What you will learn:

MATHEMATICS:

1)UNIT 1: SETS, RELATIONS AND FUNCTIONS:

Sets and their representation; Union, intersection and complement of sets andtheir algebraic properties; Power set; Relations, type of relations, equivalence relations, functions; one-one, into and onto functions, the composition of functions.

2)UNIT 2: COMPLEX NUMBERS AND QUADRATIC EQUATIONS:

Complex numbers as ordered pairs of reals, Representation of complex numbers in the form a + ib and their representation in a plane, Argand diagram, algebra of complex numbers, modulus and argument (or amplitude) of a complex number, Quadratic equations in real and complex number systems and their solutions; Relations between roots and coefficients, nature of roots, the formation of quadratic equations with given roots.

3)UNIT3: MATRICES AND DETERMINANTS:

Matrices, algebra of matrices, type of matrices, determinants and matrices of order two and three, evaluation of determinants, area of triangles usingdeterminants; Adjoint and inverse of a square matrix; Test of consistency andsolution of simultaneous linear equations in two or three variables using matrices.

4)UNIT 4: PERMUTATIONS AND COMBINATIONS:

The fundamental principle of counting, permutations and combinations; Meaningof P(n, r) and C(n, r). Simple applications.

5)UNIT 5: BINOMIAL THEOREM AND ITS SIMPLE APPLICATIONS:

Binomial theorem for a positive integral index, general term and middle termandsimple applications.

6)UNIT 6: SEQUENCE AND SERIES:

Arithmetic and Geometric progressions, insertion of arithmetic, geometric means between two given numbers, Relation between A.M and G.M.

7)UNIT 7: LIMIT, CONTINUITY AND DIFFERENTIABILITY:

Real–valued functions, algebra of functions; polynomial, rational, trigonometric, logarithmic and exponential functions; inverse functions. Graphs of simple functions. Limits, continuity and differentiability. Differentiation of the sum, difference, product and quotient of two functions. Differentiation of trigonometric, inverse trigonometric, logarithmic, exponential, composite andimplicit functions; derivatives of order upto two, Applications of derivatives: Rate of change of quantities, monotonic-Increasing and decreasing functions, Maxima and minima of functions of one variable.

8)UNIT 8: INTEGRAL CALCULAS:

Integral as an anti-derivative, Fundamental integrals involving algebraic, trigonometric, exponential and logarithmic functions. Integration by substitution, by parts and by partial fractions. Integration using trigonometric identities. Evaluation of simple integrals of the type

 The fundamental theorem of calculus, properties of definite integrals. Evaluation of definite integrals, determining areas of the regions bounded bysimple curves by simple curves in standard forms.

9)UNIT 9: DIFFRENTIAL EQUATIONS :

Ordinary differential equations, their order and degree, the solution of differential equation by the method of separation of variables, solution of a homogeneous and linear differential equation.

10)UNIT 10: CO-ORDINATE GEOMETRY :

Cartesian system of rectangular coordinates in a plane, distance formula, sections formula, locus and its equation, the slope of a line, parallel and perpendicular lines, intercepts of a line on the co-ordinate axis. Straight line: Various forms of equations of a line, intersection of lines, angles between two lines, conditions for concurrence of three lines, the distance of a point form a line, co-ordinate of the centroid, orthocentre and circumcentre of a triangle. Circle, conic sections: A standard form of equations of a circle, the general form of the equation of a circle, its radius and centre, equation of a circle whenthe endpoints of a diameter are given, points of intersection of a line and a circle with the centre at the origin and sections of conics, equations of conic sections (parabola, ellipse and hyperbola) in standard forms.

11)UNIT 11: THREE DIMENSIONAL GEOMETRY :

Coordinates of a point in space, the distance between two points, sectionformula, direction ratios and direction cosines and the angle between twointersecting lines. Equation of a line; Skew lines, the shortest distance betweenthem and its equation.

12)UNIT 12: VECTOR ALGEBRA :

Vectors and scalars, the addition of vectors, components of a vector in twodimensions and three-dimensional spaces, scalar and vector products.

13)UNIT 13: STATISTICS AND PROBABILITY :

Measures of dispersion; calculation of mean, median, mode of grouped andungrouped data, calculation of standard deviation, variance and meandeviation for grouped and ungrouped data. Probability: Probability of an event, addition and multiplication theorems of probability, Baye’s theorem, probabilitydistribution of a random variable.

14)UNIT 14: TRIGONOMETRY :

Trigonometrical identities and trigonometrical functions, inverse trigonometrical functions their properties

PHYSICS:

1)UNIT 1: Units and Measurements

Units of measurements, System of units, SI Units, fundamental and derived units, least count, significant figures, Errors in measurements. Dimensions of Physics quantities, dimensional analysis and its applications.

