About JEE Mains 2021
Joint Entrance Exam Main (JEE Main) is the national level computer-based test conducted twice a year(in the month of January 2021 as well as in April 2021) by the National Testing Agency for the purpose of admissions to the undergraduate engineering courses in top engineering institutes in India like IITs, NITs, CFTIs and other renowned institutions. In addition, it is also the screening cum qualifier test for JEE Advanced. Validity of the result is one year.
JEE MAINS 2021 HIGHLIGHTS
| Events | January Session Dates | April Session Dates |
|---|---|---|
| Release of Notification | November 2020 | January 2021 |
| Starting of Registration process | December 2020 | 1st week of February 2021 |
| Image correction starts | December 2020 | February 2021 |
| End of registration | December 2020 | 1st week of March 2021 |
| Last date of fee payment & uploading of images | December 2020 | 2nd week of March 2021 |
| Application Correction starts | January 2021 | March 2021 |
| Release of Admit card | January 2021 | 3rd week of March 2021 |
| JEE Main Exam | 2nd week of January 2021 | 2nd week of April 2021 |
| Display of Answer key | January 2021 | April 2021 |
| Declaration of Result | February 2021 | Last week of April 2021 |
| Counselling process starts | June/ July 2021 |
Eligibility Criteria for JEE Main 2021
HRD Minister has announced a relaxation in JEE Main eligibility criteria for NITs and CFITs admissions. Candidates who pass their class XII examination will be eligible to apply. The NTA JEE Main 2020 eligibility criteria which the candidates need to meet includes guidelines for age, requisite academic qualifications, subjects studied in 10+2, pass percentage etc. Candidates may check the detailed eligibility criteria below before applying for JEE Main 2020.
| JEE Main 2020 Age Criteria | There is no age limit for appearing for the exam |
|---|---|
| Qualifying Examination | Candidates must have passed class 12 or equivalent exam in 2019 or 2020. Candidates appearing for class XII board examination in 2020 will be also eligible |
| Subjects to study in 10+2 or equivalent | Candidates must have studied a minimum of 5 subjects which will be considered. They are Mathematics, Physics, Chemistry/ Biology/ Biotechnology/ Technical Vocational Subject, Language and any other subject |
| Qualifying Examination | Candidates must have passed class 12 or equivalent exam in 2018 or 2019. Candidates appearing for class XII board examination in 2020 will be also eligible |
| Relaxation is 10+2 for JEE Main 2020 | Candidates who have obtained pass marks in class 12 or equivalent are eligible. |
| Number of attempts | All aspirants can appear twice in a year. Students can appear for JEE Main for three years consecutively therefore the total attempts allowed for each student will be six in three years |
Documents Required at Exam
- JEE Main admit card
- A valid photo ID (passport, college/school ID card, driving license)
- One passport size photograph
- PwD category candidates will have to carry a copy of the PwD certificate in the prescribed format.
JEE Main 2020 Admit Card
JEE Main 2021 admit card will be released by January 2021(for January2021 Session) and 3rd week of March 2021(April Session) by NTA. Candidates who will apply can download their JEE Main April admit card in online mode. Candidates will have carry the JEE Main admit card to the exam centre along with a valid photo ID.
How to download JEE Main 2021 Admit Card?
- Candidates have to click on the download link given on the NTA JEE Main website
- They must enter their Application Number and Date of Birth in the JEE Main login window.
- The admit card of JEE Main will be displayed. Candidates must ascertain that the details are correct.
- They must print the same and safe keep it as it will be needed during counselling and admissions.
What to carry to the exam hall ?
- Admit Card along with Self Declaration (Undertaking) downloaded from the NTA website (a clear printout on A4 size
- paper) duly filled in.
- A simple transparent Ball Point Pen
- A valid photo id proof
- A passport size photograph (same as in application form)
- PwD certificate if applicable
- Personal hand sanitizer (50 ml)
Details mentioned in JEE Main 2020 admit card
- Name of Candidate
- Father's Name
- Date of Birth
- Gender
- Category
- State of Eligibility
- JEE Main Roll Number
- Paper for which appearing
- JEE Main 2020 Application Number
- JEE Main Exam Centre Name and Address
- Exam Date and Time (Shift) of JEE Main 2020
- Photograph and Signature of Candidate
- Parent's signature
Unable to download the admit card?
Candidates who are unable to download their admit card must call the JEE Main helpline numbers from 10 am to 5 pm at 0120 6895200 OR send an email to jeemain-nta@nic.in giving their JEE Main 2020 application number and also the confirmation page.
JEE Main 2021 Exam Pattern
NTA has released the JEE Main 2020 exam pattern for Paper 1 for the B.Tech aspirants. The JEE Main exam pattern specifies the subjects, types of questions asked, number of questions, duration of exam, marking scheme. mode of exam and language etc. The details of the exam pattern of JEE Main Paper 1 are given below.
