**JCECE UG 2021 Syllabus**

{tab=JCECE UG Physics Syllabus}

**JCECE UG 2021 Physics Syllabus**

**Physical World and Measurement : ** Physics – scope and excitement; nature of physical laws; physics, technology and society. Need for measurement : Units of measurement; systems of units; Sl units, fundamental and derived units. Length, mass and time measurements; accuracy and precision of measuring instruments; errors in measurement, significant figures. Dimensions of phycical quantities, dimensional analysis and its applications.

**Kinematics : ** Frame of reference. Motion in a straight line : Position-time graph, speed and velocity. Uniform and non-uniform motion, average speed and instantaneous velocity. Uniformly accelerated motion, velocity-time position-time graphs, reactions for uniformly accelerated motion ( graphical treatment ).

Elementary concepts of differentiation and integration fro describing motion. Scalar and vector quantities : position and displacement vectorsgeneral vectors and notation equality of vectors, multiplication of vectors by a real number, addition and subtraction of vectors. Relative velocity. Unit vector; Resolution of a vector in plane-rectangular components. motion in a plane. Cases of uniform circular motion .

**Laws of Motion : ** Intuitive concept of force. Inertia, Newton’s first law of motion; momentum and Newton’s second law of motion; impulse; Newton’s third law of motion. Law of conservation of linear momentum and its applications. Equilibrium of concurrent forces. Static and kinetic friction, laws of friction, rolling friction. Dynamics of uniform circular motion : Centripetal force, examples of circular motion ( vehicle on level circular road, vehicle on banked road ).

**Work, Energy and Power : ** Scalar product of vectors. Work done by a constant force and a variable force; kinetic energy, work-energy theorem, power. Notion of potential energy, potential energy of a spring, conservative forces : conservation of mechanical energy ( kinetic and potential energies ); non-conservative forces : elastic and inelastic collisions in one and two dimensions.

**Motion of System of Particles and Rigid Body : ** Centre of mass of a two-particle system, momentum conversation and center of mass motion. Centre of mass of a rigid body; centre of mass of uniform rod. Vector product of vectors; moment of force, torque, angular momentum, conservation of angular momentum with some examples. Equilibrium of rigid bodies, rigid body rotation and equations of rotational motion, comparison of linear and rotational motions; moment of inertia, radius of gyration. Values of moments of inertia for simple geometrical objects ( on derivation ). Statement of parallel and perpendicular axes theorems and their applications

**Gravitation : ** Keplar’s laws of planetary motion. The universal law of gravitation. Acceleration due to gravity and its variation with altitude and depth. Gravitational potential energy; gravitational potential. Escape velocity. Orbital velocity of a satellite. Geo stationary satellites.

**Properties of Bulk Matter : ** Elastic behaviour, Stress-strain relationship, Hooke’s law, Young’s modulus, bulk modulus, shear, modulus of rigidity. Pressure due to a fluid column; Pascal’s law and its applications ( hydraulic lift and hydraulic brakes ). Effect of gravity of fiuid pressure. Viscosity, Stokes’ law, terminal velocity, Reynold’s number, streamline and turbulent flow. Bernoulli’s theorem and its applications.

**Behaviour of Perfect Gas and Kinetic Theory : ** Equation of state of a perfect gas, work done on compressing a gas. Kinetic theory of gases-assumptions, concept of pressure. Kinetic energy and temperature; rms speed of gas molecules, degrees of freedom, law of equipartition of energy ( statement only ) and application to specific heats of gases; concept of mean free path. Avogadro’s number.

**Oscil llations and Waves : ** Periodic motion-period, frequency, displacements as a function of time. Periodic functions. Simple harmonic motion ( S.H.M ) and its equation; phase, oscillations of a spring restoring force and force constant, energy in S.H.M -kinetic and potential energies; simple pendulum-derivation of expression for its time period free, forced and damped oscillations ( qualitative ideas only ), resonance. Wave motion. Longitudinal and transverse waves, speed of wave motion. displacement relation for a progressive wave. Principle of superposition of waves, reflection of waves, standing waves in strings and organ pipes, fundamental mode and harmonics, Beats, Doppler effect.

Unit I : Electrostatics Electric Charges; Conservation of charge, Coulomb’s law force between two point charges, forces between multiple charges; superposition principle and continuous charge distribution. Electric field, electric field due to a point charge, electric field lines, electric dipole, electric field due to a dipole, torque on a dipole in uniform electric field. Electric flux, statement of Gauss’s theorem and its applications to find field due to infinitely long straight wire, uniformly charged infinite plane sheet and uniformly charged thin spherical shell ( field inside and outside ).