2)UNIT 2: Kinematics

The frame of reference, motion in a straight line, speed and velocity, uniformand non-uniform motion, average speed and instantaneous velocity, uniformlyaccelerated motion, velocity-time, position-time graph, relations for uniformlyaccelerated motion, relative velocity. Motion in a plane, projectile motion, uniform circular motion.

3)UNIT 3: Laws of Motion

Force and inertia, Newton’s first law of motion, momentum, Newton’s secondLaw 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 and its applications: vehicle on a level circular road, vehicle on a banked road.

4)UNIT 4: Work, Energy and Power

Work done by a constant force and a variable force, kinetic and potential energies, work-energy theorem, power. The potential energy of a spring, conservation of mechanical energy, conservative and non- conservative forces, motion in a vertical circle. Elastic and inelastic collisions in one and two dimensions

5)UNIT 5: Rotational Motion

Centre of mass of a two-particle system, centre of mass of a rigid body. Basic concepts of rotational motion, moment of a force, torque, angular momentum, conservation of angular momentum and its applications. The moment of inertia, the radius of gyration, values of moments of inertia for simple geometrical objects, parallel and perpendicular axes theorems and their applications. Equilibrium of rigid bodies, rigid body rotation and equations of rotational motion, comparison of linear and rotational motions.

6)UNIT 6: Gravitation

The universal law of gravitation. Acceleration due to gravity and its variationwith altitude and depth. Kepler’slaw of planetary motion. Gravitational potential energy, gravitational potential. Escape velocity, motion of a satellite, orbital velocity, time period and energy of satellite.

7)UNIT 7: Properties of Solids and Liquids

Elastic behaviour, stress-strain relationship, Hooke’s Law, Young’s modulus, bulk modulus and modulus of rigidity.

Pressure due to a fluid column, Pascal’s law and its applications, effect of gravityon fluid pressure, viscosity, Stoke’s law, terminal velocity, streamline andturbulent flow, critical velocity, Bernoulli’s principle and its applications. Surface energy and surface tension, angle of contact, excess of pressure across a curved surface, application of surface tension: drops, bubbles and capillary rise. Heat, temperature, thermal expansion, specific heat capacity, calorimetry, change of state, latent heat. Heat transfer: conduction, convection and radiation.

8)UNIT 8: Thermodynamics

Thermal equilibrium and the concept of temperature, zeroth lawof thermodynamics, heat, work and internal energy. The first lawof thermodynamics, isothermal and adiabatic processes. The second lawof thermodynamics: reversible and irreversible processes.

9)UNIT 9: Kinetic Theory of Gases

Equation of state of a perfect gas, work done on compressing a gas, kinetic theory of gases: assumptions, the concept of pressure, kinetic interpretation of temperature, RMS speed of gas molecules, degrees of freedom, lawof equipartition of energy and applications to specific heat capacities of gases, mean free path, Avogadro’s number.

10)UNIT 10: Oscillations and Waves

Oscillations and periodic motion: time period, frequency, displacement 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: derivationof expression for its time period. Wave motion, longitudinal and transverse waves, speed of the travelling wave, 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.

11)UNIT 11: Electrostatics

Electric charges: conservation of charge, Coulomb’s law forces between twopoint charges, forces between multiple charges, superposition principle andcontinuous 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 a uniformelectric field. Electric flux, Gauss’s law and its applications to find field due to infinitely longuniformly charged straight wire, uniformly charged infinite plane sheet anduniformly charged thin spherical shell. Electric potential and its calculation for a point charge, electric dipole andsystem of charges, potential difference, equipotential surfaces, electrical potential energy of a system of two point charges and of electric dipole in anelectrostatic field. Conductors and insulators, dielectrics and electric polarization, capacitors andcapacitance, the combination of capacitors in series and parallel and capacitance of a parallel plate capacitor with and without dielectric medium between the plates, energy stored in a capacitor.

12)UNIT 12: Current Electricity

Electric current: drift velocity, mobility and their relation with electric current, Ohm’s law, electrical resistance, I-V characteristics of Ohmic and non-ohmic conductors, electrical energy and power, electrical resistivity and conductivity, series and parallel combinations of resistors, temperature dependence of resistance. Internal resistance, potential difference and emf of a cell, a combination of cells in series and parallel. Kirchhoff’s laws and their applications, Wheatstone bridge, Metre Bridge.

