JEE Advanced Sample Paper

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DETAILS

Type of Sample Paper

JEE Advanced sample papers with solutions PDF

Time Allowed to Solve the Sample Paper

180 minutes 

Number of Sections in the JEE Advanced sample paper PDF download

Three Sections

• Physics
• Chemistry
• Maths 

Total Number of Questions and Marks

• 51 questions
• 180 marks 

Types of Questions 

Four Types

• MRQ- Multiple Response Questions
• MCQ- Multiple Choice Questions
• NUM- Numerical Value Questions
• MATCH- Matching Questions

Marking Scheme 

MRQ

• +4 marks for correct response 
• -2 marks for incorrect response
• +1-3 marks for partially correct response

MCQ

• +3 marks for right answer
• -1 mark for wrong answer

NUM

• +4 marks for correct response
• 0 marks for incorrect response

MATCH

• +3 marks for right answer
• -1 mark for wrong answer

Availability of JEE Advanced sample papers free download PDF

At www.selfstudys.com 

• JEE Advanced Sample Paper Set 1

• JEE Advanced Sample Paper Set 2

• JEE Advanced Sample Paper Set 3

• JEE Advanced Sample Paper Set 4

• JEE Advanced Sample Paper Set 5

JEE ADVANCED SAMPLE PAPER SYLLABUS

Physics 

General 

General units and dimensions, dimensional analysis; least count, significant figures; Methods of measurement and error analysis for physical quantities of the following experiments: Experiments based on Vernier calipers and screw gauge (micrometer), Determination of g using simple pendulum, Young’s modulus - elasticity of the material Surface tension of water by capillary rise and effect of detergents. Specific heat of liquid using a calorimeter, focal length of a concave mirror and a convex lens using the u-v method, Speed of sound using resonance column, Verification of Ohm’s law using a voltmeter and ammeter, and specific resistance of the material of a wire using meter bridge and post office box. 

Mechanics 

Kinematics in one and two dimensions (Cartesian coordinates only), projectiles; Uniform circular motion; Relative velocity. 

Newton’s laws of motion; Inertial and uniformly accelerated frames of reference; Static and dynamic friction; Kinetic and potential energy; Work and power; Conservation of linear momentum and mechanical energy. 

Systems of particles; Centre of mass and its motion; Impulse; Elastic and inelastic collisions.

Rigid body, moment of inertia, parallel and perpendicular axes theorems; Angular momentum; Torque; Rolling without slipping of rings, cylinders, and spheres; Equilibrium of rigid bodies.

Linear and angular simple harmonic motions.

Hooke’s Law, Young’s modulus.

Law of gravitation; Gravitational potential and field; Acceleration due to gravity; Kepler’s law, Geostationary orbits, Motion of planets and satellites in circular orbits; Escape velocity. 

Pressure in a fluid; Pascal’s law; Buoyancy; Stoke’s law; Terminal velocity; Bernoulli’s theorem and its applications. Wave motion (plane waves only), longitudinal and transverse waves, superposition of waves, Progressive and stationary waves; Vibration of strings and air columns; Resonance; Beats; Speed of sound in gases; and Doppler effect (in sound). 

Thermal Physics

Thermal expansion of solids, liquids, and gases; Calorimetry, latent heat; Heat conduction in one dimension; Elementary concepts of convection and radiation; Newton’s law of cooling; Ideal gas laws; Specific heats; Isothermal and adiabatic processes, bulk modulus of gases; Equivalence of heat and work; First law of thermodynamics and its applications (only for ideal gases); Second law of thermodynamics; reversible and irreversible processes, Carnot engine and its efficiency; Blackbody radiation: absorptive and emissive powers; Kirchhoff’s law; Wien’s displacement law, Stefan’s law. 

Electricity and Magnetism 

Coulomb’s law; Electric field and potential; Electric potential energy of a system of point charges and of electrical dipoles in a uniform electrostatic field; Electric field lines; Flux of an electric field; Gauss’s law and its application in simple cases. 

Capacitance; Parallel plate capacitor with and without dielectrics; Capacitors in series and parallel; Energy stored in a capacitor.

Electric current; Ohm’s law; Series and parallel arrangements of resistances and cells; Kirchhoff’s law and simple applications.

Biot-Savart’s law and Ampere’s law; Magnetic field near a current-carrying straight wire.

The magnetic moment of a current loop; Effect of a uniform magnetic field on a current loop; Moving coil galvanometer, voltmeter, ammeter, and their conversions. 

Electromagnetic induction: Faraday’s law, Lenz’s law; Self and mutual inductance; RC, LR, LC, and LCR (in series) circuits with d.c. and a.c. sources. 

Electromagnetic Waves

Electromagnetic waves and their characteristics. Electromagnetic spectrum (radio waves, microwaves, infrared, visible, ultraviolet, x-rays, gamma rays) including elementary facts about their uses.

