EXAM SYLLABUS
PHYSICS
Mechanics and Properties of Matter
Circular motion
Angular displacement, Angular velocity, Angular acceleration, Relation between linear and angular velocity. Uniform circular motion, Radial acceleration, centripetal and centrifugal forces, Banking of roads.
Gravitation
Newton’s law of gravitation, periodic time, binding energy and escape velocity of a satellite, weightlessness condition in a satellite.
Rotational Motion
Centre of mass of a two particle system, its generalization to ‘n’ particals, rigid body and its centre of mass, definition of moment of inertia it’s physical significance, radius of gyration, K. E. of a rotating body, torque, M.I. of principle of perpendicular and parallel axes its application to M. I. of uniform rod and disc with proof. Angular momentum and its conservation.
Oscillations
Explanation of periodic motion, Simple Harmonic Motion (S. H. M.), uniform circular motion and S. H. M., phase of S. H. M., K. E. and P. E. in cases of S. H. M., composition of the two S. H. M., having same period and parallel to each other (Analytical treatment), simple pendulum, angular S. H. M., magnet vibrating in the uniform magnetic induction.
Elasticity
General explanation of elastic property (a few examples) plasticity, deformation, Definition of stress and strain, Hooke’s law. Elastic constants Y, K, N, and O. Determination of Young’s modulus by Searle’s method, observation on a wire under applied increasing load, calculation of work done in stretching a thin uniform wire.
Properties of fluids
Behavior of liquid surfaces, its explanation on the basis of molecular theory, surface energy, surface tension, Angle of contact, capillary action.
Sound
Wave motion
Explanation of formation of wave, simple harmonic progressive waves, longitudinal and transverse types of waves, deflection of sound waves. Change o f phase, superposition of sound waves, explanation of formation of beats, Doppler effect.
Stationary waves
Study of vibrations on strings, explanation of formation of stationary waves on strings, study of Vibrations of air columns, forced vibrations, resonance. Experiments like sonometer, resonance tube, Mold’s experiment to study stationary waves.
Heat and Thermodynamics
Kinetic theory of gases
Assumptions of kinetic theory, mean free path, derivation for pressure of a gas in the container on the basis of Kinetic theory of gases, Derivation of Boyle’s law, specific heat at constant volume and pressure (Cp and CV). Method of determination of Cp, Mayor’s relation, internal and external latent heat.
Radiation
Absorption, emission, reflection of heat radiations, Corresponding Coefficients and relation between them, Perfectly black body, emissive power, emissivity, Kirchhoff’s law of radiation, it’s theoretical proof, Ritche’s experiment, Prevost’s theory of exchange of heat, Stefan’s law. Newton’s law of cooling and radiation correction.
Thermodynamics
Thermodynamic state, equation of state isothermals, pressure temperature phase diagram, Vander waal’s equation of state.
LIGHT
Wave theory of Light
Newton’s corpuscular theory, wave theory of light , wave front and wave normal, Huygen’s principle construction of plane and spherical wave front Reflection and refraction at plane surfaces, Ray optics as a limiting case of wave optics, scattering of light.
Interference of light
Interference of light, conditions for producing steady, interference pattern, Young’s experiment Analytical treatment of interference bands, Measurement of wave length by biprism experiment.
ELECTRICITY AND MAGNETISM
Electrostatics
Gauss’s Flux theorem, its proof and applications, mechanical force on unit area of charged conductor energy per unit volume. Capacity of a parallel plate condenser with a dielectric, Energy of a changed condenser, Condensers in series and parallel.
Current Electricity
Flow of current in a conductor, sources of e.m.f., simple cell, electric current, Ohm’s law, Kirchhoff’s laws, Wheatstone’s bridge, Potentiometer.
Magnetic effect of current
Moving coil galvanometer, ammeter, voltmeter, sensitivity and accuracy of moving coil galvanometer Theory and construction of Tangent Galvanometer, sensitivity and accuracy of TG.
Magnetism
Magnetic induction at any point due to a magnetic dipole; Magnetic potential at any point due to a magnetic dipole; Diamagnetism, Paramagnetism, Ferromagnetism on the basis of domain theory, Curie temperature.