13)UNIT 13: Magnetic Effects of Current and Magnetism

Biot – Savart law and its application to the current carrying circular loop, Ampere’s law and its applications to infinitely long current carrying straight wire and solenoid. Force on a moving charge in uniform magnetic and electric fields, force on a current-carrying conductor in a uniform magnetic field, the force between twoparallel currents carrying conductors-definition of ampere, torque experiencedby a current loop in a uniform magnetic field: Moving coil galvanometer, its sensitivity and conversion to ammeter and voltmeter. Current loop as a magnetic dipole and its magnetic dipole moment, bar magnet as an equivalent solenoid, magnetic field lines, magnetic field due to a magnetic dipole (bar magnet) along its axis and perpendicular to its axis, torque on a magnetic dipole in a uniform magnetic field, para-, dia- and ferromagnetic substances with examples, the effect of temperature on magnetic properties

14)UNIT 14: Electromagnetic Induction and Alternating Currents

Electromagnetic induction: Faraday’s law, induced emf and current, Lenz’s law, eddy currents, self and mutual inductance. Alternating currents, peak and RMS value of alternating current/voltage, reactance and impedance, LCR series circuit, resonance, power in AC circuits, wattless current, AC generator and transformer.

15)UNIT 15: Electromagnetic Waves

Displacement current, electromagnetic waves and their characteristics, transverse nature of electromagnetic waves, electromagnetic spectrum(radiowaves, microwaves, infrared, visible, ultraviolet, X-rays, Gamma rays), applications of electromagnetic waves.

16)UNIT 16: Optics

Reflection of light, spherical mirrors, mirror formula. Refraction of light at plane and spherical surfaces, thin lens formula and lens maker formula, total internal reflection and its applications, magnification, power of a lens, combination of thin lenses in contact, refraction of light through a prism, microscope and astronomical telescope (reflecting and refracting ) and their magnifying powers. Wave optics: wavefront and Huygens ‘Principle, laws of reflection andrefraction using Huygens principle. Interference: Young’s double-slit experiment and expression for fringe width, coherent sources and sustainedinterference of light. Diffraction due to a single slit, width of central maximum. Polarization: plane-polarized light, Brewster’s law, uses of plane- polarizedlight and Polaroid

17)UNIT 17: Dual Nature of Matter and Radiation

Dual nature of radiation, Photoelectric effect, Hertz and Lenard’s observations, Einstein’s photoelectric equation, particle nature of light. Matter waves: wave nature of particle, de- Broglie relation.

18)UNIT 18: Atoms and Nuclei

Alpha-particle scattering experiment, Rutherford’s model of atom, Bohr model, energy levels, hydrogen spectrum. Composition and size of nucleus, atomic masses, mass-energy relation, mass defect, binding energy per nucleon and its variation with mass number, nuclear fission and fusion.

19)UNIT 19: Electronic Devices

Semiconductors, semiconductor diode: I-V characteristics in forward andreverse bias, diode as a rectifier; I-V characteristics of LED, the photodiode, solar cell, Zener diode, Zener diode as a voltage regulator. Logic gates (OR. AND. NOT. NAND and NOR).

20)UNIT 20: Experimental Skills

Familiarity with the basic approach and observations of the experiments andactivities:

1. Vernier calipers -its use to measure the internal and external diameter anddepth of a vessel.

2. Screw gauge-its use to determine the thickness/ diameter of thin sheet/wire.

3. Simple pendulum-dissipation of energy by plotting a graph between the square of amplitude and time.

4. Metre scale – the mass of a given object by the principle of moments.

5. Young’s modulus of elasticity of the material of a metallic wire.

6. Surface tension of water by capillary rise and effect of detergents,

7. Co-efficient of viscosity of a given viscous liquid by measuring the terminal velocity of a given spherical body.

8. Speed of sound in air at room temperature using a resonance tube,

9. Specific heat capacity of a given (i) solid and (ii) liquid by method of mixtures.

10. The resistivity of the material of a given wire using a metre bridge.

11. The resistance of a given wire using Ohm’s law.

12. Resistance and figure of merit of a galvanometer by half deflection method.

13. The focal length of (i) Convex mirror (ii) Concave mirror and (iii)Convex lens, using the parallax method.

14. The plot of the angle of deviation vs angle of incidence for a triangular prism.

15. The refractive index of a glass slab using a travelling microscope.

16. Characteristic curves of a p-n junction diode in forward and reverse bias.

17. Characteristic curves of a Zener diode and finding reverse breakdownvoltage.

18. Identification of diode, LED, resistor, a capacitor from a mixed collectionof such items

CHEMISTRY:

PHYSICAL CHEMISTRY

1)UNIT I: SOME BASIC CONCEPTS IN CHEMISTRY

Matter and its nature, Dalton’s atomic theory, Concept of atom, molecule, element and compound, Lawsofchemical combination, Atomic and molecular masses, mole concept, molar mass, percentage composition, empirical and molecular formulae, Chemical equations and stoichiometry.

