#### Joint Entrance Exam (JEE Mains) 2021 Notification Released

##### Last Updated on: 2021-01-21

<<< Submission of JEE Mains-2021 Online Application Form: 16.12.2020 to 23.01.2021 >>>

### What is JEE Mains ?

JEE Mains(Joint Entrance Examination) is an Engineering Entrance examination for admission into Undergraduate Engineering Programs at NITs, IIITs, Other Centrally Funded Technical Institutions, Institutions funded by participating State Governments and other Institutions. The Paper-1 (B. E./B. Tech.) of JEE (Main) will also be considered for JEE (Advanced), which the candidate should appear for getting admitted into the undergraduate programmes offered by the 23 IITs located in the country.

• CBSE(Central Board of Secondary Education) will be conducting the Joint Entrance Examination (JEE) Main 2021 in four sessions on
(Session 1): 23, 24, 25 & 26 February 2021
(Session 2): 15, 16, 17 & 18 March 2021
(Session 3): 27, 28, 29 & 30 April 2021
(Session 4): 24, 25, 26, 27 & 28 May 2021
• From 16th DEC-2020, Online registration for JEE Mains-2021 will be opened. Here you can find how to apply for JEE mains-2021, Examination Centres, Syllabus, Important Dates, Seat Matrix and courses availability.

### Important points in JEE Mains-2021:

• The Paper 1 of JEE (Main) 2021 will be held in February 2021 followed by next three Sessions in March, April, and May 2021. This is being done to ensure that the JEE (Main) 2021 does not interfere with the Board examinations, which may be held at different times across the States/UTs. Paper 2A & Paper 2B (B. Arch & B. Planning) will be held only twice a year (February & May 2021)
• The NTA has decided to provide choices in one section to cater to the decision of different Boards across the country regarding the reduction of syllabus. However, the total number of questions to be attempted will remain the same (Physics - 25, Chemistry - 25 and Mathematics - 25), wherever applicable.

#### Year of Appearance in Qualifying Examination

• Only those candidates who have passed Class 12/ equivalent examination in 2019, 2020 or 2021; or those who are appearing in Class 12/ equivalent examination in 2021, are eligible to appear in JEE (Main) 2021.

#### Mode of Application: Online Only

3 Simple Steps to be followed to apply online

1. Fill the Online Application Form, choose your Password and note down system generated Application Number.
2. Upload Scanned Images of Photograph and Signature
3. Pay Examination Fee by debit/credit card or e-Challan of Syndicate/Canara/ICICI Bank

#### JEE Mains-2021 exam shall have two papers

• Paper-I: For B.E/B.Tech
• Paper-II: For B.Arch/ B.Planning

#### Application Fees:

The fee (in Indian Rupees) for JEE(Main)-2021 is as follows:

Paper(s) Appearing Type of Candidates
FOR EXAMINATION CENTRE OPTED IN INDIA
male female Transgender
General/GenEWS/OBC(NCL)(SC/ST/PWD)(General/OBC)(SC/ST/PWD)
Paper 1: B.E./B. Tech
or Paper 2A: B. Arch
or Paper 2B: B.Planning
650 325 325 325 325
Paper 1: B.E./B. Tech & Paper 2A: B. Arch
or
Paper 1: B.E./B. Tech & Paper 2B: B. Planning
or
Paper 1: B.E./B.Tech, Paper 2A: B. Arch & Paper 2B: B.Planning
or
Paper 2A: B. Arch & Paper 2B: B.Planning
1300 650 650 650 650
FOR EXAMINATION CENTRE OPTED IN FOREIGN COUNTRY
Paper 1: B.E./B. Tech
or
Paper 2A: B. Arch
or
Paper 2B: B.Planning
3000 1500 1500 1500 1500
Paper 1: B.E./B. Tech & Paper 2A: B. Arch
or
Paper 1: B.E./B. Tech & Paper 2B: B. Planning
or
Paper 1: B.E./B.Tech, Paper 2A: B. Arch & Paper 2B: B.Planning
or
Paper 2A: B. Arch & Paper 2B: B.Planning
6000 3000 3000 3000 3000

#### Mode of Payment:

• (through Credit Card /Debit Card (except Master/Visa Card) / NetBanking/UPI)

• The Admit Card can be downloaded from JEE (Main) website from 2nd week of February, 2021

### Scheme of Examination:

PAPER SUBJECTS TYPE OF QUESTIONS MODE OF EXAMINATIONS
Paper 1:
B.E./B.Tech.
Mathematics, Physics & Chemistry Objective Type - Multiple Choice Questions (MCQs) & Questions for which answer is a numerical value, with equal weightage to Mathematics, Physics & Chemistry "Computer Based Test (CBT)" mode
Paper 2A: B. Arch Part-I: Mathematics Objective Type - Multiple Choice Questions (MCQs) & Questions for which answer is a numerical value "Computer Based Test (CBT)" mode only
Part-II: Aptitude Test Objective Type - Multiple Choice Questions (MCQs)
Part-III: Drawing Test Questions to test drawing aptitude "Pen & Paper Based" (offline) mode to be attempted on Drawing sheet
Paper 2B: B. Planning Part-I: Mathematics Objective Type - Multiple Choice Questions (MCQs) & Questions for which answer is a numerical value "Computer Based Test (CBT)" mode only
Part-II: Aptitude Test Objective Type - Multiple Choice Questions (MCQs)
Part-III: Planning Based Questions Objective Type - Multiple Choice Questions (MCQs)

#### Medium of Question Papers:

S. No. Language Examination Centres
1 English All Examination Centres
2 Hindi All Examination Centres in India
3 English and Assamese Examination Centres in Assam
4 English and Bengali Examination Centres in West Bengal, Tripura and Andaman & Nicobar Island
5 English and Gujarati Examination Centres in Gujarat, Daman and Diu, Dadra and Nagar Haveli
6 English and Kannada Examination Centres in Karnataka
7 English and Marathi Examination Centres in Maharashtra
8 English and Malayalam Examination Centres in Kerala and Lakshadweep
9 English and Odia Examination Centres in Odisha
10 English and Punjabi Examination Centres in Punjab, Chandigarh and Delhi
11 English and Tamil Examination Centres in Tamil Nadu, Puducherry and Andaman & Nicobar Island
12 English and Telugu Examination Centres in Andhra Pradesh and Telangana
13 English and Urdu All Examination Centres in India

