Mechanical Engineering at IIT Bombay

June 22, 201339 Insightful Publications

The Engineering, Agriculture and Medical Common Entrance Test (EAMCET) is being conducted by Jawaharlal Nehru Technological University Kakinada (JNTUK) on behalf of Andhra Pradesh State Council of Higher Education (APSCHE). This Examination is for admission into various professional courses offered in the University/Private Colleges in the State of Andhra Pradesh. Below are a few important chapters and concepts you need to consider while studying for this exam:

Electric Current,

Electric Currents in Conductors,

Ohm’s law,

Drift of Electrons and the Origin of Resistivity,

Limitations of Ohm’s Law,

Resistivity of various Materials,

Temperature Dependence of Resistivity,

Electrical Energy,

Power, Combination of Resistors — Series and Parallel,

Cells,

emf,

Internal Resistance,

Cells in Series and in Parallel,

Kirchhoff’s Laws,

Wheatstone Bridge,

Meter Bridge,

Potentiometer.

Electric Currents in Conductors,

Ohm’s law,

Drift of Electrons and the Origin of Resistivity,

Limitations of Ohm’s Law,

Resistivity of various Materials,

Temperature Dependence of Resistivity,

Electrical Energy,

Power, Combination of Resistors — Series and Parallel,

Cells,

emf,

Internal Resistance,

Cells in Series and in Parallel,

Kirchhoff’s Laws,

Wheatstone Bridge,

Meter Bridge,

Potentiometer.

Thermal equilibrium,

Zeroth law of thermodynamics,

Heat,

Internal Energy and work,

First law of thermodynamics,

Specific heat capacity,

Thermodynamic state variables and equation of State,

Thermodynamic process,

Quasi-static Isothermal Process,

Adiabatic Process,

Isochoric Process,

Cyclic process,

Heat engines,

Refrigerators and heat pumps,

Second law of thermodynamics,

Reversible and irreversible processes,

Carnot engine,

Carnot’s theorem.

Zeroth law of thermodynamics,

Heat,

Internal Energy and work,

First law of thermodynamics,

Specific heat capacity,

Thermodynamic state variables and equation of State,

Thermodynamic process,

Quasi-static Isothermal Process,

Adiabatic Process,

Isochoric Process,

Cyclic process,

Heat engines,

Refrigerators and heat pumps,

Second law of thermodynamics,

Reversible and irreversible processes,

Carnot engine,

Carnot’s theorem.

Electrostatic Potential,

Potential due to a Point Charge,

Potential due to an Electric Dipole,

Potential due to a System of Charges,

Equipotential Surfaces,

Potential Energy of a System of Charges,

Potential Energy in an External Field,

Electrostatics of Conductors, Dielectrics and Polarisation,

Capacitors and Capacitance,

The Parallel Plate Capacitor,

Effect of Dielectric on Capacitance,

Combination of Capacitors,

Energy Stored in a Capacitor,

Van de Graaff Generator.

Potential due to a Point Charge,

Potential due to an Electric Dipole,

Potential due to a System of Charges,

Equipotential Surfaces,

Potential Energy of a System of Charges,

Potential Energy in an External Field,

Electrostatics of Conductors, Dielectrics and Polarisation,

Capacitors and Capacitance,

The Parallel Plate Capacitor,

Effect of Dielectric on Capacitance,

Combination of Capacitors,

Energy Stored in a Capacitor,

Van de Graaff Generator.

The Bar Magnet,

Magnetism and Gauss’s Law,

The Earth’s Magnetism,

Magnetisation and Magnetic Intensity,

Magnetic Properties of Materials,

Permanent Magnets and Electromagnets.

Magnetism and Gauss’s Law,

The Earth’s Magnetism,

Magnetisation and Magnetic Intensity,

Magnetic Properties of Materials,

Permanent Magnets and Electromagnets.

The Scalar Product,

Notions of work and kinetic energy :

The work-energy theorem,

Work,

Kinetic energy,

Work done by a variable force,

The work-energy theorem for a variable force,

The concept of Potential Energy,

The conservation of Mechanical Energy,

The Potential Energy of a spring,

Various forms of energy:

the law of conservation of energy,

Heat,

Chemical Energy,

Electrical Energy,

The Equivalence of Mass and Energy,

Nuclear Energy,

The Principle of Conservation of Energy,

Power, Collisions,

Elastic and Inelastic Collisions,

Collisions in one dimension,

Coefficent of Restitution and its determination,

Collisions in Two Dimensions.