2)UNIT 2: ATOMIC STRUCTURE

Nature of electromagnetic radiation, photoelectric effect, spectrum of the hydrogen atom, Bohr model of ahydrogen atom – its postulates, derivation of the relations for the energy of the electron and radii of thedifferent orbits, limitations of Bohr’s model, dual nature of matter, de Broglie’s relationship, Heisenberguncertainty principle, elementary ideas of quantum mechanics, the quantum mechanical model of the atomand its important features, concept of atomic orbitals as one-electron wave functions, variation of \(\psi\)and\(\psi^2\) with r for 1s and 2s orbitals, various quantum numbers (principal, angular momentumand magneticquantum numbers) and their significance, shapes of s, p and d – orbitals, electron spin and spin quantumnumber, rules for filling electrons in orbitals – Aufbau principle, Pauli’s exclusion principle andHund’srule, electronic configuration of elements and extra stability of half-filled and completely filled orbitals.

3)UNIT 3: CHEMICAL BONDING AND MOLECULAR STRUCTURE

Kossel-Lewis approach to chemical bond formation, the concept of ionic and covalent bonds. Ionic Bonding: Formation of ionic bonds, factors affecting the formation of ionic bonds; calculationoflattice enthalpy. Covalent Bonding: Concept of electronegativity, Fajan’s rule, dipole moment, Valence Shell ElectronPairRepulsion (VSEPR ) theory and shapes of simple molecules. Quantum mechanical approach to covalent bonding: Valence bond theory – its important features, theconcept of hybridization involving s, p and d orbitals, resonance. Molecular Orbital Theory – Its important features, LCAOs, types of molecular orbitals (bonding, antibonding), sigma and pi-bonds, molecular orbital electronic configurations of homonuclear diatomicmolecules, the concept of bond order, bond length and bond energy. Elementary idea of metallic bonding, hydrogen bonding and its applications.

4)UNIT 4: CHEMICAL THERMODYNAMICS

 Fundamentals of thermodynamics: System and surroundings, extensive and intensive properties, statefunctions, entropy, types of processes.

The first law of thermodynamics – Concept of work, heat, internal energy and enthalpy, heat capacity, molar heat capacity, Hess’s law of constant heat summation, Enthalpies of bond dissociation, combustion, formation, atomization, sublimation, phase transition, hydration, ionization and solution. The second law of thermodynamics – Spontaneity of processes, ΔS of the universe and ΔG of the system as criteria for spontaneity. ΔG°(Standard Gibbs energy change) and equilibrium constant.

5)UNIT 5: SOLUTIONS

Different methods for expressing the concentration of solution – molality, molarity, mole fraction, percentage (by volume and mass both), the vapour pressure of solutions and Raoult’s Law- Ideal andnonideal solutions, vapour pressure – composition, plots for ideal and non- ideal solutions, Colligativeproperties of dilute solutions – a relative lowering of vapour pressure, depression of freezing point, theelevation of boiling point and osmotic pressure, determination of molecular mass using colligativeproperties, abnormal value of molar mass, van’t Hoff factor and its significance.

6)UNIT 6: EQUILIBRIUM

Meaning of equilibrium is the concept of dynamic equilibrium.

Equilibria involving physical processes: Solid-liquid, liquid-gas, gas-gas and solid-gas equilibria, Henry’s law. General characteristics of equilibrium involving physical processes.

Equilibrium involving chemical processes: Law of chemical equilibrium, equilibriumconstants (Kp and Kc) and their significance, the significance of ΔG and ΔG° in chemical equilibrium, factors affectingequilibrium concentration, pressure, temperature, the effect of catalyst, Le Chatelier’s principle.

Ionic equilibrium: Weak and strong electrolytes, ionization of electrolytes, various concepts of acids andbases (Arrhenius, Bronsted – Lowry and Lewis) and their ionization, acid-base equilibria (includingmultistage ionization) and ionization constants, ionization of water, pH scale, common ioneffect, hydrolysis of salts and pH of their solutions, the solubility of sparingly soluble salts, solubility products and buffer solutions.

7)UNIT 7: REDOX REACTIONS AND ELECTROCHEMISTRY

Electronic concepts of oxidation and reduction, redox reactions, oxidation number, rules for assigningoxidation number and balancing of redox reactions.

Electrolytic and metallic conduction, conductance in electrolytic solutions, molar conductivities andtheirvariation with concentration, Kohlrausch’s law and its applications.

Electrochemical cells – Electrolytic and Galvanic cells, different types of electrodes, electrode potentialsincluding standard electrode potential, half-cell and cell reactions, emf of a Galvanic cell anditsmeasurement, Nernst equation and its applications, relationship between cell potential and Gibbs’ energychange, dry cell and lead accumulator, fuel cells.

8)UNIT 8: CHEMICAL KINETICS

Rate of a chemical reaction, factors affecting the rate of reactions: concentration, temperature, pressureand catalyst, elementary and complex reactions, order and molecularity of reactions, rate law, rateconstant and its units, differential and integral forms of zero and first-order reactions, theircharacteristics and half-lives, the effect of temperature on the rate of reactions, Arrhenius theory, activation energy and its calculation, collision theory of bi-molecular gaseous reactions (no derivation).