#### Exam Pattern:

Paper Subject Section A Section B Total Marks
Paper1: B.E./ B. Tech. in Computer Based Test (CBT) mode: Mathematics 20* 10* 100
Physics 20* 10* 100
Chemistry 20* 10* 100
Total 90 300
*Each Subject will have two sections. Section A will be of Multiple-Choice Questions (MCQs) and Section B will contain Questions whose answers are to be filled in as a numerical value. In Section B, candidates have to attempt any five questions out of 10. There will be no negative marking for Section B.
Paper 2A (B. Arch) Mathematics (Part I) 20* 10* 100
Aptitude Test (Part II) 50 200
Drawing Test (Part III) 02 100
Total 82 400
*20 questions will be MCQs and 5 questions will have answers to be filled as a numerical value out of 10. There will be no negative marking for numerical value. Drawing Test (Part-III) in Pen & Paper Based (offline) mode, to be attempted on drawing sheet of A4 size.
Paper 2B (B. Planning) Part-I: Mathematics 20* 10* 100
Part-II: Aptitude Test 50 200
Part-III: Planning Based Objective Type MCQs 25 100
Total 105
*20 questions will be MCQs and 5 questions will have answers to be filled as a numerical value out of 10. There will be no negative marking for numerical value.
* One mark will be deducted for every wrong answer

### Syllabus ofJEE Mains-2021:

#### UNIT 1: Sets, Relations and Functions

• Sets and their representation: Union, intersection and complement of sets and their algebraic properties; Power set; Relation, 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 number, modulus and argument (or amplitude) of a complex number, square root of a complex number, triangle inequality, Quadratic equations in real and complex number system and their solutions Relations between roots and coefficient, nature of roots, the formation of quadratic equations with given roots.

#### UNIT 3: Matrices and Determinants:

• Matrices, algebra of matrices, type of matrices, determinants and matrices of order two and three, properties of determinants, evaluation of determinants, area of triangles using determinants, Adjoint and evaluation of inverse of a square matrix using determinants and elementary transformations, Test of consistency and solution of simultaneous linear equations in two or three variables using determinants and matrices.

#### UNIT 4: Permutations and Combinations:

• The fundamental principle of counting, permutation as an arrangement and combination as section, Meaning of P (n,r) and C (n,r), simple applications.

#### UNIT 5: Mathematical Induction:

• Principle of Mathematical Induction and its simple applications.

#### UNIT 6: Binomial Theorem and its Simple Applications:

• Binomial theorem for a positive integral inde, General term and Middle term, Properties of Binomial coefficients and simple applications

#### UNIT 7: Sequences and Series:

• Arithmetic and Geometric progressions, insertion of arithmetic, geometric means between two given numbers, Relation between A.M and G.M sum up to n terms of special series; Sn, Sn2, Sn3. Arithmetico-Geometric progression.

#### UNIT 8: Limit, Continuity and Differentiability:

• Real - valued functions, algebra of functions, polynomials, rational, trigonometric, logarithmic and exponential functions, inverse function. 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 and implicit functions; derivatives of order up to two, Rolle's and Lagrange's Mean value Theorems, Applications of derivatives: Rate of change of quantities, monotonicIncreasing and decreasing functions, Maxima and minima of functions of one variable, tangents and normal.

#### UNIT 9: Integral Calculus:

• 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
$$\int{\frac{dx}{{{x}^{2}}\pm {{a}^{2}}}},\,\,\int{\frac{dx}{\sqrt{{{x}^{2}}\pm {{a}^{2}}}}},\,\,\int{\frac{dx}{{{a}^{2}}-{{x}^{2}}}},\,\,\int{\frac{dx}{\sqrt{{{a}^{2}}-{{x}^{2}}}}},\,\,\int{\frac{dx}{a{{x}^{2}}+bx+c}},$$
$$\int{\frac{dx}{\sqrt{a{{x}^{2}}+bx+c}}},\,\,\int{\frac{\left( px+q \right)dx}{a{{x}^{2}}+bx+c}},\,\,\int{\frac{\left( px+q \right)dx}{\sqrt{a{{x}^{2}}+bx+c}}}$$
$$\int{\sqrt{{{a}^{2}}\pm {{x}^{2}}}\,dx},\,\,\int{\sqrt{{{x}^{2}}-{{a}^{2}}}}\,dx$$
Integral as limit of a sum, Fundamental Theorem of Calculus, Properties of definite integrals, Evaluation of definite integrals, determining areas of the regions bounded by simple curves in standard form.

#### UNIT 10: Differential Equations:

• Ordinary differential equations, their order and degree. Formation of differential equations. Solution of differential equations by the method of separation of variables, Solution of homogeneous and linear differential equations of the type:
$$\frac{dy}{dx}+p\left( x \right)y=q\left( x \right)$$

#### UNIT 11: Co - Ordinate Geometry:

• Cartesian system of rectangular coordinates in a plane, distance formula, sections formula, locus and its equation, translation of axes, the slope of a line, parallel and perpendicular lines, intercepts of a line on the co-ordinate axis.
Straight Lines: 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, equations of internal and external by sectors of angles between two lines coordinate of the centroid, orthocentre and circumcentre of a triangle, equation of the family of lines passing through the point of intersection of two lines.
Circles, conic sectons: A standard form of equations of a circle, the general form of the equation of a circle, its radius and central, equation of a circle when the endpoints of a diameter are given, points of intersection of a line and a circle with the centre at the origin and condition for a line to be tangent to a circle, equation of the tangent, sections of conics, equations of conic sections (parabola, ellipse and hyperbola) in standard forms, condition for Y = mx +c to be a tangent and point (s) of tangency.

#### UNIT 12: Three Dimensional Geometry:

• Coordinates of a point in space, the distance between two points, section formula, directions ratios and direction cosines, the angle between two intersecting lines. Skew lines, the shortest distance between them and its equation. Equations of a line and a plane in different forms, the intersection of a line and a plane, coplanar lines.

