IIT JAM

• Cell Biology

  6 में से 5 टॉपिक

  • Structure of prokaryotic and eukaryotic cells
  • Membrane structure and function
  • Organelles and internal organization of the eukaryotic cell
  • Cell communication – signalling pathways: endocrine and paracrine signalling
  • Extracellular matrix and apoptosis

• Biochemistry

  4 टॉपिक

  • Structure and function of biological macromolecules
  • Enzymes – basic mechanisms of enzyme catalysis and regulation, Hill coefficient, Michaelis-Menten kinetics, enzyme inhibition, vitamins as coenzymes
  • Bioenergetics – free-energy change, high-energy compounds, biological oxidation-reduction reactions and reduction potential
  • Metabolism – glycolysis, TCA cycle and their regulation, oxidative phosphorylation, photosynthesis, nitrogen fixation, urea cycle

• Genetics

  5 टॉपिक

  • Mendelian inheritance
  • Exception to Mendelian law of independent assortment
  • Genetic interactions, linkage, recombination and chromosome mapping, Chromosomal mutations
  • Genetic disorders
  • Population Genetics

• Molecular Biology

  8 में से 5 टॉपिक

  • Landmark experiments that established DNA is the genetic material
  • DNA replication
  • Proof-reading and repair of DNA
  • DNA recombination
  • Transcription

• Evolution and Ecology

  11 में से 5 टॉपिक

  • Darwinian view – natural selection, fossil record and descent with modification
  • Different types of speciation
  • Phylogenetic classification
  • Origin of life – abiotic synthesis of biological macromolecules, protocell, dating fossils and origin of multicellularity
  • Climate patterns

इस विषय के 34 टॉपिक में से 24 दिखाए गए हैं।सभी 34 टॉपिक देखें →

• Microbiology

  12 में से 5 टॉपिक

  • Microbial genetics - transformation, conjugation and transduction
  • Structural features of viruses, bacteria, fungi and protozoa
  • Pathogenic microorganisms
  • Nutrition-based classification of microbes
  • Microbial metabolism

• Plant Biology

  11 में से 5 टॉपिक

  • Types of tissues and organs
  • Primary and secondary growth
  • Morphogenesis
  • Transport in vascular plants
  • Plant nutrition

• Animal Biology

  5 टॉपिक

  • Digestive, circulatory, respiratory, excretory, nervous, reproductive and endocrine systems
  • Basics of immunology – Innate and adaptive immunity, Immune cells, immunoglobulins and major histocompatibility complexes
  • Animal development – Fertilization, embryonic pattern formation, cleavage, gastrulation, cellular differentiation and morphogenesis
  • Mammalian cell culture, animal cloning
  • Transgenic animals

इस विषय के 28 टॉपिक में से 15 दिखाए गए हैं।सभी 28 टॉपिक देखें →

• Biochemical and Microscopy Techniques

  5 टॉपिक

  • Chromatography
  • Centrifugation
  • Electrophoresis
  • ELISA, Western blotting and immunostaining
  • Principles of light, fluorescence and electron microscopy

• Molecular Biology Techniques

  6 में से 5 टॉपिक

  • DNA cloning – plasmid vectors, and restriction enzymes
  • Polymerase Chain Reaction
  • Expression of cloned eukaryotic genes in bacteria
  • Hybridization techniques
  • DNA sequencing

• Computational Biology

  5 टॉपिक

  • Bioinformatics
  • Sequence and structure databases
  • DNA, RNA and protein sequence analysis
  • Secondary structure and 3D structure prediction
  • Biochemical databases

• Instrumental Techniques – Spectroscopy

  4 टॉपिक

  • fundamentals of molecular spectroscopy, emission and absorption spectroscopy, UV-Vis, circular dichroism, FTIR and 1-D proton NMR spectroscopy, basics of mass spectrometry
  • Basics of calorimetry
  • Basic concepts of crystallography
  • Flowcytometry

इस विषय के 20 टॉपिक में से 19 दिखाए गए हैं।सभी 20 टॉपिक देखें →

• Structure and properties of Atoms

  2 टॉपिक

  • Bohr’s theory
  • Periodicity in properties

• Bonding in molecules

  3 टॉपिक

  • Chemical bonding
  • Complex formation
  • Physical and chemical basis of molecular interactions