INORGANIC CHEMISTRY:

9)UNIT 9: CLASSIFICATION OF ELEMENTS AND PERIODICITY IN PROPERTIES

Modern periodic law and present form of the periodic table, s, p. d and f block elements, periodic trendsinproperties of elements atomic and ionic radii, ionization enthalpy, electron gain enthalpy, valence, oxidation states and chemical reactivity.

10)UNIT 10: p- BLOCK ELEMENTS

Group -13 to Group 18 Elements General Introduction: Electronic configuration and general trends in physical and chemical propertiesofelements across the periods and down the groups, unique behaviour of the first element in each group.

11)UNIT 11: d – and f- BLOCK ELEMENTS

Transition Elements – General introduction, electronic configuration, occurrence and characteristics, general trends in properties of the first-row transition elements – physical properties, ionization enthalpy, oxidation states, atomic radii, colour, catalytic behaviour, magnetic properties, complex formation, interstitial compounds, alloy formation, preparation, properties and uses of K2Cr2O7 and KMnO4.

Inner Transition Elements Lanthanoids – Electronic configuration, oxidation states and Lanthanoid contraction.

Actinoids – Electronic configuration and oxidation states.

12)UNIT 12: COORDINATION COMPOUNDS

Introduction to coordination compounds. Werner’s theory, ligands, coordination number, denticity, chelation, IUPAC nomenclature of mononuclear co-ordination compounds, isomerism, Bonding: Valencebond approach and basic ideas of Crystal field theory, colour and magnetic properties, importanceofcoordination compounds (in qualitative analysis, extraction of metals and in biological systems).

ORGANIC CHEMISTRY

13)UNIT 13: PURIFICATION AND CHARACTERISATION OF ORGANIC COMPOUNDS

Purification – Crystallization, sublimation, distillation, differential extraction and chromatography-principles and their applications.

Qualitative analysis – Detection of nitrogen, sulphur, phosphorus and halogens.

Quantitative analysis (basic principles only) – Estimation of carbon, hydrogen, nitrogen, halogens, sulphur and phosphorus.

Calculations of empirical formulae and molecular formulae, numerical problems in organic quantitative analysis,

14)UNIT 14: SOME BASIC PRINCIPLES OF ORGANIC CHEMISTRY

Tetravalency of carbon, shapes of simple molecules – hybridization (s and p): classification of organiccompounds based on functional groups and those containing halogens, oxygen, nitrogen and sulphur, homologous series: Isomerism – structural and stereoisomerism.

Nomenclature (Trivial and IUPAC)

Covalent bond fission – Homolytic and heterolytic, free radicals, carbocations and carbanions, stabilityofcarbocations and free radicals, electrophiles and nucleophiles.

Electronic displacement in a covalent bond – Inductive effect, electromeric effect, resonance and hyperconjugation

Common types of organic reactions– Substitution, addition, elimination and rearrangement.

15)UNITS 15:HYDROCARBONS

Classification, isomerism, IUPAC nomenclature, general methods of preparation, properties and reactions.

Alkanes – Conformations: Sawhorse and Newman projections (of ethane), mechanismof halogenationofalkanes.

Alkenes – Geometrical isomerism, mechanism of electrophilic addition, addition of hydrogen, halogens, water, hydrogen halides (Markownikoffs and peroxide effect), Ozonolysis and polymerization.

Alkynes – Acidic character, addition of hydrogen, halogens, water and hydrogen halides, polymerization.

Aromatic hydrocarbons – Nomenclature, benzene – structure and aromaticity, mechanismof electrophilicsubstitution, halogenation, nitration.

Friedel-Craft’s alkylation and acylation, directive influence of the functional group in mono- substitutedbenzene.

16)UNIT 16: ORGANIC COMPOUNDS CONTAINING HALOGENS

General methods of preparation, properties and reactions, nature of C-X bond, mechanisms ofsubstitution reactions

Uses, environmental effects of chloroform, iodoform, freons and DDT.

17)UNIT 17: ORGANIC COMPOUNDS CONTAINING OXYGEN

General methods of preparation, properties, reactions and uses.

ALCOHOLS,PHENOLS AND ETHERS

Alcohols: Identification of primary, secondary and tertiary alcohols, mechanism of dehydration.

Phenols: Acidic nature, electrophilic substitution reactions, halogenation, nitration and sulphonation, Reimer – Tiemann reaction.

Ethers: Structure.

Aldehyde and Ketones: Nature of carbonyl group, nucleophilic addition to >C=Ogroup, relativereactivities of aldehydes and ketones, important reactions such as – Nucleophilic addition reactions(addition of HCN, NH3 and its derivatives), Grignard reagent, oxidation, reduction (Wolf Kishner andClemmensen), the acidity of � -hydrogen. Aldol condensation, Cannizzaro reaction, Haloformreaction, chemical tests to distinguish between aldehydes and ketones.

