Sparsh Academy

What is JEE Main?

The Joint Entrance Examination, JEE (Main) is a national level entrance exam conducted by NTA for admission to Undergraduate Engineering Programs (B.E. / B. Tech.) at NITs, IIITs, other Centrally Funded Technical Institutions (CFTIs) and Institutions / Universities funded / recognized by participating State Governments and admission to B. Arch and B. Planning courses in the country. JEE (Main) is also an eligibility test for JEE (Advanced), which is conducted for admission to IITs.

JEE Main registration Statistics

	2022	2023	2024	2025
Total Registered Candidates (Jan- Session)	8,72,970	8,60,064	12,21,624	13,11,544

Eligibility Criteria:

Age Criteria

For appearing in the JEE (Main) - 2025, there is no age limit for the candidates. The candidates who have passed the class XII / equivalent examination in 2023, 2024 or appearing in 2025 irrespective of their age can appear in JEE (Main) - 2025 examination. However, the candidates may be required to fulfill the age criteria of the Institute(s) to which they are desirous of taking admission.

List of Qualifying Examinations (QE)

The final examination of the 10+2 system, conducted by any recognized Central/ State Board, such as the Central Board of Secondary Education, New Delhi; Council for the Indian School Certificate Examinations, New Delhi; etc.
Intermediate or two-year Pre-University examination conducted by a recognized Board/ University.
Final examination of the two-year course of the Joint Services Wing of the National Defense Academy
Senior Secondary School Examination conducted by the National Institute of Open Schooling with a minimum of five subjects.
Any Public School/ Board/ University examination in India or any foreign country is recognized as equivalent to the 10+2 system by the Association of Indian Universities (AIU).
Higher Secondary Certificate Vocational Examination.
A Diploma recognized by AICTE or a State board of technical education of at least 3 years duration.
General Certificate Education (GCE) examination (London/Cambridge/Sri Lanka) at the Advanced (A) level.
High School Certificate Examination of the Cambridge University or International Baccalaureate Diploma of the International Baccalaureate Office, Geneva.
Candidates who have completed the Class XII (or equivalent) examination outside India or from a Board not specified above should produce a certificate from the Association of Indian Universities (AIU) to the effect that the examination they have passed is equivalent to the Class XII Examination.
In case the Class XII Examination is not a public examination, the candidate must have passed at least one public (Board or Pre-University) examination earlier.

Year of Appearance in Qualifying Examination.

Candidates those who have passed the Class XII / equivalent examination in 2024, 2025 or those who are appearing in the Class XII / equivalent examination in 2026, are eligible to appear in JEE (Main) - 2026. Candidates who passed the Class XII / equivalent examination in 2023 or before are not eligible to appear in JEE (Main) - 2023.

State of Eligibility.

State code of eligibility means the code of the State from where the candidate has passed the Class XII (or equivalent) qualifying examination by virtue of which the candidate becomes eligible to appear in JEE (Main). It is important to note that the State code of eligibility does NOT depend upon the native place or the place of residence of the candidate. For example, if a candidate appears for the Class XII(or equivalent) qualifying examination from an Institution situated in New Delhi and is a resident of Noida, Uttar Pradesh, then the candidate’s State code of eligibility will be Delhi and NOT Uttar Pradesh.

If a candidate has passed the Class XII (or equivalent) qualifying examination from one State but appeared for improvement from another State, the candidate’s State code of eligibility will be from where the candidate first passed the Class XII (or equivalent) examination and NOT the State from where the candidate has appeared for improvement.

Candidates passed / appearing for Class XII from NIOS should select the State of Eligibility according to the State in which the study Centre is located.

For Indian nationals passing the Class XII (or equivalent) examination from Nepal/Bhutan, the State code of eligibility will be determined based on a permanent address in India as given in the passport of the candidate.

The State code of eligibility for OCI passing the Class XII (or equivalent) examination in India is at par with Indian nationals. However, OCI passing the Class XII (or equivalent) examination from an institution abroad are eligible for Other State quota seats or All India quota seats (but NOT for Home State quota seats) in all NITs, IIITs and Other-CFTIs.

Reservations:

Reservations Indian nationals belonging to certain categories are admitted under the seats reserved for them in accordance with the rules prescribed by the Government of India. The categories and the extent of reservation are as follows:

1. General category belonging to Economically Weaker Section (GEN- EWS) – 10% of seats in every course. The benefit of reservation will be given only to those General category candidates who satisfy the conditions given in the OM No. 20013/01/2018-BC-II dated 17 January 2019, issued by the Ministry of Social Justice and Empowerment. The criteria for GEN-EWS will be as per the prevailing norms and/or notifications of the Government of India.

