How to Prepare
(1) Applications of Matrices and Determinants
Adjoint, Inverse-Properties, Computation of inverses, a solution of a system of linear equations by matrix inversion method. Rank of a Matrix - Elementary transformation on a matrix, consistency of a system of linear equations, Cramer’s rule, Non-homogeneous equations, homogeneous linear system, rank method.
(2) Vector Algebra
Scalar Product–Angle between two vectors, properties of the scalar product, applications of dot products. Vector Product - Right handed and left handed systems, properties of vector product, applications of the cross product. The product of three vectors - Scalar triple product, properties of the scalar triple product, vector triple product, vector product of four vectors, scalar product of four vectors. Lines - Equation of a straight line passing through a given point and parallel to a given vector, passing through two given points (derivations are not required). The angle between two lines. Skew lines - Shortest distance between two lines, condition for two lines to intersect, the point of intersection, collinearity of three points. Planes - Equation of a plane (derivations are not required), passing through a given point and perpendicular to a vector, given the distance from the origin and unit normal, passing through a given point and parallel to two given vectors, passing through two given points and parallel to a given vector, passing through three given non-collinear points, passing through the line of intersection of two given planes, the distance between a point and a plane, the plane which contains two given lines, angle between two given planes, angle between a line and a plane. Sphere - Equation of the sphere (derivations are not required) whose centre and radius are given, equation of a sphere when the extremities of the diameter are given.
(3) Complex Numbers
Complex number system, Conjugate – properties, ordered pair representation. Modulus – properties, geometrical representation, meaning, polar form, principal value, conjugate, sum, difference, product, quotient, vector interpretation, solutions of polynomial equations, De Moivre’s theorem and its applications. Roots of a complex number - nth roots, cube roots, fourth roots.
(4) Analytical Geometry
Definition of a Conic - General equation of a conic, classification with respect to the general equation of a conic, classification of conics with respect to eccentricity. Parabola - the Standard equation of a parabola (derivation and tracing the parabola are not required), other standard parabolas, the process of shifting the origin, the general form of the standard equation, some practical problems. Ellipse - Standard equation of the ellipse (derivation and tracing the ellipse are not required), x2/a2 + y2/b2 = 1, (a > b), Other standard form of the ellipse, general forms, some practical problems, Hyperbola - standard equation (derivation and tracing the hyperbola are not required), x2/a2 – y2/ b2 = 1, Other form of the hyperbola, parametric form of comics, chords. Tangents and Normals - Cartesian form and Parametric form, the equation of chord of contact of tangents from a point (x1, y1), Asymptotes, Rectangular hyperbola –standard equation of a rectangular hyperbola.
(5) Differential Calculus – Applications I
Derivative as a rate measure - the rate of change - velocity - acceleration - related rates - Derivative as a measure of slope - tangent, normal and angle between curves. Maxima and Minima. Mean value theorem - Rolle’s Theorem – Lagrange Mean Value Theorem - Taylor’s and Maclaurin’s series, l’ Hôpital’s Rule, stationary points - increasing, decreasing, maxima, minima, concavity-convexity, points of inflexion.
(6) Differential Calculus – Applications II
Errors and approximations- absolute, relative, percentage errors, curve tracing, partial derivatives - Euler’s theorem.
(7) Integral Calculus & its Applications
Properties of definite integrals, reduction formulae for six and costs (only results), Area, length, volume and surface area
(8) Differential Equations
Formation of differential equations, order and degree, solving differential equations (1st order) - variable separable homogeneous, linear equations. Second order linear equations with constant coefficients f(x) = Ex, sin mix, cos mix, x, x2.
(9a) Discrete Mathematics
Mathematical Logic - Logical statements, connectives, truth tables, Tautologies.
(9b) Groups :
Binary Operations - Semigroups - monoids, groups (Problems and simple properties only), the order of a group, the order of an element.
(10) Probability Distributions
Random Variable, Probability density function, distribution function, mathematical expectation, variance, Discrete Distributions - Binomial, Poisson, Continuous Distribution - Normal distribution2.