• Chemical kinetics, thermodynamics, and equilibrium

  3 टॉपिक

  • Chemical equilibrium
  • Chemical thermodynamics (first and second law)
  • Chemical kinetics (zero and first order reactions)

• Physical and chemical properties of compounds

  8 में से 5 टॉपिक

  • Chemical catalysis
  • Acid-base concepts
  • Concepts of pH and buffer
  • Conjugative effects and resonance
  • Inductive effects

• Chemistry of organic compounds

  10 में से 4 टॉपिक

  • Hydrocarbons
  • Alkyl halides
  • Alcohols
  • Aldehydes

इस विषय के 26 टॉपिक में से 17 दिखाए गए हैं।सभी 26 टॉपिक देखें →

• General mathematics

  23 में से 4 टॉपिक

  • Sets
  • Relations and Functions
  • Logarithms
  • Complex numbers

• Probability & Statistics

  4 टॉपिक

  • Mean, median, mode and standard deviation
  • Random variables
  • Poisson, normal and binomial distributions
  • Correlation and regression analysis

इस विषय के 27 टॉपिक में से 8 दिखाए गए हैं।सभी 27 टॉपिक देखें →

• General physics

  22 में से 4 टॉपिक

  • Units and measurements
  • Motion in one and two dimensions
  • Laws of motion
  • Work and kinetic energy

इस विषय के 22 टॉपिक में से 4 दिखाए गए हैं।सभी 22 टॉपिक देखें →

• Basic Mathematical Concepts (10+2 Level)

  7 में से 4 टॉपिक

  • Functions
  • maxima and minima
  • integrals
  • ordinary differential equations

इस विषय के 7 टॉपिक में से 4 दिखाए गए हैं।सभी 7 टॉपिक देखें →

• Atomic and Molecular Structure

  8 में से 4 टॉपिक

  • Planck’s black body radiation, Photoelectric effect, Bohr’s theory, de Broglie postulate, Heisenberg’s Uncertainty Principle
  • Schr¨odinger’s wave equation (including mathematical treatment), postulates of quantum mechanics, normalized and orthogonal wave functions, its complex conjugate (idea of complex numbers) and significance of Ψ2
  • Operators
  • Particle in one- dimension box, radial and angular wave functions for hydrogen atom, radial probability distribution

• Gaseous State

  6 में से 4 टॉपिक

  • Kinetic molecular model of a gas: collision frequency
  • collision diameter
  • mean free path and viscosity of gases
  • Maxwell-Boltzmann distribution: molecular velocities, law of equipartition of energy, molecular basis of heat capacities

• Liquid State

  3 टॉपिक

  • Physical properties of Liquid, vapour pressure, surface tension and co-efficient of viscosity and their applications
  • effect of concentration of solutes on surface tension and viscosity
  • effect of temperature on viscosity of liquids

• Solid State

  6 में से 4 टॉपिक

  • Unit Cells, Miller indices, crystal systems and Bravais Lattices, elementary applications of vectors to crystal systems
  • X-ray diffraction, Bragg’s Law, Structure of NaCl, CsCl, and KCl, diamond, and graphite
  • Close packing in metals and metal compounds, semiconductors, insulators
  • Defects in crystals, lattice energy

• Chemical Thermodynamics

  4 टॉपिक

  • Mathematical treatment: Exact and in-exact differentials, partial derivatives, Euler’s reciprocity, cyclic rule
  • Reversible and irreversible processes
  • Laws of thermodynamics, thermochemistry, thermodynamic functions, such as enthalpy, entropy, and Gibbs free energy, their properties and applications
  • Partial molar quantities, dependence of thermodynamic parameters on composition, Gibbs Duhem equation, chemical potential and its applications

• Chemical and Phase Equilibria

  16 में से 4 टॉपिक

  • Law of mass action
  • Kp, Kc, Kx and Kn
  • Effect of temperature on K
  • Le-Chatelier principle

• Electrochemistry

  10 में से 4 टॉपिक

  • Conductivity, equivalent and molar conductivity and their properties
  • Kohlrausch law
  • DebyeH¨uckel-Onsager equation
  • Ionic velocities, mobilities, transference numbers