JEE Main Exam Pattern (Paper 1)
| JEE Main exam mode | Computer based | |||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| JEE Main 2020 exam duration | 3 hours | |||||||||||||||
| Number of shifts in JEE Main 2020 | There will be two shifts per day: (9:30 am to 12:30 pm and 2:30 pm to 5:30 pm) | |||||||||||||||
| Type of Questions | Multiple Choice Questions- 60 Numerical questions - 15 | |||||||||||||||
| JEE Main Paper Pattern in detail |
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| Marking Scheme for MCQs |
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| Difficulty levels of questions | Maths and Aptitude - Class 11 and Class 12 standard | |||||||||||||||
JEE Main Paper 2 Exam Pattern
B.Arch or B.Plan aspirants appearing for JEE Main Paper II must be conversant with the exam pattern. The JEE Main 2020 exam pattern (Paper 2) allows students to know what to expect in the exam in terms of types of questions, marking scheme, language, mode and more. Paper 2 of JEE Main is separate for B.Arch and B.Plan applicants. While both have aptitude and mathematics common, B.Acrh students must take up the drawing test while the B.Plan applicants must answer the planning section. Candidates can check the exam pattern of JEE Main 2020 below.
JEE Main 2020 Exam Pattern (Paper 2) for B.Arch
| JEE Main exam mode | Computer based | |||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| JEE Main 2020 exam duration | 3 hours | |||||||||||||||
| Language of JEE Main | English/ Hindi. Gujarati allowed for students from Gujarat, Damn & Diu only | |||||||||||||||
| Number of shifts in JEE Main 2020 | There will be two shifts per day: (9:30 am to 12:30 pm and 2:30 pm to 5:30 pm) | |||||||||||||||
| Type of Questions | For Maths and Aptitude -Multiple choice questions (MCQs) and Numerical Questions (NQs) Drawing - questions requiring drawing | |||||||||||||||
| JEE Main Paper Pattern in detail |
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| Marking Scheme for MCQs |
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| Difficulty levels of questions | Maths and Aptitude - Class 11 and Class 12 standard | |||||||||||||||
JEE Main Exam Pattern (Paper 2) for B.Plan
| Parameters | Particulars |
|---|---|
| Exam Mode of JEE Main | Computer-based test (CBT) |
| Exam Duration of JEE Main | 3 hours |
| Subjects | Mathematics, General Aptitude and Planning |
| Total number and type of questions | Maths - 20 MCQ questions and 5 numerical uestions Aptitude - 50 MCQs Planning - 25 questions. |
| Marking Scheme | 4 marks for a correct answer -1 for an incorrect answer. No negative marks for numerical questions |
| Maximum Marks | 400 |
| Medium of paper | English or Hindi (Candidates from Gujarat, Daman & Diu and Dadra and Nagar Haveli can opt for Gujarati as well) |
JEE Main Paper 1 Syllabus
Mathematics: Unit 01
Sets, relations and functions |
|---|
| Sets and their representation |
| Union |
| Intersection and complement of sets and their algebraic properties |
| Power set |
| Relation |
| Types of relations |
| Equivalence relations |
| Functions |
| One-one, into and onto functions |
| Composition of functions |
Complex number and quadratic equations |
|---|
| Complex numbers as ordered pairs or 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 of a complex number |
| Square root of a complex number |
| Triangle inequality |
| Quadratic equation in real and complex number system and their solutions |
| Relation between roots and co-efficients |
| Nature of roots |
| Formation of quadratic equations with given roots |
Matrices and determinants |
|---|
| Matrices |
| Algebra of matrices |
| Types 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 |
Permutations and combinations |
|---|
| Fundamental principle of counting |
| Permutation as an arrangement and combination as selection |
| Meaning of P (n, r) and C (n, r). Simple applications |
Mathematical induction |
|---|
| Principle of mathematical induction and its simple applications |
Binomial theorem and its simple applications |
|---|
| Binomial theorem for a positive integral index |
| General term and middle term |
| Properties of binomial coefficients and simple applications |
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 |
Limit, continuity and differentiability |
|---|
| Real functions |
| Valued functions |
| Algebra of functions |
| Polynomial functions |
| Rational functions |
| Trigonometric functions |
| Logarithmic and exponential functions |
| Inverse functions |
| Graphs of simple functions |
| Limits, continuity and differentiability |
| Differentiation or 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 |
| Monotonic - increasing and decreasing functions |
| Maxima and minima of functions of one variable |
| Tangents and normals |
Integrals 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 |
| Integral as limit or 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 |
Differential equations |
|---|
| Ordinary differential equations and their order and degree |
