West Bengal Joint Entrance Examinations or WBJEE 2014 is a common entrance exam. WBJEE 2014 is conducted by West Bengal Joint Entrance Examinations Board for getting admission into the undergraduate courses in Engineering / Technology / Architecture / Medical / Dental and Pharmacy in universities or colleges in West Bengal. Here is the full eligibility criteria and syllabus of WBJEE 2014.
WBJEE 2014 Eligibility Criteria: The students need the following criteria to take WBJEE 2014 exam.
- Candidates must be a citizen of India.
- The admission for degree courses in Engineering / Technology & B.Pharm courses the candidates must possess at least 50% of marks in Physics, Chemistry and Mathematics in their higher secondary examination. For SC / ST / PD candidates 40% marks considered as their minimum marks. The candidates must have not less than 30% in English subject in their higher secondary examination (for all categories). Candidates must be at least 17 (seventeen) years of age as on 31.12.2013. There is no upper age limit.
- For Architecture the students should cleared NATA (National Aptitude Test in Architecture) conducted by the Council of Architecture, New Delhi and necessary document in this regard is to be produced at the time of Counseling.
- For Marine Engineering Courses Candidates must pass Higher Secondary Examination (10+2 level) or its equivalent examination with a minimum of 60% marks in Physics, Chemistry and Mathematics taken together and with at least 50% marks in English either in 10th or in 12th Standard besides having individual pass marks in each of Physics, Chemistry, Mathematics, English and Vernacular (or any other fifth subject). Candidates must be at least 17 (seventeen) years of age or above as on 31.12.2013 and must not be above 25 (twenty five) years of age as on 31.07.2013; as per guidelines of appropriate authority.
WBJEE 2014 Paper Pattern:
The test question paper is separated into two parts. The first part consists of object type questions (80% marks) and 2nd part is of short answer type questions (20% marks). Every question is provided with four choices with one right answer.
The exam will consist of 3 papers-
- Mathematics (100 Marks)
- Physics (75 Marks)
- Chemistry (75 Marks)
WBJEE 2014 Syllabus: WBJEE-2014 Examination, candidates need to appear in 3 (three) papers in the form of written test, to be conducted physically at various Examination Centers with Pen and Paper i.e. as Offline Examination. The subjects will be: i) Mathematics, ii) Physics & iii) Chemistry.
Mathematics syllabus for WBJEE 2014
Unit 1: Algebra
A.P., G.P., H.P.: Definitions of A. P. and G.P.; General term; Summation of first n-terms; A.M. and G.M.; Definitions of H.P. (only 3 terms) and H.M.; Finite arithmetico-geometric series.
Unit 2: Logarithms
Definition; General properties; Change of base.
Unit 3: Complex Numbers
Definition and properties of complex numbers; Complex conjugate; Triangle inequality; Square root of complex numbers; Cube roots of unity; D’Moivre’s theorem (statement only) and its elementary applications.
Unit 4: 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
Unit 5: Permutation & 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
Unit 6: 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)
Unit 7: Binomial Theorem (positive integral index)
Statement of the theorem, general term, middle term, equidistant terms, properties of binomial coefficients.
Unit 8: 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. Determinant of a square matrix. Properties of determinants (statement only). Minor, cofactor and adjoint of a matrix. Nonsingular matrix. Inverse of a matrix. Finding area of a triangle. Solutions of system of linear equations. (Not more than 3 variables).
Unit 9: Sets
Relations and 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.
Unit 10: Probability
Classical definition, addition rule, conditional probability and Bayes’ theorem, independence, multiplication rule.
Unit: 11 Trigonometry
Trigonometric ratios, compound angles, multiple and submultiple angles, general solution of trigonometric equations. Properties of triangles, inverse trigonometric functions
Unit: 12 Differential Calculus
Functions, composition of two functions and inverse of a function, limit, continuity, derivative, chain rule, derivatives of implicit functions and of functions defined parametrically.
