Candidates who will be taking the** West Bengal Joint Entrance Exam** (WBJEE) for the coming academic admission of 2020 session needs to direct their study routine with a specific planning. The awareness of the **WBJEE Syllabus 2020** should be one of the top priorities of candidates to begin their preparation with. That means, the preparation for the **WBJEE 2020 Examination** must start with the WBJEE Syllabus. The Syllabus for the WBJEE 2020 will include topics from 11th and 12th standard Physics, Chemistry and Mathematics. Other than that candidates will have to go through the **WBJEE Exam Pattern 2020**.

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## About WBJEE 2020 Exam

- The candidate seeking admission to Engineering and Technology degree courses in the state of West Bengal, it is mandatory that the candidate must appear for WBJEE 2020 or
**JEE Main 2020**. - Candidates will be required to appear in two papers for WBJEE, i.e. Paper 1 and Paper 2. Paper 1 will be for Mathematics and Paper 2 will be for Physics and Chemistry Combined.
- Candidates appearing in both Paper-I and Paper-II and who are awarded GMR ranks will be eligible for admission in Engineering/ Technology/ Architecture/ Pharmacy Courses in all institutes.

## WBJEE Syllabus 2020 – Mathematics

Algebra | A.P., G.P., H.P | Definitions of A. P. and G.P.; General term; Summation of first n-terms of series ∑n, ∑n2, ∑n3; Arithmetic/Geometric series, A.M., G.M. and their relation; Infinite G.P. series and its sum |

Logarithms | Definition; General Properties; Change of Base. | |

Complex Numbers | Definition in terms of ordered pair of real numbers and properties of complex numbers; Complex conjugate; Triangle inequality; amplitude of complex numbers and its properties; Square root of complex numbers; Cube roots of unity; De Moivre’s theorem (statement only) and its elementary applications. Solution of quadratic equation in complex number system. | |

Polynomial equation | nth degree equation has exactly n roots (statement only); Quadratic Equations: Quadratic equations with real coefficients; Relations between roots and coefficients; Nature of roots; Formation of a quadratic equation, sign and magnitude of the quadratic expression a x 2 +bx+c (where a, b, c are rational numbers and a ≠ 0). | |

Permutation and combination | Permutation of n different things taken r at a time (r ≤ n). Permutation of n things not all different. Permutation with repetitions (circular permutation excluded). Combinations of n different things taken r at a time (r ≤ n). Combination of n things not all different. Basic properties. Problems involving both permutations and combinations | |

Principle of mathematical induction | Statement of the principle, proof by induction for the sum of squares, sum of cubes of first n natural numbers, divisibility properties like 22n — 1 is divisible by 3 (n ≥ 1), 7 divides 32n+1+2n+2 (n ≥ 1) | |

Binomial theorem (positive integral index) | Statement of the theorem, general term, middle term, equidistant terms, and properties of binomial coefficients. | |

Matrices | Concepts of m x n (m ≤ 3, n ≤ 3) real matrices, operations of addition, scalar multiplication and multiplication of matrices. Transpose of a matrix. The determinant of a square matrix. Properties of determinants (statement only). Minor, cofactor and adjoint of a matrix. Nonsingular matrix. Inverse of a matrix. Finding the area of a triangle. Solutions of system of linear equations. | |

Sets, Relations and Mappings | Mappings: Idea of sets, subsets, power set, complement, union, intersection and difference of sets, Venn diagram, De Morgan’s Laws, Inclusion / Exclusion formula for two or three finite sets, Cartesian product of sets. | |

Relation and its properties. Equivalence relation | Equivalence relation — definition and elementary examples, mappings, range and domain, injective, surjective and bijective mappings, the composition of mappings, inverse of a mapping. | |

Statistics and Probability | Measure of dispersion, mean, variance and standard deviation, frequency distribution. Addition and multiplication rules of probability, conditional probability and Bayes’ Theorem, independence of events, repeated independent trails and Binomial distribution. | |

Trigonometry | Trigonometric functions, addition and subtraction formulae, formulae involving multiple and submultiple angles, general solution of trigonometric equations. Properties of triangles, inverse trigonometric functions and their properties. | |

Coordinate geometry of two dimensions | Distance formula, section formula, area of a triangle, condition of collinearity of three points in a plane. Polar co-ordinates, transformation from Cartesian to polar coordinates and vice versa. Parallel transformation of axes. | |

Concept of locus, locus problems involving all geometrical configurations, Slope of a line. Equation of lines in different forms, angle between two lines. Condition of perpendicularity and parallelism of two lines. Distance of a point from a line. Distance between two parallel lines. Lines through the point of intersection of two lines. Angle bisector | ||

