WBJEE 2015 - All about West Bengal Joint Entrance Examinations (WBJEE) Notification, Eligibility, Syllabus, Exam Date, Admit Card, Question Sample Papers, Answer Key, Merit List, Counseling Schedule, Preparation Tips & more for entrance examination will be held on 5th & 6th May, 2015.
West Bengal Joint Entrance Examination or commonly known as WBJEE is a state level entrance exam of West Bengal for admission to the undergraduate courses in Engineering / Technology / Architecture / Medical / Dental and Pharmacy in universities or colleges in the state.
WBJEE 2015 Eligbility Criteria:
- The candidate must be a citizen of India.
- For admissions to B Pharm course the candidate must pass in the 12th (HSC) class examination with a minimum of 50% of aggregate marks in the subjects of Physics, Chemistry and Mathematics, in case the candidate belongs to a reserved category this percentage would be 40%.
WBJEE 2015 Important Dates:
Confirmation page printing available till | 31.03.2015. (11:59 PM) |
Candidate Correction window (based on Board feedback and self-induced errors) along with upload of correct testimonials | 09.03.2015. (10:30 AM)
to 16.03.2015. (11:59 PM) |
Publication of Downloadable Admit Card in wbjeeb.nic.in | 02.04.2015. (10:30 AM) |
Date of Examination
Biological Sciences Mathematics Physics & Chemistry |
05.05.2015. (1 PM to 4 PM)
06.05.2015. (12 Noon to 2 PM) 06.05.2015. (3 PM to 5 PM) |
Publication of Results | By 20th June 2015 |
WBJEE 2015 Exam Pattern:WBJEE 2015 Selection Procedure:
After the announcement of the WBJEE Pharmacy 2015 Result, a merit list for central counseling according to which the candidates who have been called for counseling will be awarded seats will be announced.
The WBJEE 2015 Entance Exam will consist of three papers:
- Mathematics (100 Marks)
- Physics (75 Marks)
- Chemistry (75 Marks)
The following question categories would be there in WBJEE 2015 Exam:
Paper |
Category I |
Category II |
Category III |
Sectional Marks |
Mathematics |
60 Questions 1 Mark each |
15 Questions 2 Marks each |
5 Questions 2 Marks each |
100 |
Physics |
45 Questions 1 Mark each |
10 Questions 2 Marks each |
5 Questions 2 Marks each |
75 |
Chemistry |
45 Questions 1 Mark each |
10 Questions 2 Marks each |
5 Questions 2 Marks each |
75 |
WBJEE 2015 Syllabus for Examination:
WBJEE 2015 Syllabus for Physics:
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.
Elasticity: Hooke's law, elastic modulii, Poisson's ratio, elastic energy
Mechanics & General properties of matter
- 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.
- Scalars and vectors: Addition, subtraction, multiplication of vectors
- Kinematics in one, two and three dimensions, projectiles, uniform circular motion, centripetal force, centrifugal force, relative velocity
- 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.
- Work, Power and Energy, conservative and non-conservative forces, conservation of energy, collision (elastic and inelastic).
- (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
Vibrations: Simple Harmonic Motion, equation of motion, damped and forced vibrations, resonance, superposition of SHM.
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.
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.
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.
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.
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.
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, Metre bridge, potentiometer. Heating effect of current, thermoelectricity, see beck and Peltier effect. Chemical effect of current, Faraday's law of electrolysis, primary and secondary cells
Electromagnetism: Magnetic effects of Current, Biot Savart's law, magnetic field due to an infinite line charge, circular coil and solenoid, Ampere's circuital law, Lorentz force, Fleming's left hand rule, force between two current carrying conductors, magnetic moment of a current loop, magnetic dipole, torque experienced by a current carrying coil in a uniform magnetic field, galvanometer, current sensitivity, conversion of galvanometer to voltmeter and ammeter. Magnetic field of earth. tangent galvanometer, magnetic properties of materials : Dia, para and ferromagnet, permeability, susceptibility. Electromagnetic induction : 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
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
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
WBJEE 2015 Syllabus for Chemistry:
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.
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
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); Fajan's Rule. Directionality of covalent bonds, shapes of poly-atomic molecules (examples); Concept of hybridization of atomic orbitals (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).
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
Gaseous state
Measurable properties of gases. Boyle's Law and Charles Law, absolute scale of temperature, kinetic theory of gases, ideal gas equation — average, root mean square and most probable velocities and their relationship with temperature. Dalton's Law of partial pressure, Graham's Law of gaseous diffusion. Deviations from ideal behavior. Liquefaction of gases, real gases, van der Waal's equation; Numerical problems
Physical Chemistry of Solutions
Colloidal Solutions — differences from true solutions; Hydrophobic and hydrophilic colloids (examples and uses); Coagulation and peptization of colloids; Dialysis and its applications; Brownian motion; Tyndall effect and its applications; Elementary idea of emulsion, surfactant and micelle.