2. Other Backward Classes belonging to the Non-Creamy Layer (OBC- NCL) – 27% of seats in every course.

a) OBCs should be listed in the current updated central list of OBCs (http://www.ncbc.ac.in).

b) OBCs present in the State list but not covered in the central list of OBCs (as per the list in http://www.ncbc.ac.in) are NOT eligible to claim the reservation.

c) The criteria for OBC-NCL will be as per the notification of the Government of India.

d) Candidates belonging to the creamy layer of OBC are NOT entitled to reservation. Such candidates are treated as belonging to the general (GEN), i.e. unreserved category, and they will be eligible only for the OPEN seats – the seats for which all candidates are eligible.

3. Scheduled Caste (SC) – 15% of seats in every course.

4. Scheduled Tribe (ST) – 7.5% of seats in every course.

5. Persons with Disability/ Persons with Benchmark Disability (PwD/ /PwBD) – 5% seats in each of the GENERAL, GEN-EWS, OBC- NCL, SC and ST category seats.

Scheme of Examination

Subject combinations for each paper, type of questions in each paper and mode of examination are given in the table below:

PAPER	SUBJECTS	TYPE OF QUESTIONS	MODE OF EXAMINATION
Paper 1: B.E./B. Tech.	Mathematics, Physics and Chemistry	Objective Type - Multiple Choice Questions (MCQs) and Questions for which the answer is a numerical value, with equal weightage to Mathematics, Physics and Chemistry	“Computer Based Test (CBT)” mode only
Paper 2A: B. Arch	Part-I: Mathematics	Objective Type - Multiple Choice Questions (MCQs) and Questions for which the answer is a numerical value	“Computer Based Test (CBT)” mode only
	Part-II: Aptitude Test	Objective Type - Multiple Choice Questions (MCQs)	“Computer Based Test (CBT)” mode only
	Part-III: Drawing Test	Questions to test drawing aptitude	“Pen and Paper Based” (offline) mode to be attempted on a Drawing sheet of A4 size.
Paper 2B: B. Planning	Part-I: Mathematics	Objective Type - Multiple Choice Questions (MCQs) and Questions for which the 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)

Pattern of Examination

Paper 1: B.E./ B. Tech. in Computer Based Test (CBT) mode:
1	Subject-wise distribution of Questions, Total Number of Questions, and Marks		Subject	Section A	Section B		Marks
			Mathematics	20	05		100
			Physics	20	05		100
			Chemistry	20	05		100
			Total	75			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. There will be negative marking for incorrect answer in Section A and Section B. For each question in Section B, a candidate has to enter the correct integer value of the answer using the mouse and the on- screen virtual numeric keypad in the place designated to enter the answer. For Section B, the answer should be rounded off to the nearest integer.
2	Marking Scheme	Correct Answer or the Most Appropriate Answer				Four marks (+4)
		Incorrect Answer				Minus one mark (-1)
		Unanswered / Marked for Review				No mark (0)

Paper 2A (B. Arch): Mathematics (Part-I) and Aptitude Test (Part-II) in Computer Based Test (CBT) mode and Drawing Test (Part-III) in Pen and Paper Based (offline) mode, to be attempted on a drawing sheet of A4 size.
1	Subject-wise distribution of Questions, Total Number of Questions, and Marks	Subject	Number of Questions	Marks
		Part I: Mathematics	20 (Section A) and 05 (Section B)	100
		Part II: Aptitude test	50	200
		Part III: Drawing Test	02	100
		Total	77	400
	20 questions will be MCQs and 05 (five) questions will have answers to be filled as a numerical value. There will be negative marking for both Section A and Section B (except Drawing Test). For each question in Section B, a candidate has to enter the correct integer value of the answer using the mouse and the on-screen virtual numeric keypad in the place designated to enter the answer. The answer should be rounded off to the nearest integer.
2	Marking Scheme for MCQs/Numerical Value	Correct Answer or the most appropriate Answer		Four marks (+4)
		Incorrect Answer/Multiple Answer		Minus one mark (-1)
		Unanswered /Marked for Review		No mark (0)
	Marking Scheme for Drawing Test (Part III)	Two questions are to be evaluated out of 100 marks.