Electromagnetic Induction
Electromagnetic Induction, Faraday’s experiment, law of the electromagnetic induction, proof of e= dœ)/dt, Eddy currents, self and mutual inductance, induction coil earth coil, coil rotating in a uniform magnetic induction, alternating currents, reactance and impedance, power in A. C. circuits, Electromagnetic oscillations, Electromagnetic spectrum (Elementary facts, uses and application)
MODERN PHYSICS
Electrons and photons
Discovery of an electron, change and mass of electron, photoelectric effect, Einstein’s equation. Photoelectric cell and its application.
Atoms, molecules and nuclei Rutherford’s model of an atom, Bohr model energy quantization, H2 spectrum, composition of nucleus, Radioactivity, mass energy relation.
Thermionic emission of solid state devices
Thermionic emission, diode, its construction and use’ as a half wave and full wave rectifier. Triode, its construction and use as an amplifier (Qualitative idea)
Semi- conductor
P-type and N- type semi conductors, P- N junction diodes, P- N junction diode as rectifier, and transistor as amplifier.
CHEMISTRY
Atomic Structure and Nature of Chemical Bonds
i. Introduction, electronic theory of valency, limitations:
ii. VB. Theory- postulates, overlapping of atomic orbitals.
a. S- S in H2 molecule
b. P- P in halogen molecule
c. S- P in Hexmolecule
iii The concept of hybrid orbitals and geometry of molecules
a. Tetrahedral (SP3) hybridization in CH4, Nh3, H2O
b. Trigonal hybridization (SP2) in BF3, and C2H4
c. Diagonal hybridization (SP) in Bef, and C2H2
iii. Bond Energy – Average Bond energy, factors affecting bond energy
iv. The uncertainty principle, orbitals and Quantum numbers shapes of orbitals, Electronic
configuration of atoms.
Chemical Thermodynamics and Energetics
i. Introduction
ii. Concepts in Thermodynamics- System, isolated, closed and open system, Homogeneous and heterogeneous system Thermodynamic equilibrium, nature and type of processes, isothermal and adiabatic processes, reversible and irreversible processes.
iii. Nature of work and heat, units of energy and work in thermodynamics, work of pressure, volume, maximum work in reversible isothermal process, simple numerical problems.
iv. First law of Thermodynamics- Relation between mass and energy, internal energy, change in internal energy and mathematical deduction of the first law of Thermodynamics. q = E+ W, Simple numerical problems Second law of Thermodynamics: Entropy, free energy, spontaneity of a chemical reaction, free energy change and chemical equilibrium, free energy as energy available for useful work.
v. Enthalpy (H) of a system, change in enthalpy mathematical derivation, numerical problem and conversion of H related to endothermic and exothermic reaction.
vi. Thermochemistry Endothermic and exothermic reaction, heat of reaction, heat of neutralization, Head of formation ?H = [H(Product )- H(Reactant)}, effect of temperature on heat of reaction (Kirchoof’s equation), numerical problem.
vii. Internal energy and change in internal energy.
viii. Hess’s Law of const. heat summation – definition and explanation
Electrochemistry
i. Introduction
ii. Electrolysis, electrolytic cells
iii. Faraday’s laws of electrolysis, simple numerical problem
iv. Electrochemical cells- Construction, working of simple voltatic cell (Daniel Cell), convention used in S the representation of galvanic cell, use of salt bridge, type of electrodes, hydrogen electrode, calomel electrode and measurement of electrode potentials
v. Concept of electrode potential – electronation and deelectronation ( Nerst Theory) , S. D. P. and e. m. f of a cell e. m. f. series, its applications, simple numerical problems on e. m. f. of cell.
vi. Common types of cells – Dry cell accumulator.
Ionic Equilibrium
i. Introduction
ii. Arhenius theory of acids and bases
iii. Lowry and Bronsted concepts of acids and bases
iv. Lewis concept of acids and bases
v. Strong and weak acid and bases, degree of dissociation, dissociation constant, Ostwald dilution
formula. Simple problems
vi. Ionisation of water, lonic product of water (Kw)
vii. H ion concentration, pH and pOH – pH + pOH= 14 numerical problems
viii. Commonion effects, Buffer solution, Mechanism of buffer action, solubility product its application numerical problems on solubility product
ix. Hydrolysis of salts, Hydrolysis constant, Relation between hydrolysis constant and dissociation constant.