Frictional electricity, charges and their conservation; Coulomb’s law – forces between two point electric charges. Forces between multiple electric charges – superposition principle. Electric field – Electric field due to a point charge, electric field lines; Electric dipole, electric field intensity due to a dipole – behaviour of the dipole in a uniform electric field – application of electric dipole in a microwave oven. Electric potential – potential difference – electric potential due to a point charge and due a dipole. Equipotential surfaces – Electrical potential energy of a system of two point charges. Electric flux – Gauss’s theorem and its applications to find field due to (1) infinitely long straight wire (2) uniformly charged infinite plane sheet (3) two parallel sheets (4) uniformly charged thin spherical shell (inside and outside) Electrostatic induction – capacitor and capacitance – Dielectric and electric polarisation – parallel plate capacitor with and without dielectric medium–applications of capacitor – energy stored in a capacitor. Capacitors in series and in parallel – action of points – Lightning arrester – Van de Graaff generator.
Unit-2. Current Electricity
The electric current – flow of charges in a metallic conductor – Drift velocity and mobility and their relation with electric current. Ohm’s law, electrical resistance. V-I characteristics – Electrical resistivity and conductivity. Classification of materials in terms of conductivity – Superconductivity (elementary ideas) – Carbon resistors – colour code for carbon resistors – Combination of resistors – series and parallel – Temperature dependence of resistance – Internal resistance of a cell – Potential difference and emf of a cell. Kirchoff’s law – illustration by simple circuits – Wheatstone’s Bridge and its application for the temperature coefficient of resistance measurement – Metre bridge – Special case of Wheatstone bridge – Potentiometer – principle – comparing the emf of two cells. Electric power – Chemical effect of current – Electrochemical cells Primary (Voltaic, Lechlanche, Daniel) – Secondary – rechargeable cell – lead acid accumulator.
Unit – 3. Effects of Electric Current
Heating effect. Joule’s law – Experimental verification. Thermoelectric effects – Seebeck effect – Peltier effect – Thomson effect – Thermocouple, thermal emf, neutral and inversion temperature. Thermopile. Magnetic effect of electric current – Concept of magnetic field, Oersted’s experiment – Biot-Savart law – Magnetic field due to an infinitely long current carrying straight wire and circular coil – Tangent galvanometer – Construction and working – Bar magnet as an equivalent solenoid – magnetic field lines. Ampere’s circuital law and its application. Force on a moving charge in the uniform magnetic field and electric field – cyclotron – Force on current carrying conductor in a uniform magnetic field, forces between two parallel current carrying conductors – definition of ampere. Torque experienced by a current loop in a uniform magnetic field- moving coil galvanometer – Conversion to ammeter and voltmeter – Current loop as a magnetic dipole and its magnetic dipole moment – Magnetic dipole moment of an m revolving electron.
Unit–4.Electromagnetic Induction and Alternating
Current Electromagnetic induction – Faraday’s law – induced emf and current – Lenz’s law. Self-induction – Mutual induction – Self inductance of a long solenoid – mutual inductance of two
long solenoids. Methods of inducing emf – (1) by changing magnetic induction (2) by changing area enclosed by the coil (3) by changing the orientation of the coil (quantitative treatment) analytical treatment can also be included. AC generator – commercial generator. (Single phase, three phase). Eddy current – Applications – Transformer – Long distance transmission. Alternating current–measurement of AC – AC circuit with resistance – AC circuit with inductor – AC circuit with capacitor – LCR series circuit – Resonance and Q – factor: power in AC circuits.
Unit – 5. Electromagnetic Waves and Wave Optics
Electromagnetic waves and their characteristics – Electromagnetic spectrum, Radio, microwaves, Infrared, visible, ultraviolet – X-rays, gamma rays. Emission and Absorption spectrum – Line, Band and continuous spectra – Fluorescence and phosphorescence. Theories of light – Corpuscular – Wave – Electromagnetic and Quantum theories. Scattering of light – Rayleigh’s scattering – Tyndal scattering – Raman effect – Raman spectrum – Blue colour of the sky and reddish appearance of the sun at sunrise and sunset. Wavefront and Huygen’s principle – Reflection, Total internal reflection and refraction of plane wave at a plane surface using wave fronts. Interference – Young’s double slit experiment and expression for fringe width – coherent source – interference of light. Formation of colours in thin films – analytical treatment – Newton’s rings. Diffraction – differences between interference and diffraction of light – diffraction grating. Polarisation of light waves – polarisation by reflection – Brewster’s law-double refraction – Nicol prism – uses of plane polarised light and polaroids – rotatory polarisation – polarimeter
Unit – 6. Atomic Physics
Atomic structure – discovery of the electron – specific charge (Thomson’s method) and charge of the electron (Millikan’s oil drop method) – alpha scattering – Rutherford’s atom model. Bohr’s model – energy quantisation – energy and wave number expression – Hydrogen spectrum – energy level diagrams – sodium and mercury spectra-excitation and ionisation potentials. Sommerfeld’s atom model. X-rays–production, properties, detection, absorption, diffraction of X-rays – Laue’s experiment – Bragg’s law, Bragg’s X-ray spectrometer – X-ray spectra – continuous and characteristic X-ray spectrum – Mosley’s law and atomic number. Masers and Lasers – spontaneous and stimulated emission – normal population and population inversion – Ruby laser, He – Ne laser – properties and applications of laser light – holography.