Notions of work and kinetic energy :

The work-energy theorem,

Work,

Kinetic energy,

Work done by a variable force,

The work-energy theorem for a variable force,

The concept of Potential Energy,

The conservation of Mechanical Energy,

The Potential Energy of a spring,

Various forms of energy:

the law of conservation of energy,

Heat,

Chemical Energy,

Electrical Energy,

The Equivalence of Mass and Energy,

Nuclear Energy,

The Principle of Conservation of Energy,

Power, Collisions,

Elastic and Inelastic Collisions,

Collisions in one dimension,

Coefficent of Restitution and its determination,

Collisions in Two Dimensions.

Transverse and longitudinal waves,

Displacement relation in a progressive wave,

The speed of a travelling wave,

The principle of superposition of waves,

Reflection of waves,

Beats,

Doppler effect.

Displacement relation in a progressive wave,

The speed of a travelling wave,

The principle of superposition of waves,

Reflection of waves,

Beats,

Doppler effect.

Periodic and oscillatory motions,

Period and frequency,

Displacement,

Simple harmonic motion (S.H.M.),

Simple harmonic motion and uniform circular motion,

Velocity and acceleration in simple harmonic motion,

Force law for Simple harmonic Motion,

Energy in simple harmonic motion,

Some systems executing Simple Harmonic Motion,

Oscillations due to a spring,

The Simple Pendulum,

Damped simple harmonic motion,

Forced oscillations and resonance.

Period and frequency,

Displacement,

Simple harmonic motion (S.H.M.),

Simple harmonic motion and uniform circular motion,

Velocity and acceleration in simple harmonic motion,

Force law for Simple harmonic Motion,

Energy in simple harmonic motion,

Some systems executing Simple Harmonic Motion,

Oscillations due to a spring,

The Simple Pendulum,

Damped simple harmonic motion,

Forced oscillations and resonance.

Classification of Metals,

Conductors and Semiconductors,

Intrinsic Semiconductor,

Extrinsic Semiconductor,

p-n Junction,

Semiconductor diode,

Application of Junction Diode as a Rectifier,

Special Purpose p-n Junction Diodes,

Junction Transistor,

Digital Electronics and Logic Gates,

Integrated Circuits.

Conductors and Semiconductors,

Intrinsic Semiconductor,

Extrinsic Semiconductor,

p-n Junction,

Semiconductor diode,

Application of Junction Diode as a Rectifier,

Special Purpose p-n Junction Diodes,

Junction Transistor,

Digital Electronics and Logic Gates,

Integrated Circuits.

Aristotle’s fallacy,

The law of inertia,

Newton’s first law of motion,

Newton’s second law of motion,

Newton’s third law of motion,

Impulse,

Conservation of momentum,

Equilibrium of a particle,

Common forces in mechanics,

friction, Circular motion,

Motion of a car on a level road,

Motion of a car on a Banked road,

Solving problems in mechanics.

The law of inertia,

Newton’s first law of motion,

Newton’s second law of motion,

Newton’s third law of motion,

Impulse,

Conservation of momentum,

Equilibrium of a particle,

Common forces in mechanics,

friction, Circular motion,

Motion of a car on a level road,

Motion of a car on a Banked road,

Solving problems in mechanics.

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Rate of a chemical reaction; Factors influencing rate of a reaction: dependance of rate on concentration- rate expression and rate constant- order of a reaction, molecularity of a reaction; Integrated rate equations-zero order reactions-first order reactions- half life of a reaction; Pseudo first order reaction; Temperature dependence of the rate of a reaction -effect of catalyst; Collision theory of chemical reaction rates.
Kossel - Lewis approach to chemical bonding, Octet rule, Representation of simple molecules, formal charges, limitations of octat rule; Ionic or electrovalent bond - Factors favourable for the formation of ionic compounds-Crystal structure of sodium chloride, Lattice enthalpy; General properties of ionic compounds; Bond Parameters - bond length, bond angle, and bond enthalpy, bond order, resonance-Polarity of bonds dipole moment; Valence Shell Electron Pair Repulsion (VSEPR) theories; Predicting the geometry of simple molecules; Valence bond theory-Orbital overlap concept-Directional properties of bonds-overlapping of atomic orbitals strength of sigma and pi bonds- Factors favouring the formation of covalent bonds; Hybridisation- different types of hybridization involving s, p and d orbitals- shapes of simple covalent molecules; Coordinate bond -definition with examples; Molecular orbital theory - Formation of molecular orbitals, Linear combination of atomic orbitals (LCAO)-conditions for combination of atomic orbitals - Energy level diagrams for molecular orbitals -Bonding in some homo nuclear diatomic molecules- H2, He2, Li2, B2, C2, N2 and O2; Hydrogen bonding-cause of formation of hydrogen bond - Types of hydrogen bonds-inter and intra molecular-
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General properties of hydrogen bonds.
Group 1 Elements : Alkali metals; Electronic configurations; Atomic and Ionic radii; Ionization enthalpy; Hydration enthalpy; Physical properties; Chemical properties; Uses; General characteristics of the compounds of the alkali metals: Oxides; Halides; Salts of oxo Acids; Anomalous properties ofLithium: Differences and similarities with other alkali metals, Diagonal relationship; similarities between Lithium and Magnesium; Some important compounds of Sodium: Sodium Carbonate; Sodium Chloride; Sodium Hydroxide; Sodium hydrogen carbonate; Biological importance of Sodium and Potassium.