| Formation of differential equations |
| Solution of differential equations by the method of separations of variables |
| Solution of differential equations by the method of separations of variables,solution of homogeneous and linear differential equations of the type : dy/dx+p(x)y=q(x) |
Co-ordinate geometry |
|---|
| Cartesian system of rectangular co-ordinates 10 in a plane |
| Distance formula |
| Section formula |
| Locus and its equation |
| Translation of axes |
| Slope of a line |
| Parallel and perpendicular lines |
| Intercepts of a line on the coordinate axes |
| Various forms of equations of a straight line |
| Intersection of lines |
| Angles between two lines |
| Conditions for concurrence of three lines |
| Distance of a point from a line |
| Equations of internal and external bisectors of angles between two lines |
| Coordinates of centroid |
| Orthocentre and circumcentre of a triangle |
| Equation of family of lines passing through the point of intersection of two lines |
| Standard form of equation of a circle |
| General form of the equation of a circle, its radius and centre |
| Equation of a circle when the end points 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 cones |
| Equation of conic sections in standard forms |
| Condition for y = mx + c to be a tangent and point (s) of tangency |
Three-dimensional geometry |
|---|
| Coordinates of a point in space |
| Distance between two points |
| Section formula |
| Direction ratios and direction cosines |
| Angle between two intersecting lines |
| Skew lines and the shortest distance between them and its equation |
| Equations of a line and a plane in different forms |
| Intersection of a line and a plane |
| Coplanar lines |
Vector algebra |
|---|
| Vectors and scalars |
| Addition of vectors |
| Components of a vector in two dimensions and three dimensional space |
| Scalar and vector products |
| Scalar and vector triple product |
Statistics and probability |
|---|
| Measures of dispersion |
| Calculation of mean and median |
| Mode of grouped and ungrouped data calculation of standard deviation |
| Variance and mean deviation for grouped and ungrouped data |
| Probability of an event |
| Addition and multiplication theorems of probability |
| Baye's theorem |
| Probability distribution of a random variate |
| Bernoulli trials and binomial distribution |
Trigonometry |
|---|
| Trigonometrical identities and equations, trigonometrical functions |
| Inverse trigonometrical functions and their properties |
| Heights and distances |
Mathematical reasoning |
|---|
| Statements |
| Logical operations and, or, implies, implied by, if and only if |
| Understanding of tautology |
| Contradiction |
| Converse and contrapositive |
Physics: Unit 01
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 physical quantities |
| Dimensional analysis and its applications |
Kinematics |
|---|
| Frame of reference |
| Motion in a straight line |
| Position-time graph |
| Speed and velocity |
| Uniform and non-uniform motion |
| Average speed and instantaneous velocity uniformly accelerated motion |
| Velocity-time graph |
| Position-time graphs |
| 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 |
Laws of motion |
|---|
| Force and inertia |
| Newton's first law of motion |
| Momentum |
| Newton's second law of motion |
| Impulse |
| Newton's third law or 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 |
Work, energy and power |
|---|
| Work done by a constant force and a variable force |
| Kinetic and potential energies |
| Work energy theorem |
| Power |
| Potential energy of a spring |
| Conservation of mechanical energy |
| Conservative and non-conservative forces |
| Elastic and inelastic collisions in one and two dimensions |
Rotational motion |
|---|
| Centre of mass or a two-particle system |
| Centre of mass of a rigid body |
| Basic concepts of rotational motions |
| Moment of a force |
| Torque |
| Angular momentum |
| Conservation of angular momentum and its applications |
| Moment of inertia |
| 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 |
Gravitation |
|---|
| The universal law of gravitation |
| Acceleration due to gravity and its variation with altitude and depth |
| Kepler's laws of planetary motion |
| Gravitational potential energy |
| Gravitational potential |
| Escape velocity |
| Orbital velocity of a satellite |
| Geo-stationary satellites |
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 or state |
| Heat transfer-conduction |
| Convection and radiation |
| Newton's law of cooling |
Thermodynamics |
|---|
| Thermal equilibrium |
| Zeroth law of thermodynamics |
| Concept of temperature |
| Heat, work and internal energy |
| First law of thermodynamics |
| Second law of thermodynamics |
| Reversible and irreversible processes |
| Carnot engine and its efficiency |
Kinetics theory of gases |
|---|
| Equation of state of a perfect gas, work done on compressing a gas |
| Kinetic theory of gases - assumptions |
| Concept of pressure |
| Kinetic energy and temperature |