Equation of a circle with a given centre and radius. Condition that a general equation of second degree in x, y may represent a circle. Equation of a circle in terms of endpoints of a diameter. Equation of tangent, normal and chord. Parametric equation of a circle. Intersection of a line with a circle. Equation of common chord of two intersecting circles. | ||

Definition of conic section, Directrix, Focus and Eccentricity, classification based on eccentricity. Equation of Parabola, Ellipse and Hyperbola in standard form, their foci, directrices, eccentricities and parametric equations. | ||

Coordinate Geometry of three dimensions | Direction cosines and direction ratios, distance between two points and section formula, equation of a straight line, equation of a plane, distance of a point from a plane. | |

Calculus | Differential calculus | Functions, domain and range set of functions, Composition of two functions and inverse of a function, limit, continuity, derivative, chain rule and derivative of functions in various forms. Concept of differential. |

Rolle’s Theorem and Lagrange’s Mean Value theorem (statement only). Their geometric interpretation and elementary application. L’Hospital’s rule (statement only) and applications. Second-order derivative. | ||

Integral calculus | Integration as a reverse process of differentiation, indefinite integral of standard functions. Integration by parts. Integration by substitution and partial fraction. Definite integral as a limit of a sum with equal subdivisions. The fundamental theorem of integral calculus and its | |

Differential Equations | Formation of ordinary differential equations, solution of homogeneous differential equations, separation of variables method, linear first order differential equations. | |

Application of Calculus | Tangents and normals, conditions of tangency. Determination of monotonicity, maxima and minima. Differential coefficient as a measure of rate. Motion in a straight line with constant acceleration. Geometric interpretation of definite integral as area, calculation of area bounded by elementary curves and Straight lines. Area of the region included between two elementary curves. | |

Vectors | Addition of vectors, scalar multiplication, dot and cross products, scalar triple product. |

## WBJEE Syllabus 2020 – Physics

Physical World, Measurements, Units & dimensions | Physical World, Measurements, Units & dimensions Units & Dimensions of physical quantities, dimensional analysis & its applications, error in measurements, significant figures. | |

Kinematics | Scalars & vectors, representation of vectors in 3D, dot & cross product & their applications, elementary differential & integral calculus, time-velocity & relevant graphs, equations of motion with uniform acceleration. | |

Laws of motion | Newton’s laws of motion, using algebra & calculus, inertial & non inertial frames, conservation of linear momentum with applications, elastic & inelastic collisions, impulse centripetal force, banking of roads, relative velocity, projectile motion & uniform circular motion Work, power, energy: Work, power, energy Work, work-energy theorem, power, energy, work done by constant & variable forces, PE & KE, conservation of mechanical energy, conservative and non-conservative forces, PE of a spring, | |

Motion of centre of mass, connected systems, Friction | Centre of mass of two-particle system, motion of connected system, torque, equilibrium of rigid bodies, moments of inertia of simple geometric bodies (2D) [without derivation] conservation of angular momentum, friction and laws of friction. | |

Gravitation | Kepler’s laws, (only statement) universal law of gravitation, acceleration due to gravity (g), variation of g, gravitational potential & PE, escape velocity, orbital velocity of satellites, geostationary orbits. | |

Bulk properties of matter | Elasticity, Hooke’s law, Young’s modulus, bulk modulus, shear, rigidity modulus, Poisson’s ratio elastic potential energy | |

Viscosity | Coefficient of viscosity, streamline & turbulent motion, Reynold’s number, Stoke’s law, terminal velocity, Bernoulli’s theorem. | |

Thermodynamics | Thermal equilibrium (Zeroth law of thermodynamics), heat, work & internal energy. 1st law of thermodynamics, isothermal & adiabatic processes, 2nd law of thermodynamics, reversible & irreversible processes. | |

Kinetic theory of gases | Equation of state of a perfect gas, kinetic theory of gases, assumptions in Kinetic theory of gases, concept of pressure. & temperature; rms speed of gas molecules; degrees of freedom, law of equipartition of energy (introductory ideas) & application to specific heats of gases; mean free path, Avogadro number. | |

Electrostatics | Conservation of electric charges, Coulomb’s law-force between two-point charges, forces between multiple charges; superposition principle & continuous charge distribution. Electric field, & potential due to a point charge & distribution of charges, electric field lines electric field due to a dipole; torque on a dipole in uniform electric field; electric flux, Gauss’ theorem & its simple applications, conductors & insulators, free charges & bound charges inside a conductor; dielectrics & electric polarisation, capacitors & capacitance, combination of capacitors in series & in parallel, capacitance of a parallel plate capacitor with & without dielectric medium between the plates, energy stored in a capacitor. | |