#### UNIT 13: Vector Algebra:

• Vectors and scalars, the addition of vectors, components of a vector in two dimensions and three-dimensional space, scalar and vector products, scalar and vector triple product

#### UNIT 14: Statistics and Probability:

• Measures of discretion; calculation of mean, median, mode of grouped and ungrouped data calculation of standard deviation, variance and mean deviation for grouped and ungrouped data.
Probability: Probability of an event, addition and multiplication theorems of probability, Baye's theorem, probability distribution of a random variate, Bernoulli trials and binomial distribution.

#### UNIT 15: Trigonometry:

• Trigonometrical identities and equations, trigonometrical functions, inverse trigonometrical functions and their properties, heights and distance.

#### UNIT 16: Mathematical Reasoning:

• Statement logical operations and, or, implies, implied by, if and only if, understanding of tautology, contradiction, converse and contrapositive.

The syllabus contains two Section- A and B, Section - A pertains to the Theory Part having 80% weightage, while Sections - B contains practical component (Experimental Skills) having 20 % Weightage.

### SECTION - A

#### UNIT 1: Physics and Measurements:

• Physics, technology and society, S I Units, fundamental and derived units, least count, accuracy and precision of measuring instruments, Errors in measurement, Dimensions of Physics quantities, dimensional analysis and its applications.

#### UNIT 2: Kinematics

• The 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 graph, relations for uniformly accelerated motion, Scalars and Vectors, Vector. Addition and subtraction, zero vector, scalar and vector products, Unit Vector, Resolution of a Vector. Relative Velocity, Motion in a plane, Projectile Motion, Uniform Circular Motion.

#### UNITS 3: Laws of Motion:

• Force and inertia, Newton's First law of motion; Momentum, Newton's Second Law of motion, Impulses; 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.

#### UNIT 4: Work, Energy and Power:

• Work done by a content force and a variable force; kinetic and potential energies, work-energy theorem, power.
The potential energy of spring conservation of mechanical energy, conservative and neoconservative forces; Elastic and inelastic collisions in one and two dimensions.

#### UNIT 5: Rotational Motion:

• Centre of the mass of a two-particle system, Centre of the mass of a rigid body; Basic concepts of rotational motion; a 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. Rigid body rotation equations of rotational motion.

#### UNIT 6: Gravitation:

• The universal law of gravitation. Acceleration due to gravity and its variation with altitude and depth. Kepler's law of planetary motion. Gravitational potential energy; gravitational potential. Escape velocity, Orbital velocity of a satellite. Geo stationary satellites.

#### UNIT 7: Properties of Solids and Liquids:

• Elastic behaviour, Stress-strain relationship, Hooke's Law. Young's modulus, bulk modulus, modulus of rigidity. Pressure due to a fluid column; Pascal's law and its applications. Viscosity. Stokes' law. terminal velocity, streamline and turbulent flow. Reynolds number. Bernoulli's principle and its applications. Surface energy and surface tension, angle of contact, 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. Newton's law of cooling.

#### UNIT 8: Thermodynamics:

• Thermal equilibrium, zeroth law of thermodynamics, the concept of temperature. Heat, work and internal energy. The first law of thermodynamics. The second law of thermodynamics: reversible and irreversible processes. Carnot engine and its efficiency.

#### 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 energy and temperature: RMS speed of gas molecules: Degrees of freedom. Law of equipartition of energy, applications to specific heat capacities of gases; Mean free path. Avogadro's number

#### UNIT 10: Oscillations and Waves:

• Periodic motion - 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 - derivation of expression for its time period: Free, forced and damped oscillations, resonance. Wave motion - Longitudinal and transverse waves, speed of a wave. Displacement relation for a progressive wave. Principle of superposition of waves, a reflection of waves. Standing waves in strings and organ pipes, fundamental mode and harmonics. Beats. Doppler Effect in sound.

#### UNIT 11: Electrostatics

• Electric charges:Conservation of charge. Coulomb's law-forces 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 a uniform electric field.
• Electric Flux: Gauss's law and its applications to find field due to infinitely long uniformly charged straight wire, uniformly charged infinite plane sheet and uniformly charged thin spherical shell. Electric potential and its calculation for a point charge, electric dipole and system of charges; Equipotential surfaces, Electrical potential energy of a system of two point charges in an electrostatic field
Conductors and insulators. Dielectrics and electric polarization, capacitor, the combination of capacitors in series and parallel, capacitance of a parallel plate capacitor with and without dielectric medium between the plates. Energy stored in a capacitor.

#### UNIT 12: Current Electricity:

• Electric current. Drift velocity. Ohm's law. Electrical resistance. Resistances of different materials. V-l characteristics of Ohmic and non-ohmic conductors. Electrical energy and power. Electrical resistivity. Colour code for resistors; Series and parallel combinations of resistors; Temperature dependence of resistance.
Electric Cell and its 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. Potentiometer - principle and its applications.

#### UNIT 13: Magnetic Effects of Current and Magnetism:

• Biot - Savart law and its application to 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. Cyclotron.
Force on a current-carrying conductor in a uniform magnetic field. The force between two parallel current carrying conductorsdefinition of ampere. Torque experienced by a current loop in a uniform magnetic field: Moving coil galvanometer, its current 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; Earth's magnetic field and magnetic elements. Para-, dia- and ferromagnetic substances. Magnetic susceptibility and permeability. Hysteresis. Electromagnets and permanent magnets.

#### UNIT 14: Electromagnetic Induction and Alternating Current:

• 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: Quality factor, power in AC circuits, wattless current. AC generator and transformer.

#### UNIT 15: Electromagnetic Waves:

• Electromagnetic waves and their characteristics, Transverse nature of electromagnetic waves, Electromagnetic spectrum (radio waves, microwaves, infrared, visible, ultraviolet. X-rays. Gamma rays), Applications of e.m. waves.

#### UNIT 16: Optics:

• Reflection and refraction of light at plane and spherical surfaces, mirror formula. Total internal reflection and its applications. Deviation and Dispersion of light by a; prism; Lens Formula. Magnification. Power of a Lens. Combination of thin lenses in contact. Microscope and Astronomical Telescope (reflecting and refracting ) and their magnifying powers.
Wave optics: wavefront and Huygens' principle. 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. Polarization, plane-polarized light: Brewster's law, uses of plane-polarized light and Polaroid.