| RMS speed of gas molecules |
| Degrees of freedom |
| Law of equipartition of energy |
| Applications to specific heat capacities of gases |
| Mean free path |
| Avogadro's number |
Oscillations and waves |
|---|
| Periodic motion-period |
| Frequency |
| Displacement as a function of time |
| Periodic functions |
| Simple harmonic motion 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 or expression for its time period |
| Free, forced and damped oscillations |
| Resonance |
| Wave motion, phase, amplitude and velocity of wave |
| Longitudinal and transverse waves |
| Speed of a wave |
| Displacement relation for a progressive wave |
| Principle of superposition of waves |
| Reflection of waves |
| Standing waves in strings and organ pipes |
| Beats |
| Doppler effect in sound |
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 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 or charges |
| Equipotential surfaces |
| Electrical potential energy of a system of two point charges in an electrostatics field |
| Conductors and insulators |
| Dielectrics and electric polarization |
| Capacitor |
| Combination of capacitors in series and in parallel |
| Capacitance or a parallel plate capacitor with and without dielectric medium between the plates |
| Energy stored in a capacitator |
Current electricity |
|---|
| Electric current |
| Drift velocity |
| Ohm's law |
| Electrical resistance |
| Resistances of different materials |
| V-I 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 |
| Combination of cells in series and in parallel |
| Kirchhoff's laws and their applications |
| Wheatstone bridge |
| Metre bridge |
| Potentiometer and its principle and its applications |
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 |
| Force between two parallel current carrying conductors |
| Definition of ampere |
| Torque experienced by a current loop in uniform magnetic field |
| Moving coil galvanometer and 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 ferro magnetic substance |
| Magnetic susceptibility and permeability |
| Hysteresis |
| Electromagnets and permanent magnets |
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 |
| Quality factor |
| Power in AC circuits |
| Wattless current |
| AC generator and transformer |
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 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 |
| Polansation |
| Plane polarized light |
| Brewster's law |
| Uses of plane polarized light and polaroids |
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 and Broglie relation |
| Davisson-Germer experiment |
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, Its variation with mass number |
| Mass defect |
| Binding energy per nucleon and its variation with mass number |
| Nuclear fission and fusion |
Electronic devices |
|---|
| Semiconductors: Semiconductor diode |
| 1-V characteristics in forward and reverse bias |
| Diode as a rectifier |
| I-V characteristics or LED |
| Photodiode |
| Solar cell and Zener diode |
| Zener diode as a voltage regulator |
| Junction transistor |
| Transistor action |
| Characteristics or a transistor |
| Transistor as an amplifier and oscillator |
| Logic gates or, and, not, nand and nor |
| Transistor as a switch |
Communications system |
|---|
| Propagation of electromagnetic waves in the atmosphere |
| Sky and space wave propagation |
| Need for modulation |
| Amplitude and frequency modulation |
| Bandwidth of signals |
| Bandwidth of transmission medium |
| Basic elements of a communication system |
Experimental skills |
|---|
| Familiarity with the basic approach and observations of the experiments and activities |
| Vernier callipers and its use to measure internal and external diameter and depth of a vessel |
| Screw gauge and its use to determine thickness/diameter of thin sheet/wire |
| Simple pendulum-dissipation of energy by plotting a graph between square of amplitude and time |
| Meter scale and mass or a given object by principle of moments |
| Young's modulus of elasticity of the material of a metallic wire |
| Surface tension of water by capillary rise and effect of detergents |
| Co-efficient or viscosity of a given viscous liquid by measuring terminal velocity of a given spherical body |
| Plotting a cooling curve for the relationship between the temperature of a hot body and time |
| Speed of sound in air at room temperature using a resonance tube |
| Specific heat capacity of a given solid and liquid by method of mixtures |
| Resistivity of the material of a given wire using metre bridge |
| Resistance of a given wire using Ohm's law |
| Potentiometer |
| Comparison or EMF of two primary cells |
| Determination of internal resistance of a cell |
| Resistance and figure of merit of a galvanometer by half deflection method |
| Focal length of |
| Convex mirror |
| Concave mirror |
| Convex Iens using parallax method |
| Plot of angle of deviation vs angle of incidence for a triangular prism |
| Refractive index of a glass slab using a travelling microscope |