Electric potential, potential difference, electric potential due to a point charge, a dipole and system of charges, equipotential surfaces, electrical potential energy of a system of two point charges and of electric dipole in an electrostatic field. Conductors and insulators, free charges and bound charges inside a conductor, Dielectrics and electric polarisation, capacitors and capacitance, combination of capacitors in series and in parallel, capacitance of a parallel plate capacitor with and without dielectric medium between the plates, energy stored in a capacitor. Van de Graaff generator.

**Current Electricity : ** Electric current, flow of electric charges in a metallic conductor, drift velocity, mobility and their relation with electric current, Ohm’s law, electrical resistance, V-I characteristics ( linear and non-linear ), electrical energy and power, electrical resistivity and conductivity. Cardon resistors, colour code for carbon resistors, series and parallel combinations of resistors, temperature dependence of resistance. Internal resistance of a cell, potential difference and emf of a cell, combination of cells in series and in parallel. Kirchhoff’s laws and simple applications. Wheatstone bridge, metttre bridge. Potentiometer – principle and its applications to measure potential difference and for comparing emf of two cells; measurement of internal resistance of a cell.

**Magnetic Effects of current and Magnetism : ** Concept of magnetic field, Oersted’s experiment. Biot – Savart law and its application to current carrying circular loop. Ampere’s law and its applications to infinitely long straight wire, straight and toroidal solenoids. Force on a moving charge in uniform magnetic and electric fields. Cyclotron. Force on a current-carrying conductor in a uniform magnetic field. Force between two parallel current-carrying conductors-definition of ampere. Torque experienced by a current loog in uniform magnetic field; moving coil galvanometer-its current sensitivity and conversion to ammeter and voltmeter. Current loog as a magnetic dipole and its magnetic dipole moment.

Mangetic dipole moment of a revolving electron. Magnetic field intensity due to magnetic dipole ( bar magnet ) along its axis and perpendicular to its axis. Torque on a magnetic dipole ( bar magnet ) in a uniform magnetic field; bar magnet as an equivalent solenoid, magnetic field lines; Earth’s magnetic field and magnetic elements. Para-dia-and ferro magnetic substances, with examples. Electromagnets and factors affecting their strengths. Permanent magnets.

**Electromagnetic and Alternating Currents : ** Electromagnetic induction; Faraday’s law, induced emf and current; Lenz’s Law, Eddy currents. Self and mutual inductance. Need for displacement current. Alternating currents, peak and rms value of alternating current / voltage; reactance and impedance; LC oscillations ( qualitative treatment only ), LCR series circuit, resonance; power in AC circuits, wattless current. AC generator and transformer.

**Electromagnetic waves : ** Electromagnetic waves and their characteristics ( qualitative ideas only ). Transverse nature of electromagnetic waves. Electromagnetic spectrum ( radio waves, microwaves, infrared, visible, ultraviolet, X-rays, gamma rays ) including elementary facts about their uses.

**Optics : ** Reflection of light, spherical mirrors, mirror formula. Refraction of light, total internal reflection an its applications, optical fibres, refraction at spherical surfaces, lenses, thin lens formula, lens-maker’s formula Magnification, power of a lens, combination of thin lenses in contact. Refraction and dispersion of light through a prism. Scattering of light – blue colour of the sky and reddish appearance of the sun at sunrise and sunset. Optical instruments : Human eye, image formation and accommodation, correction of eye defects ( myopia, hypermetropia, presbyopia and astigmatism ) using lenses. Microscopes and astronomical telescopes ( reflecting and refracting ) and their magnifying powers.

Wave optics : wave front and Huygens’ principle, reflection and refraction of plane wave at a plane surface using wave fronts. Proof of laws of reflection and refraction using Huygens’ principle. Interference, young’s double slit experiment and expression for fringe width, coherent sources and sustained interference of light. Diffraction due to a single slit, width of central maximum. Resolving power of microscopes and astronomical telescopes. Polarisation, plane polarised light; Brewster’s law, uses of plane polarised light and Polaroids.

**Dual Nature of Matter and Radiation : ** Dual nature of radiation. Photoelectric effect, Hertz and Lenard’s observational; Einstein’s photoelectric equation particle nature of light. Matter waves-wave nature of particles, de Broglie relation. Davisson- Germer experiment.