• Chemical Kinetics

  10 में से 4 टॉपिक

  • Order and molecularity of a reaction, differential and integrated form of rate expressions
  • Kinetics of opposing, parallel, and consecutive reactions
  • Steady state approximation in reaction mechanisms
  • Chain reactions

• Adsorption

  5 में से 4 टॉपिक

  • Gibbs adsorption equation
  • adsorption isotherm
  • types of adsorption
  • surface area of adsorbents

• Spectroscopy

  2 टॉपिक

  • Beer-Lambert’s law
  • fundamental concepts of rotational, vibrational, electronic and magnetic resonance spectroscopy

इस विषय के 70 टॉपिक में से 37 दिखाए गए हैं।सभी 70 टॉपिक देखें →

• Basic Concepts in Organic Chemistry and Stereochemistry

  3 टॉपिक

  • Electronic effects (resonance, inductive, hyperconjugation) and steric effects and its applications (acid/base property)
  • optical isomerism in compounds with and without any stereocenters (allenes, biphenyls)
  • conformation of acyclic systems (substituted ethane/n-propane/n-butane) and cyclic systems, substituted cyclohexanes, and polycyclic (cis and trans decalins) systems

• Organic Reaction Mechanism and Synthetic Applications

  8 में से 4 टॉपिक

  • Chemistry of reactive intermediates (carbocations, carbanions, free radicals, carbenes, nitrenes, benzynes)
  • nucleophilic substitution, elimination reactions and mechanisms
  • Hofmann-Curtius- Lossen rearrangement, Wolff rearrangement, Simmons-Smith reaction, Reimer-Tiemann reaction, Michael reaction, Darzens reaction, Wittig reaction and McMurry reaction
  • Pinacolpinacolone, Favorskii, benzilic acid rearrangement, Baeyer-Villeger reaction

• Qualitative Organic Analysis

  2 टॉपिक

  • Identification of functional groups by chemical tests
  • elementary UV, IR and 1H NMR spectroscopic techniques as tools for structural elucidation of simple organic molecules

• Natural Products Chemistry

  1 टॉपिक

  • Chemistry of alkaloids, steroids, terpenes, carbohydrates, amino acids, peptides and nucleic acids

• Aromatic and Heterocyclic Chemistry

  2 टॉपिक

  • Monocyclic, bicyclic and tricyclic aromatic hydrocarbons, and monocyclic compounds with one hetero atom: synthesis, reactivity and properties, aromaticity
  • Electrophilic and nucleophilic aromatic substitution reactions

इस विषय के 16 टॉपिक में से 12 दिखाए गए हैं।सभी 16 टॉपिक देखें →

• Periodic Table

  2 टॉपिक

  • Periodic classification of elements, Aufbau’s principle, periodicity
  • Variations of orbital energy, effective nuclear charge, atomic, covalent, and ionic radii, ionization enthalpy, electron gain enthalpy, and electronegativity with atomic number, electronic configuration of diatomic molecules (first and second row elements)

• Extractions of Metals

  2 टॉपिक

  • General methods of isolation and purification of elements
  • Principles and applications of Ellingham diagram

• Chemical Bonding and shapes of molecules

  9 में से 4 टॉपिक

  • Ionic bond: Packing of ions in crystals, radius ratio rule, Born-Land´e equation, Kapustinskii expression, Madelung constant, Born-Haber cycle, solvation energy, polarizing power and polarizability
  • Fajan’s rules
  • Covalent bond: Lewis structure, valence bond theory. Hybridization, molecular orbital theory, molecular orbital diagrams of diatomic and simple polyatomic molecules and ions
  • Multiple bonding (σ and π bond approach) and bond lengths

• Main Group Elements (s and p blocks)

  11 में से 4 टॉपिक

  • Reactions of alkali and alkaline earth metals with oxygen, hydrogen and water
  • Alkali and alkaline earth metals in liquid ammonia
  • Gradation in properties of main group element in a group
  • Inert pair effect

• Transition Metals (d block)