Group 2 Elements: Alkaline earth elements; Electronic configuration; Ionization enthalpy; Hydration enthalpy; Physical properties, Chemical properties; Uses; General characteristics of compounds of the Alkaline Earth Metals: Oxides, hydroxides, halides, salts of oxoacids (Carbonates; Sulphates and Nitrates); Anomalous behavior of Beryllium; its diagonal relationship with Aluminium; Some important compounds of calcium: Preparation and uses of Calcium Oxide; Calcium Hydroxide; Calcium Carbonate; Plaster of Paris; Cement; Biological importance of Calcium and Magnesium.

Some Basic Concepts - Properties of matter - uncertainty in Measurement-significant figures, dimensional analysis; Laws of Chemical Combinations - Law of Conservation of Mass, Law of Definite Proportions, Law of Multiple Proportions, Gay Lussac’s Law of Gaseous Volumes, Dalton’s Atomic Theory, Avogadro Law, Principles, Examples; Atomic and molecular masses- mole concept and molar mass. Concept of equivalent weight; Percentage composition of compounds and calculations of empirical and molecular formulae of compounds; Stoichiometry and stoichiometric calculations; Methods of Expressing concentrations of solutions-mass percent, mole fraction, molarity, molality and normality; Redox reactions-classical idea of redox reactions, oxidation and reduction reactions-redox reactions in terms of electron transfer; Oxidation number concept; Types of Redox reactions-combination, decomposition, displacement and disproportionation reactions; Balancing of redox reactions - oxidation number method Half reaction (ion-electron) method; Redox reactions in Titrimetry.
Need to classify elements; Genesis of periodic classification; Modern periodic law and present form of the periodic table; Nomenclature of elements with atomic number greater than 100; Electronic configuration of elements and the periodic table; Electronic configuration and types of elements s,p,d.and f blocks; Trends in physical properties: (a) Atomic radius, (b) Ionic radius (c)Variation of size in inner transition elements, (d) Ionization enthalpy, (e) Electron gain enthalpy, (f) Electro negativity; Periodic trends in chemical properties: (a) Valence or Oxidation states, (b) Anomalous properties of second period elements - diagonal relationship; Periodic trends and chemical reactivity.
GROUP-15 ELEMENTS : Occurrence- electronic configuration, atomic and ionic radii, ionisation enthalpy, electronegativity, physical and chemical properties; Dinitrogen-preparation, properties and uses; Compounds of nitrogen-preparation and properties of ammonia; Oxides of nitrogen; Preparation and properties of nitric acid; Phosphorous-allotropic forms; Phosphine-preparation and properties; Phosphorous halides; Oxoacids ofphosphorous

GROUP-16 ELEMENTS: Occurrence- electronic configuration, atomic and ionic radii, ionisation enthalpy, electron gain enthalpy, electronegativity, physical and chemical properties; Dioxygen-preparation, properties and uses; Simple oxides; Ozone-preparation, properties, structure and uses; Sulphur-allotropic forms; Sulphur dioxide-preparation, properties and uses; Oxoacids of sulphur; Sulphuric acid-industrial process of manufacture, properties and uses.

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GROUP-17 ELEMENTS: Occurrence, electronic configuration, atomic and ionic radii, ionisation enthalpy, electron gain enthalpy, electronegativity, physical and chemical properties; Chlorine- preparation, properties and uses; Hydrogen chloride- preparation, properties and uses; Oxoacids of halogens; Interhalogen compounds.