Electrolytic Solutions — Specific conductance, equivalent conductance, ionic conductance, Kohlrausch's law, Faraday's laws of electrolysis, applications. Numerical problems.
Non-electrolytic Solutions — Types of solution, vapour pressure of solutions. Raoult's Law; Colligative properties — lowering of vapour pressure, elevation of boiling point, depression of freezing point, osmotic pressure and their relationships with molecular mass (without derivations); Numerical problems.
Ionic and Redox Equilibria
Ionic equilibria — ionization of weak electrolytes, Ostwald's dilution law. Ionization constants of weak acids and bases, ionic product of water, the pH - scale, pH of aqueous solutions of acids and bases; Buffer solutions, buffer action
and Henderson equation.
Acid-base titrations, acid-base indicators (structures not required).
Solubility and Solubility Products.
Common ion effect (no numerical problems).
Redox Equilibria — Oxidation-Reduction reactions as electron transfer processes, oxidation numbers, balancing of redox reactions by oxidation number and ion-electron methods.
Standard electrode potentials (E°), Electrochemical series, feasibility of a redox reaction. Significance of Gibb's equation: _G° = - nF_E° (without derivation), no numerical problems. Redox titrations with (examples); Nernst equations (Numerical problems).
Chemical Energetics and Chemical Dynamics:
Chemical Energetics — Conservation of energy principle, energy changes in physical and chemical transformations. First law of thermodynamics; Internal energy, work and heat, pressure-volume work; Enthalpy. Internal energy change (_E) and Enthalpy change (_H) in a chemical reaction. Hess's Law and its applications
(Numerical problems). Heat of reaction, fusion and vapourization; Second law of thermodynamics; Entropy; Free energy; Criterion of spontaneity.
Chemical Equilibria — The Law of mass action, dynamic nature of chemical equilibria. Equilibrium constants, Le Chatelier's Principle. Equilibrium constants of gaseous reactions (Kp and Kc) and relation between them (examples). Significance of _G and _G°.
Chemical Dynamics — Factors affecting the rate of chemical reactions (concentration, pressure, temperature, catalyst). Arrhenius equation and concept of activation energy.
Order and molecularity (determination excluded); First order reactions, rate constant, half-life (numerical problems), examples of first order and second order reactions.
Chemistry of Non-metallic Elements and their Compounds
Carbon — occurrence, isotopes, allotropes (graphite, diamond, fullerene); CO and CO, production, properties and uses.
Nitrogen and Phosphorus — occurrence, isotopes, allotopes, isolation from natural sources and purification, reactivity of the free elements. Preparation, properties, reactions of NH3, PH3 , NO, NO2, HNO2, HNO3, P4O10, H3PO3 and H3PO4.
Oxygen and Sulphur — Occurrence, isotopes, allotropic forms, isolation from natural sources and purification, properties and reactions of the free elements. Water, unusual properties of water, heavy water (production and uses). Hydrogen peroxide and ozone (production, purification, properties and uses).
Chemistry of Metals:
General principles of metallurgy - occurrence, concentration of ores, production and purification of metals, mineral wealth of India.
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).
Principles of chemistry involved in electroplating, anodizing and galvanizing.
Halogen
Halogens - comparative study, occurrence, physical states and chemical reactivities of the free elements, peculiarities of Fluorine and iodine; Hydracids of halogens (preparation, properties, reactions and uses), interhalogen compounds (examples); Oxyacids of chlorine
Chemistry of Metals:
General principles of metallurgy - occurrence, concentration of ores, production and purification of metals, mineral wealth of India.
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).
Principles of chemistry involved in electroplating, anodizing and galvanizing.
Chemistry in Industry
Large scale production (including physicochemical principles where applicable omitting technical details and uses of individual items).
Heavy Chemicals: Sulphuric acid (contact process), Ammonia (Haber's process), Nitric acid (Ostwald's process), sodium bi-carbonate and sodium carbonate (Solvey process).
Polymers, Polythene, Nylon-66, rubber from natural source, vulcanization. Electrochemicals - sodium hydroxide, chlorine, bleaching powder as byproducts, Fuel Gases - LPG, CNG. Silicon carbide and silicones.
Environmental Chemistry
Common modes of pollution of air, water and soil. Ozone layer, ozone hole - important chemical reactions. Green House effect; Smog; Pollution of water by domestic and industrial effluents; Pollutantspesticides, fertilizers and plastics
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).
Electronic Effects — inductive, resonance and hyperconjugation. Stability of carbocation, carbanion and free radicals; Rearrangement of carbocation; Electrophiles and nucleophiles, tautomerism in â-dicarbonyl compounds, acidity and basicity of simple organic compounds.
Aliphatic Compounds
Alkanes -- Preparation from alkyl halides and carboxylic acids; Reactions — halogenation and combustion.
