BCECEB DECE LE Admit Card 2021 to release tomorrow
Bihar Combined Entrance Competitive Examination Board
Diploma Entrance Competitive Examination [Lateral Entry]
( Advt No : DECE(LE) – 2021/01 )
Name of the Post
BCECEB DECE LE Admit Card 2021 to release tomorrow
Post related Short Information
Bihar Combined Entrance Competitive Examination Board published the advertisement for the Entrance Test for Admission in DECE(LE) – 2021 and this advertisement details is published firstly on only Sarkari Plan website. All candidates who are interested in this published advertisement of the vacancy, We suggest please read the notification. If candidate want to apply the application form of this notification , then we suggest please read this notification and then apply application form.
Post Publish Date
26-08-2021
Post Update Date
26-08-2021
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Important Dates
- Online Registration Starting Date : 05.07.2021
- Online Registration Closing Date : 05.08.2021 (11:59 P.M.)
- Last date of payment through Challan after submission of Online Application form of Registered candidate (Up to Banking hour) : 07.08.2021
- Last date of payment through Net Banking / Debit Card / Credit Card after submission of the Online Application Form of Registered Candidate : 09.08.2021 (11:59 P.M.)
- Online Editing of Application Form : 10.08.2021 to 11.08.2021(11:59 P.M.)
- (vi) Issue of Online Admit Card : Notified Soon
- (vii) Proposed Date of Examination : Notified Soon
Application Fees
- UR/BC/EBC / SC / ST / DQ : Rs. 2200
Age Limit ( Reference Date : 01/08/2021 )
- Minimum Age for ITICAT :14 Years
Exam Center
All Bihar
Total Post
1124
Qualification
Passed 10+2 Examination with Physics / Mathematics / Chemistry / Computer Science / Electronics /Information Technology / Biology / Informatics Practices / Biotechnology / Technical Vocational Subject /Agriculture / Engineering Graphics / Business Studies / Entrepreneurship (Any of the three)
OR
10th + (2 years ITI) with appropriate Trade in that order shall be eligible for admission to Second Year Diploma Courses of appropriate Programme
(The Affiliating Body will offer suitable bridge courses such as Mathematics, Physics, Engineering drawing,etc, for the students coming from diverse backgrounds to achieve desired learning outcomes of the programme).
Important Links
Apply Online : Click Here
How to Apply : Click Here
Download Prospectus : Click Here
Official Website : Click Here
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Syllabus for DECE(LE) Entrance
Physics
Introduction and measurement
Science and scientific method, Physics and its relation with society, Technology and other branches of
Science Physics Quantities and their measurement units system of units, s.i. system, Fundamental and
Derived Units. Dimensions and their applications. Accuracy and Precision, Systematic and random errors. Gaussian distribution for random errors. Standard deviation, RMS value, Combination of errors, Order of magnitude, Significant figures, Rounding off
Mathematical Tools
Scalar and vector quantities, vector addition and substraction, Unit vectors, Null vector Resolution method for vector addition and subtraction, Scalar and vector Products. Concept of Differentiation and Integration as applied in Physics. Cartesian Coordinate system. Graphs-plotting and interpreting. Interpretation of slopes of chords and tangents, Curvature, Maxima and Minima, Area under a curve.
Kinematics of Particles
Concept of particles, Uniform rectilinear motion, Uniformly accelerated rectilinear motion-their graphical representation, Freely falling bodies. Motion in two and three- dimensions. Projectile motion, Change of frame and relative velocity.
Force and Laws of Motion
Interactions and Force, Basic idea about the fundamental forces of Nature (Gravitational, Electromagnetic and Nuclear forces), Force and Motion : Newton’s first law of motion, Concurrent forces and equilibrium, momentum, Inertial and Non-Inertial reference frames. Newton’s second law of motion, Impulse. Newton’s third law of motion. Conservation of Linear momentum. Motion of connected bodies. Rocket propulsion, Static and kinetic friction, Laws of friction, Rolling friction, Lubrication, motion on rough inclined surface, Uniform circular motion, Centripetal force and acceleration, Centripetal force of a pseudo force, Banking of roads, motion of vertical circle conical pendulum.
