AMU MCA Entrance

• Mechanics

  7 टॉपिक

  • Concept of inertial and non-inertial frames of reference
  • fictitious forces
  • conservative and non-conservative forces
  • Centre of mass for a system of particles
  • motion of the centre of mass
  • Expressions for kinetic energy, linear momentum and angular momentum for a system of particles in terms of centre of mass values
  • Central forces and the law of conservation of angular momentum

• Rotational Motion

  8 टॉपिक

  • Transformation equations for a frame of reference rotating with respect to an inertial frame of reference
  • Coriolis force
  • Energy and moment of inertia and moment of inertia as a tensor
  • principal axes
  • angular momentum and kinetic energy of rotation with respect to principal axis
  • moment of inertia for a spherical shell and solid sphere
  • rolling bodies
  • Central force, Kepler’s laws

• Special Relativity

  8 टॉपिक

  • Postulates of special theory of relativity
  • Lorentz transformations
  • velocity addition
  • length contraction and time dilation
  • variation of mass with velocity
  • relativistic form of Newton’s second law
  • equivalence of mass and energy
  • relativistic transformations of momentum and energy

• Electricity and Magnetism

  16 में से 9 टॉपिक

  • Gauss’s law
  • Dielectrics
  • polarization of dielectrics
  • Poisson and Laplace’s equations in dielectric
  • polarizability
  • Clausius-Mossotti relation
  • Capacitors
  • Continuity equation
  • transient currents

• Optics

  16 में से 9 टॉपिक

  • Fermat’s principle and its applications
  • Chromatic and spherical aberrations, removal
  • Coma
  • astigmatism
  • curvature of the field
  • distortion
  • Interference of light waves, coherence
  • Fresnel’s biprism
  • Newton’s rings

• Fraunhofer diffraction

  5 टॉपिक

  • Fraunhofer diffraction at two and N slits
  • diffraction grating
  • grating spectrum
  • Rayleigh criterion of resolution
  • resolving power of grating

• Electronics

  13 में से 9 टॉपिक

  • BJT Amplifier
  • α, β and their relation
  • hybrid parameters
  • Characteristics of their simple circuits
  • load line
  • Q-point and its change due to temperature variation
  • BJT biasing: fixed biasing, self-bias, stability factor
  • RC coupled amplifier, its frequency response characteristics
  • Feedback in amplifiers

• Mathematical Method

  8 टॉपिक

  • Cauchy’s integral theorem
  • Cauchy’s integral formula
  • Taylor and Laurent series
  • Cauchy’s residue theorem
  • Gradient, divergence and curl
  • Gauss’s theorem
  • Green’s theorem
  • Stoke’s theorem

• Legendre function

  7 टॉपिक

  • The polynomial solution of the Legendre equation
  • the Legendre function of the second kind
  • the generating function
  • Rodrigues’ formula
  • orthogonality relation
  • Associated Legendre functions and its orthogonality property
  • Laguerre functions

• Modern Physics

  21 में से 9 टॉपिक

  • Black body radiation experiment and Planck’s hypothesis
  • Photoelectric effect
  • Compton effect
  • Wave function and its simple properties
  • Alpha-particle scattering experiment
  • Rutherford’s model of atom; Bohr model, energy levels hydrogen spectrum
  • Composition and size of nucleus, atomic masses
  • Radioactivity – alpha, beta and gamma particles and their properties
  • Mass-energy relation

इस विषय के 109 टॉपिक में से 79 दिखाए गए हैं।सभी 109 टॉपिक देखें →

• Calculus

  28 टॉपिक

  • Successive differentiation
  • Derivatives of higher order
  • nth derivative of well-known functions
  • Leibnitz’s theorem (without proof)
  • Expansion of functions
  • Maclaurin’s theorem and Taylor’s theorem (without proof)
  • Indeterminate forms
  • Asymptotes of the algebraic curves
  • parallel asymptotes
  • Asymptotes parallel to x-axis and y-axis
  • Curvature
  • Angle between radius vector and tangent
  • derivative of arc length in cartesian, parametric and polar form
  • Calculation of curvature in cartesian, parametric and polar form
  • Radius of curvature in the three forms
  • Multiple points
  • convexity and concavity of a curve
  • points of inflexion
  • Tracing of cartesian curves
  • Idea of some well known polar curves
  • Functions of two or more variables
  • partial differential coefficients
  • Homogeneous functions
  • Euler’s theorem on homogeneous functions
  • Gamma functions
  • Length of curves for cartesian, parametric and polar equations
  • Intrinsic equation from cartesian, parametric and polar equations
  • Volume and Surfaces of solids of revolution of cartesian, parametric and polar curves