Adsorption Colloids
i. Introduction
ii. Adsorption as a surface phenomenon, difference in type of adsorption and absorption, factors affecting adsorption, types of adsorption.
iii. Freundlich’s adsorption isotherm, Applications in water purification, catalyst, adsorption indicate and chromatography
iv. Colloids- Introduction, colloidal state of matter disperse phase, dispersion medium, few examples colloidal solutions.
v. Preparation of colloidal solutions:
a. Dispersion method (electrical and mechanical)
b. Condensation methods (Oxidation and reduction) properties of colloidal solutions, general properties, (electrophoresis and electroosomsis) coagulation.
vi. Gels- Definition, example, types, properities and uses
vii. Emulsion- Definition, examples, type, (D/W, W/O)prosperities and uses.
viii. Application of colloids- food, medicine, sewage, precipitation of smoke.
Nuclear and Radiochemistry
i. Introduction
ii. Characteristics of nucleons, mass number, atomic number, isotopes and isobars.
iii. Nuclear stability, mass defect, binding energy, average binding energy, simple numerical problem on binding energy.
iv. Radioactivity – Radioactive decay, nature of radiations, radioactive disintegration constant, half
life period, mathematical derivation for the decay constant- and halflife (t1/2, simple numerical problems, Artificia radioactivity and artificial transmutation of elements.
v. Nuclear reactions. Radio isotopes and their uses- carbon dating, production of synthetic elements, medicine, agriculture.
Chemical of Third Row Elements
i. Introduction
ii. Position of third row elements in periodic table
iii. Electronic Configuration
iv. Periodic trend- reducing and oxidizing characters, ionization potential, electropositive and electronegative character and hence metallic and non- metallic character.
v. Nature of bonding in crystal lattice
vi. Explanation of prosperities of metallic solids- conductivity, metallic luster, malleability, ductility.
vii. Acidic and basic character of oxides and hydroxyl compounds of third row elements. Hydrogen – Position in periodic table, isotopes, properties, reaction and uses). Oxygen- Position in periodic table, preparation, reaction uses, ozone. Water and hydrogen peroxide structure of water molecule, physical and chemical prosperities of water, hard and soft water. Hydrogen peroxides- Preparation, properties, structure and uses. Nitrogen- Preparation, properties, uses, compounds of nitrogen.
Fluorine and Hydrogen Fluoride
i. Introduction
ii. Position of halogens in – periodic table, electronic configuration, general principles of halogens
iii. Fluorine- Occurrence, preparation, properties, reaction and uses.
iv. Hydrogen- fluoride and hydrofluoric acid- preparation, properties, reaction uses
Silicon
i. Introduction
ii. Position of silicon in periodic table, electronic configuration
iii. Silicon- occurrence, preparation, properties and uses
iv. Silicates, structure of simple silicates, nature of Si-O bond, tetrahedral geometry of Si 04 units in silicates. Halogen
Derivatives of Alkanes
i. Introduction
ii. Classification, Mono, di, tri and tetrahalogen derivations of alkanes.
iii. Monohalogen derivatives (alkylhalides)
a. Nomenclature- Trivial and I. U. P. A. C. system
b. Preparation
c. Halogenation of alkanes
d. Addition of Hx to alkanes
e. Action of P and PXs to Sod2 on alcohols (Ethyl bromide C2H5Br to be taken as a representative member)
iv. Reactions of alky halides
a. Substitution reactions with Akalies KCN, Ammonia, Sodium alkoxide, R- COOAg
b. Wurtz reaction
c. Formation of Grignards reagent
d. Elimination – Action of alcoholic KOH
v. a. Introduction of Homolytic and heterolytic fission explanation of fission taking compound A- B
1. A- B 0A +B Homolytic
2. A- B0A + B- Heterolytic
b. Types of reagents
1. Electrophillic with suitable examples
2. Nucleuophillic with suitable examples
c. Mobility of electrons in single and double bonds
1. Inductive effect
2. Electromeric effect
vi. SN1 and SN2 reaction mechanism:
a. Mechanism of alkaline hydrolysis of methyl bromide (SN2 mechanism)
b. Alkaline hydrolysis oft – Butyl bromide (SN1 mechanism)
vii. Optical activity:
Following points are to be emphasized : polarization of light by Nicol prism Asymmetric carbon atom optically active (compounds, definition with example of lactic acid (Dextro, Leavo and Racemic forms) Optically activity of 2- chlorobutane to be discussed on the following points presence of asymmetric Carbon atom Two non- superimposable mirror image structures Amixture and its optical inactivity.