| Characteristic curves of a p-n junction diode in forward and reverse bias |
| Characteristic curves of a Zener diode and finding reverse break down voltage |
| Characteristic curves of a transistor and finding current gain and voltage gain |
| Identification of diode, LED, transistor, IC, resistor, capacitor from mixed collection of such items |
| Using multimeter to: i) Identify base of a transistor, ii) distinguish between NPN and PNP type transistor, iii) See the unidirectional flow of current in case of a diode and an LED, iv) Check the correctness or otherwise of a given electronic component |
Chemistry: Unit 01
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 |
States of matter |
|---|
| Gaseous state |
| Measurable properties of gases |
| Gas laws-Boyles Iaw,Charles law,Graham's law of diffusion,Avogadro's law and Dalton's law of partial pressure |
| Concept of absolute scale of temperature |
| Ideal gas equation |
| Kinetic theory of gases, average, root mean square and most probable velocities and their relation with temperature |
| 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 |
| Solid state: Classification of solids |
| Molecular, ionic, covalent and metallic solids |
| Elementary idea of amorphous and crystalline solids |
| Bragg's law and its applications |
| Unit cell and lattices |
| Packing in solids |
| Voids |
| Calculations involving unit cell parameters |
| Imperfection in solids |
| Electrical and magnetic properties |
Atomic structure |
|---|
| Thomson and Rutherford atomic models and their limitations |
| Nature of electromagnetic radiation |
| Photoelectric effect |
| Spectrum of hydrogen atom and its postulates |
| Bohr model of hydrogen atom and its postulates |
| Derivation of the relations for 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 mechanical model of atom and its important features |
| Concept of atomic orbitals as one electron wave functions |
| Lectron wave functions: variation of Ѱand Ѱ² with r for Is and 2s orbitals: various quantum numbers |
| 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 |
Chemical bonding and molecular structure |
|---|
| Kossel - lewis approach to chemical bond formation |
| Concept of ionic and covalent bonds |
| Ionic bonding and 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 theory and shapes of simple molecules |
| Quantum mechanical approach to covalent bonding |
| Valence bond theory and its important features |
| Resonance |
| Molecular orbital theory and its important features |
| LCAOS |
| Types of molecular orbitals |
| Sigma and pi-bonds |
| Molecular orbital electronic configurations of homo nuclear diatomic molecules |
| Concept of bond order |
| Bond length and bond energy |
| Elementary idea of metallic bonding |
| Hydrogen bonding and its applications |
Chemical thermodynamics |
|---|
| Fundamentals of thermodynamics |
| System and surroundings |
| Extensive and intensive properties |
| State functions |
| Types of processes |
| First law or thermodynamics |
| Concept of work, heat, internal energy and enthalpy |
| Heat capacity and molar heat capacity |
| Hess's law of constant heat summation |
| Enthalpies of bond dissociation |
| Combustion |
| Formation |
| Atomization |
| Sublimation |
| Phase transition |
| Hydration |
| Ionization and solution |
| Second law of thermodynamics |
| Spontaneity of processes |
| ∆S of the universe and ∆G of the system as criteria for spontaneity |
| Standard Gibbs energy change and equilibrium constant |
Solutions |
|---|
| Different methods for expressing concentration of solution |
| Molality, molarity, mole fraction, percentage, vapour pressure of solutions and Raoult's law |
| Ideal and non-ideal solutions |
| Composition of vapour pressure |
| Plots for ideal and non-ideal solutions |
| Colligative properties of dilute solutions |
| Relative lowering of vapour pressure |
| Depression of freezing point |
| 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 |
Equilibrium |
|---|
| Meaning of equilibrium |
| 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 |
| Law of chemical equilibrium |
| Equilibrium constants and their significance |
| Significance of ∆G and ∆G' in chemical equilibria |
| Factors affecting equilibrium concentration, pressure and temperature |
| Effect of catalyst |
| Le Chatelier's principle |
| Ionic equilibrium |
| Weak and strong electrolytes |
| Ionization of electrolytes |
| Various concepts of acids and bases and their ionization |
| Acid - base equilibria and ionization constants |
| Ionization of water |
| Ph scale |
| Common ion effect |
| Hydrolysis of salts and pH of their solutions |
| Solubility of sparingly soluble salts and solubility products |
| Buffer solutions |
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 |
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 |
| 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 and their characteristics,rate of a chemical reaction |