Current Electricity | Electric current, & conductor, drift velocity’ mobility & their relation with electric current; Ohm’s law, electrical resistance, Ohmic and non-Ohmic conductors, electrical energy & power, carbon resistors, colour codes, combination of resistances, temperature dependence of resistances, electric cell, emf and internal resistance of an electric cell, PD, combination of cells, secondary cells, (introductory) Kirchoff’s laws of the electrical network, simple applications, the principle of Wheatstone bridge, metre bridge and potentiometer and their uses, thermoelectricity; Seebeck effect; Peltier effect, thermo emf. | |

Magnetics | Current loop as a magnetic dipole & its magnetic dipole moment, magnetic dipole moment of a revolving electron, magnetic field intensity due to a magnetic dipole bar magnet along its axis & perpendicular to its axis, torque on a magnetic dipole (bar magnet) in a uniform magnetic field; magnet as an equivalent solenoid, magnetic field lines; Earth’s magnetic field & its magnetic elements. para-, dia- & ferromagnetic substances, with examples. Electromagnets & the factors affecting their strengths, permanent magnets. | |

Magnetic effect of current | Concept of magnetic field, Oersted’s experiment, Biot – Savart law & its application to current carrying circular loop; Ampere’s law & its applications to infinitely long straight wire, straight and toroidal solenoids; force on a moving charge in uniform magnetic & electric fields, cyclotron frequency; 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 a uniform magnetic field; moving coil galvanometer-its current sensitivity & conversion to ammeter & voltmeter, Inter-conversion of voltmeter & ammeter & change of their ranges. | |

Electromagnetic induction & alternating current: | Electromagnetic induction; Faraday’s laws, induced emf & current; Lenz’s Law, eddy currents, self & mutual induction, alternating currents, peak and RMS value of alternating current and voltage; reactance and impedance; LR & CR circuits, phase lag & lead, LCR series circuit, resonance; power in AC circuits, watt less current. | |

Electromagnetic waves | Electromagnetic waves and their characteristics (qualitative ideas only), transverse nature of electromagnetic waves, electromagnetic spectrum, applications of the waves from the different parts of the spectrum | |

Optics I (Ray optics) | Reflection of light, spherical mirrors, mirror formula. Refraction of light, total internal reflection & its applications, optical fibres, refraction at spherical surfaces, lenses, thin lens formula, lensmaker’s formula. Newton’s relation: Displacement method to find position of images (conjugate points) Magnification, power of a lens, combination of thin lenses in contact, combination of a lens & a mirror refraction and dispersion of light through a prism; optical instruments, human eye, image formation & accommodation, correction of eye defects (myopia, hypermetropia) using lenses, microscopes & astronomical telescopes (reflecting & refracting) & their magnifying powers. | |

Optics II (Wave Optics) | Scattering of the light – blue colour of the sky, elementary idea of Raman effect; wave optics: wavefront & Huygens’ principle, reflection & refraction of plane wave at a plane surface using wavefronts. Proof of laws of reflection & refraction using Huygens’ principle Interference, Young’s double slit experiment & expression for fringe width, coherent sources, Fraunhofer diffraction due to a single slit, Particle nature of light & wave-particle dualism: Photoelectric effect, Hertz and Lenard’s observations; Einstein’s photoelectric equation – particle nature of light, matter waves; wave nature of particles, de Broglie relation. Atomic Physics: Alpha-particle scattering expt Rutherford’s nuclear atom model of atom; Bohr model of hydrogen atom, energy levels in a hydrogen atom, hydrogen spectrum, continuous & characteristic x-rays. Nuclear Physics: Composition & size of nucleus, atomic masses, isotopes, isobars; isotones, radioactivity – alpha, beta & gamma particles/ rays & their properties; radioactive decay law; mass-energy relation, mass defect; binding energy per nucleon & its variation with mass number; nuclear fission & fusion. Solid-state Electronics: Energy bands in solids (qualitative ideas only), conductors, insulators & semiconductors; semiconductor diode – I-V characteristics in forward & reverse bias, diode as a rectifier. I-V characteristics of LED, photodiode, solar cell & Zener diode; Zener diode as a voltage regulator, junction transistor (BJT), transistor action, characteristics of a BJT, BJT as an amplifier (CE configuration) & oscillator; logic gates (OR, AND, NOT, NAND & NOR). |

## WBJEE Syllabus 2020 – Chemistry

Atoms, Molecules and Chemical Arithmetic | For WBJEE Syllabus 2020, read Dalton’s atomic theory; Gay Lussac’s law of gaseous volume; Avogadro’s Hypothesis and its applications. Atomic mass; Molecular mass; Equivalent weight; Valency; Gram atomic weight; Gram molecular weight; Gram equivalent weight and mole concept; Chemical formulae; Balanced chemical equations; Calculations (based on mole concept) involving common oxidation – reduction, neutralization, and displacement reactions; Concentration in terms of mole fraction, molarity, molality and normality. Percentage composition, empirical formula and molecular formula; Numerical problems. |