viii. Dihalogen Derivatives:
Preparation of C2H4CI2 Two isomers
a. Ethylene dichloride
b. Ethylidence chloride
Preparation of ethylene dichloride by
a. Addition of CI2 to ethane
b. Ethylene glycol and PCI5
Preparation of ethylidence chloride from
a. Acetaldehyde and PCI5
b. Acetylene and HCI
ix. Trihalogen Derivatives of CH4 :
Preparation of chloroform and lodoform General physical and chemical properties
a. Reduction
b. Oxidation
c. Hydrolysis
d. Carbylamine reaction
e. Action of HNO3
Organic Hydroxy Compounds
i. Introduction
Alcohols- introduction – classification Nomenclature-
1. Trival system
2. I. U.P. A. C system
Preparation method
Hydrolysis of alky halides
Hydration of Alkene by acid Reduction of Aldehydes and ketones by
a. Catalytic method using Nickel
b. Na- Hg/ H2O
Properties and Reactions:
General Physical and Chemical Properties
Reaction with:
a. Na, Hx, PCB, PCI5
b. Dehydration
c. Oxidation of primary, secondary and tertiary alcohols
ii. Phenols:
Aromatic hydroxyl compounds- Phenol as a representative compounds
a. Chlorobenzene
b. Benzene Sulphonic acid
c. Cumene
iii. Physical properties and chemical reactions
a. Halogenation
b. Nitration,
c. Sulphonation
Distinction between alcohol and phenol, uses of phenol
Aldehydes and Ketones:
i. Introduction
ii. Preparation
Oxidation of alcohols
Hydrolysis of gemdihalides
From Grignard reagent,
iii. From calcium salt of acids
Reactions :
a. Addition to Carbony1 compounds HCN, NaHCO3 NH3, Grignard reagent
b. Condensation reactions- (NH2OH), C5H5NHNH2
c. Aldol condensation , Acetaldehyde with dil alkali, similar reactions with ketones.
d. Cannizzaro’s reaction- Action of conc. NaOH on formaldehyde
e. Reduction of Aldehydes and Ketones, catalytic hydrogenation
f. Reducing properties of Aldehydes Fehling solution, Tollen’s reagent, Schiff’s reagent.
Acids and Esters
i. Introduction
ii. Preparation (acids)
a. Oxidation of primary alcohols, aldehyde
b. Hydrolysis of alky1 cyanides
c. Grignard reagent and CO2
iii. Reactions:
a. Acidic properties
b. Antyride formation by using P205
c. Ester formation
iv. Amide formation
v. Esters
a. Introduction
b. Preparation: Acid and Alcohol, Alcohol and acid anhydride Alcohol and acid chloride Alkylhalide and Ag- salt of acid
c. Reaction of ethyl acetate Hydrolysis with acid and alkali Action of Grignard reagent Uses of esters
Ethers
i. Introduction
ii. Definition: Classification, simple and mixed ethers
Preparation:
a. Williamson’s synthesis
b. Continuous etherification process
c. Alcohol and Diazomethane
iii. Physical and chemical properities:
a. Action of HI on simple and mixed ethers in cold and hot
b. Hydrolysis by dil. H2SO4 uses of dethyl ether
Amines
i. Introduction
ii. Definition : Classification- Nomenclature
iii. Preparation
a. Haloalkanes and Ammonia
b. Reduction of Oxime, nitriles and nitroalkanes.
iv. Properties : Physical and Chemical
a. Basic nature on the basis of Lewis concept
b. Acetylation by acetyl chloride and acetic anhy dride
c. Action of HNO2 on primary, Secondary and tertiary amines yielding quaternary ammonium salts.
Carbohydrates, Proteins and Fats
i. Introduction
ii. Carbohydrates: Classification, mono di and polysaccharide preparation of glucose from surcrose and starch
iii. Proteins: Classification, simple conjugated and drived proteins . Hydrolysis of proteind to produce amino acids peptide linkage colour tests:
1) Biuret test
2) Millon’s test
iv. Fats and Oils:
Glycerol- as atrihydroxy alcohol, fatty acid Esters of glycerol with fatty acids Saponification, Hydrogenation.