Optics 

Rectilinear propagation of light; Reflection and refraction at plane and spherical surfaces; Total internal reflection; Deviation and dispersion of light by a prism; Thin lenses; Combinations of mirrors and thin lenses; Magnification.

Wave nature of light; Huygens principle, interference limited to Young’s double slit experiment. 

Diffraction due to a single slit. Polarization of light, plane polarized light; Brewster’s law, Polaroids.

Modern Physics

Atomic nucleus; Law of radioactive decay; Decay constant; Half-life and mean life; Binding energy and its calculation; Fission and fusion processes; Energy calculation in these processes.

Photoelectric effect; Bohr’s theory of hydrogen-like atoms; Characteristic and continuous X-rays, Moseley’s law; de Broglie wavelength of matter waves. 

Chemistry 

General Topics

Concept of atoms and molecules; Dalton’s atomic theory; Mole concept; Chemical formulae; Balanced chemical equations; Calculations (based on mole concept and stoichiometry) involving common oxidation-reduction, neutralization, and displacement reactions; Concentration in terms of mole fraction, molarity, molality, and normality.

States of Matter: Gases and Liquids

Gas laws and ideal gas equation, absolute scale of temperature; Deviation form ideality; van der Waals equation; Kinetic theory of gases, average, root mean square and most probable velocities and their relation with temperature; Law of partial pressures; Diffusion of gases. Intermolecular interactions: types, distance dependence, and their effects on properties; Liquids: vapor pressure, surface tension, and viscosity.

Atomic Structure

Bohr model, the spectrum of hydrogen atom; Wave-particle duality; de Broglie hypothesis; Uncertainty principle; Qualitative quantum mechanical picture of the hydrogen atom: Energies, quantum numbers, wave function, and probability density (plots only), shapes of s, p, and d orbitals; Aufbau principle; Pauli’s exclusion principle and Hund’s rule. 

Chemical Bonding and Molecular Structure

Orbital overlap and covalent bond; Hybridization involving s, p, and d orbitals only; Molecular orbital energy diagrams for homonuclear diatomic species; Hydrogen bond; Polarity in molecules, dipole moment; VSEPR model and shapes of molecules (linear, angular, triangular, square planar, pyramidal, square pyramidal, trigonal bipyramidal, tetrahedral, and octahedral).

Chemical Thermodynamics

Intensive and extensive properties, state functions, First law of thermodynamics; Internal energy, work (pressure-volume only) and heat; Enthalpy, heat capacity, standard state, Hess’s law; Enthalpy of reaction, fusion, and vaporization, and lattice enthalpy; Second law of thermodynamics; Entropy; Gibbs energy; Criteria of equilibrium and spontaneity.

Chemical and sonic Equilibrium

Law of mass action; Equilibrium constant and reaction quotient; Le Chatelier’s principle; Solubility product and its applications, common ion effect, pH and buffer solutions; Acids and bases (Bronsted and Lewis concepts); Hydrolysis of salts.

Electrochemistry 

Electrochemical cells and cell reactions; Standard electrode potentials; Electrochemical work, Nernst equation; Electrochemical series, emf of galvanic cells; Faraday’s laws of electrolysis; Electrolytic conductance, specific, equivalent, and molar conductivity, Kohlrausch’s law; Batteries: Primary and secondary, fuel cells; Corrosion.

Chemical Kinetics

Rates of chemical reactions; Order and molecularity of reactions; Rate law, rate constant, half-life; Differential and integrated rate expressions for zero and first order reactions; Temperature dependence of rate constant. Catalysis: Homogeneous and heterogeneous, activity and selectivity of solid catalysts, enzyme catalysis and its mechanism.

Solid State

Classification of solids, crystalline state, seven crystal systems, close-packed structure of solids (cubic and hexagonal), packing in fcc, bcc, and hcp lattices; Nearest neighbors, ionic radii and radius ratio, point defects.

Solutions 

Henry’s law, Raoult’s law; Ideal solutions; Colligative properties” lowering of vapor pressure, the elevation of boiling point, depression of freezing point, and osmotic pressure; Van’t Hoff factor. 

Surface Chemistry

Elementary concepts of adsorption: Physisorption and Chemisorption, Freundlich adsorption isotherm; Colloids: types, methods of preparation, and general properties; Elementary ideas of emulsions, surfactants, and micelles (only definitions and examples). 

Classification of Elements and Periodicity in Properties

Modern periodic law and the present form of the periodic table; electronic configuration of elements; periodic trends in atomic radius, ionic radius, ionization enthalpy, electron gain enthalpy, valence, oxidation states, electronegativity, and chemical reactivity. 

Coordination Compounds

Werner’s theory; Nomenclature, cis-trans and ionization isomerism, hybridization and geometrics of mononuclear coordination compounds; Bonding; Magnetic properties and color of 3-d series coordination compounds; Ligands and spectrochemical series; Stability; Importance and applications; Metal carbonyls.