Unit: 13 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.
Unit: 14 differential Equations
Formulation and solution of differential equations of the forms.
1) dy / dx = f(x).g(y)
2) dy /. dx = f(y/x)
3) dy / dx = (ax+by) / (cx+dy)
4) dy / dx = (a,x+b,y+c,) / (a,x+b,y+c, ), (a,/a2 = b,/b,)
5) dy / dx + p(x)y = Q(x)
6) d2y / dx2 + p, dy/dx + p2y = 0 with p1 and p, constants.
7) d2y/dx2 = f(x)
Physics syllabus for WBJEE 2014
Unit: 1 Mechanical & General properties of Matter
(i)Units and dimensions: Units of measurement, system of units, fundamental and derived units, S I units, dimensional analysis, Methods of measurement: Vernier scale, screw gauge, analysis of errors, significant figures.
(ii) Calars and vectors: Addition, subtraction, multiplication of vectors
(iii) Kinematics in one, two and three dimensions, projectiles, uniform circular motion, centripetal force, centrifugal force, relative velocity
(iv) Dynamics: Newton’s laws of motion; inertial frames, uniformly accelerated frame (pseudo-forces), conservation of linear momentum, rocket motion, centre of mass, impulsive forces, friction.
(v) Work, Power and Energy, conservative and non-conservative forces, conservation of energy,collision (elastic and inelastic).
(vi) Rotational motion: Torque, angular momentum and conservation of angular momentum, moment of inertia, radius of gyration, moment of inertia of objects with simple geometrical shapes, rotational kinetic energy and rolling on horizontal surface
Unit: 2 Gravitation
Laws of gravitation, gravitational field and potential, acceleration due to gravity and its variation, escape velocity, Kepler’s laws and planetary motion, motion of satellites, Geostationary orbit.
Unit: 3 Elasticity
Hooke’s law, elastic modulii, Poisson’s ratio, elastic energy.
Unit 4:Hydrostatics and Fluid Mechanics
Pressure in a fluid, Pascal’s law, Archimedes’ principle, hydraulic press. Surface energy and surface tension, capillary rise.Viscosity, streamline and turbulent motion, critical velocity, Reynold’s number, Stoke’s law, Bernoulli’s theorem.
Unit: 5 Vibrations
Simple Harmonic Motion, equation of motion, damped and forced vibrations, resonance, and superposition of SHM.
Unit: 6 Wave Motion
Elastic waves, longitudinal and transverse waves, progressive waves, superposition of waves: interference, stationary waves, beats, vibration of strings, air columns, velocity of elastic waves in different media, Doppler effect.
Unit 7: Thermal Physics
Scales of temperature, thermal expansion of solids, liquids and gases, calorimetry, change of state of matter, latent heat, transition temperature, Transmission of heat: conduction, convection, radiation, Black body radiation, absorptive and emissive powers: Kirchoff’s law, Wien’s law, Stefan’s law, Newton’s law of cooling, Kinetic theory: mean free path, pressure of an ideal gas, mean and rms velocity of molecules of a Gas, kinetic interpretation of temperature, degrees of freedom, equipartition of energy (statement only) application to mono atomic and diatonic gases.
Unit 8: Thermodynamics
First law of thermodynamics, equivalence of heat and work, intensive and extensive thermodynamic variables, reversible and irreversible processes, specific heats of gases, relation between Cp and Cv.
Unit 9: Optics
Reflection and refraction at plane and spherical surfaces, total internal reflection, thin lenses, power of a lens, combination of lenses and mirrors, deviation and dispersion by prisms, Simple and compound microscopes, astronomical telescope, human eye: defects and remedies. Coherent sources, interference of light, Young’s double slit.
Unit: 10 Current Electricity
Electric current, drift velocity and mobility. Ohm’s law, resistivity, combination of resistances in series and parallel, combination of cells. Kirchoffs laws, Wheat stone bridge, MetreBridge, potentiometer.Heating effect of current, thermoelectricity, see beck and Peltier effect. Chemical effect of current, Faraday’s law of electrolysis, primary and secondary cells.
