JEE (Main) Paper 1 (B.E./B.Tech.)

Paper 1 (B.E./B.Tech.)180 minutes300 marks

• Mathematics46

  • Sets, Relations and Functions
    • Sets, operations, power set
    • Relations, equivalence relations
    • Functions: one-one, onto, composition
  • Complex Numbers and Quadratic Equations
    • Algebra of complex numbers, Argand plane, modulus and argument
    • Quadratic equations, relation between roots and coefficients, nature of roots
  • Matrices and Determinants
    • Algebra and types of matrices
    • Determinants of order 2 and 3, area of triangle
    • Adjoint, inverse, solving linear equations, consistency
  • Permutations and Combinations
    • Fundamental principle of counting; P(n,r), C(n,r)
  • Binomial Theorem
    • Positive integral index, general and middle terms
  • Sequence and Series
    • AP and GP, arithmetic and geometric means, AM-GM relation
  • Limit, Continuity and Differentiability
    • Real functions, inverse functions, graphs
    • Limits, continuity, differentiability
    • Differentiation rules; composite and implicit functions; second derivative
    • Rate of change, monotonicity, maxima and minima
  • Integral Calculus
    • Integration by substitution, parts, partial fractions
    • Fundamental theorem, properties of definite integrals
    • Area under simple curves
  • Differential Equations
    • Order and degree
    • Variable separable, homogeneous and linear equations
  • Coordinate Geometry
    • Distance and section formulae, locus, slope
    • Straight lines; centroid, orthocentre, circumcentre
    • Circles
    • Parabola, ellipse, hyperbola (standard forms)
  • Three Dimensional Geometry
    • Distance, section formula, direction ratios and cosines
    • Equation of a line, skew lines, shortest distance
  • Vector Algebra
    • Addition and components of vectors
    • Scalar and vector products
  • Statistics and Probability
    • Mean, median, mode, standard deviation, variance, mean deviation
    • Addition and multiplication theorems, Bayes' theorem, random variable distribution
  • Trigonometry
    • Trigonometric identities and functions
    • Inverse trigonometric functions
• Physics84

  • Units and Measurements
    • Systems of units, SI units, fundamental and derived units
    • Least count, significant figures, errors in measurement
    • Dimensions and dimensional analysis
  • Kinematics
    • Motion in a straight line; uniform and non-uniform motion; x-t and v-t graphs
    • Relative velocity
    • Motion in a plane, projectile motion, uniform circular motion
  • Laws of Motion
    • Newton's laws, momentum, impulse
    • Conservation of linear momentum; equilibrium of concurrent forces
    • Static, kinetic and rolling friction
    • Dynamics of circular motion: level and banked roads
  • Work, Energy and Power
    • Work by constant and variable force; work-energy theorem; power
    • Potential energy of a spring, conservation of mechanical energy, conservative forces
    • Motion in a vertical circle
    • Elastic and inelastic collisions in one and two dimensions
  • Rotational Motion
    • Centre of mass
    • Torque, angular momentum and its conservation
    • Moment of inertia, radius of gyration, parallel and perpendicular axes theorems
    • Equilibrium of rigid bodies; equations of rotational motion
  • Gravitation
    • Universal law of gravitation; variation of g with altitude and depth
    • Kepler's laws of planetary motion
    • Gravitational potential energy and potential; escape velocity
    • Satellites: orbital velocity, time period, energy
  • Properties of Solids and Liquids
    • Elasticity: stress-strain, Hooke's law, Young's, bulk and rigidity moduli
    • Fluid pressure, Pascal's law, viscosity, Stokes' law, terminal velocity, Bernoulli's principle
    • Surface energy, surface tension, angle of contact, capillary rise
    • Thermal expansion, specific heat, calorimetry, latent heat; conduction, convection, radiation
  • Thermodynamics
    • Zeroth and first laws; heat, work and internal energy
    • Isothermal and adiabatic processes
    • Second law; reversible and irreversible processes
  • Kinetic Theory of Gases
    • Equation of state of a perfect gas; work on compressing a gas
    • Kinetic interpretation of pressure and temperature; RMS speed
    • Degrees of freedom, equipartition of energy, specific heats of gases, mean free path
  • Oscillations and Waves
    • Periodic motion, SHM, energy in SHM, spring and simple pendulum
    • Longitudinal and transverse waves, progressive wave, superposition
    • Standing waves in strings and organ pipes, harmonics, beats
  • Electrostatics
    • Charge conservation, Coulomb's law, superposition
    • Electric field, field lines, dipole, torque on a dipole
    • Electric flux, Gauss's law and applications
    • Electric potential, equipotential surfaces, potential energy
    • Conductors, dielectrics, capacitors and their combinations, energy stored
  • Current Electricity
    • Drift velocity, mobility, Ohm's law, resistivity, temperature dependence
    • Internal resistance, emf, combination of cells; series and parallel resistors
    • Kirchhoff's laws, Wheatstone bridge, metre bridge
  • Magnetic Effects of Current and Magnetism
    • Biot-Savart law, Ampere's law and applications
    • Force on moving charges and current-carrying conductors; torque on a loop
    • Moving coil galvanometer, conversion to ammeter and voltmeter
    • Magnetic dipole, bar magnet; para-, dia- and ferromagnetism
  • Electromagnetic Induction and Alternating Currents
    • Faraday's law, Lenz's law, eddy currents, self and mutual inductance
    • Peak and RMS values, reactance, impedance, LCR circuit, resonance, power
    • AC generator and transformer
  • Electromagnetic Waves
    • Displacement current; characteristics of EM waves
    • Electromagnetic spectrum and applications
  • Optics
    • Reflection, refraction, TIR, lenses, prism, optical instruments
    • Huygens' principle, interference (YDSE), diffraction, polarisation
  • Dual Nature of Matter and Radiation
    • Photoelectric effect, Einstein's equation
    • Matter waves, de Broglie relation
  • Atoms and Nuclei
    • Rutherford model, Bohr model, hydrogen spectrum
    • Nuclear size, mass defect, binding energy, fission and fusion
  • Electronic Devices
    • Semiconductors, p-n junction diode, I-V characteristics, rectifier
    • LED, photodiode, solar cell, Zener diode as regulator
    • Logic gates (OR, AND, NOT, NAND, NOR)
  • Experimental Skills
    • Vernier callipers, screw gauge, simple pendulum, metre scale
    • Young's modulus, surface tension, viscosity, speed of sound, specific heat experiments
    • Resistivity (metre bridge), Ohm's law, galvanometer, focal length, prism, diode characteristics
• Chemistry83