#### 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. DavissonGermer experiment.

#### 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, isotopes, isobars: isotones. Radioactivity- alpha. beta and gamma 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.

#### UNIT 19: Electronic Devices:

• Semiconductors; semiconductor diode: 1- V characteristics in forward and reverse bias; diode as a rectifier; I-V characteristics of LED. the 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.

#### UNIT 20: Communication System:

• Propagation of electromagnetic waves in the atmosphere; Sky and space wave propagation. Need for modulation. Amplitude and Frequency Modulation, Bandwidth of signals. the bandwidth of Transmission medium, Basic Elements of a Communication System (Block Diagram only).

### SECTION - B

#### UNIT 21: Experimental Skills:

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

1. Vernier callipers-its use to measure the internal and external diameter and depth of a vessel.
2. Screw gauge-its use to determine 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 principle of moments.
5. Young's modulus of elasticity of the material of a metallic wire.
6. Surf ace tension of water by capillary rise and effect of detergents.
7. Co-efficient of Viscosity of a given viscous liquid by measuring terminal velocity of a given spherical body.
8. Plotting a cooling curve for the relationship between the temperature of a hot body and time.
9. Speed of sound in air at room temperature using a resonance tube.
10. Specific heat capacity of a given (i) solid and (ii) liquid by method of mixtures.
11. The resistivity of the material of a given wire using metre bridge.
12. The resistance of a given wire using Ohm's law.
13. Potentiometer -
1. Comparison of emf of two primary cells.
2. Determination of internal resistance of a cell.
14. Resistance and figure of merit of a galvanometer by half deflection method.
15. Focal length of:
1. Convex mirror
2. Concave mirror, and
3. Convex lens using parallax method.
16. Plot of angle of deviation vs angle of incidence for a triangular prism.
17. Refractive index of a glass slab using a travelling microscope.
18. Characteristic curves of a p-n junction diode in forward and reverse bias.
19. Characteristic curves of a Zener diode and finding reverse break down voltage.
20. Characteristic curves of a transistor and finding current gain and voltage gain.
21. . Identification of Diode. LED, Transistor. IC. Resistor. A capacitor from a mixed collection of such items.
22. Using multimeter to:
1. Identify base of a transistor.
2. Distinguish between NPN and PNP type transistor.
3. See the unidirectional flow of current in case of a diode and an LED.
4. Check the correctness or otherwise of a given electronic component (diode, transistor or IC).

### Physical Chemistry

#### UNIT 1: Some Basic Concepts in Chemistry:

• Matter and its nature, Dalton's atomic theory: Concept of atom, molecule, element and compound: Physical quantities and their measurements in Chemistry, precision and accuracy, significant figures. S.I.Units, dimensional analysis: Laws of chemical combination; Atomic and molecular masses, mole concept, molar mass, percentage composition, empirical and molecular formulae: Chemical equations and stoichiometry.

#### UNIT 2: States of Matter:

Classification of matter into solid, liquid and gaseous states.
• Gaseous State:Measurable properties of gases: Gas laws - Boyle's law, Charle's law. Graham's law of diffusion. Avogadro's law, Dalton's law of partial pressure; Concept of Absolute scale of temperature; Ideal gas equation; Kinetic theory of gases (only postulates); Concept of average, root mean square and most probable velocities; Real gases, deviation from Ideal behaviour, compressibility factor and van der Waals equation.
• Liquid State: Properties of liquids - vapour pressure, viscosity and surface tension and effect of temperature on them (qualitative treatment only).
• Solid State: Classification of solids: molecular, ionic, covalent and metallic solids, amorphous and crystalline solids (elementary idea); Bragg's Law and its applications: Unit cell and lattices, packing in solids (fcc, bcc and hcp lattices), voids, calculations involving unit cell parameters, an imperfection in solids; Electrical and magnetic properties.

#### UNIT 3: Atomic Structure:

• Thomson and Rutherford atomic models and their limitations; Nature of electromagnetic radiation, photoelectric effect; Spectrum of the hydrogen atom. Bohr model of a hydrogen atom - its postulates, derivation of the relations for the energy of the electron and radii of the different orbits, limitations of Bohr's model; Dual nature of matter, de Broglie's relationship. Heisenberg uncertainty principle. Elementary ideas of quantum mechanics, quantum mechanics, the quantum mechanical model of the atom, 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 momentum and magnetic quantum numbers) and their significance; shapes of s, p and d - orbitals, electron spin and spin quantum number: Rules for filling electrons in orbitals - Aufbau principle. Pauli's exclusion principle and Hund's rule, electronic configuration of elements, extra stability of half-filled and completely filled orbitals.

#### UNIT4: 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; calculation of lattice enthalpy
Covalent Bonding:Concept of electronegativity. Fajan's rule, dipole moment: Valence Shell Electron Pair Repulsion (VSEPR ) theory and shapes of simple molecules.
Quantum mechanical approach to covalent bonding:Valence bond theory - its important features, the concept 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 diatomic molecules, the concept of bond order, bond length and bond energy.
Elementary idea of metallic bonding. Hydrogen bonding and its applications.

#### UNIT 5: Chemical Thermodynamics:

Fundamentals of thermodynamics: System and surroundings, extensive and intensive properties, state functions, 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; ?S of the universe and ?G of the system as criteria for spontaneity. ?G? (Standard Gibbs energy change) and equilibrium constant.

#### UNIT6: 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 and non-ideal solutions, vapour pressure - composition, plots for ideal and non-ideal solutions; Colligative properties of dilute solutions - a relative lowering of vapour pressure, depression of freezing point, the elevation of boiling point and osmotic pressure; Determination of molecular mass using colligative properties; Abnormal value of molar mass, van't Hoff factor and its significance.