Unit–7. Dual Nature of Radiation And Matter
relativity Photoelectric effect – Light waves and photons – Einstein’s photo – electric equation – laws of photo – electric emission – particle nature of energy – photoelectric equation – work function – photocells and their application. Matter waves – wave mechanical concept of the atom – wave nature of particles – De – Broglie relation – De – Broglie wavelength of an electron – electron microscope. The concept of space, mass, time – Frame of references. Special theory of relativity – Relativity of length, time and mass with velocity – (E = mc2).
Unit – 8. Nuclear Physics
Nuclear properties–nuclear Radii, masses, binding energy, density, charge – isotopes, isobars and isotones – Nuclear mass defect – binding energy. Stability of nuclei- Bain-bridge mass spectrometer. Nature of nuclear forces – Neutron – discovery – properties – artificial transmutation – particle accelerator Radioactivity – alpha, beta and gamma radiations and their properties, -decay, -decay and decay – Radioactive decay law – half life – mean life. Artificial radioactivity – radioisotopes – effects and uses Geiger – Muller counter. Radiocarbon dating – biological radiation hazards.Nuclear fission – chain reaction – atom bomb – nuclear reactor – nuclear fusion – Hydrogen bomb – cosmic rays – elementary particles.
Unit – 9. Semiconductor Devices and their Applications
Semiconductor theory – energy band in solids – difference between metals, insulators and semiconductors based on band theory – semiconductor doping – Intrinsic and Extrinsic semiconductors. Formation of P-N Junction – Barrier potential and depletion layer. – P-N Junction diode – Forward and reverse bias characteristics – diode as a rectifier – more zen diode. Zener diode as a voltage regulator – LED. Junction transistors – characteristics – transistor as a switch – transistor as an amplifier – transistor biassing – RC, LC coupled and direct coupling in amplifier – feedback amplifier – positive and negative feedback – advantages of negative feedback amplifier – oscillator – condition for oscillations – LC circuit – Colpitts oscillator. Logic gates – NOT, OR, AND, EXOR using discreet components – NAND and NOR gates as universal gates – integrated circuits. Laws and theorems of Boolean’s algebra – operational amplifier – parameters – pin-out configuration – Basic applications. Inverting amplifier. Non-inverting amplifier – summing and difference amplifiers. Measuring Instruments – Cathode Ray oscilloscope – Principle – Functional units – uses. Multimeter – construction and uses.
Unit – 10. Communication Systems
Modes of propagation, ground wave – sky wave propagation. Amplitude modulation, merits and demerits – applications – frequency modulation – advantages and applications – phase modulation. Antennas and directivity. Radio transmission and reception – AM and FM – superheterodyne receiver. T.V. transmission and reception– scanning and synchronising. Vidicon (camera tube) and picture tube – block diagram of a monochrome TV transmitter and receiver circuits. Radar – principle – applications. Digital communication – data transmission and reception – principles of fax, modem, satellite communication – wire, cable and Fibre-optical communication.
Unit -1. Atomic Structure
Dual properties of electrons-de-Broglie relation – Heisenberg’s uncertainty principle – Wave nature of an electron – Schrodinger wave equation (only equation, no derivation) – Eigen values and Eigenfunction – significance only – molecular orbital method. Application to Homo diatomic and Hetero diatomic molecules-Metallic Bond – Hybridization of atomic orbitals.Hybridization involving, p and d Orbitals – Types of forces between molecules.
Unit -2.Periodic Classification
Review of periodic properties – Calculation of atomic radii – Calculation of ionic radii-Method of determination of Ionisation potential-Factors affecting ionisation potential – Method to determine the electron affinity – Factors affecting EA-Various scales on electronegativity values.