Work, Energy and Power
Work, Kinetic energy, Power, work energy theorem for system of particle, Internal and external forces,
Conservative and dissipative forces, potential Energy, Potential energy for simple systems like simple
pendulum, electron moving around nucleus, satellite, etc. Law of conservation of Energy, Equivalence of Mass and Energy, Elastic collision in one and two dimensions, Inelastic collision in one dimension, Coefficient of restitution.
Rotation
Centre of mass for a two particle system, many particle system and for rigid body, Moment of Inertia and Radius of Gyration-their physical significance, parallel axis theorem, Perpendicular axes theorem for a lamina, calculation of moment of inertia of ring. Disk, rod rectangular bar and sphere, Torque, Couple, Equilibrium of Rigid Bodies, Relation between Torque and angular acceleration, Angular momentum, Conservation, General motion of rigid body in a plane ( Translation of centre of mass and Rotation about axis passing through centre of mass), Motion of rolling bodies.
Gravitation
Newton’s law of Universal Gravitation, Inertial and Gravitational Mass, Gravitational potential and field, their calculation for hollow and solid sphere, Acceleration due to gravity and its variation, kepler’s Laws of planetary motion (statement only), Satellites.
Properties of Matter
Interatomic and intermolecular forces, States of Matter. Solids : Elastic properties, Hooke’s law, Young’s modulus, Bulk modulus, Shear and rigidity modulus. Liquids : Cohesion and Adhesion, Surface tension, Surface energy, Angle of contact, Molecular theory for surface tension, Capillary action. Excess pressure inside a drop and soap bubble, effect of temperature of surface tension.
Gases : Kinetic theory of gases, Ideal gas law, Van der Waals equation (Derivation not required).
Fluid Dynamics : Streamlined and Turbulent motion, Viscosity, Coefficient of viscosity, Critical velocity,
Reynold’s number, Stoke’s law and its derivation using dimensional analysis, Terminal velocity, Bernoulli’s theorem and its applications (Venturi meter, Atomizer, Pitot tube, Dynamic uplift, etc.)
Heat and thermodynamics
Concept of Heat and temperature, Thermal equilibrium and Zeroth law of thermodynamics, Temperature scales, Thermometers ( Liquid in Glass, Platinum resistance, Constant volume hydrogen gas, thermometer), First law of thermodynamics, Specific heat of an ideal gas at constant volume and constant pressure, relation between them, Thermodynamic state, phase diagrams for H2O and CO2 Thermodynamic processes ( reversible and irreversible, isothermal and adiabatic), Carnot cycle, Second law of thermodynamics, efficiency of heat engines. Thermal conductivity determination by Searle’s method, Block body radiation, Wien’s displacement law, Stefan’s law , Newton’s law of cooling.
Oscillations
Periodic motion, Oscillatory motion. Simple harmonic motion, Kinetic and potential energy in SHM, Simple pendulum, Damped and forced oscillations, Resonance, Composition of SHM in one dimension and two dimensions.
Waves and Acoustics
progressive wave, equation of a travelling wave, speed of wave on a string. Longitudinal and transverse waves. Superposition of waves. Interference. Stationary wave and Beats. Sound wave in air, displacement and pressure waves, speed of sound-Newton’s formula and Laplace’s correction, Effect of temperature, pressure and humidity of velocity of sound, Laws of transverse vibration of stretched strings. Closed and open organ pipes, Doppler effect, Acoustics of buildings, Characteristics of musical sound, Musical scale, Decibel scale.
Universe
The constituents of the Universe, Planets-elementary idea about determination of their distances and masses. Starts- brightness, magnitude scale, luminosity, surface temperature, energy source of starts ( concept only). Evolution of the Universe, Cosmic background radiation, Red shift, Hubble’s law, Chandrasekhar limit, White dwarf. Neutron star and Black hole.