**Atoms & Nuclei : ** Alpha-pariticle scattering experiment, Rutherford’s model of atom; Bohr model, energy levels, hydrogen spectrum. Composition and size of nucleus, atomic masses, isotopes, isobars; isptones. Radioactivity alpha, beta and gamme particles / rays and their properties; radioactive decay law. Mass-energy relation, mass defect; binding energy per nucleon and its variation with mass number nuclear fission and fusion.

**Electronic Devices : ** Semiconductors; semiconductor diode – I – V characteristics in forward and reverse bias, diode as a rectifier; I – V characteristics of LED, photodiode, solar cell, and zener diode; zener diode as a voltage regulator Junction transistor, transistor action, characteristics of a transistor; transistor as an amplifier ( common emitter configuration ) and oscillator. Logic gates ( OR, AND, NOT, NAND, and NOR ). Transistor as a switch.

**Communication Systems : ** Elements of a communication system ( block diagram only ); bandwidth of signals ( speech, TV and digital data ); bandwidth of transmission medium. Propagation of electromagnetic waves in the atmosphere, sky and space wave

propagation. Need for modulation. Production and detection of an amplitued-modulated wave.

{tab=JCECE UG Chemistry Syllabus}

**JCECE UG 2021 Chemistry Syllabus**

**Some Basic Concepts of Chemistry : ** General Introduction : Importance and scope of chemistry. Historical approach to particulate nature of matter, laws of chemical combination, Dalton’s atomic theory : theory : concept of elements, atoms and molecules. Atomic and molecular masses. Mole concept and molar mass : percentage composition, empirical and molecular formula; chemical reactions, stoichiometry and calculations based on stoichiometry.

**Structure of Atom : ** Discovery of electron, proton and neutron, atomic number, isotopes and isobars. Thomson’s model and its limitations, Rutherford’s model and its limitations. Borh’s model and its limitations, concept of shells and subshells, dual nature of matter and light, De Broglies relationship, Heisenberg uncertainty principle, concept of orbitals, quantum numbers, shapes of s, p, and d orbitals, rules for filling electrons in orbitals-Aufbau principle, Pauli exclusion principle and Hund’s rule, electronic configuration of atoms, stability of half filled and completely filled orbitals.

**Classification of Elements and Periodicity in Properties : ** Significance and classification, brief history of the development of periodic table, modern periodic law and the present form of periodic table, periodic trends in properties of elements-atomic radii, ionic radii, inert gas radii. Ionization enthalpy, electron gain enthalpy, electro negativity, valence.

**Chemical Bonding and Molecular Structure : ** Valence electrons, ionic bond, covalent bond : bond parameters. Lewis structure, polar character of covalent bond, covalent character of ionic bond, valence bond theory, resonance, geometry of covalent molecules, VSEPR theory, concept of hybridization, involving s, p orbitals and shapes of some simple molecules, molecular orbital; theory of homo nuclear diatomic molecules ( qualitative idea only ), hydrogen bond.

**States of Matter : ** gases and liquids : Three states of matter. Intermolecular interactions, type of bonding, melting and boiling points. Role of gas laws in elucidating the concept of the molecule, Boyle’s law, Charles law, Gay Lussac’s law, Avogadro’s law, ldeal behaviour, empirical derivation of gas equation, Avogadro’s number. Ideal gas equation. Derivation from ideal behaviour, liquefaction of gases, critical temperature. Liquid State-Vapour pressure, viscosity and surface tension ( qualitative idea only, no mathematical derivations. )

**Thermodynamics : ** Concepts of System, types of systems, surroundings. Work, heat, energy, extensive and intensive properties, state functions. First law of thermodynamics – internal energy and enthalpy, heat capacity and specific heat, measurement of ÎU and ÎH, Hess’s law of constant heat summation, enthalpy of : bond dissociation, combustion, formation, atomization, sublimation. Phase transition, ionization, and dilution. Introduction of entropy as a state function, free energy change for spontaneous and non-spontaneous process, equilibrium.

**Equilibrium : ** Equilibrium in physical and chemical processes, dynamic nature e of equilibrium, law of mass action, equilibrium constant, factors affecting equilibrium – Le Chatelier’s principle; ionic equilibrium – ionization of acids and bases, strong and weak electrolytes, degree of ionization, concept of pH. Hydrolysis of salts ( elementary idea ). Buffer solutions. Solubility product, common ion effect ( with illustrative examples ).