  6 में से 4 टॉपिक

  • Characteristics of d-block elements
  • oxide, hydroxide and salts of first row metals
  • coordination complexes: structure, isomerism, reaction mechanism and electronic spectra
  • VB, MO and crystal field theoretical approaches for structure, color and magnetic properties of metal complexes

• Bioinorganic Chemistry

  3 टॉपिक

  • Essentials and trace elements of life
  • basic reactions in the biological systems and the role of metal ions, especially Fe2+, and Zn2+
  • structure and function of myoglobin, hemoglobin and carbonic anhydrase

• Instrumental Methods of Analysis

  3 टॉपिक

  • Basic principles
  • instrumentations and simple applications of conductometry, potentiometry and UV-vis spectrophotometry
  • analyses of water, air and soil samples

• Analytical Chemistry

  7 में से 4 टॉपिक

  • Principles of qualitative and quantitative analysis
  • Acid-base, oxidation- reduction and complexometric titrations using EDTA
  • Precipitation reactions
  • Use and types of indicators

इस विषय के 43 टॉपिक में से 26 दिखाए गए हैं।सभी 43 टॉपिक देखें →

• Consumer theory

  6 में से 4 टॉपिक

  • Preference
  • utility and representation theorem
  • budget constraint, choice
  • demand (ordinary and compensated)

• Theory of production and cost

  5 में से 4 टॉपिक

  • Production technology, isoquants
  • production function with one and more inputs
  • returns to scale
  • short run and long run costs

• General equilibrium and welfare

  3 टॉपिक

  • Equilibrium and efficiency under pure exchange and production
  • welfare economics
  • theorems of welfare economics

• Market structure

  4 टॉपिक

  • Perfect competition, monopoly
  • pricing with market power
  • price discrimination (first, second and third)
  • monopolistic competition and oligopoly

• Game theory

  7 में से 4 टॉपिक

  • Strategic form games
  • iterated elimination of dominated strategies
  • Nash equilibrium
  • mixed extension and mixed strategy Nash equilibrium

• Public goods and market failure

  2 टॉपिक

  • Externalities
  • public goods and markets with asymmetric information (adverse selection and moral hazard)

इस विषय के 27 टॉपिक में से 21 दिखाए गए हैं।सभी 27 टॉपिक देखें →

• National income accounting

  4 टॉपिक

  • Structure
  • key concepts, measurements
  • circular flow of income - for closed and open economy, money
  • fiscal and foreign sector variables - concepts and measurements

• Behavioural and technological functions

  6 में से 4 टॉपिक

  • Consumption functions - absolute income hypothesis
  • life-cycle and permanent income hypothesis
  • random walk model of consumption
  • investment functions - Keynesian

• Business cycles and economic models (closed economy)

  7 में से 4 टॉपिक

  • Business cycles-facts and features
  • the Classical model of the business cycle
  • the Keynesian model of the business cycle
  • simple Keynesian cross model of income and employment determination and the multiplier (in a closed economy)

• Business cycles and economic models (open economy)

  4 टॉपिक

  • Open economy
  • Mundell-Fleming model
  • Keynesian flexible price (aggregate demand and aggregate supply) model
  • role of monetary and fiscal policies

• Inflation and unemployment

  2 टॉपिक

  • Inflation - theories, measurement, causes, and effects
  • unemployment - types, measurement, causes, and effects

• Growth models

  2 टॉपिक

  • Harrod-Domar
  • Solow and Neo-classical growth models (AK model, Romer model and Schumpeterian growth model)

इस विषय के 25 टॉपिक में से 20 दिखाए गए हैं।सभी 25 टॉपिक देखें →

• Probability theory

  11 में से 4 टॉपिक

  • Sample space and events
  • axioms of probability and their properties
  • conditional probability and Bayes’ rule
  • independent events

• Mathematical statistics

  9 में से 4 टॉपिक

  • Random sampling
  • types of sampling
  • point and interval estimation
  • estimation of population parameters using methods of moments and maximum likelihood procedures

• Hypothesis testing

  5 में से 4 टॉपिक

  • distributions of test statistics
  • testing hypotheses related to population parameters
  • Type I and Type II errors
  • the power of a test

• Correlation and regression

  7 में से 4 टॉपिक

  • Correlation and types of correlation
  • the nature of regression analysis
  • method of Ordinary Least Squares (OLS)
  • CLRM assumptions