Ray Optics
Refraction at spherical surfaces, thin lens, combination of thin lenses in contact and separated by a distances, effect of silvering one face of a lens. Total internal reflection, optical fibre, rainbow. Optical instrumentssimple and compound microscopes, Refracting (Astronomical) and reflecting (Newtonian) Telescopes, Defects of vision and their remedies, Dispersion and deviation of light due to a prism. Dispersive power, dispersion without deviation and deviation without dispersion. Spectrometer and its use for determination of refractive index. Emission and absorption spectra (with suitable examples) Scattering of light by the atmosphere ( blue colour of the sky and the reddish appearance of Sun at sunrise and sunset, derivation not required).
Wave Optics
Wave front and Huygen’s Principle, Explanation of reflection and refraction of plane wave at plane surfaces using huygen’s principle, Coherent and non-coherent sources of light, interference of light, Young’s doubleslit experiment, Fringe width, Biprism, Diffraction of Light, Diffraction due to single sit, Polarization, Transverse nature of light waves, linearly polarized light. Brewster’s law, Use of Polarized light. Polaroids.
Electrostatics
Charges and their conservation, charge quantization, Coulomb’s Law, Electric potential and field due to a point charge and dipole in an electric field. Gauss’s theorem and its simple applications ( Field due to an infinite charged cylinder, plane sheet of charge. Charged conducting sheet, hollow conducting sphere, spherical conductor). Conductors and insulators, Concept of polarization and dielectric constant, Electrostatic induction, Capacitance, parallel plate, cylindrical and spherical capacitors, grouping of capacitors, Energy of capacitors, loss of energy due to sharing of charge Van de Graff generator.
Current Electricity
Concept of Drift velocity and Mobility, Current density and electric current, Ohm’s law, resistivity, conductivity of various materials, zero conductivity and superconductivity (elementary idea). Carbon resistors and their colour code, temperature dependence of resistance, Kirchoff’s current and voltage laws and their simple applications, Whetstone bridge and its application in meter bridge, Principle of Potentiometer and its application for comparison of emf.
Thermal and Chemical effect of current
Heating effect of current Joule’s law, Thermocouple, elementary idea of Seebeck, peltier and Thomson effect, Faraday’s law of electrolysis and their verification, Dry cell, Lead accumulator, Nickel-cadmium cell, Button cells.
Magnetic effect of current
Oersted’s experiment. Biot Savart law, magnetic field due to a straight ware and a circular loop carrying current, magnetic field due to a solenoid, Moving coil galvanometer and its conversion in to an ammeter and a voltmeter. Force on a conductor carrying current, torque on a current loop in a magnetic field, force between two parallel conductors carrying current, definition of Ampere.
Electromagnetic Induction and Alternating Current
Faraday’s and Lenz’s lays self and mutual induction- deduction of coefficients, eddy currents, Induced emf in a coil rotating in a uniform magnetive field. Alternative voltage and current, RMS, Peak and average values of voltage and current Reactance and impedance for L, C and R, Behaviour of circuits with L,C and R (Phasor diagrams only), Power factor, resonant circuits, Q-factor. Electrical machines and devices- transformer, AC Generator, Choke and starter.
Magnetism
Properties of bar magnets, field and potential due to a magnetic dipole, Current loop as a magnetic dipole, torque on a magnetic dipole placed in a uniform magnetic field lones, Comparison of magnetic fields due to a bar magnet and a solenoid carrying current. Earth’s magnetic field and elementary idea about its origin, Para dia and ferromagnetic substances with examples, Electomagnets and permanent magnets, elementary idea about modern theory of magnetism.
Electromagnetic waves (Qualitative treatment)
History of electromagnetic waves ( Contributions of Maxwell, Hertz, Bose, Marconi), Electromagnetic spectrum ( radiowaves, microwave infrared, optical, ultraviolet, x-ray and Gamma rays). Simple ideas about their properties and applications.