**Redox Reactions : ** Concept of oxidation and reduction, redox reactions, oxidation number, balancing redox reactions, applications of redox reactions.

**Hydrogen : ** Position of hydrogen in periodic table, occurrence, isotopes, preparation, properties and uses of hydrogen; hydrides – ionic, covalent and interstitial, physical and chemical properties of water, heavy water, hydrogen peroxide-preparation, reactions and structure; hydrogen as a fuel

**S-Block Elements ( Alkali and Alkaline earth metals ) Group 1 and Group 2 elements : ** General introduction, electronic configuration, occurrence, anomalous properties of the first element of each group, diagonal relationship, trends in the variation of properties ( such as ionization enthalpy, atomic and ionic radii ), trends in chemical reactivity with oxygen, water, hydrogen and halogens; uses.

**Preparation and properties of some important compounds : ** Sodium carbonate, sodium chloride, sodium hydroxide and sodium hydrogen carbonate, biological importance of sodium and potassium. CaO, CaCO3 and industrial use of lime and limestone, biological importance of Mg and Ca

**Some P-Block Elements : General introduction to p-Block Elements Group 13 elements : ** General introduction, electronic configuration, occurrence, Variation of properties, oxidation states, trends in chemical reactivity, anomalous properties of first element of the group; Boron-physical and chemical properties, some important compounds : borax, boric acids, boron hydrides. Aluminium : uses, reactions with acids and alkalies. Group 14 elements : General introduction, electronic configuration, occurrence, variation of properties, oxidation states, trends in chemical reactivity, anomalous behaviour of first element, Carbon – catenation, allotropic forms, physical and chemical properties; uses of some important compounds : oxides. Important compounds of silicon and a few uses : silicon tetrachloride, silicones, silicates and zeolites.

Organic Chemistry – Some Basic Principles and Techniques General introduction method, qualitative and quantitative analysis, classification and IUPAC nomenclature of organic compounds Electronic displacements in a covalent bond : free radicals, carbocations, carbanions; heterophiles and nucleophiles, types of organic reactions.

**Hydrocarbons : Classification of hydrocarbons : ** Alkanes-Nomenclature, isomerism, conformations ( ethane only ), physical properties, chemical reactions including free radical mechanism or halogenation, combustion and pyrolysis. Alkenes-Nomenclature, structure of double bond ( ethene ) geometrical isomerism, physical properties, methods of preparation, chemical reactions : addition of hydrogen, halogen, water, hydrogen halides ( Markovnikov’s addition and peroxide effect ), ozonolysis, oxidation mechanism of electrophilic addition.

Alkynes-Nomenclature, structure of triple bond ( ethyne ), physical properties, Methods of preparation, chemical reactions : acidic character of alkynes, addition reaction of -hydrogen, halogens, hydrogen halides and water. Aromatic hydrocarbons : Introduction, IUPAC nomenclature; Benzene : resonance aromaticity; chemical properties : mechanism of electrophilic substitution. nitration sulphonation, halogenation, Friedel Craft’s alkylation and acylation : directive influence of functional group in mono-substituted benzene; carcinogenicity and toxicity.

**Environmental Chemistry : ** Environmental pollution – air, water and soil pollution, chemical reactions in atmosphere, smog, major atmospheric pollutants; acid rain, ozone and its reactions effect of depletion of ozone layer, greenhouse effect and global warming – pollution due to industrial wastes; green chemistry as an alternative tool for reducing pollution, strategy for control of environmental pollution.

**Solid State : ** Classification of solids based on different binding forces : molecular, ionic, covalent and metallic solids, amprophous and crystalline solids ( elementary idea ), unit cell in two dimensional and three dimensional lattices, calculation of density of unit cell, packing in solids, voids, number of atoms per unit cell in a cubic unit cell, point defects, electrical and magnetic properties.

**Solutions : ** Types of solutions, expression of concentration of solutions of solids in liquids, solubility of gases in liquids, solid solutions, colligative properties -relative lowering of vapour pressure, elevation of Boiling Point, depression of freezing point, osmotic pressure, determination of molecular masses using colligative properties, abnormal molecular mass.

**Electrochemistry : ** Redox reactions, conductance in electrolytic solutions, specific and molar conductivity variations of conductivity with concentration, Kohlrausch’s Law, electrolysis and laws of electrolysis ( elementary idea ), dry cell-electrolytic cells and Galvanic cells; lead accumulator, EMF of a cell, standard electrode potential, Nernst equation and its application to chemical cells, fuel cells; corrosion.