Carboxylic Acids: Acidic strength and factors affecting it

18)UNIT 18: ORGANIC COMPOUNDS CONTAINING NITROGEN

General methods of preparation, properties, reactions and uses.

Amines: Nomenclature, classification, structure, basic character and identification of primary, secondaryand tertiary amines and their basic character.

Diazonium Salts: Importance in synthetic organic chemistry

19)UNIT 19: BIOMOLECULES

General introduction and importance of biomolecules.

CARBOHYDRATES – Classification, aldoses and ketoses, monosaccharides (glucose and fructose) andconstituent monosaccharides of oligosaccharides (sucrose, lactose and maltose).

PROTEINS – Elementary idea of  \(\alpha\)-amino acids, peptide bond, polypeptides, proteins: primary, secondary, tertiary and quaternary structure (qualitative idea only), denaturation of proteins, enzymes.

VITAMINS – Classification and functions. NUCLEIC ACIDS – Chemical constitution of DNA and RNA, biological functions of nucleic acids.

Hormones (General introduction)

20)UNIT 20: PRINCIPLES RELATED TO PRACTICAL CHEMISTRY

Detection of extra elements (Nitrogen, sulphur, halogens) in organic compounds, detectionof thefollowing functional groups, hydroxyl (alcoholic and phenolic), carbonyl (aldehyde and ketones) carboxyl and amino groups in organic compounds

• The chemistry involved in the preparation of the following: Inorganic compounds, Mohr’s salt, potash alum. Organic compounds: Acetanilide, p-nitro acetanilide, aniline yellow, iodoform.
• The chemistry involved in the titrimetric exercises – acids, bases and the use of indicators, oxalic-acid vs KMnO4, Mohr’s salt vs KMnO4
• Chemical principles involved in the qualitative salt analysis:

Cations – Pb 2+, Cu 2+, Al3+ , Fe 3+ , Zn 2+ , Ni2+ , Ca 2+ , Ba 2+ , Mg 2+ , NH4+

Anions- CO3 2− , S 2-, SO4 2− , NO3 -, NO2 -, Cl -, Br -, I – ( Insoluble salts excluded).

Chemical principles involved in the following experiments:

1. Enthalpy of solution of CuSO4

2. Enthalpy of neutralization of strong acid and strong base.

3. Preparation of lyophilic and lyophobic sols.

4. Kinetic study of the reaction of iodide ions with hydrogen peroxide at room temperature.

                      

   Syllabus for JEE (Main) Paper 2A (B.Arch.) – Mathematics, Aptitude Test and Drawing Test 

    Part – I MATHEMATICS

UNIT 1: SETS, RELATIONS AND FUNCTIONS: Sets and their representation; Union, intersection and complement of sets and their algebraic properties; Power set; Relations, type of relations, equivalence relations, functions; one-one, into and onto functions, the composition of functions.

UNIT 2: COMPLEX NUMBERS AND QUADRATIC EQUATIONS: Complex numbers as ordered pairs of reals, Representation of complex numbers in the form a +ib and their representation in a plane, Argand diagram, algebra of complex numbers, modulus and argument (oramplitude) of a complex number, Quadratic equations in real and complex number systems andtheirsolutions; Relations between roots and coefficients, nature of roots, the formation of quadratic equationswith given roots.

UNIT3: MATRICES AND DETERMINANTS: Matrices, algebra of matrices, type of matrices, determinants and matrices of order two andthree, evaluation of determinants, area of triangles using determinants; Adjoint and inverse of a square matrix; Test of consistency and solution of simultaneous linear equations in two or three variables using matrices.

UNIT 4: PERMUTATIONS AND COMBINATIONS: The fundamental principle of counting, permutations and combinations; Meaning of P(n, r) and C(n,r)  Simple applications

UNIT 5: BINOMIAL THEOREM AND ITS SIMPLE APPLICATIONS: Binomial theorem for a positive integral index, general term and middle term and simple applications.

UNIT 6: SEQUENCE AND SERIES: Arithmetic and Geometric progressions, insertion of arithmetic, geometric means between twogivennumbers, Relation between A.M and G.M.

UNIT 7: LIMIT, CONTINUITY AND DIFFERENTIABILITY: Real–valued functions, algebra of functions; polynomial, rational, trigonometric, logarithmic andexponential functions; inverse functions. Graphs of simple functions. Limits, continuityanddifferentiability. Differentiation of the sum, difference, product and quotient of two functions. Differentiation of trigonometric, inverse trigonometric, logarithmic, exponential, composite and implicit functions; derivatives of order upto two, Applications of derivatives: Rate of change of quantities, monotonic-Increasing and decreasing functions, Maxima and minima of functions of one variable.