Atomic and Nuclear Physics
Discovery of electron, Rutherford scattering experiment, Bohr model of atom, hydrogen spectrum, Photoelectric effect, particle nature of light, Einstein’s photoelectric equation, photocell, matter waves, De Broglie relation. Composition of nucleus, Size of nucleus, atomic number and mass number, mass-energy per nucleon with mass number, Radioactivity, α, β, and γ rays. Simple explanation of α, β, and γ decay. Radioactive decay law, half life and mean life, nature of nuclear forces, nuclear fission and fusion.
Semiconductor devices
Energy bands in solids, band gap conductors semiconductors and insulators, P-n junction semiconductor diode, diole as a rectifier, solar cell, LED, Junction transistor, transistor action, collector amplifiers ( elementary idea), Logic gates (AND, OR and NOT gates) and combination of gats NAND and NOR), Binary number system and Boolean algebra, Truth table.
Basics of Communication (Qualitative treatment)
Analog and digital signals and their mutual conversion, Amplitude, Frequency and pulse modulation
and their demodulation, Principles of digital transmission and retrieval of information, Fax and Modem. Space communication-Propagation of electromagnetic waves in the atmosphere, Sky and space wave propagation, Satellite communication, Applications in Remote Sensing. Line communication two wire lines, cables, telephone links, Optical communication-optical fibres, Basic principles of Lasers and their applications, elementary principles of light modulation.
Chemistry
PHYSICAL CHEMISTRY
Mole concept and related numerical analysis
Laws of chemical combination. Mole concept, equivalent weights, atomic weights, molecular weight,
eudiometry, problems based on chemical equations.
Oxidation and reduction
Oxidation-reduction as electron transfer processes, Oxidation numbers, calculation of oxidation numbers, balancing of redox equations by oxidation number method and ion-electron method, equivalent weights of oxidants and reductants, Roles of K2Cr2O7′ KMnO4O3, H2O2, SO2, I2, FeSO4
States of matter
(A) Gaseous stste, Kinetic theory of gases, equation of state, Grahams law of diffusion, Root Mean
Square Velocity. Graphical distribution of molecular speeds of ideal gases and the effect of temperature, Most probable, velocity, average speed, Van der Waals equation and significance of Van der waals constants.
(B) The liquid state, Properties of liquids, Concept of vapour pressure, surface tension and viscosity
(C) The Solid State. The crystalline state and types of erystals. Seven crystal systems and 14 Bravais
lattices, close packing in crystals, fee, ccp and bcc lattices.
Atomic structure
The Bohr and Sommerfeld models and related calculations, Spectral distribution and the Rydberg constant, deBroglie concept and Heisenberg Uncertainty Principle. The three dimensional atom as in quantum mechanics, Shapes of orbitals, Quantum numbers, Aufbau principle, Hund’s rule, Pauli exclusion principle, electronic configuration of elements, and ions (upto at no.34)
Radioactivity
Artificial and natural radioactivity,α, β and γ cause of radioactivity disintegration law, group displacement law, half-life period, average life, mass defect, binding energy, balancing of nucleate reactions, Fission and fusion, isotopes and their uses, isobars and isotones
Chemical bonding
Octet concept, Types of bond- ionic covalent, coordinate, hydrogen bond ; Vander Waals attractions σ−π and ζ− (tau) bonds, Hybridisation VSEPR theory, dipole moment, resonance, shape of molecules and jons (CH4, N H3, H2O, SO4-2 and NO3-), Concept of molecular orbitals, MO diagrams of some homonuclear and hetronuclear diatomic molecules (H2, N2, CO and NO)
Acids, bases and salts
Classical concepts, modern concepts (Bronsted-Lowis and SHAB Principles). Salts and their classifications pH and pOH, pKa and pKb, relative strengths of acids and bases, buffer solutions.
Volumetry
Standard solutions and primary standards, strength parameter (normality, molarity, molality, %age, mole fraction and ppm). Acid-base titration and indicators (phenolphthalein and methyl orange), redox titrationpemanganometry dichrometry, volume strength of H2 O 2 solution
Energetics
Bond energy and enthalpy of reaction, exo and endo-thermic reactions, first law of thermodynamics, internal energy, pressure-volume-works relationships for gases, enthalpy, extensive and intensive, properties of formation, combustion, neutralization, hydrogenation,fusion and vaporization, Resonance energy.