इस विषय के 32 टॉपिक में से 16 दिखाए गए हैं।सभी 32 टॉपिक देखें →

• Indian economy before 1950

  2 टॉपिक

  • Transfer of tribute
  • deindustrialization of India

• Planning and Indian development

  3 टॉपिक

  • Planning models
  • relation between agricultural and industrial growth
  • challenges faced by Indian planning

• Indian economy after 1991

  3 टॉपिक

  • Balance of payments crisis in 1991
  • major aspects of economic reforms in India after 1991
  • reforms in trade and foreign investment

• Banking, finance and macroeconomic policies

  5 में से 4 टॉपिक

  • aspects of banking in India
  • CRR and SLR
  • financial sector reforms in India
  • fiscal and monetary policy

• Inequalities in social development

  3 टॉपिक

  • India’s achievements in health
  • education and other social sectors
  • disparities between Indian States in human development

• Poverty

  2 टॉपिक

  • Methodology of poverty estimation
  • Issues in poverty estimation in India

• India’s labour market

  2 टॉपिक

  • unemployment
  • labour force participation rates

इस विषय के 20 टॉपिक में से 19 दिखाए गए हैं।सभी 20 टॉपिक देखें →

• Preliminaries and functions

  11 में से 4 टॉपिक

  • Set theory and number theory
  • elementary functions: quadratic, polynomial, power, exponential, logarithmic
  • functions of several variables
  • graphs and level curves

• Differential calculus

  10 में से 4 टॉपिक

  • Limits
  • continuity and differentiability
  • mean value theorems
  • Taylor’s theorem

• Integral calculus

  3 टॉपिक

  • Definite integrals
  • fundamental theorems
  • indefinite integrals and applications

• Differential equations, and difference equations

  2 टॉपिक

  • First order difference equations
  • first order differential equations and applications

• Linear algebra

  6 में से 4 टॉपिक

  • Matrix representations and elementary operations
  • systems of linear equations: properties of their solution
  • linear independence and dependence, rank, determinants
  • eigenvectors and eigenvalues of square matrices

• Optimization

  9 में से 4 टॉपिक

  • Local and global optima: geometric and calculus-based characterisations, and applications
  • multivariate optimization
  • constrained optimization and method of Lagrange multiplier
  • second order condition of optima

इस विषय के 41 टॉपिक में से 21 दिखाए गए हैं।सभी 41 टॉपिक देखें →

• The Planet Earth

  8 में से 4 टॉपिक

  • Origin of the Solar System and the Earth
  • Internal structure, composition, and age of the Earth
  • Pressure-temperature-density variations within the Earth
  • Principles of radiometric dating (Rb-Sr, Sm-Nd, 14C)

इस विषय के 8 टॉपिक में से 4 दिखाए गए हैं।सभी 8 टॉपिक देखें →

• Geomorphology

  5 में से 4 टॉपिक

  • Weathering, erosion, deposition
  • Endogenous and exogenous processes of landform development
  • Soil formation
  • River and drainage basin/drainage pattern, network characteristics

इस विषय के 5 टॉपिक में से 4 दिखाए गए हैं।सभी 5 टॉपिक देखें →

• Structural Geology

  8 में से 4 टॉपिक

  • Concept of dip, strike, rake and plunge
  • Contour lines
  • Rule of ‘V’s and outcrop patterns
  • Interpretation of geological maps

इस विषय के 8 टॉपिक में से 4 दिखाए गए हैं।सभी 8 टॉपिक देखें →

• Paleontology

  6 में से 4 टॉपिक

  • Major stages in the evolution of life forms
  • Fossils and their mode of preservation
  • Application of macrofossils in age determination and paleoenvironmental interpretations
  • Morphology, major evolutionary trends and ages of important groups of invertebrates – Brachiopoda, Mollusca, Trilobita, Echinodermata

इस विषय के 6 टॉपिक में से 4 दिखाए गए हैं।सभी 6 टॉपिक देखें →

• Stratigraphy

  7 में से 4 टॉपिक

  • Principles of stratigraphy
  • Litho-, chrono- and bio-stratigraphic classification
  • Stratigraphic correlation techniques
  • Archaean cratons of Peninsular India (Dharwar, Singhbhum and Aravalli)