**Chemical Kinetics : ** Rate of a reaction ( average and instantaneous ), factors affecting rates of reaction; concentration, temperature, catalyst, order and molecularity of a reaction, rate law and specific rate constant, integrated rate equations and half life ( only for zero and first order reactions ); concept of collision theory ( elementary idea, no mathematical treatment )

**Surface Chemistry : ** Adsorption – physisorption and chemisorption; factors affecting adsorption of gases on solids; catalysis : homogenous and heterogeneous, activity and selectivily : enzyme catalysis; colloidal state : Distinction between true solutions, colloids and suspensions; lyophilic, lyophobic, multimolecular and macromolecular clloids; properties of colloids; Tyndall effect, Brownian movement, electrophoresis, coagulation; emulsion – typesof emulsions

**General Principles and Processes of Isolation of Elements : ** Principles and methods of extraction – concentration, oxidation, reduction electrolytic method and refining; occurrence and principles of extraction of aluminium, copper, zinc and lron….

**P-Block Elements : Group 15 elements : ** General introduction, electronic configuration, occurrence, oxidation states, trends in physical and chemical properties; nitrogen – perparation, properties and uses; compounds of nitrogen preparation and properties of ammonia and nitric acid, oxides of nitrogen ( structure only ) Phosphorous-allotropic forms; compounds of phosphorous : preparation and properties of phosphine, halides ( PCI_{3}, PCI_{5} ) and oxoacids ( elementary idea only )

**Group 16 elements : ** General introduction, electronic configuration, oxidation states, occurrence, trends in physical and chemicla properties, dioxygen : preparation, properties and uses; simple oxides; Ozone. Sulphurallotropic forms; compounds of sulphur : preparation, properties and uses of sulphur dioxide; sulphuric acid : industrial process of manufacture, properties and uses, oxoacids of sulphur ( structures only ).

**Group 17 elements : ** General introduction, electronic configuration, oxidation states, occurrence, trends in physical and chemical properties; compounds of halogens : preparation, properties and uses of chlorine and hydrochloric aoid, interhalogen compounds, oxoacids of halogens ( structures only )

**Group 18 elements : ** General introduction, electronic configuration. Occurrence, trends in physical and chemical properties, uses.

**D and F Block Elements : ** General introduction, electronic configuration, occurrence and characteristics of transition metals, general trends in properties of the first row transition metals – metallic character, ionization enthalpy, oxidation states, ionic radii, colour catalytic property, magnetic properties, interstitial compounds, alloy formation. Preparation and properties of K_{2}Cr_{2}O_{7} and KMnO_{4}

**Lanthanoids** – electronic configuration, oxidation states, chemical reactivity and lanthanoid contraction.

**Actinoids** – Electronic configuration, oxidation states,

**Coordination Compounds : ** Coordination compounds – Introduction, ligands, coordination number colour, magnetic properties and shapes. IUPAC nomenclature of mononuclear coordination compounds. bonding; isomerism, importance of coordination compounds ( in qualitative analysis, extraction of metals and biological systems ).

**Haloalkanes and Haloarenes. Haloalkanes : ** Nomenclature, nature of C-X bond, physical and chemical properties mechanism of substitution reactions.

**Haloarenes : ** Nature of C-X bond, substitution reactions ( direvtive influence of halogen for monosubstituted compounds only ) Uses and environmental effects of – dichloromethane, trichloromethane, tetrachloromethane, iodoform, freons, DDT,

**Alcohols, Phenols and Ethers : Ahenols : ** Nomenclature, methods of preparation, physical and chemical properties ( of primary alcohols only ); identification of primary, secondary and tertiary alcohols; mechanism of dehydration, uses of methanol and ethanol. Phenols : Nomenclature, methods of preparation, physical and chemical properties, acidic nature of phenol, electrophillic substitution reactions, uses of phenols.

**Ethers : ** Nomenclature, methods of preparation, physical and chemical properties, uses.

**Aldehydes, Ketones and Carboxylic Acids : Aldehydes and Ketones : ** Nomenclature, nature of carbonyl group methods of preparation, physical and chemical properties mechanism of nucleophilic addition, reactivity of alpha hydrogen in aldehydes; uses.

**Caboxylic Acids : ** Nomenclature, acidic nature, methods. of preparation, physical and chemical properties; uses. Organic compounds containing Nitrogen

**Amines : ** Namenclature, classification, structure, methods of preparation, physical and chemical properties, uses, identification of primary, secondary and tertiary amines. Diazonium salts : Preparation, chemical reactions and importance in synthetic organic chemistry.