Chemical and related equilibria
Law of mass action, equilibrium constant Le Chatelier’s principle, Equilibrium constants of the following reactions- gaseous dissociation of HI, SO3 and PCI5, Esterification and formation of ammonia. Relation between K and ∆ G
Colligative properties of solutions
Relative lowering of vapour pressure, elevation of boiling point, depression of freezing points, osmotic pressure, ideal and non-ideal solutions, Vant Hoff factor- dissociation and association, Henry’s faw
Chemical Kinetics
Rate of chemical reactions, factors affecting rate of reactions, molecularity and order of reactions, rate constants of first order reaction and its characteristics, temperature dependence of rate constant-Arrhenius equation
Electrochemistry
Faraday’s law, Electrolytic conductance- specific, equivalent and molar conductivities, kohalarausch’s law, Electrochemical cells and their cell reactions. Electrode potential, electrochemical series, simple calculations based on emf of galvanic cells
Surface chemistry
Elementary idea of adsorption (excluding isotherms), Colloids and their types, Properties
of colloids, elementary concepts of emulsions, surfactants and micelles.
INORGANIC CHEMISTRY
Periodicity of elements
The long periodic table, classification of elements in terms of s,p, d and f meteoroids, periodicity and enthalpy of ionization, electron affinity and electronegativty.
Transition elements
3d series only. General characteristics, Oxidation states and their stability colur, magnetic properties,
complexing properties and catalytic properties.
Metallurgy, Ores and minerals, gaugue, flux and slag
Commonly occurring ores of iron, copper, lead, magnesium, aluminium, mercury, zinc, silver, gold and tin. General principles and reactions involved in carbon reduction (Fe and Sn), self reduction methods (Cu and Pb), electrolytic reduction method (Al and Mg), cyanide process (Ag and au).
Chemistry of non metals and their compounds
Carbon- oxides, carbides, halides, fluorene, Industrial fuels, calorific value of fuels, Nitrogen- N2, NH2
and HNO3, phosphourous- PH3 oxides, orthometer and pyro-oxy-acis. Sulphur SO2, H2S, H2
S O4 (contact processonly), Halogens- Hydrides, oxides and oxyacids, Inter-halogens. Noble gases, Isolation and fluorides of Xe.
Principles of qualitative analysis
Systematic grouping of cations and related group reagents, test for anions (other than
fluorides,phosphates,silicates and borates)
Preparation of important compounds and their uses
NaOH, Na, CO310H2O. Ca (OCI) Cl. Ca (OH)2, MgSO4,7H2O, CuSO4, 5H2O, FeSO4, 7H2O, ZnSO4, 7H2O, AgNO3, KMnO4, K2 Cr2O, Mohrs salt, potash alum, plaster of Paris, calomel, corrosive sublimate, vermillion and nesslers reagent.
Fertilizers – nitrogen and phosphorous containing
Pollution – water and air
ORGANIC CHEMISTRY
- Fundamentals. Hybridisation of carbon, structural formulae of organic compounds. Catenation, spatial
arrangements around sp3 sp2 hybridised carbon atoms, Homologous series and classification of organic
compounds, functional groups, nomenclature (IUPAC) of hydrocarbons, mono-and bi-functional group
containing compounds. Physical properties of organic, compounds – boiling. pt, melting pt, solubility and
density. - Isomerism – structural including keto-enol tautomerism, confirmation of ethane and butane- Newmann’s
projection only. geometrical isomerism – cis and trans, optical isomerism with reference to one and two
stereo-geinc centres (RS nomenclature not required). - General concept – of Organic reactions. Fission of bonds. reaction intermediates- carbocations, free
radicals and carbanions, acidity and basicity due to inductive and resonance effects, Nucleophiles and
electrophiles, types of organic reactions-addition substitution and elimination. - Principle – involved in the preparation of organic compounds and related chemical reactions.