Atomic Structure | Concept of Nuclear Atom |

Radioactivity and Nuclear Chemistry | For WBJEE Syllabus 2020, read Radioactivity α-, β-, γ rays and their properties; Artificial transmutation; Rate of radioactive decay, decay constant, half-life and average age life period of radio-elements; Units of radioactivity; Numerical problems. Stability of the atomic nucleus – effect of neutron-proton (n/p) ratio on the modes of decay, group displacement law, radioisotopes and their uses (C, P, Co and I as examples) isobars and isotones (definition and examples), elementary idea of nuclear fission and fusion reactions |

The Periodic Table and Chemical Families | Modern periodic law (based on atomic number); Modern periodic table based on electronic configurations, groups (Gr. 1-18) and periods. Types of elements – representative (s-block and p- block), transition (d-block) elements and inner transition (f-block/lanthanides and actinides) and their general characteristics. Periodic trends in physical and chemical properties – atomic radii, valency, ionization energy, electron affinity, electronegativity, metallic character, acidic and basic characters of oxides and hydrides of the representative elements (up to Z = 36). Position of hydrogen and the noble gases in the periodic table; Diagonal relationships. |

Chemical Bonding and Molecular Structure | Valence electrons, the Octet rule, electrovalent, covalent and coordinate covalent bonds with examples; Properties of electrovalent and covalent compounds. Limitations of Octet rule (examples); Fajans Rule. Directionality of covalent bonds, shapes of polyatomic molecules (examples); Concept of hybridization of atomic orbitals (qualitative pictorial approach): sp, sp2, sp3 and dsp2. Molecular orbital energy diagrams for homonuclear diatomic species. |

Coordination Compounds | Introduction, Double salts and complex salts, coordination compounds (examples only), Werner’s theory, coordination number (examples of coordination number 4 and 6 only), colour, magnetic properties and shapes, IUPAC nomenclature of mononuclear coordination compounds. |

States of Matter | Solid States; Liquid States; Gaseous State |

Chemical Energetics and Chemical Dynamics | Chemical Energetics; Chemical Equilibria; Order and molecularity; Chemical Dynamics; |

Physical Chemistry of Solutions | Colloidal Solutions; Electrolytic Solutions; Non-electrolytic Solutions; |

Ionic and Redox Equilibria | Ionic equilibria; Acid-base titrations, acid; Redox Equilibria: Oxidation; |

Hydrogen | Position of hydrogen in periodic table, occurrence, isotopes, preparation, properties and uses of hydrogen, hydrides-ionic covalent and interstitial; physical and chemical properties of water, heavy water, hydrogen peroxide – preparation, reactions and structure and use; hydrogen as a fuel. |

Chemistry of Non-Metallic Elements and their Compounds | Carbon; Oxygen and Sulphur; Halogens; |

Chemistry of Metals | General principles of metallurgy; Lanthanoids; Actinoids; |

Chemistry in Industry | Large scale production and uses of Sulphuric acid, Ammonia, Nitric acid, sodium bicarbonate and sodium carbonate. |

Polymers | Natural and synthetic polymers, methods of polymerization |

Surface Chemistry | Adsorption |

Environmental Chemistry | Common modes of pollution of air, water and soil. Ozone layer, ozone hole |

Chemistry of Carbon Compounds | Hybridization of carbon; Conformations of ethane and n-butane; Electronic Effects. |

Compounds | Alkanes; Alkenes and Alkynes; Oxymercuration. |

Haloalkanes and Haloarenes | Haloalkanes; |

Alcohols | Preparation of alcohols from carbonyl compounds and esters; Reaction; Ethers; Aldehydes and Ketones; Reaction; Carboxylic Acids; Aliphatic Amines; |

Aromatic Compounds | Benzene; Amines; Haloarenes; Phenols; Aromatic Aldehydes |

Application Oriented chemistry | Main ingredients, their chemical natures (structures excluded) and their side effects, if any, of common antiseptics, analgesics, antacids, vitamin-C. |

Introduction to Bio-Molecules | Carbohydrates; ADP and ATP; |

Principles of Qualitative Analysis | Detection of water-soluble non-interfering Acid and Basic Radicals by dry and wet tests from among: Acid Radicals: Cl-, S2-, SO4 2-, NO3– , CO3 2- Basic Radicals: Cu2+, Al3+, Fe3+, Fe2+, Zn2+, Ca2+, Mg2+, Na+ , NH4+ . |

## Download WBJEE Syllabus PDF

**Note- The above details are as per the syllabus of 2019 session. The information will be updated on next in career after the release of official notification.**