• Geometry

  65 टॉपिक

  • General Equations
  • pair of straight line through origin
  • lines joining the origin to the intersection of a curve and a line
  • The conic section
  • Equation to a conic section
  • Intersection of a straight line and a conic
  • Equation of a tangent to a conic
  • Condition of tangency
  • Pair of tangents from a point
  • Chord of contact of a pair of tangents to a conic
  • Pole and polar
  • Conjugate points
  • Conjugate lines
  • The condition of conjugacy
  • Chord with a given middle point
  • Centre of a conic and diameter
  • Equation of the conic when the origin is transferred to the centre
  • Conjugate diameters
  • Change of rectangular axes without change of origin
  • Removal of xy-term
  • Invariants
  • Nature of conic
  • Tracing of Parabola
  • The asymptotes of hyperbola
  • Conjugate hyperbola
  • Asymptotes
  • The length and position of axes
  • Coordinate of foci
  • Polar equation of a conic when focus is at the pole
  • Directrices
  • Tracing of the conic
  • Equation of the Chord when the vectorial angles of the extremities are given
  • Equation of the tangent at the point whose vectorial angle is α
  • Normal, Polar
  • Direction cosines of a line
  • Projection of a segment
  • Angles between two lines
  • Distance of a point from a line
  • Equation of a plane
  • Length of perpendicular from a point to a plane
  • Cylinder and its Equation
  • Right circular cylinder
  • Equation of a right circular cylinder
  • Equation of a cone
  • Equation of a cone when the vertex is at the origin
  • Condition for general equation of second degree to represent a cone
  • Tangent plane to a cone
  • A property of the tangent plane to a cone
  • Reciprocal cone
  • Cone with three mutually perpendicular generators
  • Number of mutually perpendicular generators
  • The standard equation of central conicoids
  • The tangent plane
  • Condition of tangency of a plane
  • Section with a given centre
  • Locus of the mid-points of a system of parallel chords
  • The Polar plane
  • Polar lines
  • Enveloping cone
  • Classification of central conicoids
  • The Normal
  • Normals from given point
  • Conjugate diametral plane and diameters of Ellipsoid
  • Paraboloid (elliptic and hyperbolic)
  • Tangent plane to a paraboloid

• Numerical Analysis

  36 टॉपिक

  • Absolute, relative and percentage errors
  • General error formula
  • Error in series approximation
  • Solution of algebraic and transcendental equations
  • The bisection and Regulafalsi method
  • Iteration methods namely, Newton-Raphson method
  • Generalized Newton’s method
  • Solution of system of linear equations using direct methods such as matrix inversion, Gauss elimination and LU decomposition including some iteration methods namely, Jacobi and Gauss-Siedel methods
  • The algebraic eigen value problems using iterative and Householder methods
  • Symbols of Δ,∇, E, E-1, D, µ and δ
  • Newton-Gregory Forward and Backward difference formulae
  • Gauss’s, Stirling’s and Bessel’s formulae
  • Lagrange’s formula
  • Divided Differences and their properties
  • Newton’s general interpolation formula
  • Inverse interpolation formula
  • Interpolation with cubic splines
  • Numerical Differentiation and Integration
  • Numerical differentiation of tabular and non-tabular functions including error estimations
  • Numerical integration using Gauss quadrature formulae
  • Trapezoidal, Simpson’s 1/3- and 3/8-Rule
  • Weddle’s Rule and Newton-Cotes Formula including error estimation
  • Curve fitting and approximations
  • Least squares curve fitting procedures
  • Different types of approximations
  • Least squares polynomial approximation
  • Chebyshev polynomials and its application in various approximations
  • Ordinary differential equations
  • Euler’s and modified Euler’s methods
  • Picard’s method
  • Taylor series method
  • Runge-Kutta methods of 2nd and 4th order
  • Multi-step methods
  • Milne-Simpson method
  • Adam Bashforth-Moulton method
  • Boundary value problems using Finite Difference method