Synthetic Fibres
i. Introduction
ii. Definition of fibers: Classification as – natural and artificial fibres
iii.Preparation: properties and used of Nylon 6, Nylon 66. Terylene, Teflon, PVC, Polystyrene.
BIOLOGY (BOTANY)
Section (A): General Biology And Botany
General Biology
Continuity of life
i. Mendel’s laws of inheritance, with reference to Mendel’s experiments with peas, ideas of factors, Monohybrid and Dihybrid ratio.
ii. Genes – Packaging of hereditary material, prokaryotes, bacterial chromosomes, plasmid and eukarytic chromosomes Genetic material, DNA replication; Genetic Code and Central dogma of protein synthesis.
iii. Cell division-cell cycle, mitosis and meiosis significance.
Applications of Biology
i. Domestication pf plants: improvement of crop plants – Principals of plant breeding and technique of hybridization
Application of Tissue: Culture.
Use of fertilizers and pesticides – Their advantages and disadvantages; Biological method of Pest control.
ii. Bio- energy:- Bio-gas, plants as sources of hydro carbons for producing Petroleum to
iii. Bio-technology:- Fermentation and manufacture of Alcohols, Antibiotics and Vitamins.
Multicelluarity, Plants Life
i. Concept of species – Various taxons and catergories, Hirearchial levers of classification, Binomial nomenclature, principles of classification.
ii. Conquest of land- Life history of Gern (Nephrolepis). Cycas and angiosperms (Hisbiscus, jowar, Bajra)- Anatmoy, development of seed habit, flower and fruit . (Development of Reporductive structure not excepted)
iii. Physiology
Transpiration : Transpiration and exchange of gases, stomatal mechanism.
Photosynethesis: Ultra – structure and function of chloroplast, photochemical pathways, significance.
Respiration: Ultra- structure and function of mitochondrion, glycolysis, krebs cycle, electron transport system, fermentation, significance.
Growth: Plant hormones and growth regulation, action of plants hormones in relation to seed dormancy and germination, apical dominance.
Reproduction : Asexual and sexual Brief accopunt of mode sexual reproduction in multicelluar lower plants- antheridium and archegonium. Sexual reproduction in angiosperms Pollination, structure of male and female gametophytwes, fertilization, formation of endosperm, seed and fruit.
BIOLOGY (ZOOLOGY)
Section (B) – General Biology And Zoology Evolution of life
Evolution: Definition, Darwin’s theory of natural selection ( Common origin, recombination as a source of variability, Role of selection on variation, adaptation, reproductive isolation and speciation).
ii) Human evolution: Paleontological evidence , Brief idea of the Dryopithecus, Australopithecus, Homo- erectus, Homo- meanunderthalensis, Cro- magnon, Homo- sapiens,
Continuity of life
i. Sex determination and sex linkage in man.
ii. Domestication of animals-introduction of poultry, fisheries.
Sericulture and apiculture. Principles of animal breeding major animal diseases and their control
iii. Human diseases and their control + Hepatitis, AIDs, Leprosy, Cancer.
iv. Community Health Services – Blood bank smoking. Alcoholism, drug addiction –Physiological symptoms and their measures.
v. Pollution – Air, Water-effect and control.
vi. Human population – Growth, problems and control.
Multicellularity
Structure and functions of animal life with reference to mammals:
i. Circulation – Closed vascular system, Heart – Structure and pumping action, Arterial blood pressures.
ii. Excretion and Osmo–regulation: Aminotelism, uriotelism, uricorelism, Excreton of water and urea, with special reference to main, role of kidney, in regulation of plasma, osmoregularity on the basis of structure of nephron: role of skin and lungs, in excretion.
iii. Hormonal Co-ordination: Morphological and histological structure of pituitary and thyroid glands, Important hormones of pituitary and thyroid and their role as messengers and regulators.
iv. Nervous Co-ordination: Central, Peripheral, autonomous nervous system, receptors and effectors, reflection.
v. Locomotion-Joints, muscle movements.
vi. Skeleton – Brief account of human skeleton.
vii. Reproduction: Human reproduction, female reproductive cycle, embryonic development up to three germinal layers.
viii. Classification of chordata: Pisces, Amphibia, Reptilia, Aves, Mammals, highlighting major characters with two examples of each class.