Paper 2B (B. Planning) Part-I: Mathematics, Part-II: Aptitude Test, and Part-III: Planning- Based Questions in Computer-Based Test (CBT) mode.
1	Subject-wise distribution of Questions, Total Number of Questions, and Marks	Subject		Number of Questions		Marks
		Part-1 Mathematics		20 (Section A) and 05 (Section B)		100
		Part-II: Aptitude Test		50		200
		Part-III: Planning		25		100
		Total		100		400
	20 questions will be MCQs and 05 (five) questions will have answers to be filled as a numerical value. There will be negative marking for both Section A and Section B (except Drawing Test). For each question in Section B, enter the correct integer value of the answer using the mouse and the on-screen virtual numeric keypad in the place designated to enter the answer. The answer should be rounded off to the nearest integer.
2	Marking Scheme for MCQs/Numerical Value		Correct Answer or the most appropriate Answer		Four marks (+4)
			Incorrect Answer/Multiple Answer		Minus one mark (-1)
			Unanswered /Marked for Review		No mark (0)

Duration of Test

Paper	Subjects	Total Time Duration
Paper	Subjects	For Non-PwD/PwBD Candidates	*For PwD /PwBD Candidates (who are eligible for scribe)
Paper 1 (B.E. / B. Tech.)	Physics, Chemistry, and Mathematics	03 hours	04 hours
Or Paper 2A (B. Arch)	Or Mathematics, Aptitude Test, and Drawing Test
Or Paper 2B (B. Planning)	Or Mathematics, Aptitude Test, and Planning Based Questions
Paper 2A (B. Arch) and Paper 2B (B. Planning)	Mathematics, Aptitude Test, Drawing Test, and Planning Based Questions	03 hours 30 minutes	04 hours 10 minutes

Syllabus for JEE (Main) - 2025

Syllabus for JEE Main Paper 1 (B.E./B.Tech.)- Mathematics, Physics and Chemistry

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 (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.

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 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 two given numbers, Relation between A.M and G.M.

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 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 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 by simple curves by simple curves in standard forms.

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 of the type 𝑑

UNIT 10 : CO-ORDINATE GEOMETRY

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 when the 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.

UNIT 11 : THREE DIMENSIONAL GEOMETRY

Coordinates of a point in space, the distance between two points, section formula, direction ratios and direction cosines and the angle between two intersecting lines. Equation of a line; Skew lines, 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 and three-dimensional spaces, scalar and vector products.

UNIT 13 : STATISTICS AND PROBABILITY

Measures of dispersion; 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 variable.

UNIT 14 : TRIGONOMETRY

Trigonometrical identities and trigonometrical functions, inverse trigonometrical functions their properties.

PHYSICS

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.

UNIT 2 : Kinematics

The frame of reference, motion in a straight line, 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, relative velocity. Motion in a plane, projectile motion, uniform circular motion.

UNIT 3 : Laws of Motion

Force and inertia, Newton’s first law of motion, momentum, Newton’s second Law of motion, impulse, Newton’s third Law of motion. Law of conservation of linear momentum and its applications, equilibrium of concurrent forces. Static and Kinetic friction, laws of friction, rolling friction. Dynamics of uniform circular motion, centripetal force and its applications : vehicle on a level circular road, vehicle on a banked road.

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.

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.

UNIT 6 : Gravitation

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

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.

UNIT 8 : Thermodynamics

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

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, law of equipartition of energy and applications to specific heat capacities of gases, mean free path, Avogadro's number.

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: derivation of 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.

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, potential difference, equipotential surfaces, electrical potential energy of a system of two point charges and of electric dipole in an electrostatic field. Conductors and insulators, dielectrics and electric polarization, capacitors and capacitance, 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.

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.

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 two parallel currents carrying conductors-definition of ampere, torque experienced by 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.

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.

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.

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 sustained interference 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.

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.

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.

UNIT 19 : Electronic Devices

Semiconductors, semiconductor diode: I-V characteristics in forward and reverse 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).

UNIT 20 : Experimental Skills

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

1. Vernier calipers -its use to measure the internal and external diameter and depth 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 break down voltage.

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

CHEMISTRY

PHYSICAL CHEMISTRY

UNIT I : SOME BASIC CONCEPTS IN CHEMISTRY

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

UNIT 2 : ATOMIC STRUCTURE

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, the quantum mechanical model of the atom and its important features, concept of atomic orbitals as one-electron wave functions, variation of 1 and 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 and extra stability of half-filled and completely filled orbitals.