• Differential Equations

  63 टॉपिक

  • Exact differential equations
  • Integrating factors
  • Total differential equations
  • Differential equations of first order but not of first degree
  • Equations solvable for p, y and x
  • Clairaut’s equations
  • Linear differential equations of order n
  • Homogeneous and non-homogeneous differential equations of order n with constant coefficients
  • Complementary functions
  • Different forms of particular integrals
  • Linear differential equations with non-constant coefficients
  • Reduction of order method
  • The Cauchy-Euler’s equation of order n
  • The Legendre’s linear equation
  • Methods of undetermined coefficients and variation of parameters
  • Series solution of differential equations
  • Frobenius method
  • Different cases
  • Bessel, Legendre and hypergeometric differential equations and their solutions
  • Simultaneous total different equations
  • Equations of the form dx/P=dy/Q=dz/R
  • Methods of grouping and multipliers
  • Solution of a system of linear differential equation with constant coefficients
  • An equivalent triangular system
  • Degenerate case
  • Laplace transforms
  • Linearity of Laplace transforms
  • First shifting property
  • Table of Laplace transforms
  • Inverse Laplace transforms
  • Laplace transform of derivative and integrals
  • Unit step function and its Laplace transform
  • Second shifting property
  • Unit impulsive function and its Laplace transform
  • Convolution and periodic function theorems
  • Solution of linear differential equations with constant coefficients using Laplace transform methods
  • Formation and solution of a partial differential equations
  • Equations easily integrable
  • Linear partial differential equations of first order
  • Non-linear partial differential equation of first order and their different forms
  • Charpit’s method
  • Homogeneous linear partial differential equations with constant coefficients
  • Different cases for complimentary functions and particular integrals
  • Non-homogeneous partial differential equations with constant coefficients
  • Classification of second order linear partial differential equations
  • Method of separation of variables
  • Fourier series
  • Even and odd functions and their Fourier series
  • Change of interval
  • Vibration of stretched string
  • One and two dimensional heat flow
  • Solution of Laplace equation in Cartesian and polar co-ordinates
  • Variation of a functional
  • Variational problems
  • Euler’s equations and its various cases
  • Externals
  • Functional depending on n unknown functions
  • Functionals depending on higher derivatives
  • Variational problems in parametric form
  • Isoperimetric problem
  • Canonical form of Euler’s equation
  • Functionals depending on functions of several independent variables
  • Ostrogradsky’s equation

• Advanced Calculus

  32 टॉपिक

  • Functions of several variables
  • Contour lines
  • Level curves and level surfaces
  • Limits and continuity for functions of two and more variables
  • Partial derivatives
  • Partial derivatives and continuity
  • Differentiability
  • The chain rule for functions of two and three variables
  • Directional derivatives
  • Gradient vectors
  • Tangent planes
  • Linearization and differentials
  • Extreme values and saddle points
  • Local and absolute maxima / minima
  • The method of Lagrange multipliers (with one constraint only)
  • Taylor’s series for function of two variables
  • Partial derivatives with constrained variables
  • Double integral over a rectangle region
  • Double integral as volume
  • Double integral over non rectangular regions
  • Fubini’s Theorem
  • Area of a region in a plane
  • Transformation of double integral from Cartesian to polar co-ordinates and vice-versa
  • Spherical and cylindrical co-ordinates
  • Triple integral in Cartesian, Cylindrical and spherical co-ordinates
  • Line integral
  • Gradient field
  • Green’s Theorem in a plane
  • Evaluation of line integral using Green’s Theorem
  • Surface Area
  • Surface integral
  • Strokes Theorem

• Algebra

  24 टॉपिक

  • Binary operations
  • definitions of Group, Ring and Field with examples
  • vector spaces
  • subspaces
  • span of a set
  • sum of subspaces
  • linear dependence and independence
  • dimension and basis
  • coordinates of a vector relative to the ordered basis
  • dimension theorem
  • Linear transformation and its properties
  • range and kernel of a linear transformation
  • rank and nullity of linear transformation
  • rank-nullity theorem
  • inverse of linear transformation
  • The vector space L(U,V) and its dimension
  • composition of linear transformations
  • matrix associated with a linear transformation
  • linear transformation associated with a matrix
  • matrix as a linear transformation and its rank and nullity
  • Elementary row operations and row- reduced echelon form
  • inverse of a matrix through elementary row operation
  • solution of a system of linear equations
  • eigen-values, eigen-vectors

