**WBJEE 2021 Syllabus** will consist of questions asked from Mathematics, Chemistry, and Physics. WBJEE 2021 Examination is organized by the West Bengal Joint Entrance Examinations Board. WBJEE is a state-level examination for West Bengal students. Qualified students of the entrance examination will get admissions into various government and private colleges in West Bengal. WBJEE is entrance test provided to offer admissions in multiple UG programmes in engineering, technology, architecture and pharmacy. Candidates can check the details of the complete WBJEE syllabus 2021 in this article,

## WBJEE 2021 Syllabus

Contents

Students must go through the WBJEE syllabus before preparing for the entrance examination. The question paper for the test will contain various subjects like physics, chemistry, and mathematics. Students can go through the syllabus through this article.

### Physics Syllabus

The syllabus for Physics includes:

**Physical World, Measurements, Units & Dimensions:** Units & dimensions, Measurements, Physical World, error in measurements, , significant figures dimensional analysis & its applications.

**Bulk Properties of Matter:** Young’s modulus, Elasticity, Hooke’s law, bulk modulus, Poisson’s ratio elastic potential energy, rigidity modulus, shear, buoyancy, Pascal’s law, Fluid pressure: Effect of gravity on fluid pressure Pressure due to a fluid column, phenomena involving surface tension, Surface tension: angle of contact, Surface energy, capillary rise.

**Laws of Motion:** Newton’s laws of Motion using algebra & calculus, Work, conservation of linear momentum with applications, elastic & inelastic collisions, banking of roads, relative velocity, , inertial & non inertial frames, impulse centripetal force, projectile motion & uniform circular motion, power, energy Work, work done by constant & variable forces, work-energy theorem, forces, PE of a spring, PE & KE, conservation of mechanical energy, Motion of centre of mass, conservative and non-conservative, connected systems, Motion of connected system, torque, the equilibrium of rigid bodies, Friction: Centre of the mass of the two-particle system, conservation of angular momentum moments of inertia of simple geometric bodies (2D) [without derivation], friction and laws of friction.

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

**Current Electricity:** Electric current, & conductor, Ohm’s law, electrical resistance, drift velocity’ mobility & their Relation with electric current, colour codes, Ohmic and non-Ohmic conductors, carbon resistors, the combination of resistances, electrical energy & power, the temperature dependence of resistance, variety of cells, secondary cells, (introductory) Kirchhoff’s laws of the electrical network, electric cell, simple applications, emf and internal resistance of an electric cell, the principle of Wheatstone bridge, thermoelectricity, Peltier effect, thermo emf, See beck effect, meter bridge and potentiometer & their uses.

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

**Oscillations & Waves:** Periodic Motion –period, frequency, Simple harmonic Motion (SHM) & its equation; phase, time-displacement equation, restoring force & force const, energy in SHM- KE & PE, resonance wave motion, the equation for progressive wave, free, forced & damped oscillations (initial ideas), SHM in different systems, longitudinal & transverse waves, factors affecting the velocity of sound in air, sound waves, principles of superposition of waves, Newton’s formula & Laplace’s correction, the reflection of waves, fundamental mode, beats, standing waves in strings & organ pipes, harmonics &overtones, Doppler effect.

**Electromagnetic Waves:** Transverse nature of electromagnetic waves Electromagnetic waves and their characteristics (qualitative ideas only), electromagnetic spectrum, applications of the waves from the different parts of the spectrum.

**Atomic Physics:** Alpha-particle scattering experiment Rutherford’s nuclear atom model of the atom, energy levels in a hydrogen atom, hydrogen spectrum, Bohr model of the hydrogen atom, continuous & characteristic x-ray’s.

**Optics II (Wave Optics):** Scattering of light – blue colour of the sky, reflection & refraction of plane wave at a plane surface using wave optics: wavefront & Huygens’ principle, elementary idea of Raman effect, wavefronts, Young’s double-slit experiment & expression for fringe width, proof of laws of reflection & refraction using Huygens’ principle Interference, coherent sources, Fraunhofer diffraction due to a single slit.

**Solid-state Electronics:** Energy bands in solids (qualitative ideas only), semiconductor diode – I-V characteristics in forward & reverse bias, solar cell & Zener diode conductors, insulators & semiconductors, diode as a rectifier; I-V characteristics of LED, photodiode, Zener diode as a voltage regulator,characteristics of a BJT, BJT as an amplifier (CE configuration) & oscillator, junction transistor (BJT), transistor action, logic gates (OR, AND, NOT, NAND & NOR).