MATHEMATICS
1. Mathematical Logic
Statements - Introduction, sentences and statement, truth value of statement, open sentences, compound statement, quantifier and quantified statements, logical connectives : conjunction, disjunction, negation, implication/ conditional, biconditional, truth tables of compound statements, examples related to real life and mathematics, statement patterns and logical equivalence - tautology, contradiction, contingency, duality, negation of compound statement, contrapositive, converse, inverse, algebra of statements-idempotent law, associative law, commutative law, distributive law, identity law, complement law, involution law, DeMorgan’s laws, difference between converse, contrapositive, contradiction, application-introduction to switching circuits (simple examples).
2. Matrices
Elementary transformation of a matrixrevision of cofactor and minor, elementary row transformation, elementary column transformation, inverse of a matrixexistance and uniqueness of inverse of a matrix, inverse by elementary transformation, adjoint method, application-solution of system of linear equations by – reduction method, inversion method.
3. Trigonometric functions
Trigonometric equations-general solution of trigonometric equation of the type: sinθ = 0, cosθ = 0, tanθ = 0, sinθ = sinα, cosθ = cosα, tanθ = tanα, sin 2 θ = sin 2 α, cos 2 θ = cos 2 α, tan 2 θ = tan 2 α, acosθ + bsinθ = C solution of a triangle : polar coordinates, sine rule, cosine rule, projection rule, area of a triangle, application, Hero’s formula, Napier Analogues, inverse trigonometric functions- definitions, domain, range, principle values, graphs of inverse trigonometric function, properties of inverse functions.
4. Pair of straight lines
Pair of lines passing through origincombined equation, homogenous equation, theorem-the joint equation of a pair of lines passing through origin and its converse, acute angle between the lines represented by ax 2 +2hxy+by 2 =0, condition for parallel lines, condition for perpendicular lines, pair of lines not passing through origin-combined equation of any two lines, condition that the equation ax 2 +2hxy+by 2 +2gx+2fy+c=0 should represent a pair of lines (without proof), acute angle between the lines (without proof), condition of parallel and perpendicular lines, point of intersection of two lines.
5. Circle
Tangent of a circle-equation of a tangent at a point to 1) standard circle,2) general circle, condition of tangency only for line y = mx + c to the circle x 2 + y 2 = a 2 , tangents to a circle from a point outside the circle, director circle, length of tangent segments, normal to a circle-equation of normal at a point.
6. Conics
Tangents and normals-equations of tangent and normal at a point for parabola, ellipse, hyperbola; condition of tangency for parabola; ellipse, hyperbola; tangents in terms of slope for parabola, ellipse, hyperbola, tangents from a point outside conics, locus of points from which two tangents are mutually perpendicular, properties of tangents and normals to conics (without proof).
7. Vectors
Revision, Collinearity and coplanarity of vectors : linear combination of vectors, condition of collinearity of two vectors, conditions of coplanarity of three vectors, section formula : section formula for internal and external division, midpoint formula, centroid formula, scaler triple product : definition, formula, properties, geometrical interpretation of scalar triple product, application of vectors to geometrymedians of a triangle are concurrent, altitudes of a triangle are concurrent, angle bisectors of a triangle are concurrent, diagonals of a parallelogram bisect each other and converse, median of trapezium is parallel to the parallel sides and its length is half the sum of parallel sides, angle subtended on a semicircle is right angle.
8. Three dimensional geometry
Direction cosines and direction ratios: direction angles, direction cosines, direction ratios, relation between direction ratio and direction cosines, angle between two lines, condition of perpendicular lines.
9. Line
Equation of line passing through given point and parallel to given vector, equation of line passing through two given points, distance of a point from a line, distance between two skew lines, distance between two parallel lines (vector approach).