#### UNIT 7: Equilibrium

Meaning of equilibrium, the concept of dynamic equilibrium.
• Equilibria involving physical processes: Solid-liquid, liquid - gas and solid-gas equilibria, Henry's law. General characteristics of equilibrium involving physical processes.
• Equilibria involving chemical processes: Law of chemical equilibrium, equilibrium constants (Kp and Kc) and their significance, the significance of $$\Delta G$$ and $$\Delta {{G}^{0}}$$ in chemical equilibrium, factors affecting equilibrium concentration, pressure, temperature, the effect of catalyst; Le Chatelier's principle.
• Ionic Equilibrium: Weak and strong electrolytes, ionization of electrolytes, various concepts of acids and bases (Arrhenius. Bronsted - Lowry and Lewis) and their ionization, acid-base equilibria (including multistage ionization) and ionization constants, ionization of water. pH scale, common ion effect, hydrolysis of salts and pH of their solutions, the solubility of sparingly soluble salts and solubility products, buffer solutions.

#### UNIT 8: Redox Reactions and Electrochemistry:

• Electronic concepts of oxidation and reduction, redox reactions, oxidation number, rules for assigning oxidation number, balancing of redox reactions.
• Electrolytic and metallic conduction, conductance in electrolytic solutions, molar conductivities and their variation with concentration: Kohlrausch's law and its applications.
• Electrochemical cells - Electrolytic and Galvanic cells, different types of electrodes, electrode potentials including standard electrode potential, half - cell and cell reactions, emf of a Galvanic cell and its measurement: Nernst equation and its applications; Relationship between cell potential and Gibbs' energy change: Dry cell and lead accumulator; Fuel cells.

#### UNIT 9: Chemical Kinetics:

• Rate of a chemical reaction, factors affecting the rate of reactions: concentration, temperature, pressure and catalyst; elementary and complex reactions, order and molecularity of reactions, rate law, rate constant and its units, differential and integral forms of zero and first-order reactions, their characteristics and half-lives, the effect of temperature on the rate of reactions, Arrhenius theory, activation energy and its calculation, collision theory of bimolecular gaseous reactions (no derivation).

#### UNIT-10: Surface Chemistry:

• Adsorption - Physisorption and chemisorption and their characteristics, factors affecting adsorption of gases on solids - Freundlich and Langmuir adsorption isotherms, adsorption from solutions.
• Catalysis - Homogeneous and heterogeneous, activity and selectivity of solid catalysts, enzyme catalysis and its mechanism.
• Colloidal state - Distinction among true solutions, colloids and suspensions, classification of colloids - lyophilic. lyophobic; multimolecular. macromolecular and associated colloids (micelles), preparation and properties of colloids - Tyndall effect. Brownian movement, electrophoresis, dialysis, coagulation and flocculation: Emulsions and their characteristics

### INORGANIC CHEMISTRY

#### UNIT 11: Classification of Elements and Periodicity in Properties:

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

#### UNIT 12: General Principles and Processes of Isolation of Metals:

• Modes of occurrence of elements in nature, minerals, ores; Steps involved in the extraction of metals - concentration, reduction (chemical and electrolytic methods) and refining with special reference to the extraction of Al. Cu, Zn and Fe; Thermodynamic and electrochemical principles involved in the extraction of metals

#### UNIT 13: Hydrogen:

• Position of hydrogen in periodic table, isotopes, preparation, properties and uses of hydrogen; Physical and chemical properties of water and heavy water; Structure, preparation, reactions and uses of hydrogen peroxide; Classification of hydrides - ionic, covalent and interstitial; Hydrogen as a fuel

#### UNIT 14: S - Block Elements (Alkali and Alkaline Earth Metals)

Group - I and 2 Elements
• General introduction, electronic configuration and general trends in physical and chemical properties of elements, anomalous properties of the first element of each group, diagonal relationships.
• Preparation and properties of some important compounds - sodium carbonate and sodium hydroxide and sodium hydrogen carbonate; Industrial uses of lime, limestone. Plaster of Paris and cement: Biological significance of Na, K. Mg and Ca.

#### UNIT 15: P- Block Elements:

##### Group -13 to Group 18 Elements
• General Introduction: Electronic configuration and general trends in physical and chemical properties of elements across the periods and down the groups; unique behaviour of the first element in each group.
##### Group - 13
• Preparation, properties and uses of boron and aluminium; Structure, properties and uses of borax, boric acid, diborane, boron trifluoride, aluminium chloride and alums.
##### Group - 14
• The tendency for catenation; Structure, properties and uses of Allotropes and oxides of carbon, silicon tetrachloride, silicates, zeolites and silicones.
##### Group - 15
• Properties and uses of nitrogen and phosphorus; Allotrophic forms of phosphorus; Preparation, properties, structure and uses of ammonia, nitric acid, phosphine and phosphorus halides $$\left( PC{{l}_{3}},\text{ }PCl{{ }_{3}} \right);$$, Structures of oxides and oxoacids of nitrogen and phosphorus.
##### Group - 16
• Preparation, properties, structures and uses of ozone: Allotropic forms of sulphur; Preparation, properties, structures and uses of sulphuric acid (including its industrial preparation); Structures of oxoacids of sulphur.
##### Group - 17
• Preparation, properties and uses of hydrochloric acid; Trends in the acidic nature of hydrogen halides; Structures of Interhalogen compounds and oxides and oxoacids of halogens.
##### Group - 18
• Occurrence and uses of noble gases; Structures of fluorides and oxides of xenon.

#### UNIT 16: 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 $${{K}_{2}}\text{ }C{{r}_{2}}\text{ }{{\text{O}}_{7}}$$ and $$KMn{{O}_{4}}$$.
##### Inner Transition Elements
• Lanthanoids - Electronic configuration, oxidation states and lanthanoid contraction.
• Actinoids - Electronic configuration and oxidation states.

#### UNIT 17: Co - Ordination Compounds:

• Introduction to co-ordination compounds. Werner's theory; ligands, co-ordination number, denticity. chelation; IUPAC nomenclature of mononuclear co-- ordination compounds, isomerism; Bonding-Valence bond approach and basic ideas of Crystal field theory, colour and magnetic properties; Importance of co-- ordination compounds (in qualitative analysis, extraction of metals and in biological systems).

#### UNIT 18: Environmental Chemistry:

• Environmental pollution - Atmospheric, water and soil.
• Atmospheric pollution - Tropospheric and Stratospheric
• Tropospheric pollutants - Gaseous pollutants: Oxides of carbon, nitrogen and Sulphur, hydrocarbons; their sources, harmful effects and prevention; Greenhouse effect and Global warming; Acid rain;
• Particulate pollutants: Smoke, dust, smog, fumes, mist; their sources, harmful effects and prevention.
• Stratospheric pollution - Formation and breakdown of ozone, depletion of ozone layer - its mechanism and effects.
• Water Pollution - Major pollutants such as, pathogens, organic wastes and chemical pollutants; their harmful effects and prevention.
• Soil pollution - Major pollutants such as: Pesticides (insecticides, herbicides and fungicides), their harmful effects and prevention. Strategies to control environmental pollution.