इस विषय के 7 टॉपिक में से 4 दिखाए गए हैं।सभी 7 टॉपिक देखें →

• Mineralogy

  6 में से 4 टॉपिक

  • Symmetry and forms in common crystal classes
  • Miller indices
  • Twinning and twinning laws
  • Isomorphism, polymorphism, solid solution and exsolution

इस विषय के 6 टॉपिक में से 4 दिखाए गए हैं।सभी 6 टॉपिक देखें →

• Petrology

  14 में से 4 टॉपिक

  • Igneous rocks – classification and texture
  • Forms of igneous bodies
  • Evolution and diversification of magma
  • Use of binary systems to understand melting and crystallization behaviour of rocks and magmas

इस विषय के 14 टॉपिक में से 4 दिखाए गए हैं।सभी 14 टॉपिक देखें →

• Economic Geology

  5 में से 4 टॉपिक

  • Physical properties of common economic minerals
  • Processes of formations of ore mineral deposits-magmatic concentration, hydrothermal processes, oxidation and supergene sulphide enrichment, residual and mechanical concentration
  • Mode of occurrence and distribution of metallic and non-metallic mineral deposits in India
  • Ore grade and reserve estimation

इस विषय के 5 टॉपिक में से 4 दिखाए गए हैं।सभी 5 टॉपिक देखें →

• Applied Geology

  6 में से 4 टॉपिक

  • Basics of groundwater geology
  • Types of aquifers, porosity and permeability
  • Groundwater flow
  • Principles of engineering geology

इस विषय के 6 टॉपिक में से 4 दिखाए गए हैं।सभी 6 टॉपिक देखें →

• Sequences and Series of Real Numbers

  11 में से 4 टॉपिक

  • convergence of sequences
  • bounded and monotone sequences
  • Cauchy sequences
  • Bolzano-Weierstrass theorem

• Functions of One Real Variable

  12 में से 4 टॉपिक

  • limit
  • continuity
  • intermediate value property
  • differentiation

इस विषय के 23 टॉपिक में से 8 दिखाए गए हैं।सभी 23 टॉपिक देखें →

• Functions of Two or Three Real Variables

  5 में से 4 टॉपिक

  • limit
  • continuity
  • partial derivatives
  • total derivative

• Integral Calculus

  4 टॉपिक

  • double and triple integrals
  • change of order of integration
  • calculating surface areas and volumes using double integrals
  • calculating volumes using triple integrals

• Differential Equations

  9 में से 4 टॉपिक

  • Bernoulli’s equation
  • exact differential equations
  • integrating factors
  • orthogonal trajectories

इस विषय के 18 टॉपिक में से 12 दिखाए गए हैं।सभी 18 टॉपिक देखें →

• Basic algebra

  2 टॉपिक

  • Permutations and Combinations
  • Binomial Theorem

• Matrices

  8 में से 4 टॉपिक

  • systems of linear equations
  • rank
  • nullity
  • rank-nullity theorem

• Finite Dimensional Vector Spaces

  8 में से 4 टॉपिक

  • linear independence of vectors
  • basis
  • dimension
  • linear transformations

• Groups

  8 में से 4 टॉपिक

  • cyclic groups
  • abelian groups
  • non-abelian groups
  • permutation groups

इस विषय के 26 टॉपिक में से 14 दिखाए गए हैं।सभी 26 टॉपिक देखें →

• Sequences and Series of real numbers

  13 में से 4 टॉपिक

  • Sequences of real numbers, their convergence, and limits
  • Cauchy sequences and their convergence
  • Monotonic sequences and their limits
  • Limits of standard sequences

इस विषय के 13 टॉपिक में से 4 दिखाए गए हैं।सभी 13 टॉपिक देखें →

• Differential Calculus of one variable

  9 में से 4 टॉपिक

  • Limits of functions of one real variable
  • Continuity and differentiability of functions of one real variable
  • Properties of continuous and differentiable functions of one real variable
  • Rolle’s theorem and Lagrange’s mean value theorems