UNIT 8: INTEGRAL CALCULAS: Integral as an anti-derivative, Fundamental integrals involving algebraic, trigonometric, exponential andlogarithmic functions. Integration by substitution, by parts and by partial fractions. Integrationusingtrigonometric identities. Evaluation of simple integrals.

The fundamental theorem of calculus, properties of definite integrals. Evaluation of definite integrals, determining areas of the regions bounded by simple curves in standard forms.

UNIT 9: DIFFRENTIAL EQUATIONS :

Ordinary differential equations, their order and degree, the solution of differential equation by the methodof separation of variables, solution of a homogeneous and linear differential equation of the type

\(\frac{dy}{dx}+p\left(x\right)y=q\left(x\right)\)

UNIT 10: CO-ORDINATE GEOMETRY : Cartesian system of rectangular coordinates in a plane, distance formula, sections formula, locus anditsequation, the slope of a line, parallel and perpendicular lines, intercepts of a line on the co-ordinate axis.

Straight line: Various forms of equations of a line, intersection of lines, angles between twolines, conditions for concurrence of three lines, the distance of a point form a line, co-ordinate of the centroid, orthocentre and circumcentre of a triangle.

Circle, conic sections: A standard form of equations of a circle, the general form of the equation of a circle, its radius and centre, equation of a circle when the endpoints of a diameter are given, points of intersectionof a line and a circle with the centre at the origin and sections of conics, equations of conic sections(parabola, ellipse and hyperbola) in standard forms.

UNIT 11: THREE DIMENSIONAL GEOMETRY:

Coordinates of a point in space, the distance between two points, section formula, direction ratios anddirection cosines and the angle between two intersecting lines. Equation of a line; Skewlines, the shortest distance between them and its equation.

UNIT 12: VECTOR ALGEBRA :

Vectors and scalars, the addition of vectors, components of a vector in two dimensions andthree-dimensional spaces, scalar and vector products

UNIT 13: STATISTICS AND PROBABILITY :

Measures of dispersion; calculation of mean, median, mode of grouped and ungrouped data, calculationofstandard deviation, variance and mean deviation for grouped and ungrouped data. Probability: Probabilityof an event, addition and multiplication theorems of probability, Baye’s theorem, probability distributionof arandom variable.

UNIT 14: TRIGONOMETRY :

Trigonometrical identities and trigonometrical functions, inverse trigonometrical functions andtheirproperties.

 

  Part –II APTITUDE TEST

UNIT – 1 Awareness of persons: Buildings, Materials. Objects, Texture related to Architecture and Build-environment, Visualizing three- dimensional objectsfrom two-dimensional drawings. Visualizing. Different sides of three- dimensional objects. Analytical Reasoning Mental Ability (Visual, Numerical and Verbal)

UNIT – 2 Three dimensional- perception: Understanding and appreciation of scale and proportions ofobjects, building forms and elements, colour texture harmony and contrast Design and drawingofgeometrical or abstract shapes and patterns in pencil. Transformation of forms both 2Dand 3Dunion, subtraction rotation, development of surfaces and volumes, Generation of plans, elevations and 3Dviewsof objects, creating two-dimensional and three-dimensional compositions using given shapes and forms.

 Part – III DRAWING TEST

Sketching of scenes and activities from memory of urbanscape (public space, market, festivals, street scenes, monuments, recreational spaces, etc.). landscape (riverfronts. Jungle. Gardens, trees. Plants, etc.)and rural life.

 

    Syllabus for JEE (Main) Paper 2B (B.Planning) – Mathematics, Aptitude Test and Planning 

    Part – I MATHEMATICS

 

UNIT 1: SETS, RELATIONS AND FUNCTIONS: Sets and their representation; Union, intersection and complement of sets and their algebraic properties; Power set; Relations, type of relations, equivalence relations, functions; one-one, into and onto functions, the composition of functions.

UNIT 2: COMPLEX NUMBERS AND QUADRATIC EQUATIONS: Complex numbers as ordered pairs of reals, Representation of complex numbers in the form a +ib and their representation in a plane, Argand diagram, algebra of complex numbers, modulus and argument (oramplitude) of a complex number, Quadratic equations in real and complex number systems and their solutions; Relations between roots and coefficients, nature of roots, the formation of quadratic equations with given roots.

UNIT3: MATRICES AND DETERMINANTS: Matrices, algebra of matrices, type of matrices, determinants and matrices of order two andthree, evaluation of determinants, area of triangles using determinants; Adjoint and inverse of a square matrix; Test of consistency and solution of simultaneous linear equations in two or three variables using matrices.

UNIT 4: PERMUTATIONS AND COMBINATIONS: The fundamental principle of counting, permutations and combinations; Meaning of P(n, r) and C(n, r), Simple applications.

UNIT 5: BINOMIAL THEOREM AND ITS SIMPLE APPLICATIONS: Binomial theorem for a positive integral index, general term and middle term and simple applications.