| Factors affecting the rate of reactions,concentration, temperature, pressure and catalyst,effect of temperature on rate of reactions |
| Arrhenius theory |
| Activation energy and its calculation |
| Collision theory of bimolecular gaseous reactions |
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 and lyophobic |
| Multi molecular |
| Macromolecular and associated colloids |
| Preparation and properties of colloids |
| Tyndall effect |
| Brownian movement |
| Electrophoresis |
| Dialysis |
| Coagulation and flocculation |
| Emulsions and their characteristics |
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 |
General principles and process of Isolation of metals |
|---|
| Mode of occurrence of elements in nature |
| Minerals |
| Ores |
| Steps involved in the extraction or metals |
| Concentration |
| Reduction and refining with special reference to the extraction of Al, Cu, Zn and Fe |
| Thermodynamic and electrochemical principles involved in the extraction of metals |
Hydrogen |
|---|
| Position of hydrogen in periodic table |
| Isotopes |
| Preparation, properties and uses of hydrogen |
| Physical and chemical properties of water and heavy water |
| Structure and preparation of hydrogen peroxide |
| Reactions and uses of hydrogen peroxide |
| Classification of hydrides |
| Classification of ionic, covalent and interstitial |
| Hydrogen as a fuel |
S - block elements - alkali and alkaline earth metals |
|---|
| General introduction of group 1 and 2 Elements |
| Electronic configuration and general trends in physical and chemical properties of elements |
| Anomalous properties of the first element of each group |
| Diagonal relationships |
| Preparation & 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 |
P - block elements |
|---|
| General Introduction of Group 13 to 18 Elements |
| Electronic configuration and general trends in physical and chemical properties of elements across the periods and down the groups |
| Unique behaviour or the first element in each group |
P - block elements - group 13 elements |
|---|
| Preparation, properties and uses of boron and aluminium |
| Structure, properties and uses of borax, boric acid, diborane, boron trifluoride, aluminium chloride and alums |
| Structure, properties and uses of boric acid |
| Structure, properties and uses of diborane |
| Structure, properties and uses of boron trifluoride |
| Structure, properties and uses of aluminium chloride and alums |
P - block elements - group 14 elements |
|---|
| Tendency for catenation |
| Structure, properties and uses of allotropes and oxides of carbon, silicon tetrachloride, silicates. Zeolites and silicones |
P - block elements - group 15 elements |
|---|
| Properties and uses or nitrogen and phosphorus |
| Allotrophic forms of phosphorus |
| Preparation, properties, structure and uses of ammonia, nitric acid, phosphine and phosphorus halides |
| Structures of oxides and oxoacids of nitrogen and phosphorus |
P - block elements - group 16 elements |
|---|
| Preparation, properties, structures and uses of ozone |
| Allotropic forms or sulphur |
| Preparation, properties, structures and uses of sulphuric acid |
| Structures of oxoacids of sulphur |
P - block elements - group 17 elements |
|---|
| 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 |
P - block elements - group 18 elements |
|---|
| Occurrence and uses of noble gases |
| Structures of fluorides and oxides of xenon |
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 and catalytic behaviour |
| Magnetic properties |
| Complex formation |
| Interstitial compounds |
| Alloy formation |
| Preparation, properties and uses of K, Cr, O, and KMnO4 |
| Inner Transition Elements |
| Electronic configuration of lanthanoids |
| Actinoids-oxidation states and lanthanoid contraction |
| Electronic configuration and oxidation states of actinoids |
Co-ordinations compound |
|---|
| Introduction to co-ordination compounds |
| Werner's theory |
| Ligands |
| Co-ordination number |
| Denticity |
| Chelation |
| IUPAC nomenclature of mononuclear co-ordination compounds |
| Isomerism - Structural and stereoisomerism |
| Bonding |
| Valence bond approach and basic ideas of crystal field theory |
| Colour and magnetic properties |
| Importance of co-ordination compounds |
Environmental chemistry |
|---|
| Environmental pollution |
| Atmospheric, water and soil |
| Atmospheric pollution |
| Tropospheric and stratospheric |
| Tropospheric pollutants - Gaseous pollutants |
| Oxides of carbon, nitrogen and sulphur, hydrocarbons and their sources |
| Harmful effects and prevention |
| Greenhouse effect and global warming |
| Acid rain |
| Particulate pollutants-smoke, dust, smog. fumes, mist and their sources,harmful effects and prevention |
| Stratospheric pollution |
| Formation and breakdown of ozone |
| Depletion or ozone layer and its mechanism and effects |
| Water pollution |
| Major pollutants such as pathogens, organic wastes and chemical pollutants and their harmful effects and prevention |
| Soil pollution |
| Major pollutants such as pesticides their harmful effects and prevention |