### Syllabus for Mathematics

**Algebra AP, GP, HP:** Definitions of A. P. and GP; General term Arithmetic/Geometric series, A.M., GM and their Relation; Summation of first n-terms of series ∑n, ∑n²,∑n3; Infinite GP series and its sum.

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

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

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

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

**Co-ordinate Geometry of Three Dimensions:** Direction cosines and direction ratios, equation of a straight line, equation of a plane, the distance between two points and section formula, the distance of a point from a plane.

**Sets, Relations and Mappings:** Idea of sets, subsets, power set, complement, union, intersection and difference of sets, Venn diagram, Inclusion/ Exclusion formula for two or three finite sets, Relation and its properties, De Morgan’s Laws, Cartesian product of sets, Equivalence relation — definition and elementary examples, injective, subjective and bijective mappings, mappings, range and domain, the composition of mappings, the inverse of a mapping.

**Integral Calculus:** Integration by parts, indefinite integral of standard functions, : Integration as a reverse process of differentiation, Integration by substitution and partial fraction, Fundamental theorem of integral calculus and its applications Properties of definite integrals, , Definite integral as a limit of a sum with equal subdivisions.

**Logarithms:** Definition; General properties, Change of the base.

**Polynomial Equation:** nth degree equation has precisely n roots (statement only), Relations between roots and coefficients, Quadratic Equations: Quadratic equations with real coefficients, Nature of roots; Formation of a quadratic equation sign and magnitude of the quadratic expression ax2 +bx+c (where a, b, c are rational numbers and a ≠ 0).

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

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

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

### Syllabus for Chemistry

**Atomic Structure:** Concept of Nuclear Atom – electron, proton and neutron (charge and mass), Rutherford’s model and its limitations, atomic number, Extranuclear structure; Line spectra of the hydrogen atom, Bohr’s model of the hydrogen atom and its rules, Quantization of energy (Planck’s equation E = hν), Somerfield’s modifications (elementary idea), The four quantum numbers, The Aufbau Principle; Pauli’s Exclusion Principle and Hund’s Rule, ground state electronic configurations of many-electron atoms and monoatomic ions.

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

**The Periodic Table and Chemical Families:** Modern periodic law (based on the atomic number), Modern periodic table based on electronic configurations, 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, groups (Gr. 1-18) and periods.

**Gaseous State: **The absolute scale of temperature, Boyle’s Law and Charles Law, kinetic theory of gases, Measurable properties of gases, root mean square and most probable velocities and their relationship with temperature, , Grahams Law of gaseous diffusion, Liquefaction of gases, real gases, van der Waals equation, Numerical problems, ideal gas equation – average, Daltons Law of partial pressure, Deviations from ideal behaviour

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

**Chemical Dynamics:** Factors affecting the rate of chemical reactions (concentration, pressure, temperature, catalyst), Arrhenius equation and concept of activation energy, Concept of collision theory, Order and molecularity (determination excluded), First order reactions, half-life (numerical problems), examples of first-order and second-order reactions, the rate constant.

**Environmental Chemistry:** Common modes of pollution of air, water and soil, critical chemical reactions in the atmosphere, Smog; major atmospheric pollutants, Global warming pollution due to industrial wastes, Ozone layer, ozone hole, Green House effect, green chemistry as an alternative tool for reducing pollution, strategies for control of environment pollution.

**Hybridization of Carbon:** Isomerism – constitutional and stereoisomerism, IUPAC nomenclature of simple organic compounds – hydrocarbons, σ – and π – bonds, Geometrical and optical Isomerism of compounds containing up to two asymmetric carbon atoms, mono and functional molecules only (alicyclic and heterocyclic compounds excluded).

**General Principles of Metallurgy:** Occurrence, the concentration of ores, the mineral wealth of India, production and purification of metals, Typical metals (Na, Ca, Al, Fe, Cu and Zn) – occurrence, extraction, purification (where applicable), properties and reactions with air, water, acids and non-metals. Manufacture of steels and alloy steel (Bessemer, Open-Hearth and LD process). Chemistry in Industry Ammonia (Haber’s process), uses of Sulphuric acid (contact process), Nitric acid (Ostwald’s method), Large scale production (including physicochemical principles where applicable, omitting technical details)sodium carbonate (Solvey process).

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