Unit: 11 Electrostatics
Coulomb’s law, electric field and potential, flux of electric field, Gauss’ law, electric field and potential due to an infinite line charge, charged infinite sheet, solid spheres and spherical shells.Electric dipole and field due to dipole. Capacitance, spherical and parallel plate capacitors, energy stored in a capacitor, series and parallel combination of capacitors.
Unit: 12 Electromagnetic Inductions
Magnetic flux, Faraday’s laws of electromagnetic induction, Lenz’s law, self and mutual induction,Flemings right hand rule, Alternating current, peak and rms value of alternating current; generator, D.C. motor and transformer Qualitative idea of electromagnetic wave and its spectrum.
Unit: 13 Modern Physics
Bohr’s atomic model for hydrogen like atom, hydrogen spectrum, x-ray emission, Moseley’s law, wave particle duality, de Broglie’s hypothesis, photo-electric effect .Constituents of atoms, isotopes, mass defect, mass-energy equivalence, binding energy. radioactivity – α, β, γ radiation, half life, mean life, fission, fusion. Energy bands in solids, intrinsic and doped semiconductors, p-n junction diode, rectifier, pnp and npn transistors, common emitter characteristics. Binary number, AND, OR, NOT, NAND and NOR gates.
Chemistry syllabus for WBJEE 2014
Unit 1: Atoms, Molecules and Chemical Arithmetic
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
Unit 2: Atomic Structure
Concept of Nuclear Atom — electron, proton and neutron (charge and mass), atomic number; Rutherford’s model and its limitations; Extra nuclear structure; Line spectra of hydrogen atom. Quantization of energy (Planck’s equation E = hν); Bohr’s model of hydrogen atom and its limitations, Sommerfelds modifications (elementary idea); The four quantum numbers, ground state electronic configurations of many electron atoms and mono-atomic ions; The Aufbau Principle; Pauli’s Exclusion Principle and Hund’s Rule. Uncertainty principle; The concept of atomic orbitals, shapes of s, p and d orbitals (pictorial approach) Radioactivity and Nuclear Chemistry
Radioactivity — α-, β-, γ-rays and their properties; Artificial transmutation; Rate of radioactive decay, decay constant, half-life and average life period of radio-elements; Units of radioactivity, Numerical problems. Stability of the atomic nucleus — effect of neutron—proton (nip) 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.
Unit 3: The periodic Table & 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, Electro negativity, 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
Unit 4: Chemical Bonding & 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); Fajan’s Rule. Directionality of covalent bonds, shapes of poly-atomic molecules (examples); Concept of hybridization of atomic orbital’s (qualitative pictorial approach) : sp, sp2, sp3 and dsp2. Molecular orbital energy diagrams for homonuclear diatomic species – bond order and magnetic properties. Valence Shell Electron Pair Repulsion (VSEPR) concept (elementary idea) — shapes of molecules. Concept of resonance (elementary idea), resonance structures (examples). Elementary idea about electro negativity, bond polarity and dipole moment, inter- and intra- molecular hydrogen bonding and its effects on physical properties (mp, bp and solubility); Hydrogen bridge bonds in diborane.Double salts and complex salts, co-ordination compounds (examples only), co-ordination number (examples of co-ordination number 4 and 6 only).
Unit: 5 Solubility and Solubility Products
Common ion effect (no numerical problems).
Unit: 6 Chemistry of Carbon Compounds
Hybridization of carbon – σ- and π-bonds.Isomerism -constitutional and stereoisomerism; Geometrical and optical isomerism of compounds containing upto two asymmetric carbon atoms. IUPAC nomenclature of simple organic compounds- hydrocarbons, mono and bifunctional molecules only (alicyclic and heterocyclic compounds excluded).Conformations of ethane and n-butane (Newman projection only).