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; 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 4 : CHEMICAL THERMODYNAMICS

Fundamentals of thermodynamics: System and surroundings, extensive and intensive properties, state functions, 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.

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 and nonideal 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 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, equilibrium constants (Kp and Kc) and their significance, the significance of ΔG and ΔG° 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, solubility products and buffer solutions.

UNIT 7 : REDOX REACTIONS AND ELECTROCHEMISTRY

Electronic concepts of oxidation and reduction, redox reactions, oxidation number, rules for assigning oxidation number and 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 8 : 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 bi-molecular gaseous reactions (no derivation).

INORGANIC CHEMISTRY

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 trends in properties of elements atomic and ionic radii, ionization enthalpy, electron gain enthalpy, valence, oxidation states and chemical reactivity.

UNIT 10 : 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.

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.

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 : Valence bond approach and basic ideas of Crystal field theory, colour and magnetic properties, importance of coordination compounds (in qualitative analysis, extraction of metals and in biological systems).

ORGANIC CHEMISTRY

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.

UNIT 14 : 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.

UNITS 15 : 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 16 : ORGANIC COMPOUNDS CONTAINING HALOGENS

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 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=O group, relative reactivities of aldehydes and ketones, important reactions such as - Nucleophilic addition reactions (addition of HCN, NH3 and its derivatives), Grignard reagent, oxidation, reduction (Wolf Kishner and Clemmensen), the acidity of a-hydrogen. Aldol condensation, Cannizzaro reaction, Haloform reaction, chemical tests to distinguish between aldehydes and ketones. Carboxylic Acids: Acidic strength and factors affecting it.

UNIT 18 : 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 19 : 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 a-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)

UNIT 20 : 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 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

UNIT 2 : COMPLEX NUMBERS AND QUADRATIC EQUATIONS

Complex numbers as ordered pairs of reals, Representation of complex numbers in the forma +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.

UNIT3 : MATRICES AND DETERMINANTS

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 two given numbers, Relation between A.M and G.M.

UNIT 7 : LIMIT, CONTINUITY AND DIFFERENTIABILITY

UNIT 8 : INTEGRAL CALCULAS

UNIT 9 : DIFFRENTIAL EQUATIONS

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 when the endpoints of a diameter are given, points of inter-section 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.

UNIT 11 : THREE DIMENSIONAL GEOMETRY

UNIT 12 : VECTOR ALGEBRA

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

UNIT 13 : STATISTICS AND PROBABILITY

Measures of dispersion; 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 variable.

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, Texture related to Architecture and Build-environment, Visualizing three- dimensional objects from 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 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 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 urban scape (public space, market, festivals, street scenes, monuments, recreational spaces, etc.). landscape (riverfronts. Jungle. Gardens, trees. Plants, etc.) and rural life. To be conducted in a Drawing sheet.

Note: Candidates are advised to bring pencils, own geometry box set, crassest and colour pencils and crayons for the Drawing Test.

Syllabus for JEE (Main) Paper 2B (B. Planning)

Mathematics, Aptitude Test and Planning Part - I

MATHEMATICS

UNIT 1 : SETS, RELATIONS AND FUNCTIONS

UNIT 2 : COMPLEX NUMBERS AND QUADRATIC EQUATIONS

Complex numbers as ordered pairs of reals, Representation of complex numbers in the forma +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.

UNIT3 : MATRICES AND DETERMINANTS

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 two given numbers, Relation between A.M and G.M.

UNIT 7 : LIMIT, CONTINUITY AND DIFFERENTIABILITY

UNIT 8 : INTEGRAL CALCULAS

UNIT 9 : DIFFRENTIAL EQUATIONS

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 when the 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.

UNIT 11 : THREE DIMENSIONAL GEOMETRY

UNIT 12 : VECTOR ALGEBRA

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

UNIT 13 : STATISTICS AND PROBABILITY

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 and Build-environment, Visualizing three-dimensional objects from 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 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 plans, elevations and 3D views of objects, creating two-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, government programs etc.

UNIT-2 SOCIAL SCIENCES

The idea of nationalism, nationalism in India, pre-modern world, 19th-century global economy, colonialism and colonial cities, industrialization, 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, globalization, the concept of development, poverty; Population structure, 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.

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