Unit -3. P – Block Elements
Group – 13 General trends-Potash alum – Preparation, Properties and uses – Group 14 General trends –Silicates – Types and structure – Silicones-Structure and uses – Extraction of lead – Group – 15 General trends – Phosphorous-Allotropes and extraction – Compounds of phosphorous – Group – 16 General trends – H2SO4 – Manufacture and properties. – Group – 17 General characteristics. Physical and Chemical properties – Isolation of fluorine and its properties – Interhalogen compounds Group – 18 Inert gases – Isolation, properties and uses.
Unit - 4. D – Block Elements
General characteristics of D-block elements – First transition series –Occurrence and principles of extraction – chromium, copper and zinc – Alloys – Second transition series – Occurrence and principles of extraction of silver – Third transition series – Compounds – K2Cr2O7, CuSO45H2O, AgNO3, Hg2Cl2, ZnCO3, Purple of Cassius.
Unit -5. F – Block Elements
General characteristics of F-block elements and extraction – Comparison of Lanthanides and Actinides – Uses of lanthanides and actinides.
Unit- 6. Coordination Compounds and Bio-Coordination Compounds
An introduction – Terminology in chemistry – IUPAC nomenclature of coordination compounds – Isomerism in compounds – Structural isomerism – coordination mononuclear coordination Geometrical isomerism in 4 – coordinate, 6 – coordinate complexes – Theories on coordination compounds – Werner’s theory (brief) – Valence Bond theory – Crystal field theory – Uses of coordination compounds – Biocoordination compounds. Haemoglobin and chlorophyll.
Unit -7.Nuclear Chemistry
Nuclear energy nuclear fission and fusion – Radiocarbon dating – Nuclear reaction in sun-Uses of radioactive isotopes.
Unit -8. Solid State –II
Types of packing in crystals-X-Ray crystal structure – Types of ionic crystals – Imperfections in solids – Properties of crystalline solids–Amorphous solid.
Unit -9. Thermodynamics – II
Review of I law – Need for the II law of thermodynamics – Spontaneous and non-spontaneous processes – Entropy – Gibb’s free energy – Free energy change and chemical equilibrium – Third law of thermodynamics.
Unit -10. Chemical Equilibrium – II
Applications of a law of mass action – Le Chatlier’s principle.
Unit -11.Chemical Kinetics-II
First order reaction and pseudo first order reaction – Experimental determination of first order reaction method of determining an order of reaction – temperature dependence of rate constant – Simple and complex reactions.
Unit- 12. Surface Chemistry
Adsorption-Catalysis-Theory of catalysis-Colloids- Preparation of colloids-Properties of colloids-Emulsions.
Unit- 13. Electrochemistry – I
Conductors, insulators and semiconductors – Theory of electrical conductance – Theory of strong electrolytes – Faraday’s laws of electrolysis – Specific resistance, specific conductance, equivalent and molar conductance – Variation of conductance with dilution – Kohlrabi's law – Ionic product of water, pH and pOH – Buffer solutions – Use of pH values.
Unit- 14. Electrochemistry – II
Cells-Electrodes and electrode potentials-Construction of cell and EMF – Corrosion and its preventions-commercial production of chemicals-Fuel cells.
Unit -15. Isomerism In Organic Chemistry
Geometrical isomerism – Conformations of cyclic compounds – Optical isomerism – Optical activity – Chirality – Compounds containing chiral centres-D-L and R-S notation – Isomerism in benzene.
Unit- 16. Hydroxy Derivatives
Nomenclature of alcohols – Classification of alcohols – General methods of preparation of primary alcohols – Properties Methods of the distinction between three classes of alcohols 1°, 2° and 3°) – Methods of preparation of dihydric alcohols. (glycol) – Properties – Uses – Methods of preparation of trihydric alcohols – Properties – Uses – Aromatic alcohols – Methods of preparation of benzyl alcohol Properties – Uses – Phenols – Manufacture of phenols – Properties – Chemical properties – Uses of Phenols.
Unit -17. Ethers
Ethers-General methods of preparation of aliphatic ethers – Properties – Uses – Aromatic ethers – Preparation of anisole – Reactions of anisole – Uses.