| Strategies to control environmental pollution |
Purification and characteristics of organic compounds |
|---|
| Purification |
| Crystallization |
| Sublimation |
| Distillation |
| Differential extract ion and chromatography |
| Principles and their applications |
| Qualitative analysis |
| Detection of nitrogen, sulphur, phosphorus and halogens |
| Quantitative analysis |
| Estimation of carbon, hydrogen, nitrogen, halogens, sulphur and phosphorus |
| Calculations or empirical formulae and molecular formulae |
| Numerical problems in organic quantitative analysis |
Some basic principles of organic chemistry |
|---|
| Tetra valency of carbon |
| Shapes of simple molecules |
| Hybridization of 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 of 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 |
| Electrometric effect |
| Resonance and hyper conjugation |
| Common types of organic reactions |
| Substitution, addition, elimination and rearrangement |
Hydrocarbons |
|---|
| Classification |
| Isomerism - Structural and stereoisomerism |
| IUPAC nomenclature |
| General methods of preparation, properties and reactions |
| Alkanes |
| Conformations |
| Sawhorse and Newman projections |
| Mechanism of halogenation of alkanes |
| Alkenes |
| Geometrical isomerism |
| Mechanism of electrophilic addition |
| Addition of hydrogen, halogens, water, hydrogen halides |
| 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 functional group in mono-substituted benzene |
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 |
Organic compounds containing oxygen |
|---|
| General Methods of Preparation, Properties, Reactions and Uses |
| Alcohols Phenols and Esther |
| Identification of primary, secondary and tertiary alcohols |
| Mechanism of dehydration |
| Phenols |
| Acidic nature |
| Electrophilic substitution reactions, halogenation, nitration, sulphonation, Friedel-Crafts alkylation and acylation |
| Halogenation, nitration and sulphonation |
| Reimer-Tiemann reactionEthers |
| 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 |
| Grignard reagent |
| Oxidation |
| Reduction |
| Acidity of α-hydrogen |
| Aldol condensation |
| Cannizzaro reaction |
| Haloform reaction |
| Chemical tests to distinguish between aldehydes and ketones |
| Carboxylic acids: formation of esters, acid chlorides and amides, ester hydrolysis |
| Acidic strength and factors affecting it |
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 |
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 |
Biomolecules |
|---|
| General introduction and importance or biomolecules |
| Classification of carbohydrates |
| Aldoses and ketoses |
| Monosaccharides and constituent monosaccharides of oligosaccharides |
| Proteins |
| Elementary Idea of α-amino acids, peptide bond, polypeptides |
| Primary, secondary, tertiary and quaternary structure of proteins |
| Denaturation of proteins and enzymes |
| Classification and functions of vitamins |
| Nucleic acid |
| Chemical constitution of DNA and RNA |
| Biological functions of nucleic acids |
Chemistry in everyday life |
|---|
| Chemicals in medicines-Analgesies,tranquilizers,antiseptics,disinfectants,antimicrobials,antifertility drugs,antibiotics,antacids,antihistamins-their meaning and common examples |
| Chemicals in food-Preservatives,artificial sweatening agents-common examples, Cleansing agents - -Soaps and detergents,cleansing action |
Principles related to practical chemistry |
|---|
| Detection of extra elements in organic compounds |
| Detection of the functional groups |
| Alcoholic and phenolic |
| Aldehyde and ketone |
| Carboxyl and amino groups in organic compound |
| Chemistry involved in the preparation or the following: Inorganic compounds: Mohr's salt,potash alum; Organic compounds:Acetanilide,P nitroacetanilide,aniline yellow,iodoform |
| Chemistry involved in the titrimetric exercise |
| Acids, bases and the use of indicators |
| Oxalic-acid vs mohr's salt vs KMnO4 |
| Chemical principles involved in the qualitative salt analysis |
| Cations |
| Anions |
| Chemical principles involved in the experiments |
| Enthalpy of solution of CuSO4 |
| Enthalpy or neutralization of strong acid and strong base |
| Preparation of lyophilic and lyophobic sols |
| Kinetic study or reaction of iodide with hydrogen peroxide at room temperature |
JEE Main Paper 2 Syllabus
Drawing: Unit 01
Awareness of person, place, building and materials |
|---|
| Objects |
| Texture related to architecture and build-environment |
| Visualising three dimensional objects from two dimensional drawings |
| Visualising different sides or three dimensional objects |
| Analytical reasoning mental ability (visual,numerical and verbal) |
Three-dimensional |
|---|
| Perception: understanding and appreciation of scale and proportion of objects,building forms and elements,colour texture,harmony and contrast |
| Design and drawing or geometrical or abstract shapes and patterns in pencil |
| Transformation of forms both 2D and 3D union |