**Biomolecules Carbohydrates** – Classification ( aldoses and ketoses ), monosaccahrides ( glucose and fructose ), oligosaccharides ( sucrose, lactose, maltose ), polysaccharides ( starch, cellulose glycogen ), importance.

**Proteins** – Elementary idea of ex- amino acids, peptide bond, polypeptides proteins, primary structure, secondary structure, tertiary structure and quaternary structure ( qualitative idea only ), denaturation of proteins, enzymes. Vitamins – Classification and functions.

**Nucleic Acids** : DNA & RNA.

**Polymers : ** Classification – natural and synthetic, methods of polymerization ( addition and condensation ), copolymerization. Some important polymers : natural and synthetic like polythene, nylon, polyesters, bakelite, rubber.

**Chemistry in Everyday life : **

1. Chemicals in medicines – analgesics, tranquilizers, antiseptics, disinfectants, antimicrobials, antifertility dmgs, antibiotics, antacids, antihistamines.

2. Chemicals in food – preservatives, artificial sweetening agents.

3. Cleansing agents – soaps and detergents, cleansing action.

{tab=JCECE UG Mathematics Syllabus}

**JCECE UG Mathematics Syllabus 2017**

**Sets and Function**

**1. Sets : ** Sets and their representations. Empty set. Finite & Infinite sets. Equal sets, Subsets. Susets of the set of real numbers especially intervals ( with notations ). Power set. Universal set. Venn diagrams. Union and Intersection of sets. Difference of sets. Complement of a set.

**2. Relations & Functions : ** Ordered pairs, Cartesian product of sets. Number of elements in the cartesian product of two finite sets. Cartesian product of the reals with itself ( upto R x R x R ). Definition of relation, pictorial diagrams, domain, codomain and range of a relation, Function as a special kind of relation from one set to another. Pictorial representation of function, domain and range of these functions, constant, identity, polynomial, rational, modulus, signum and greatest integer functions with their graphs. Sum, difference, product and quotients of functions.

**3. Trigonometric Functions : ** Positive and negative angles, Measuring angles in radians & in degrees and conversion from one measure to another. Definition of trigonometric functions with the help of unit circle, Truth of the identity sin^{2} x+cos^{2}x= 1, for all x. Signs of trigonometric functions and sketch of their graphs, Expressing sin ( x+y ) and cos ( x+y ) in terms of sin x, sin y, cos x & cos y.

**Algebra**

**1. Principle of Mathematical Induction : ** Processes of the proof by induction, motivating the application of the method by looking at natural numbers as the lest inductivesubset of realnumbers. The principle of mathematical induction and simpleapplications.

**2. Complex Numbers and Quardratic Equations : ** Need for complex numbers, especially – 1, to be motivated by inability to solve every quadratic equation, Brief description of algebraic properties of complex numbers. Argand plane and polar representation of complex numbers. Statement of Fundamental Theorem of Algebra, solution of quadratic equations in the complex number system.

**3. Linear Inequalities : ** Linear inequalities. Algebraic solutions of linear inequalities in one varibale and their representation on the number line. Graphical solution of linear inequalities in two variables, solution of system of linear inequalities in two varibales-graphically.

**4. Permutations & Theorem : ** Fundamental principle counting. Factorial n. permutations and combinations, derivation of formula and their connections, simple applications.

**5. Binomial Theorem : ** History, statement and proof of the binomial theorem for positive integral indices. Pascal’s triangle, general and middle term in binomial expansion, simple applications.

**6. Sequence and Series : ** Sequence and Series. Arithmetic progression ( A.P. ) arithmetic mean ( A.M. ) Geometric progression ( G.P. ) general term of a G.P. sum of n terms of a G.P. geometric mean ( G.M. ) relation between A.M. and G.M. sum to n terms of the special series. 3n, 3n^{2} and 3n^{3}

**Coordinate Geometry**

**1. Straight Lines : ** Briet recall of 2D from earlier classes. Slope of a line and angle between two lines. Various forms of equations of a line : parallel to axes, point-slope form, slopeintercept form, two-point from, intercepts form and normal form. General equation of a line. Distance of a point from a line.