(a) Alkanes – from unsaturated hydrocarbons, alkyl halides and carboxylic acids, combustion and
mono-halogenation of alkanes, cracking and refining of petroleum, octane number.
(b) Alkenes – Form alkyl halides and alcohols, their chemical reactions with Cl2
,aqueous acis, quos KMnO4, ozone and boron hydride Markownikoff and anti-markinokoff addition, hydrogenation of alkenes.
(c) Alkynes- from metal acetylide and halogen derivatives, reduction, some electrophilic additions, acidity of acetylene.
(d) Halogen derivatives of alkanes – form alcohol, alkynes and alkynes, Chloroform, haloform reactions, nucleophilic substitution and elimination reaction in monohalogen derivatives, an elementary treatment of Grignard reagent.
(e) Alcohol – from alkyl halides, aldehydes’ and ketones, Reactions of alcohols-oxidation esterification, dehydration and reaction with PCl5
(f) Ether- form alkyl halide and alcohol. Reactions Hl, PCL5 and acetyl chloride.
(g) Aldehydes and ketones – from alcohol, alkynes, carboxylic acid salts, Reactions with hydroxylamine, phenyl hydrazine, Tollens reagent, Aldol condensation, Prekin reaction Canizzaro reaction and Benzoin condensation.
(h) Carboxylic acids and their derivatives- from cyanides alcohos and esters. reactions with PCl5
alcohol ammonia, Rosenmund’s reduction.
(h) Carbosylic acids and their derivatives- from cyanides alcohols and esters. Reactions with
PCl5, alcohol ammonia, Rosenmund’s reduction.
(i) Aromatic compounds – aromaticity, benzene, phenol and aniline, Diazo coupling. - Polymer – natural and synthetic- rubber, polythene, PVC, polyester, techniques of polymerisation.
MATHEMATICS
- Set Theory — Sets and their representation, Finite and infinite sets, Empty Set, Equal sets, (Union, Intersection and Difference). Application of sets, ordered pairs, Cartesian product of sets, Relations, domain, co-domain and range, function-into and onto functions, One-one into and one-one onto functions, constant functions, Identity functions, composition of functions, Invertible functions, Binary operations.
- Boolean Algebra — Boolean Algebra as an algebraic structure, Principle of duality, Boolean functions, conditional and biconditional statements, valid arguments, switching circuits, Applications of Boolean algebra to switching circuits.
- Mathematical Logic — Statements, use of venn diagram in logic, Negation operation. Basic logical
connectives and compound statements including their negations, Truth tables, Tautology, Duality, Algebra of statements. Application of logic in solving simple problems. - Algebra — complex numbers, representation of complex numbers as points on Agrand Plane, algebra of complex numbers, real and imaginary parts, modulus and argument of complex numbers. Triangle inequality, Polar representations of complex numbers. Square root of a complex number, cube roots of unit, Demoivre’s Theorem with application to find the nth rooth of a complex number. Sequence and examples of finite and infinite sequences, A.P.G.P., H.P. relation between AM Σ n, Σn2, Σ n5 & HM, evaluation of GM.
- Quadratic equations and expressions — Revision of “Solutions of Quadratic Equations by factorizations and by using formula, Relations between roots and coefficients, nature of Roots, Formation of Quadratic equations with given roots”. Symmetric functions of roots, equations reducible to quadratic forms, extreme values of quadratic expressions in one variable, conditions for resolutions into linear factors of a quadratic expressions in two variables. Permutations and combinations and problems based on them, principle of mathematical Induction and simple applications. Binomial theorem : Statements, Proof of Binomial theorem for positive integral index and problems, statements only of Binomial theorem for any index, exponentials functions and logarithmic functions.
- Matrices and Determinants — Concepts of a matrix, types of matrices, equality of Matrices (only real entries). Addition, scalar multiplication and multiplication of matrices, statements and important results on operations of matrices, Determinants of square matrix, properties of determinants, Minors and cofactors, solving system of linear equations, Transpose, adjoint and inverse of matrix. Consistency and inconsistency of system of a linear equations in 2 and 3 variable using inverse of a matrix.