### ORGANIC CHEMISTRY

#### UNIT 19: 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, phosphorus.
• Calculations of empirical formulae and molecular formulae; Numerical problems in organic quantitative analysis.

#### UNIT 20: Some Basic Principles of Organic Chemistry:

Tetravalency of carbon: Shapes of simple molecules - hybridization (s and p): Classification of organic compounds 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; stability of carbocations 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.

#### UNIT 21: Hydrocarbons:

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

• Alkanes- Conformations: Sawhorse and Newman projections (of ethane): Mechanism of halogenation of alkanes.
• 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: Mechanism of electrophilic substitution: halogenation, nitration.
Friedel - Craft's alkylation and acylation, directive influence of the functional group in mono-substituted benzene.

#### UNIT 22: Organic Compounds Containing Halogenes:

• General methods of preparation, properties and reactions; Nature of C-X bond; Mechanisms of substitution reactions.
Uses: Environmental effects of chloroform, iodoform freons and DDT.

#### UNIT 23: 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 = 0 group, relative reactivities of aldehydes and ketones; Important reactions such as - Nucleophilic addition reactions (addition of $$HCN,\text{ }N{{H}_{3}}$$ and its derivatives), Grignard reagent; oxidation; reduction (Wolff Kishner and Clemmensen); acidity of $$\alpha$$-hydrogen, aldol condensation, Cannizzaro reaction, Haloform reaction; Chemical tests to distinguish between aldehydes and Ketones.
##### Carboxilic Acids
Acidic strength and factors affecting it.

#### UNIT 24: Organic Compounds Containing Nitrogen

• General methods of preparation. Properties, reactions and uses.
• Amines: Nomenclature, classification structure, basic character and identification of primary, secondary and tertiary amines and their basic character.
• Diazonium Salts: Importance in synthetic organic chemistry.

#### UNIT 25: Polymers

• General introduction and classification of polymers, general methods of polymerization - Addition and condensation, copolymerization.
• Natural and synthetic, rubber and vulcanization, some important polymers with emphasis on their monomers and uses - polythene, nylon, polyester and bakelite.

#### UNIT 26: Biomolecules

• General introduction and importance of biomolecules.
• CARBOHYDRATES - Classification; aldoses and ketoses: monosaccharides (glucose and fructose) and constituent monosaccharides of oligosaccharides (sucrose, lactose and maltose).
• PROTEINS - Elementary Idea of ?-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.

#### UNIT 27: Chemistry in Everyday Life

• Chemicals in Medicines - Analgesics, tranquillizers, antiseptics, disinfectants, antimicrobials, anti-fertility drugs, antibiotics, antacids. Anti-histamines - their meaning and common examples.
• Chemicals in food - Preservatives, artificial sweetening agents - common examples.
• Cleansing agents - Soaps and detergents, cleansing action.

#### UNIT 28: Principles Related to Practical Chemistry

• Detection of extra elements (Nitrogen, Sulphur, halogens) in organic compounds; Detection of the following 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 $$KMn{{0}_{4}}$$ Mohr's salt vs $$KMn{{0}_{4}}$$.
• Chemical principles involved in the qualitative salt analysis:
Cations -$$P{{b}^{2+}}\text{, C}{{\text{u}}^{2+}},\,\,A{{l}^{3}},\text{ }F{{e}^{3+}},\text{ }Z{{n}^{2+}},\text{ }N{{i}^{2+}},\text{ }C{{a}^{2+}},\text{ }B{{a}^{2+}},\text{ }M{{g}^{2+}},\text{ }NH_{4}^{+}.$$
Anions - $$CO_{3}^{2-},\,\,\,{{S}^{2-}},\,SO_{4}^{2-},\text{ }NO_{3}^{-},\text{ }NO_{2}^{-},\text{ }C{{l}^{-}},\text{ }B{{r}^{-}},\text{ }{{\text{I}}^{-}}.$$
(Insoluble salts excluded).
• Chemical principles involved in the following experiments:
1. Enthalpy of solution of $$CuS{{O}_{4}}$$
2. Enthalpy of neutralization of strong acid and strong base.
3. Preparation of lyophilic and lyophobic sols.
4. Kinetic study of reaction of iodide ion with hydrogen peroxide at room temperature.

### Paper-2A (B.Arch)

#### UNIT 1: Sets, Relations and Functions

• Sets and their representation: Union, intersection and complement of sets and their algebraic properties; Power set; Relation, 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 number, modulus and argument (or amplitude) of a complex number, square root of a complex number, triangle inequality, Quadratic equations in real and complex number system and their solutions Relations between roots and coefficient, nature of roots, the formation of quadratic equations with given roots.

#### UNIT 3: Matrices and Determinants:

• Matrices, algebra of matrices, type of matrices, determinants and matrices of order two and three, properties of determinants, evaluation of determinants, area of triangles using determinants, Adjoint and evaluation of inverse of a square matrix using determinants and elementary transformations, Test of consistency and solution of simultaneous linear equations in two or three variables using determinants and matrices.

#### UNIT 4: Permutations and Combinations:

• The fundamental principle of counting, permutation as an arrangement and combination as section, Meaning of P (n,r) and C (n,r), simple applications.

#### UNIT 5: Mathematical Induction:

• Principle of Mathematical Induction and its simple applications.

#### UNIT 6: Binomial Theorem and its Simple Applications:

• Binomial theorem for a positive integral inde, General term and Middle term, Properties of Binomial coefficients and simple applications

#### UNIT 7: Sequences and Series:

• Arithmetic and Geometric progressions, insertion of arithmetic, geometric means between two given numbers, Relation between A.M and G.M sum up to n terms of special series; Sn, Sn2, Sn3. Arithmetico-Geometric progression.