**2. Conic Section : ** Sections of cone : circles, ellipse, parabola, hyperbola, a point, a straight line and pair of intersecting lines as a degenerated case of a conic section. Standard equations and simple properties of parabola, ellipse and hyperbola. Standard equation of a circle

**3. Introduction to Three-dimensional Geometry : ** Coordinate axes and coordinate planes in three dimensions. Coordinates of a point. Distance between two points and section formula.

**Calculus
**

**1. Limits and Derivatives : ** Derivative introduced as rate of change both as that of distance function and geometrically, intuitive idea of limit. Definition of derivative, relate it slope of tangent of the curve, derivative of sum, difference, product and quotient of functions. Derivatives of polynomial and trigonometric functions.

**Mathematical Reasoning**

**1. Mathematical Reasoning : ** Mathematically acceptable statements. Connecting words / phrases – consolidating the understanding of “if and only if ( necessary and sufficient ) condition”, “implies”, “and / or”, “implied by”, “and”, “or”, “there exists” and their use through variety of examples related to real life and Mathematics. Validating the statements involving the connecting words-difference between contradiction, converse and contapositive.

**Statistics & Probability**

**1. Statistics : ** Measure of dispersion; mean deviation, variance and standard deviation of ungrouped / grouped data. Analysis of frequency distributions with equal means but different variances.

**2. Probability : ** Random experiments : outcomes, sample spaces ( set representation ). Events : occurrence of events, ‘not’, ‘and ‘or’ events, exhaustive events, mutually exc lusive events, Axiomatic ( set theoretic ) probability, connections with the theories of earlier classes. Probability of an event, probability of ‘not’, ‘and’ & ‘or’ events.

**Relations and Functions**

**1. Relations and Functions : ** Types of relations : reflexive, symmetric, transitive and equivalence relations. One to one and onto functions, composite functions, inverse of a function. Binary operations.’

**2. Inverse Trigonometric Functions : ** Definition, range, domaia, principal value branches. Graphs of inverse trigonometric functions. Elementary properties of inverse trgonometric functions

**Algebra**

**1. Matrices : ** Concept, notation, order, equality, types of matrices, Zero matrix, transpose of a matrix, symmetric and skew symmetric matrices. Addition, multiplication and scalar multiplication of matrices, simple properties of addition, multiplication and scalar multiplication. Noncommutativity of multiplication of martices and existence of non-zero matrices whose product is the zero matrix ( restrict to square matrices of order 2 ). Concept of elementary row and column operations. Invertible matrices and proof of the uniqueness of inverse, if it exists ( Here all matrices will have real entries ).

**2. Determinants : ** Determinant of a square matrix ( up to 3 x 3 matrices ), properties of determinants, minors, cofactors and applications of determinants in finding the area of a triangle. Adjoint and inerse of a square matrix. Consistency, inconsistency and number of solutions of system of linear equations by examples, solving system of linear equations in two or three variables( having unique solution ) using inverse of a matrix

**Calculus**

**1. Continuity and Differentiability : ** Continuity and differentiability, derivative of composite functions, chain rule, derivatives of inverse trigonometric functions, derivative of implicit function. Concept of exponential and logarithmic functions and their derivative. Logarithmic differentiation. Derivative of functions expressed in parametric forms. Second order derivatives. Rolle’s and Lagranges mean Value Theorems ( without proof ) and their geometric intepretations.

**2. Applications of Derivatives : ** Applications of derivatives : rate of change, increasing / decreasing functions, tangents & normals, approximation, maxima and minima a ( first derivative test motivated geometrically and second derivative test given as a provable tool ). Simple problems ( that illustrate basic principles and understanding of the subject as well as real-life situations. )

**3. Integrals : ** Integration as inverse process of differntiation. Integration of a variety of functions by substitution, by partial fractions and by parts, only simple integrals of the type.Definite integrals as a limit of a sum, Fundamental Theorem of Calculus ( without proof ). Basic properties of definite integrals and evaluation of definite integrals.

**4. Applications of the Integrals : ** Applications in finding the area under simple curves, especially lines, areas of circles / parabolas / ellipses ( in standard form only, ) area between the two above said curves ( the region should be clearly indentifiable ).

**5. Differential Equations : ** Definition, order and degree, general and particular solutions of a differential equation. Formation of differential equation whose general solution is given. Solution of differential equations by method of separation of variables, homogeneous differential equations of first order first degree.