Alkenes and Alkynes — Preparation from alcohols; Formation of Grignard reagents and their synthetic applications for the preparation of alkanes, alcohols, aldehydes, ketones and acids; SNl and SN2 reactions (preliminary concept). Markownikoff's and anti-Markownikoff's additions; Hydroboration; Oxymercuration — demercuration,
reduction of alkenes and alkynes (H2/Lindler catalyst and Na in liquid NH3), metal acetylides. Alkyl halides -- Preparation from alcohols; Formation of Grignard reagents and their synthetic applications for the preparation of alkanes, alcohols, aldehydes, ketones and acids; SN 1 and SN2 reactions (preliminary concept).
Alcohols — Preparation from carbonyl compounds and esters. Reaction — dehydration, oxidation, esterification, reaction with sodium, ZnCl2/ HCl, phosphorous halides.
Ethers — Preparation by Williamson's synthesis; Cleavage with HCl and HI.
Aldehydes and Ketones — Preparation from esters, acid chlorides, gem-dihalides, Ca-salt of carboxylic acids. Reaction — Nucleophilic addition with HCN, hydrazine, hydroxyl amines, semi carbazides, alcohols; Aldol condensation, Clemmensen and Wolff-Kishner reduction, haloform, Cannizzaro and Wittig reactions.
Carboxylic Acids — Hydrolysis of esters (mechanism excluded) and cyanides; Hunsdicker and HVZ reactions. Aliphatic Amines — Preparation from nitro, cyano and amido compounds. Distinction of 10, 2° and 3° amines (Hinsberg method); Reaction with HNO2 ; Carbyl amine reaction.
Aromatic Compounds
Benzene — Kekule structure, aromaticity and Huckel rule. Electrophilic substitution — halogenation, sulfonation, nitration, Friedel Crafts reaction, ozonolysis. Directive influence of substituents in monosubstituted benzenes.
Amines — Preparation from reduction of nitro compounds; Formation of diazonium salts and their stability; Replacement of diazonium group with H, OH, X (halogen), CN and NO2 diazocoupling and reduction.
Haloarenes — Nucleophilic substitution, cine substitution (excluding mechanism).
Phenols — halogenation, sulfonation, nitration, Reimer-Tiemann and Kolbe reactions.
Aromatic Aldehydes — Preparation by Gattermann, Gattermann — Koch, Rosenmund and Stephen's method.Reactions — Perkin, Benzoin and Cannizzaro
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 — Pentoses and hexoses. Distinctive chemical reactions of glucose.
Aminoacids — glycine, alanine, aspartic acid, cysteine (structures). Zwitterion structures of amino acids, peptide bond.
ADP and ATP — structures and role in bioenergetics; Nucleic acids — DNA and RNA skeleton structures. Names of essential elements in biological system.
Principles of Qualitative Analysis
Detection of water soluble noninterfering Acid and Basic Radicals by dry and wet tests from among:
(a) Acid Radicals : Cl-, S2-, SO4 2-, NO-3, CO3 2-
(b) Basic Radicals: Cu2+, Al3+, Fe3+, Fe2+, Zn2+, Ca2+, Mg2+, Na+, NH4+
Detection of special elements (N, Cl, Br, I and S) in organic compounds by chemical tests. Identification of functional groups in: phenols, aromatic amines, aldehydes, ketones and carboxylic acids.
WBJEE 2015 Syllabus for Mathematics:
Algebra:
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.
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
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
ax2+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
Logarithms: Definition; General properties; Change of base.
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, properties of binomial coefficients.
Infinite series: Binomial theorem for negative and fractional index. Infinite G.P. series, Exponential and Logarithmic series with range of validity (statement only), simple applications
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).
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. Relation and its properties. Equivalence relation — definition and elementary examples, mappings, range and domain, injective, surjective and bijective mappings, composition of mappings, inverse of a mapping.
Probability: Classical definition, addition rule, conditional probability and Bayes' theorem, independence, multiplication rule.
Coordinate geometry of two dimensions
Basic Ideas: Distance formula, section formula, area of a triangle, condition of collinearity of three points in a plane.
Polar coordinates, transformation from Cartesian to polar coordinates and vice versa. Parallel transformation of axes, concept of locus, elementary locus problems.
Straight line: 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.
Circle: Equation of a circle with a given center 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 . Parametric equation of a circle. Intersection of a line with a circle. Equation of common chord of two intersecting circles.
Conics : Definition, Directrix, Focus and Eccentricity, classification based on eccentricity.
Parabola : Standard equation. Reduction of the form x = ay2+by+c or y = ax2+bx+c to the standard form y2= 4ax or x2 = 4ay respectively. Elementary properties and parametric equation of a parabola.
Ellipse and Hyperbola: Reduction to standard form of general equation of second degree when xy term is absent. Conjugate hyperbola. Simple properties. Parametric equations. Location of a point with respect to a conic.
Trigonometry
Trigonometric ratios, compound angles, multiple and submultiple angles, general solution of trigonometric equations. Properties of triangles, inverse trigonometric functions.
Calculus
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.
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. Fundamental theorem of integral calculus and its applications. Properties of definite integrals.
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)
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.