#### UNIT 8: Limit, Continuity and Differentiability:

• Real - valued functions, algebra of functions, polynomials, rational, trigonometric, logarithmic and exponential functions, inverse function. 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 and implicit functions; derivatives of order up to two, Rolle's and Lagrange's Mean value Theorems, Applications of derivatives: Rate of change of quantities, monotonicIncreasing and decreasing functions, Maxima and minima of functions of one variable, tangents and normal.

#### UNIT 9: Integral Calculus:

• 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
$$\int{\frac{dx}{{{x}^{2}}\pm {{a}^{2}}}},\,\,\int{\frac{dx}{\sqrt{{{x}^{2}}\pm {{a}^{2}}}}},\,\,\int{\frac{dx}{{{a}^{2}}-{{x}^{2}}}},\,\,\int{\frac{dx}{\sqrt{{{a}^{2}}-{{x}^{2}}}}},\,\,\int{\frac{dx}{a{{x}^{2}}+bx+c}},$$
$$\int{\frac{dx}{\sqrt{a{{x}^{2}}+bx+c}}},\,\,\int{\frac{\left( px+q \right)dx}{a{{x}^{2}}+bx+c}},\,\,\int{\frac{\left( px+q \right)dx}{\sqrt{a{{x}^{2}}+bx+c}}}$$
$$\int{\sqrt{{{a}^{2}}\pm {{x}^{2}}}\,dx},\,\,\int{\sqrt{{{x}^{2}}-{{a}^{2}}}}\,dx$$
Integral as limit of a sum, Fundamental Theorem of Calculus, Properties of definite integrals, Evaluation of definite integrals, determining areas of the regions bounded by simple curves in standard form.

#### UNIT 10: Differential Equations:

• Ordinary differential equations, their order and degree. Formation of differential equations. Solution of differential equations by the method of separation of variables, Solution of homogeneous and linear differential equations of the type:
$$\frac{dy}{dx}+p\left( x \right)y=q\left( x \right)$$

#### UNIT 11: Co - Ordinate Geometry:

• Cartesian system of rectangular coordinates in a plane, distance formula, sections formula, locus and its equation, translation of axes, the slope of a line, parallel and perpendicular lines, intercepts of a line on the co-ordinate axis.
Straight Lines: 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, equations of internal and external by sectors of angles between two lines coordinate of the centroid, orthocentre and circumcentre of a triangle, equation of the family of lines passing through the point of intersection of two lines.
Circles, conic sectons: A standard form of equations of a circle, the general form of the equation of a circle, its radius and central, equation of a circle when the endpoints of a diameter are given, points of intersection of a line and a circle with the centre at the origin and condition for a line to be tangent to a circle, equation of the tangent, sections of conics, equations of conic sections (parabola, ellipse and hyperbola) in standard forms, condition for Y = mx +c to be a tangent and point (s) of tangency.

#### UNIT 12: Three Dimensional Geometry:

• Coordinates of a point in space, the distance between two points, section formula, directions ratios and direction cosines, the angle between two intersecting lines. Skew lines, the shortest distance between them and its equation. Equations of a line and a plane in different forms, the intersection of a line and a plane, coplanar lines.

#### UNIT 13: Vector Algebra:

• Vectors and scalars, the addition of vectors, components of a vector in two dimensions and three-dimensional space, scalar and vector products, scalar and vector triple product

#### UNIT 14: Statistics and Probability:

• Measures of discretion; calculation of mean, median, mode of grouped and ungrouped data calculation of standard deviation, variance and mean deviation for grouped and ungrouped data.
Probability: Probability of an event, addition and multiplication theorems of probability, Baye's theorem, probability distribution of a random variate, Bernoulli trials and binomial distribution.

#### UNIT 15: Trigonometry:

• Trigonometrical identities and equations, trigonometrical functions, inverse trigonometrical functions and their properties, heights and distance.

#### UNIT 16: Mathematical Reasoning:

• Statement logical operations and, or, implies, implied by, if and only if, understanding of tautology, contradiction, converse and contrapositive.

#### UNIT - 1:

• Awareness of persons. Buildings, Materials.
Objects, Texture related to Architecture and Build-envirounmentVisusalising three dimensional objects from two-dimensional drawings. Visualising. 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 of objects, building forms and elements, colour texture harmony and contrast Design and drawing of geometrical or abstract shapes and patterns in pencil. Transformation of forms both 2D and 3D union, subtraction rotation, development of surfaces and volumes, Generation of Plan, elevations and 3D views of objects, Creating two dimensional and three-dimensional compositions using given shapes and forms.

#### Part - III: Drawing

• Sketching of scenes and activities from memory of urbanscape (public space, market, festivals, street scenes, monuments, recreational spaces etc). landscape (riverfronts. Jungles. Gardens, trees. Plants etc.) and rural life.
• To be conducted in a Drawing sheet.
Note: TCandidates are advised to bring pencils. Own geometry box set, crasets and colour pencils and crayons for the Drawing Test.

### Paper-2B (B.Planning)

#### UNIT 1: Sets, Relations and Functions

• Sets and their representation: Union, intersection and complement of sets and their algebraic properties; Power set; Relation, 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 number, modulus and argument (or amplitude) of a complex number, square root of a complex number, triangle inequality, Quadratic equations in real and complex number system and their solutions Relations between roots and coefficient, nature of roots, the formation of quadratic equations with given roots.

#### UNIT 3: Matrices and Determinants:

• Matrices, algebra of matrices, type of matrices, determinants and matrices of order two and three, properties of determinants, evaluation of determinants, area of triangles using determinants, Adjoint and evaluation of inverse of a square matrix using determinants and elementary transformations, Test of consistency and solution of simultaneous linear equations in two or three variables using determinants and matrices.

#### UNIT 4: Permutations and Combinations:

• The fundamental principle of counting, permutation as an arrangement and combination as section, Meaning of P (n,r) and C (n,r), simple applications.

#### UNIT 5: Mathematical Induction:

• Principle of Mathematical Induction and its simple applications.

#### UNIT 6: Binomial Theorem and its Simple Applications:

• Binomial theorem for a positive integral inde, General term and Middle term, Properties of Binomial coefficients and simple applications

#### UNIT 7: Sequences and Series:

• Arithmetic and Geometric progressions, insertion of arithmetic, geometric means between two given numbers, Relation between A.M and G.M sum up to n terms of special series; Sn, Sn2, Sn3. Arithmetico-Geometric progression.