**Vectors and Three Dimensional Geometry**

**1. Vectors : ** Vectors and scalars, magnitude and direction of a vector. Direction consines / ratios of vectors. Types of vectors ( equal, unit zero, parallel and collinear vectors ), position vector of a point, negative of a vector, components of a vector, addition of vectors, multiplication of a vector by a scalar, position vector of a point dividing a line segment in a given ratio. Scalar ( dot ) product of vecters, projection of a vector on a line. Vector ( cross ) product of vectors.

**2. three – dimensional Geometry : ** Direction consines / ratios of a line joining two points. Cartesian and vector equation of a line, coplanar and skew lines, shortest distance between two lines, Cartesian and vector equation of a plane. Angle between ( i ) two lines, ( ii ) two planes, ( iii ) a line and a plane, Distance of a point from a plane.

**Linear Programming**

**1. Linear Programming : ** Introduction, definition of related terminology such as constraints, objective function, optimization, different types of linear programming ( L.P. ) problems, mathematical formulation of L.P. problems, graphical method of solution for problems in two variables, feasible and infeasible region, feasible and infeasible solutions, optimal feasible solutions ( up to three nontrivial constraints ).

**Probability**

**1. Probability : ** Multiplication theorem on probability. Conditional probability, independent events, total probability, Bayes’s theorem, Random variable and its probability distribution, mean and variance of haphazard variable. Repeated independent ( Bernoulli ) trials and Binomial distribution.

{tab=JCECE UG Biology Syllabus}

**JCECE UG 2017 Biology Syllabus**

**I. Diversity in Living World : ** Diversity of living organisms Classification of the living organisms ( five kingdom classification, major groups and principles of classification within each kingdom. ) Systematic and binomial System of nomenclature Salient features of animal ( non chordates up to phylum level and chordates up to class level ) and plant ( major groups; Angiospems up to subclass ) classification. Botanical gardens, herbara, Zoological parks and museums

**ll Structural Organization in Animals and Plants : ** Tissues in animals and plants. Morphology, anatomy and functions of different parts of flowering plants : Root, stem, leaf, inflorescence, flower, fruit and seed. Morphology, anatormy and functions of different systems of an annelid ( earthworm ), an insect ( cockroach ) and an amphibian ( frog ).

**lll Cell : Structure and Function : **Cell : cell wall, cell membrance and cell organelles’ ( plastids, mitochondria, endoplasmic reticulum, Golgi bodies / dictyosomes, ribosomes, lysosomes, vacuoles, Centrioles ) and nuclear organization. Mitosis, meiosis, cell cycle. Basic chemical constituents of living bodies. Structure and functions of carbohydrates, proteins, lipids and nucleic acids. Enzymes : types, properties and function.

**IV Plant Physiology : ** Movement of water, food, nutrients and gasses, Plants and Water Mineral nutrition. Respiration, Photosynthesis, Plant growth and development.

**V Human Physiology : ** Digestion and absorption. Dreathing and respiration. Body fluids and circulation. Excretory products and elimination. Locomotion and movement. Control and coordination.

**l. Sexual Reproduction : ** Pollination and fertilization in flowering plants. Development of seeds and fruits. Human reproduction : reproductive system in male and female, menstrual cycle. Production of gametes, fertilization, implantation, embryo development, pregnancy and prarturation. Reproductive health – birth control, contraception and sexually transmitted diseases.

**ll Genetics and evolution : ** Mendelian inheritance. Chromosome theory of inheritance, deviations from Mendelian ratio ( gene interaction – Incomplete dominance, co-dominance, complementary genes, multiple alleles ). Sex determination in human beings : XX, XY Linkage and crossing over. Inheritance pattern of harmophilia and blood groups in human beings. DNA : replication, transcription, translation. Gene expression and regulation. Genome and Human Genome Project. DNA fingerprinting. Evolution : Theories and evidences.

**III. Biology and Human Welfare : ** Animal husbandry. Basic concepts of immunology, vaccines. Pathogens, Parasites. Plant breeding, tissue culture, food production.Microbes in household food processing, industrial production, sewage treatment and energy generation. Cancer and AIDS. Adolescence and drug / alcohol abuse.

**IV. Biotechnology and its Applications : ** Recombinant DNA technology. Applications in Health, Agriculture and Industry Genetically modified ( GM ) organisms; biosafety issues. Insulin and Bt cotton

**V. Ecology & Environment : ** Ecosystems : components, types and energy flow. Species, population and community. Ecological adaptations. Centres of diversity and conservation of biodiversity, National parks and sanctuaries. Environmental issues.

{/tabs}

#### JEE Main

Application Form Submission 16 Dec 2020 to 16 Jan 2021.