Limitations Formulating LP Model (Simple Problems Only)
  1. Obtaining Optimal Solution for Linear Programming Problem (LPP)
  2. Graphical Method
  3. Problems
  4. Simplex Method for Type of LPP and for Slack Variable Case
  5. Maximization Function
  6. Minimization Function (Simple Problem Only)
  1. Meaning
  2. (Initial Basic Feasible Solution )Assumptions
  3. Degenerate Solution
  4. North -West Corner Method- Least Cost Method -Vogels Approximation Method
  5. Assignment Problems
  6. Features
  7. Transportation Problem Vs Assignment Problem
  8. Hungarian Method (Simple Problems Only)
  1. Meaning
  2. Types of Games
  3. Basic Assumptions
  4. Finding Value of Game for Pure Strategy
  5. Mixed Strategy
  6. Indeterminate Matrix and Average Method
  7. Graphical Method
  8. Pure Strategy
  9. Saddle Point Payoff Matrix Value of Game (Simple Problems Only)

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