Unit - 18. Carbonyl Compounds
Nomenclature of carbonyl compounds – Comparison of aldehydes and ketones – General methods of preparation of aldehydes – Properties – Uses Aromatic aldehydes – Preparation of benzaldehyde – Properties – Uses – Ketones – general methods of preparation of aliphatic ketones (acetone) – Properties – Uses – Aromatic ketones – preparation of acetophenone – Properties – Uses – preparation of benzo – phenone – Properties.
Unit - 19. Carboxylic Acids
Nomenclature – Preparation of aliphatic monocarboxylic c acids – formic acid – Properties – Uses – Tests for carboxylic acid – Monohydroxy monocarboxylic acids – Lactic acid – Sources – Synthesis of lactic acid – Aliphatic dicarboxylic acids – preparation of dicarboxylic acids – oxalic and succinic acids – Properties – Strengths of carboxylic acids – Aromatic acids – Preparation of benzoic acid – Properties – Uses – Preparation of salicylic acid – Properties – Uses – Derivatives of carboxylic acids Preparation of acid chloride – acetyl chloride (CH3COCl) – Preparation – Properties – Uses – Preparation of acetamide – Properties – Preparation of acetic anhydride – Properties – Preparation of esters methyl acetate – Properties.
Unit -20. Organic Nitrogen Compounds
Aliphatic nitro compounds – Preparation of aliphatic nitroalkanes – Properties – Uses – Aromatic nitro compounds – Preparation – Properties – Uses – Distinction between aliphatic and aromatic nitro compounds – Amines – Aliphatic amines – General methods of preparation – Properties – Distinction between 1°, 2°, and 3° amines – Aromatic amines – Synthesis of benzylamine – Properties – Aniline – preparation – Properties – Uses – Distinction between aliphatic and aromatic amines – Aliphatic nitrites – Preparation – properties – Uses – Diazonium salts – Preparation of benzene diazonium chloride – Properties.
Unit -21. Biomolecules
Carbohydrates – structural elucidation – Disaccharides and polysaccharides – Proteins-Amino acids – structure of proteins – Nucleic acids – Lipids.
Unit -22. Chemistry in Action
Medicinal chemistry – Drug abuse – Dyes – classification and uses – Cosmetics – creams, perfumes, talcum powder and deodorants – chemicals in food – Preservatives artificial sweetening agents, antioxidants and edible colours – Insect repellant – pheromones and sex attractants – Rocket fuels – Types of polymers, preparation and uses
Make a proper Time Table
It is very important that you make a timetable and stick to it and you will have an exact idea of what you are required to study and the time required for it.
Concept clarity rather than rotes learning
It is essential that you have a clear idea of the formulas and concepts rather than rote learning of things for the papers. While you might require it for memorizing formulas it is important that for other stuff you make sure you clear your basics and concepts before moving on.
It is very important make small notes or a comprehensive list of formulas on each covered topic and chapter which will come in handy at the time of revision. This will require you to be regular with your work but will surely make things easy at the time of revision.
Revision of Class XI and XII concepts
Make sure that you revise your concepts from the syllabus of these classes before starting anything new as most of the engineering exams will be for admission to undergraduate courses and so the syllabi from class XI and XII becomes the testing ground to check students.
It is not possible for you to know everything in your syllabus, at least not at the time of preparation. Sooner or later you will run into a concept or so which will give you trouble and then it is best you seek guidance from an instructor or a teacher. It is necessary that you clear your doubts at regular intervals and don’t prolong things for long. Getting into a good coaching class is nothing to be ashamed off and if anything a regular coaching class will enable you to avoid roadblocks in your preparation.
Even though there may be a complete change in the exam pattern or the expected questions altogether,it is important that you practice on the sample and previous years question papers available for the engineering exam you’d be attempting. You will know the existing pattern and have a fair idea of the type of questions to expect in the paper along with the time constraint.
The paper pattern, duration of the paper and the number of questions to be attempted in the given amount of time is not something you will be able to pick up on the day of the examination. A Mock Test tests a student’s abilities as it not only provides a similar feel of real exams but also helps in building speed and confident to face the exam. Furthermore, they can improve their performance to get an extra edge in actual exams. Try to build up an Engineering Entrance Exam Test Prep MCQ Question Bank
Time management can be learnt through thorough practice and regular test taking. So it is important that you practice it and practice it well.
Most the entrance examinations will have negative marking and everyone would suggest you stay clear of questions are not sure about. But some experts are of the opinion that you answer the questions in which you are confused between an option or two because there will also be a chance of getting it right.
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