10. Plane
Equation of plane in normal form, equation of plane passing through the given point and perpendicular to given vector, equation of plane passing through the given point and parallel to two given vectors, equation of plane passing through three noncollinear points, equation of plane passing through the intersection of two given planes, angle between two planes, angle between line and plane, condition for the coplanarity of two lines, distance of a point from a plane (vector approach)
11. Linear programming problems
Introduction of L.P.P. definition of constraints, objective function, optimization, constraint equations, nonnegativity restrictions, feasible and infeasible region, feasible solutions, Mathematical formulation-mathematical formulation of L.P.P. different types of L.P.P. problems, graphical solutions for problem in two variables, optimum feasible solution.
12. Continuity
Continuity of a function at a point : left hand limit, right hand limit, definition of continuity of a function at a point, discontinuity of a function, types of discontinuity, algebra of continuous functions, continuity in interval-definition, continuity of some standard functionspolynomial, rational, trigonometric, exponential and logarithmic function.
13. Differentiation
Revision- revision of derivative, relationship between continuity and differentiability-left hand derivative and right hand derivative (need and concept), every differentiable function is continuous but converse is not true, Derivative of composite function-chain rule, derivative of inverse function, derivative of inverse trigonometric function : Derivative of implicit function definition and examples, derivative of parametric function – definition of parametric function ,exponential and logarithmic functionderivative of functions which are expressed in one of the following form a) product of functions, b) quotient of functions, c) higher order derivative, second order derivative d) [f (x) ] [g(x)]
14. Applications of derivative
Geometrical application-tangent and normal at a point, Rolle's theorem, and Mean value theorem and their geometrical interpretation (without proof), derivative as a rate measure-introduction, increasing and decreasing function, approximation (without proof), Maxima and minimaintroduction of extrema and extreme values, maxima and minima in a closed interval, first derivative test, second derivative test.
15. Integration
Indefinite integrals-methods of integration, substitution method, integrals of the various types, integration by parts (reduction formulae are not expected), integration by partial fraction-factors involving repeated and non-repeated linear factors, non-repeated quadratic factors, definite integral-definite integral as a limit of sum, fundamental theorem of integral calculus (without proof), evaluation of definite integral 1) by substitution 2) integration by parts, properties of definite integrals.
16. Applications of definite integral
Area under the curve: area bounded by curve and axis (simple problems), area bounded by two curves, volume of solid of revolution-volume of solid obtained by revolving the area under the curve about the axis (simple problems).
17. Differential equation
Definition-differential equation, order, degree, general solution, particular solution of differential equation, formation of differential equation-formation of differential equation by eliminating arbitary constants (at most two constants), solution of first order and first degree differential equation-variable separable method, homogeneous differential equation (equation reducible to homogeneous form are not expected), Linear differential equation, applications : population growth, bacterial colony growth, surface area, Newton’s laws of cooling, radioactive decay.
18. Statistics
Bivariate frequency distribution - bivariate data, tabulation of bivariate data, scatter diagram, covariance of ungrouped data, covariance for bivariate frequency distribution, Karl Pearson’s coefficient of correlation.
19. Probability distribution
Probability distribution of a random variable-definition of a random variable, discrete and continuous random variable, probability mass function (p.m.f.), probability distribution of a discrete random variable, cumulative probability distribution of a discrete random variable, expected value, variance and standard deviation of a discrete random variable, probability density function (p.d.f.), distribution function of a continuous random variable.
20. Bernoulli trials and Binomial distribution
Definition of Bernoulli trial, conditions for Binomial distribution, binomial distribution (p.m.f.), mean, variance and standard deviation, calculation of probabilities (without proof), Normal distribution : p.d.f., mean, variance and standard deviation, standard normal variable, simple problems (without proof).
Fundamental Of Computer
i. Introduction to computers
ii. Hardware
iii. Software
iv. Types of Computers
v. Concept of files and directories
vi. OS and interfaces
vii. Commonly used commands
viii. Concept of login and logout
ix. File ownership
x. Networking Fundamentals
xi. Client – server
xii. LAN, WAN
xiii. Ftp, telnet, rlogin
xiv. Internet, WWWhtml
xv. Programming in a high-level language
xvi. Algorithms, pseudo codes
Preparation Strategy
Make a proper Time Table
It is very important that you make a time table 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 rote 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.
Prepare Notes
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 basic concepts
Make sure that you revise the basic 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.
Seek guidance
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.
Sample Papers
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.
Mock tests
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
Time management can be learnt through thorough practice and regular test taking. So it is important that you practice it and practice it well.
Negative marking
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.