#### UNIT 8: Limit, Continuity and Differentiability:

• Real - valued functions, algebra of functions, polynomials, rational, trigonometric, logarithmic and exponential functions, inverse function. 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 and implicit functions; derivatives of order up to two, Rolle's and Lagrange's Mean value Theorems, Applications of derivatives: Rate of change of quantities, monotonicIncreasing and decreasing functions, Maxima and minima of functions of one variable, tangents and normal.

#### UNIT 9: Integral Calculus:

• 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
$$\int{\frac{dx}{{{x}^{2}}\pm {{a}^{2}}}},\,\,\int{\frac{dx}{\sqrt{{{x}^{2}}\pm {{a}^{2}}}}},\,\,\int{\frac{dx}{{{a}^{2}}-{{x}^{2}}}},\,\,\int{\frac{dx}{\sqrt{{{a}^{2}}-{{x}^{2}}}}},\,\,\int{\frac{dx}{a{{x}^{2}}+bx+c}},$$
$$\int{\frac{dx}{\sqrt{a{{x}^{2}}+bx+c}}},\,\,\int{\frac{\left( px+q \right)dx}{a{{x}^{2}}+bx+c}},\,\,\int{\frac{\left( px+q \right)dx}{\sqrt{a{{x}^{2}}+bx+c}}}$$
$$\int{\sqrt{{{a}^{2}}\pm {{x}^{2}}}\,dx},\,\,\int{\sqrt{{{x}^{2}}-{{a}^{2}}}}\,dx$$
Integral as limit of a sum, Fundamental Theorem of Calculus, Properties of definite integrals, Evaluation of definite integrals, determining areas of the regions bounded by simple curves in standard form.

#### UNIT 10: Differential Equations:

• Ordinary differential equations, their order and degree. Formation of differential equations. Solution of differential equations by the method of separation of variables, Solution of homogeneous and linear differential equations of the type:
$$\frac{dy}{dx}+p\left( x \right)y=q\left( x \right)$$

#### UNIT 11: Co - Ordinate Geometry:

• Cartesian system of rectangular coordinates in a plane, distance formula, sections formula, locus and its equation, translation of axes, the slope of a line, parallel and perpendicular lines, intercepts of a line on the co-ordinate axis.
Straight Lines: 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, equations of internal and external by sectors of angles between two lines coordinate of the centroid, orthocentre and circumcentre of a triangle, equation of the family of lines passing through the point of intersection of two lines.
Circles, conic sectons: A standard form of equations of a circle, the general form of the equation of a circle, its radius and central, equation of a circle when the endpoints of a diameter are given, points of intersection of a line and a circle with the centre at the origin and condition for a line to be tangent to a circle, equation of the tangent, sections of conics, equations of conic sections (parabola, ellipse and hyperbola) in standard forms, condition for Y = mx +c to be a tangent and point (s) of tangency.

#### UNIT 12: Three Dimensional Geometry:

• Coordinates of a point in space, the distance between two points, section formula, directions ratios and direction cosines, the angle between two intersecting lines. Skew lines, the shortest distance between them and its equation. Equations of a line and a plane in different forms, the intersection of a line and a plane, coplanar lines.

#### UNIT 13: Vector Algebra:

• Vectors and scalars, the addition of vectors, components of a vector in two dimensions and three-dimensional space, scalar and vector products, scalar and vector triple product

#### UNIT 14: Statistics and Probability:

• Measures of discretion; calculation of mean, median, mode of grouped and ungrouped data calculation of standard deviation, variance and mean deviation for grouped and ungrouped data.
Probability: Probability of an event, addition and multiplication theorems of probability, Baye's theorem, probability distribution of a random variate, Bernoulli trials and binomial distribution.

#### UNIT 15: Trigonometry:

• Trigonometrical identities and equations, trigonometrical functions, inverse trigonometrical functions and their properties, heights and distance.

#### UNIT 16: Mathematical Reasoning:

• Statement logical operations and, or, implies, implied by, if and only if, understanding of tautology, contradiction, converse and contrapositive.

#### UNIT - 1:

• Awareness of persons. Buildings, Materials.
Objects, Texture related to Architecture and Build-envirounmentVisusalising three dimensional objects from two-dimensional drawings. Visualising. 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 of objects, building forms and elements, colour texture harmony and contrast Design and drawing of geometrical or abstract shapes and patterns in pencil. Transformation of forms both 2D and 3D union, subtraction rotation, development of surfaces and volumes, Generation of Plan, elevations and 3D views of objects, Creating two dimensional and three-dimensional compositions using given shapes and forms

#### UNIT 1: GENERAL AWARENESS

• General knowledge questions and knowledge about prominent cities, development issues, government programmes etc.

#### UNIT 2: SOCIAL SCIENCES

• The idea of nationalism, nationalism in India, pre-modern world, 19th century global economy, colonialism and colonial cities, industrialisation, resources and development, types of resources, agriculture, water, mineral resources, industries, national economy; Human Settlements.
Power-sharing, federalism, political parties, democracy, the constitution of India.
Economic development- economic sectors, globalisation, the concept of development, poverty; Population structure, social exclusion and inequality, urbanisation, 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.
Note: The NTA has decided to provide choices in one section (Section B) to cater to the decision of different Boards across the country regarding the reduction of the syllabus. However, the total number of questions to be attempted will remain the same (Physics - 25, Chemistry - 25 and Mathematics - 25), wherever applicable.

### Seat Allocation Process and Admission Procedure:

• Candidates shall be offered admission based on their choices and All India Ranks of JEE (Main) 2021 through a Seat Allocation Process to be announced later CSAB/JoSAA.
• The authentication/verification of relevant documents in support of identification, date of birth, qualifying examination, State of eligibility, category and disability (if any) of the qualifying candidates would be done at the time of Seat Allocation/ admission process. On failing to produce any of the authentic documents, the candidate may not be considered for admission.
• Gen-EWS, SC, ST, OBC and PwD candidates will be required to produce original certificate as per prescribed formats issued by the competent authority at the time of Seat Allocation / admission process failing which they will not be considered for admission.