• Differential calculus of two variables

  8 में से 4 टॉपिक

  • Limits of functions of two real variables
  • Continuity and differentiability of functions of two real variables
  • Properties of continuous and differentiable functions of two real variables
  • Partial differentiation and total differentiation

• Integral Calculus

  10 में से 4 टॉपिक

  • Fundamental theorems of integral calculus (single integral)
  • Lebnitz’s rule and its applications
  • Differentiation under integral sign
  • Improper integrals

इस विषय के 27 टॉपिक में से 12 दिखाए गए हैं।सभी 27 टॉपिक देखें →

• Matrices and Determinants

  23 में से 4 टॉपिक

  • Rn and Cn as vector spaces over real field
  • Span of a set
  • Linear dependence and independence
  • Dimension and basis

इस विषय के 23 टॉपिक में से 4 दिखाए गए हैं।सभी 23 टॉपिक देखें →

• Descriptive Statistics

  7 में से 4 टॉपिक

  • Concepts of sample and population
  • Different types of data
  • Tabular and graphical representation of data
  • Measures of central tendency (arithmetic mean, geometric mean, harmonic mean, median, mode)

• Probability

  10 में से 4 टॉपिक

  • Random Experiments
  • Sample Space and Algebra of Events (Event space)
  • Relative frequency and Axiomatic definitions of probability
  • Properties of probability function

इस विषय के 17 टॉपिक में से 8 दिखाए गए हैं।सभी 17 टॉपिक देखें →

• Univariate Distributions

  10 में से 4 टॉपिक

  • Definition of random variables
  • Cumulative distribution function (c.d.f.) of a random variable
  • Discrete and Continuous random variables
  • Probability mass function (p.m.f.) and Probability density function (p.d.f.) of a random variable

इस विषय के 10 टॉपिक में से 4 दिखाए गए हैं।सभी 10 टॉपिक देखें →

• Multivariate Distributions

  13 में से 4 टॉपिक

  • Definition of random vectors
  • Joint and marginal c.d.f.s of a random vector
  • Discrete and continuous type random vectors
  • Joint and marginal p.m.f., joint and marginal p.d.f

इस विषय के 13 टॉपिक में से 4 दिखाए गए हैं।सभी 13 टॉपिक देखें →

• Limit Theorems

  2 टॉपिक

  • Convergence in probability, convergence in mean square, almost sure convergence, convergence in distribution, and their inter-relations
  • Weak law of large numbers, Strong law of large numbers, and Central Limit Theorem (i.i.d. and finite variance case)

• Sampling Distributions

  8 टॉपिक

  • Definitions of random sample, parameter and statistic
  • Sampling distribution of a statistic
  • Order Statistics: Definition and distribution of the rth order statistic (d.f. and p.d.f. for i.i.d. case for continuous distributions)
  • Distribution (c.d.f., p.m.f., p.d.f.) of smallest and largest order statistics (i.i.d. case for discrete as well as continuous distributions)
  • Central Chi-square distribution: Definition and derivation of p.d.f. of central x2 distribution with n degrees of freedom (d.f.) using m.g.f. Properties of central x2 distribution, additive property and limiting form of central x2 distribution
  • Central t - distribution: Definition and derivation of p.d.f. of Central t-distribution with n d.f., Properties and limiting form of central t-distribution
  • Central F-distribution: Definition and derivation of p.d.f. of Central F- distribution with (m,n) d.f. Properties of Central F-distribution, distribution of the reciprocal of F-distribution
  • Relationship between t, F and 2 distributions

इस विषय के सभी 8 टॉपिक दिखाए गए हैं।कम टॉपिक दिखाएँ

• Estimation

  12 में से 4 टॉपिक

  • Unbiasedness
  • Sufficiency of a statistic
  • Factorization theorem
  • Complete statistic

इस विषय के 12 टॉपिक में से 4 दिखाए गए हैं।सभी 12 टॉपिक देखें →

• Testing of Hypotheses

  7 में से 4 टॉपिक

  • Null and alternative hypotheses (simple and composite), Type-I and Type-II errors
  • Critical region
  • Level of significance, size and power of a test, p-value
  • Most powerful critical regions and most powerful (MP) tests