इस विषय के सभी 248 टॉपिक दिखाए गए हैं।कम टॉपिक दिखाएँ

• Descriptive Statistics

  11 में से 9 टॉपिक

  • Measures of central tendency
  • Dispersion
  • Skewnes and Kurtosis
  • Scatter diagram
  • Correlation coefficient
  • Rank correlation
  • Spearman’s and Kendall’s measures
  • Multiple correlations in three variables
  • Partial correlation in three variables

• Probability Theory

  10 में से 9 टॉपिक

  • Definition of probability
  • Discrete and Continuous sample space
  • Events
  • Independent and Mutually Exclusive Events
  • Random Experiment
  • Conditional Probability
  • Baye’s theorem and its application
  • Random Variables
  • mathematical expectation

• Probability Distributions

  6 टॉपिक

  • Uniform
  • Binomial
  • Poisson
  • Geometric
  • Hyper-geometric
  • Normal Exponential Gamma and Beta Distribution, their means, variances and other properties

• Sampling Theory

  8 टॉपिक

  • Concept of population and sampling
  • Census and sample survey
  • random sample
  • sample size
  • Non-sampling errors
  • Concept of bias and standard error of an estimate
  • sampling distributions
  • Tests of significance based on t, chi-square and F tests

• Statistical Inference

  6 टॉपिक

  • Requirements of a good estimator
  • Methods of estimation (MLE and method of moments)
  • Interval Estimation
  • Testing of hypothesis
  • simple and composite hypothesis
  • Errors of first and second type and critical region

• Design of Experiments and LPP

  5 टॉपिक

  • ANOVA for one way and two way classifications
  • Principles of Design of Experiments
  • CRD, RBD and LSD
  • General LPP
  • Graphical and Simplex Method of Solving LPP

इस विषय के 46 टॉपिक में से 43 दिखाए गए हैं।सभी 46 टॉपिक देखें →

• FUNDAMENETALS & Information Technology and Information Systems

  3 टॉपिक

  • Recent IT tools and technologies
  • SDLC
  • ERD and System Design Principals

• COMPUTER ARCHITECTURE

  9 टॉपिक

  • Number System
  • Integer and Floating Point representations
  • Addition and subtraction of signed and unsigned numbers
  • Multiplication and division of signed and unsigned numbers
  • CISC and RISC characteristics
  • Cache memory – Organization and Structure
  • Cache mapping algorithms
  • Cache replacement policies
  • Input / Output techniques

• PROGRAMMING CONCEPT

  15 में से 8 टॉपिक

  • C, C++, Java
  • arithmetic, logical bitwise and conditional operators
  • Data
  • Expressions
  • Statements
  • Control Flow
  • iteration
  • Functions

• DATA STRUCTURES AND ALGORITHMS

  14 में से 8 टॉपिक

  • Arrays
  • stacks
  • queues
  • linked lists
  • trees
  • binary search trees
  • binary heaps
  • graphs

• OPERATING SYSTEM

  6 टॉपिक

  • Operating System and its function
  • Instruction Execution
  • Interrupts
  • Memory Management
  • Scheduling
  • Case study of Linux / Unix OS

• DATABASE MANAGEMENT SYSTEM

  12 में से 8 टॉपिक

  • Database Systems Concepts & Architecture
  • Data Models, Schemas & Instances
  • DBMS Architecture & Data Independence
  • Database Languages & Interfaces
  • Data modeling using the Entity-Relationship Approach
  • Relational Database Design: Function Dependencies & Normalization for Relational Databases
  • Functional Dependencies
  • Normal forms based on primary keys (INF, 2NF, 3NF & BCNF)

• DATA COMMUNICATION AND COMPUTER NETWORKS

  19 में से 8 टॉपिक

  • Fundamentals of Data Communication and Networks
  • Network models : OSI Model
  • Peer-to-peer processes
  • Interfaces
  • Layers in OSI model
  • TCP / IP model-Architecture
  • Layers in TCP / IP model
  • Similarities

इस विषय के 78 टॉपिक में से 50 दिखाए गए हैं।सभी 78 टॉपिक देखें →