- Trigonometry — Definition of trigonometric functions, periodic functions, concept of periodic of trigonometric functions, values of trigonometric functions of particular values of x. Compound angles, multiple and submultiple angles, Tansformation formula. Conditional identities.” Graphs of sine, cosine, tangent and their reciprocal functions. General solutions of trigonometrical equations and inverse circular functions. Properties of triangles Logarithms height and distances
- Two Dimensional co-ordinate Geometry —
Cartesian system of co-ordinates, Distance formula, Area of a triangle, conditions of colinearity of 3 points, section formula, centre locus and in centre locus and its equation. Standard general equation of a straight line, Intersection of Lines, Equations of bisectors of angle between two straight lines. Angle between two line, concurrency of 3 lines, distances of a point from a line.
Translation and rotation of axes, Equation of family of lines through and intersection of two lines.
Equation of a circle, general equation of a circle equation of tangent, normal and chord to a circle.
Parametric equation of a circle intersection of a circle with a straight line or a circle. Equation of a circle through the points of intersection of two circle and that a circle and straight line. Section of a cone, Equations of the conic sections (Parabola, hyperbola, ellipse in standard forms. Equation of tangent and normal). - Calculus — Concept of a real function, its domain and range, types of functions and their graphs, Limit of a function. Continuity of a function, Intermediate value property of continuous function.
Relation between continuity and differentiability, Derivative of some simple functions from first
principle. Derivative of a function at a point, derivative of sum, difference, product and quotient of a function. Derivative of a composite function, implicit function, inverse circular functions, Derivatives of functions in parametric form, Derivatives upto order three. dy/dx as a rate measurer, geometrical interpretation of dy/dx. Equation of tangents and normals. Increasing and decreasing functions and sign of derivatives, Maxima and minimum, Rollea’s Theorem and mean value theorem (without proof). Approximation by differentials, Curve sketching of simple curves.
Integrations as the inverse process of the differentiation. Integration by substitution and by parts
,partial function and their use in integration rational function. Definite integrals and its simple properties. Definite integrals as the limit of a sum. Determination of area enclosed by standard curves (straight lines, circle, parabolas ellipse) - Differential Equations – definition, order and degree, General and particular solution, Formation of differential equations, Solutions of differential equations by variable method. Homogeneous differential equations of first order, Solution of second order differential d2 y equations —— = f(x) dx2
- Vectors – vectors and scalars, Types of vector- equal, unit zero, position vector of a point, Local and free vectors etc. Components of a vector, Addition of vectors, Multiplication by scalars, scalar and vector products of 2 vectors with their geometrical meaning, scalar and vector-triple products, Application of geometry, Moment of a vector about a line. Coplanarity of three- vector of four points using scalar triple product.
- 3-Dimensional co-ordinate geometry– co-ordinate axes and co- ordinate planes in 3 dimensional
space, coordinates of a point in space .distance between 2 points ,section formula, direction co- sines, and direction ratio of a line joining 2 points, projection of the join of 2 points on a given line, Angle between two lines whose direction cosines are given cartesian and vector equations of a line through (i) a point and parallel to a given vector (ii) two points. Collinearity of 3 points , coplanar and skew lines, Shortest distance between 2 linnes, condition of intersection of 2 lines and 2 planes and a plane. Conditions of coplanarity of 2 lines in vector and cartesian from length of perpendicular of a point from a plane by both vectors and cartesian method. Equation of a sphere, its centre, radius, diameter. - Statics– Basic concepts of laws of mechanics, and force. Resultant of coplanar, concurrent and parallel forces , couples and members, conditions of equilibrium of particle under 3 concurrent forces.
- Dynamics– Basic concepts of displacement, speed , velocity, average speed, uniform velocity uniform asseleration, resultant of 2 velocities, motion of a article in a straight line motion under gravity, projectile
motion. - Probability– Random experiments and sample space, events , probability on a discrete sample space, theorems of probability, addition rule multiplication rule, independent and independent events, experiments conditional probability repeated trials.
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