इस विषय के 7 टॉपिक में से 4 दिखाए गए हैं।सभी 7 टॉपिक देखें →

• Nonparametric Methods

  5 में से 4 टॉपिक

  • Tests of randomness based on total number of runs
  • Empirical distribution function
  • Kolmogorov-Smirnov one sample test
  • One and two sample sign tests

इस विषय के 5 टॉपिक में से 4 दिखाए गए हैं।सभी 5 टॉपिक देखें →

• Stochastic Processes

  2 टॉपिक

  • Discrete time Markov chain: transition probability matrix, higher order transition probabilities, Markov chain as a graph, Chapman-Kolmogorov equation, classification of states and chains, stability of Markov chain (stationary and limiting distributions)
  • Poisson process and its properties, interarrival and waiting times

• Mathematical Methods

  3 टॉपिक

  • Calculus of single and multiple variables, Partial derivatives, Jacobian, imperfect and perfect differentials, Taylor expansion, Fourier series, Vector algebra, Vector Calculus, Multiple integrals, Divergence theorem, Green’s theorem, Stokes’ theorem
  • First order equations and linear second-order differential equations with constant coefficients
  • Matrices and determinants, Complex numbers, Error analysis of Experimental Data: Significant digits and rounding of numbers, Types of errors, mean, median, standard deviation

• Mechanics and General Properties of Matter

  5 में से 4 टॉपिक

  • Newton’s laws of motion and applications, Velocity and acceleration in Cartesian, polar and cylindrical coordinate systems, uniformly rotating frame, centrifugal and Coriolis forces, Motion under a central force, Kepler’s laws, Gravitational Law and field, Conservative and non-conservative forces
  • System of particles, Center of mass, equation of motion of the CM, conservation of linear and angular momentum, conservation of energy, variable mass systems
  • Elastic and inelastic collisions
  • Rigid body motion, fixed axis rotations, rotation and translation, moments of Inertia and products of Inertia, parallel and perpendicular axes theorem, Principal moments and axes

इस विषय के 5 टॉपिक में से 4 दिखाए गए हैं।सभी 5 टॉपिक देखें →

• Oscillations, Waves and Optics

  17 में से 4 टॉपिक

  • Differential equation for simple harmonic oscillator and its general solution
  • Superposition of two or more simple harmonic oscillators
  • Lissajous figures
  • Damped and forced oscillations, resonance

इस विषय के 17 टॉपिक में से 4 दिखाए गए हैं।सभी 17 टॉपिक देखें →

• Electricity and Magnetism

  7 में से 4 टॉपिक

  • Coulomb’s law, Electric field and potential, Gauss’s law, Electrostatic boundary conditions, Solution of Laplace’s equation for simple cases – upto two dimensions Conductors, capacitors, Linear dielectrics, dielectric polarization, volume and surface bound charges, electrostatic energy
  • Biot-Savart law, Ampere’s law, Faraday’s law of electromagnetic induction, Self and mutual inductance
  • Alternating currents
  • Simple DC and AC circuits with R, L and C components

इस विषय के 7 टॉपिक में से 4 दिखाए गए हैं।सभी 7 टॉपिक देखें →

• Kinetic Theory, Thermodynamics

  16 में से 4 टॉपिक

  • Elements of Kinetic theory of gases
  • Velocity distribution and Equipartition of energy
  • Specific heat of Mono-, di- and tri-atomic gases
  • Ideal gas, van-der-Waals gas and equation of state

इस विषय के 16 टॉपिक में से 4 दिखाए गए हैं।सभी 16 टॉपिक देखें →

• Modern Physics

  12 में से 4 टॉपिक

  • Inertial frames and Galilean invariance
  • Postulates of special relativity
  • Lorentz transformations
  • Length contraction, time dilation

इस विषय के 12 टॉपिक में से 4 दिखाए गए हैं।सभी 12 टॉपिक देखें →

• Solid State Physics, Devices and Electronics

  16 में से 4 टॉपिक

  • Crystal structure, Bravais lattices and basis
  • Miller indices
  • X-ray diffraction and Bragg’s law
  • Intrinsic and extrinsic semiconductors, variation of resistivity with temperature

इस विषय के 16 टॉपिक में से 4 दिखाए गए हैं।सभी 16 टॉपिक देखें →