| Subtraction, rotation and development or surfaces and volumes |
| Generation of plan |
| Elevations and 3D views of objects |
| Creating two dimensional and three dimensional compositions using given shapes and forms |
| Sketching of scenes and activities from memory of urbanscape (public space,market,festivals,street scenes,monuments,recreational spaces etc.) |
| Landscape(river fronts,jungles,gardens,trees,plants etc.) and rural life |
JEE Main 2021 Books
| Best books for JEE Main Physics | |
|---|---|
| Name of the book | Author |
| Concepts of physics (Vol. 1 & Vol. 2) | by H.C Verma |
| Fundamentals of Physics | by Halliday, Resnick & walker |
| Understanding Physics: Set of books for | by D C Pandey (Arihant Publications) |
| Problems in General Physics | by I.E Irodov |
| Problems in physics | by SS Krotov |
| Problems and solution of physics | by Shashi bhushan tiwari |
| Best books for JEE Main 2021 Chemistry | |
| Name of the book | Author |
| NCERT Textbooks (for Class XI and XII) | |
| Modern Approach to Chemical Calculations | by R.C. Mukherjee |
| Organic Chemistry | by O P Tandon |
| Concise Inorganic Chemistry | by J D Lee |
| Physical Chemistry | by P.W. Atkins |
| Organic Chemistry | by Morrison & Boyd |
| Concept of Physical Chemistry | by P Bahadur |
| Best books for JEE Main 2021 Mathematics | |
| Name of the book | Author |
| Objective Mathematics | by R D Sharma |
| The Elements Of Coordinate Geometry | by S L Loney |
| Play with Graphs | by Amit M Agarwal (Arihant Publications) |
| Algebra | by Dr S K Goyal Arihant Publications |
| Differential Calculus | by Amit M Agarwal (Arihant Publications) |
| Integral Calculus | by Amit M Agarwal (Arihant Publications) |
| Complete mathematics for JEE Main | by Ravi Prakash (Author), Ajay Kumar (Author), Usha Gupta (Author) |
| Plane Trigonometry | by S L Loney |
JEE Main 2020 Exam Centers
| State | City | |
|---|---|---|
| Andaman and Nicobar Islands | Port Blair | |
| Andhra Pradesh | Chittoor Anantapur Eluru Guntur Kurnool Kakinada Nellore Rajahmundry Tirupati Vijayawada Visakhapatnam Vizianagaram Bhimavaram Ongole Srikakulam Narasaraopet Proddatur Surampalem Chirala Kadapa | |
| Assam | Dibrugarh Guwahati Jorhat Silchar Tezpur | |
| Bihar | Arrah Bhagalpur Gaya Muzaffarpur Patna Purnea Darbhanga | |
| Chandigarh | Chandigarh | |
| Chhattisgarh | Bhilai Bilaspur Raipur Durg | |
| Daman and Diu | Daman Diu | |
| Delhi | Delhi | |
| Goa | Panaji Margao | |
| Gujarat | Anand Bhavnagar Jamnagar Rajkot Surat Vadodara Valsad Junagadh Himatnagar Gandhinagar Mehsana | |
| Haryana | Ambala Faridabad Gurugram Hisar Karnal Kurukshetra Panipat Sonipat Yamuna Nagar | |
| Himachal Pradesh | Shimla Solan Hamirpur Mandi Una Kullu Bilaspur Kangra Palampur | |
| Jammu and Kashmir | Jammu Srinagar Leh Samba | |
| Jharkhand | Dhanbad Jamshedpur Ranchi Bokaro Steel City Hazaribagh | |
| Karnataka | Bellary Bidar Hassan Udupi Belgaum Bengaluru Gulbarga Hubballi Mangaluru Mysore Shivamogga Tumkur Dharwad Manipal Davanagere | |
| Kerala | Alappuzha Ernakulam Kannur Kollam Kottayam Kozhikode Malappuram Palakkad Thiruvananthapuram Thrissur Idukki Kasaragod Pathanamthitta Chengannur Angamaly Muvattupuzha | |
| Madhya Pradesh | Bhopal Gwalior Indore Jabalpur Rewa Sagar Satna Ujjain Balaghat Betul Chhindwara | |
| Maharashtra | Ahmednagar Akola Amravati Aurangabad Jalgaon Kolhapur Mumbai Nagpur Nanded Nashik Pune Solapur Thane Chandrapur Dhule Latur Raigad Ratnagiri Sangli Satara Wardha Navi Mumbai | |
| Manipur | Imphal | |
| Meghalaya | Shillong | |
| Mizoram | Aizawl | |
| Nagaland | Dimapur Kohima | |
| Odisha | Balasore Berhampur Bhubaneswar Cuttack Rourkela Sambalpur Ganjam Dhenkanal | |
| Puducherry | Puducherry | |
| Punjab | Amritsar Jalandhar Ludhiana Patiala Sangrur Fatehgarh Sahib Pathankot Bathinda Mohali | |
| Rajasthan | Ajmer Alwar Bikaner Jaipur Jodhpur Kota Sikar Udaipur Sri Ganganagar | |
| Sikkim | Gangtok | |
| Tamil Nadu | Chennai Coimbatore Kanyakumari Madurai Namakkal Salem Tiruchirappalli Tirunelveli Cuddalore Thanjavur Thoothukudi Vellore Virudhunagar Nagercoil Kanchipura Tiruvallur | |
| Telangana | Hyderabad Karimnagar Khammam Warangal Mahabubnagar Nalgonda Secunderabad K.V.Rangareddy | |
| Tripura | Agartala | |
| Uttar Pradesh | Agra Aligarh Allahabad Bareilly Ghaziabad Gorakhpur Greater Noida Noida Jhansi Kanpur Lucknow Meerut Mathura Moradabad Muzaffarnagar Varanasi Faizabad Sitapur | |
| Uttarakhand | Dehradun Haldwani Haridwar Pantnagar Roorkee Nainital | |
| West Bengal | Asansol Durgapur Hooghly Howrah Kalyani Kolkata Siliguri Burdwan | |
| Arunachal Pradesh | Itanagar Naharlagun | |
| Dadra and Nagar Haveli | Dadra and Nagar Haveli | |
| Lakshadweep | Kavaratti | |
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Joint Entrance Exam
(JEE)
Joint Entrance Exam Main (JEE Main) is the national level computer-based test conducted by the National Testing Agency.
Question Papers
JEE MAINS 2020
10/12/2020
JEE MAINS 2019
10/08/2019
JEE MAINS 2018
025/08/2018
JEE MAINS 2017
20/07/2017