UNIT 6: SEQUENCE AND SERIES: Arithmetic and Geometric progressions, insertion of arithmetic, geometric means between twogivennumbers, Relation between A.M and G.M.

UNIT 7: LIMIT, CONTINUITY AND DIFFERENTIABILITY: Real–valued functions, algebra of functions; polynomial, rational, trigonometric, logarithmic andexponential functions; inverse functions. Graphs of simple functions. Limits, continuityanddifferentiability. Differentiation of the sum, difference, product and quotient of two functions. Differentiation of trigonometric, inverse trigonometric, logarithmic, exponential, composite and implicit functions; derivatives of order upto two, Applications of derivatives: Rate of change of quantities, monotonic-Increasing and decreasing functions, Maxima and minima of functions of one variable.

UNIT 8: INTEGRAL CALCULAS: Integral as an anti-derivative, Fundamental integrals involving algebraic, trigonometric, exponential andlogarithmic functions. Integration by substitution, by parts and by partial fractions. Integrationusingtrigonometric identities. Evaluation of simple integrals

The fundamental theorem of calculus, properties of definite integrals. Evaluation of definite integrals, determining areas of the regions bounded by simple curves.

UNIT 9: DIFFRENTIAL EQUATIONS :

Ordinary differential equations, their order and degree, the solution of differential equation by the methodofseparation of variables, solution of a homogeneous and linear differential equation of the type

\(\frac{dy}{dx}+p\left(x\right)y=q\left(x\right)\)

UNIT 10: CO-ORDINATE GEOMETRY : Cartesian system of rectangular coordinates in a plane, distance formula, sections formula, locusanditsequation, the slope of a line, parallel and perpendicular lines, intercepts of a line on the co-ordinate axis.

Straight line: Various forms of equations of a line, intersection of lines, angles between two lines, conditionsforconcurrence of three lines, the distance of a point form a line, co-ordinate of the centroid, orthocentreandcircumcentre of a triangle.

Circle, conic sections: A standard form of equations of a circle, the general form of the equation of acircle, itsradius and centre, equation of a circle when the endpoints of a diameter are given, points of intersectionofaline and a circle with the centre at the origin and sections of conics, equations of conic sections (parabola,ellipse and hyperbola) in standard forms.

UNIT 11: THREE DIMENSIONAL GEOMETRY : Coordinates of a point in space, the distance between two points, section formula, directionratiosanddirection cosines and the angle between two intersecting lines. Equation of a line; Skewlines, theshortestdistance between them and its equation.

UNIT 12: VECTOR ALGEBRA : Vectors and scalars, the addition of vectors, components of a vector in two dimensions and three-dimensionalspaces, scalar and vector products.

UNIT 13: STATISTICS AND PROBABILITY : Measures of dispersion; calculation of mean, median, mode of grouped and ungrouped data, calculationofstandard deviation, variance and mean deviation for grouped and ungrouped data. Probability: Probabilityofanevent, addition and multiplication theorems of probability, Baye’s theorem, probability distributionof arandomvariable.

UNIT 14: TRIGONOMETRY : Trigonometrical identities and trigonometrical functions, inverse trigonometrical functions and their properties

 

 Part –II APTITUDE TEST

UNIT – 1 Awareness of persons, Buildings, Materials, Objects and Textures related to Architecture andBuild-environment, Visualizing three-dimensional objects from two-dimensional drawings.Visualizing different sidesof three-dimensional objects, Analytical Reasoning Mental Ability (Visual, Numerical and Verbal)

UNIT – 2 Three dimensional- perception: Understanding and appreciation of scale and proportions of objects,building forms and elements, colour texture harmony and contrast Design and drawing of geometrical orabstract shapes and patterns in pencil. Transformation of forms both 2D and 3D union, subtractionrotation,development of surfaces and volumes, Generation of plans, elevations and 3D views of objects, creatingtwo-dimensional and three-dimensional compositions using given shapes and forms.

 Part – III PLANNING

UNIT-1 GENERAL AWARENESS.

General knowledge questions and knowledge about prominent cities, development issues, governmentprograms etc.

UNIT-2 SOCIAL SCIENCES

The idea of nationalism, nationalism in India, pre-modern world, 19 th-century global economy, colonialismandcolonial cities, industrialization, resources and development, types of resources, agriculture, water, mineralresources, industries, national economy; Human Settlements.

Power-sharing, federalism, political parties, democracy, the constitution of India

Economic development- economic sectors, globalization, the concept of development, poverty; Populationstructure, social exclusion and inequality, urbanization, rural development, colonial cities.

UNIT-3 THINKING SKILLS

Comprehension (unseen passage); map reading skills, scale, distance, direction, area etc.; critical reasoning;understanding of charts, graphs and tables; basic concepts of statistics and quantitative reasoning.