  • Some Basic Concepts in Chemistry
    • Matter, Dalton's atomic theory, laws of chemical combination
    • Atomic and molecular masses, mole concept, molar mass
    • Percentage composition, empirical and molecular formulae
    • Chemical equations and stoichiometry
  • Atomic Structure
    • EM radiation, photoelectric effect, hydrogen spectrum, Bohr model
    • Dual nature, de Broglie, Heisenberg uncertainty, quantum mechanical model
    • Quantum numbers, shapes of s, p, d orbitals
    • Aufbau, Pauli, Hund's rule; electronic configuration
  • Chemical Bonding and Molecular Structure
    • Ionic bonding, lattice enthalpy
    • Electronegativity, Fajans' rule, dipole moment, VSEPR
    • Valence bond theory, hybridisation, resonance
    • Molecular orbital theory, bond order
    • Metallic bonding, hydrogen bonding
  • Chemical Thermodynamics
    • System, surroundings, state functions, types of processes
    • First law, enthalpy, Hess's law, enthalpies of reactions
    • Second law, entropy, Gibbs energy, equilibrium constant
  • Solutions
    • Molality, molarity, mole fraction, percentage
    • Vapour pressure, Raoult's law, ideal and non-ideal solutions
    • Colligative properties, van't Hoff factor
  • Equilibrium
    • Physical equilibria, Henry's law
    • Kp, Kc, Le Chatelier's principle
    • Acids and bases, pH, common ion effect, hydrolysis, solubility product, buffers
  • Redox Reactions and Electrochemistry
    • Oxidation number, balancing redox reactions
    • Conductance, molar conductivity, Kohlrausch's law
    • Galvanic cells, electrode potential, Nernst equation, batteries, fuel cells
  • Chemical Kinetics
    • Rate of reaction, order and molecularity, rate law
    • Zero and first order reactions, half-life
    • Effect of temperature, Arrhenius equation, activation energy, collision theory
  • Classification of Elements and Periodicity
    • Modern periodic law, s, p, d, f blocks
    • Atomic and ionic radii, ionization enthalpy, electron gain enthalpy, valence
  • p-Block Elements (Groups 13 to 18)
    • Electronic configuration and trends across periods and down groups
    • Unique behaviour of the first element in each group
  • d- and f-Block Elements
    • Transition elements: properties, oxidation states, colour, magnetism, catalysis
    • K2Cr2O7 and KMnO4
    • Lanthanoids, lanthanoid contraction, actinoids
  • Coordination Compounds
    • Werner's theory, ligands, coordination number, denticity, IUPAC naming
    • Isomerism in coordination compounds
    • VBT and crystal field theory, colour, magnetic properties
  • Purification and Characterisation of Organic Compounds
    • Crystallisation, sublimation, distillation, extraction, chromatography
    • Qualitative and quantitative analysis of elements; empirical formula problems
  • Some Basic Principles of Organic Chemistry
    • Classification, functional groups, IUPAC nomenclature
    • Structural and stereoisomerism
    • Bond fission, carbocations, carbanions, free radicals, electrophiles, nucleophiles
    • Inductive, electromeric, resonance, hyperconjugation
    • Substitution, addition, elimination, rearrangement
  • Hydrocarbons
    • Alkanes: conformations, halogenation mechanism
    • Alkenes: geometrical isomerism, electrophilic addition, Markovnikov, ozonolysis
    • Alkynes: acidic character, addition reactions
    • Benzene, aromaticity, electrophilic substitution, Friedel-Crafts, directive influence
  • Organic Compounds Containing Halogens
    • C-X bond, substitution mechanisms (SN1, SN2)
    • Chloroform, iodoform, freons, DDT: uses and environmental effects
  • Organic Compounds Containing Oxygen
    • Alcohols, phenols and ethers
    • Aldehydes and ketones: nucleophilic addition, aldol, Cannizzaro, haloform
    • Carboxylic acids: acidic strength
  • Organic Compounds Containing Nitrogen
    • Amines: classification, basic character, identification
    • Diazonium salts in synthesis
  • Biomolecules
    • Carbohydrates
    • Amino acids, proteins, enzymes
    • Vitamins, nucleic acids, hormones
  • Principles Related to Practical Chemistry
    • Detection of extra elements and functional groups
    • Preparation of Mohr's salt, potash alum, acetanilide, p-nitroacetanilide, aniline yellow, iodoform
    • Titrimetric exercises (acid-base, KMnO4)
    • Qualitative salt analysis