**WBJEE 2019 Syllabus** will comprise of subjects like Mathematics, Physics and Chemistry. WBJEE exam will be regulated by the West Bengal Joint Entrance Examinations Board. It is a state level exam conducted for admission in engineering, technology, architecture and pharmacy courses. Students seeking for admission in various colleges of West Bengal state can apply on the basis of WBJEE scores. Here we are providing details about the WBJEE Syllabus 2019.

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## WBJEE 2019 Syllabus

Before preparing for the exam, candidates must be aware of the WBJEE syllabus. In this examination, questions will be asked from **physics**, **chemistry** and **mathematics** subjects. Candidates can check the detailed syllabus from below:

### Syllabus for Physics:

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

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

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

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

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

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

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

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

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

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

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

### Syllabus for Mathematics:

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

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

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

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

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

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

**Co-ordinate geometry of three dimensions**: Direction cosines and direction ratios, equation of a straight line, equation of a plane, distance between two points and section formula, distance of a point from a plane.

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

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

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

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

**Principle of mathematical induction:** Statement of the principle, 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), utherford’s model and its limitations, atomic number, Extra nuclear structure; Line spectra of hydrogen atom, Bohr’s model of hydrogen atom and its limitations, Quantization of energy (Planck’s equation E = hν), Sommerfeld’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 mono – atomic ions.

**The Periodic Table and Chemical Families:** Modern periodic law (based on 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.

**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.

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

**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, rate constant.

**Hydrogen:** Occurrence, isotopes, preparation, properties and uses of hydrogen, Position of hydrogen in periodic table, 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.

**General principles of metallurgy**: Occurrence, concentration of ores, 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 L.D. process).

**Chemistry in Industry:** Large scale production (including physicochemical principles where applicable, omitting technical details) and Ammonia (Haber’s process), uses of Sulphuric acid (contact process), Nitric acid (Ostwald’s process), sodium carbonate (Solvey process).

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

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

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