GROUP-18 ELEMENTS : Occurrence, electronic configuration, ionization enthalpy, atomic radii, electron gain enthalpy, physical and chemical properties(a) Xenon-fluorine compounds- XeF2,XeF4 and XeF6 -preparation, hydrolysis and formation of fluoro anions-structures of XeF2, XeF4 and XeF6 (b) Xenon-oxygen compounds XeO3 and XeOF4 - their formation and structures

d AND f BLOCK ELEMENTS : Position in the periodic table; Electronic configuration of the d-block elements; General properties of the transition elements (d-block) -physical properties, variation in atomic and ionic sizes of transition series, ionisation enthalpies, oxidation states, trends in the M2+/M and M3+/M2+ standard electrode potentials, trends in stability of higher oxidation states, chemical reactivity and Eθ properties, formation of coloured ions, formation of complex compounds, catalytic properties, formation of interstitial compounds, alloy formation; Some important compounds of transition elements-oxides and oxoanions of metals-preparation and properties of potassium dichromate and potassium permanganate-structures of chromate, dichromate, manganate and permanganate ions; Inner transition elements(f-block)-lanthanoids- electronic configuration-atomic and ionic sizes-oxidation states- general characteristics; Actinoids-electronic configuration atomic and ionic sizes, oxidation states, general characteristics and comparison with lanthanoids; Some applications of d and f block elements.

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Important units in MATHS
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a) Addition of Vectors : Vectors as a triad of real numbers - Classification of vectors - Addition of vectors - Scalar multiplication - Angle between two non zero vectors - Linear combination of vectors - Component of a vector in three dimensions - Vector equations of line and plane including their Cartesian equivalent forms.b) Product of Vectors : Scalar Product - Geometrical Interpretations - orthogonal projections - Properties of dot product - Expression of dot product in i, j, k system - Angle between two vectors - Geometrical Vector methods - Vector equations of plane in normal form - Angle between two planes - Vector product of two vectors and properties - Vector product in i, j, k system - Vector Areas - Scalar Triple Product - Vector equations of plane in different forms, skew lines, shortest distance and their Cartesian equivalents. Plane through the line of intersection of two planes, condition for coplanarity of two lines, perpendicular distance of a point from a plane, Angle between line and a plane. Cartesian equivalents of all these results - Vector Triple Product – Results.

a) Measures of Dispersion - Range - Mean deviation - Variance and standard deviation of ungrouped/grouped data - Coefficient of variation and analysis of frequency distribution with equal means but different variances.b) Probability : Random experiments and events - Classical definition of probability, Axiomatic approach and addition theorem of probability - Independent and dependent events - conditional probability- multiplication theorem and Bayee’s theorem.

c) Random Variables and Probability Distributions: Random Variables - Theoretical discrete distributions – Binomial and Poisson Distributions.

a) Limits and Continuity: Intervals and neighbourhoods – Limits - Standard Limits – Continuity. b) Differentiation: Derivative of a function - Elementary Properties - Trigonometric, Inverse Trigonometric, Hyperbolic, Inverse Hyperbolic Function – Derivatives - Methods of Differentiation -Second Order Derivatives.

d) Integration : Integration as the inverse process of differentiation- Standard forms -properties of integrals - Method of substitution- integration of Algebraic, exponential, logarithmic, trigonometric and inverse trigonometric functions - Integration by parts - Integration- Partial fractions method - Reduction formulae.

e) Definite Integrals: Definite Integral as the limit of sum - Interpretation of Definite Integral as an area - Fundamental theorem of Integral Calculus – Properties - Reduction formulae - Application of Definite integral to areas.

f)Differential equations: Formation of differential equation-Degree and order of an ordinary differential equation - Solving differential equation by

i) Variables separable method, ii) Homogeneous differential equation, iii) Non - Homogeneous differential equation, iv) Linear differential equations.
Permutations and Combinations: Fundamental Principle of counting – linear and circular permutations- Permutations of ‘n’ dissimilar things taken ‘r’ at a time - Permutations when repetitions allowed - Circular permutations - Permutations with constraint repetitions - Combinations-definitions, certain theorems and their applications.Complex Numbers: Complex number as an ordered pair of real numbers- fundamental operations - Representation of complex numbers in the form a+ib - Modulus and amplitude of complex numbers –Illustrations - Geometrical and Polar Representation of complex numbers in Argand plane- Argand diagram.

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