Isolation of Metals

Metal ores and their concentration; extraction of crude metal from concentrated ores; thermodynamic and electrochemical principles of metallurgy; cyanide process; refining.

Environmental Chemistry

Atmospheric pollution; water pollution; soil pollution; industrial waste; strategies to control environmental pollution; green chemistry.

Basic Principles of Organic Chemistry

Hybridization of carbon; 𝝈 and 𝝅 bonds; Shapes of simple organic molecules; aromaticity; Structural and geometrical isomerism; Stereoisomers and stereochemical relationship of compounds containing only up to two asymmetric centers. 

Chemistry in Everyday Life

Drug-target interaction; Therapeutic action, and examples (excluding structures) of antacids, antihistamines, tranquilizers, analgesics, antimicrobials, and antifertility drugs; Artificial sweeteners (names only); soaps, detergents, and cleansing action.

Maths 

Sets, Relations, and Functions

Sets and their representations, different kinds of sets, algebra of sets, intersection, complement, difference and symmetric difference of sets and their algebraic properties, De-Morgan’s law of union, intersection, difference, and practical problems based on them.

Cartesian product of finite sets, ordered pair, relations, domain and codomain of relations, equivalence relation. 

Function as a special case of relation, functions as mapping, domain, codomain, range of functions, invertible functions, even and odd functions, onto and one-to-one functions, special functions, sum, difference, product, and composition of functions. 

Algebra 

Algebra of complex numbers, addition, multiplication, conjugation, polar representation, properties of modulus and principal argument, triangle inequality, cube roots of unity, geometric interpretations. 

Statement of the fundamental theorem of algebra, Quadratic equations with real coefficients, symmetric functions of roots. 

Arithmetic and geometric progressions, infinite geometric series; the sum of the first n natural numbers.

Matrices 

Matrices as a rectangular array of real numbers, equality of matrices, addition, multiplication by a scalar and product of matrices, transpose of a matrix, elementary row, and column transformations, determinant of a square matrix of order up to three, adjoint of a matrix, properties of these matrix operations, diagonal, symmetric, and skew-symmetric matrices and their properties. 

Probability and Statistics

Random experiment, sample space, different types of events (impossible, simple, compound), addition and multiplication rules of probability, conditional probability, independence of events, total probability, Bayes Theorem, computation of probability of events using permutations and combinations. 

The measure of central tendency and dispersion, mean, median, mode, mean deviation, standard deviation, and variance of grouped and ungrouped data, analysis of the frequency distribution with the same mean but different variance, random variable, mean, and variance of the random variable. 

Trigonometry 

Trigonometric functions, their periodicity, and graphs, addition and subtraction formulae, formulae involving multiple and sub-multiple angles, general solution of trigonometric equations.

Inverse trigonometric functions and their elementary properties. 

Analytical Geometry 

Two dimensions: Cartesian coordinates, the distance between two points, section formulae, and the shift of origin.

Equation of a straight line in various forms, the angle between two lines, distance of a point from a line; Lines through the point of intersection of two given lines, equation of the bisector of the angle between two lines, concurrency of lines; Centroid, orthocentre, incentre, and circumcentre of a triangle.

Equation of a circle in various forms, equations of tangent, normal, and chord. Parametric equations of a circle, intersection of a circle with a straight line or a circle, equation of a circle through the points of intersection of two circles, and those of a circle and a straight line. Equations of a parabola, ellipse, and hyperbola in standard form, their foci, directrices and eccentricity, parametric equations, equations of tangent and normal. Locus problems.

Three dimensions: Distance between two points, direction cosines, and direction ratios, equation of a straight line in space, skew lines, the shortest distance between two lines, equation of a plane, the distance of a point from a plane, the angle between two lines, the angle between two planes, the angle between a line and a plane, coplanar lines. 

Differential Calculus

Limit of a function at a real number, continuity of a function, limit, and continuity of the sum, difference, product, and quotient of two functions, L’Hospital rule of evaluation of limits and functions. 

Continuity of composite functions, intermediate value property of continuous functions.

Derivative of a function, derivative of the sum, difference, product, and quotient of two functions, chain rule, derivatives of a polynomial, rational, trigonometric, inverse trigonometric.

Tangents and normals, increasing and decreasing functions, Rolle’s theorem and Lagrange’s mean value theorem, geometric interpretation of the two theorems, derivatives up to order two of implicit functions.

Integral Calculus

Integration as the inverse process of differentiation, indefinite integrals of standard functions, definite integrals as the limit of sums, definite integral and their properties, fundamental theorem of integral calculus. 

Integration by parts, integration by the methods of substitution and partial functions, and application of definite integrals to the determination of areas bounded by simple curves. Formation of ordinary differential equations, solution of homogeneous differential equations of first order and first degree. 

Vectors 

Addition of vectors, scalar multiplication, dot and cross products, scalar and vector triple products, and their geometrical interpretations.