OJEE Syllabus 2020: Odisha Joint Entrance Exam body conducts the exam for admission to Undergraduate Courses in (Lateral Entry) Engineering & Technology, Pharmacy. Post-graduation courses are also taken into account. Thus the candidates who want to pursue engineering from Odisha must prepare themselves for the OJEE 2020. For the exam, the syllabus plays an important role. Students must be aware of the syllabus if they are preparing for the OJEE exam. There will be 120 questions, 2 hours duration (Engineering Maths, Engineering Mechanics, and Basic Electrical Engineering, 40 each) for the lateral entry B.Tech exam. Read the article to know about the OJEE B.Tech Syllabus 2020 (Lateral Entry).
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OJEE Syllabus for B.Tech 2020
Look into the syllabus as per the subject wise. Check the syllabus separately for the lateral entry (diploma) and lateral entry stream (+3 Sc./ BSc).
Lateral Entry (Diploma)
Basic Electrical Engineering (40 Questions)
Concept of Source and Load
Concept of resistance
Series and Parallel DC circuits
Faraday’s Laws of Electromagnetic Induction
Fleming’s Left 7 Hand Rule and Right-Hand Rule.
Generation of alternating emf
Difference between DC and AC
Time period, Frequency
Amplitude factor and Form factor
Phasor diagram representation of AC values
AC through pure resistance
inductance and capacitance
AC through RL
RC and RLC circuits
Impedance Triangle and Power Triangle.
Generation of Electrical Power
Principle of operation of different electrical power generating plants such as Thermal, Hydro-Electric and Nuclear power plants with their block diagrams
Concept of single-phase Transformer and its application.
Conversion of Electrical Energy
DC machine and its main parts.
DC generators: Principle of operation and emf equation.
DC motors: Principle of operation, classification, torque equation and applied voltage V-back emf Eb relation.
Starters used for DC motors.
Use of different types of DC generators and motors.
Principle of operation of three-phase and single-phase induction motors.
Types and use of three-phase and single-phase induction motors.
Wiring and Power billing
Types of wiring and their comparison
The layout of household wiring (single line diagram)
Basic protective devices in household wiring
Calculation of Power used in small electrical appliances and installation
Calculation of Energy consumption in small electrical installations
Earthing installation, types (Pipe and Plate earthing) and uses.
Introduction to measuring instruments
The expression for Torque in measuring instruments
Use of PMMC and MI type of instruments( Ammeters and Voltmeters)
Connection diagram of AC/DC ammeter, voltmeter, energy meter and wattmeter for single-phase electrical system only
Introduction to storage devices and their types
Charging, Discharging and Maintenance of Lead-Acid battery.
OJEE Mathematics Syllabus (40 Questions)
Definition of complex number
Conjugate of complex number
Modulus and amplitude of a complex number.
Algebra of complex numbers.
Cube root of unity and their properties
De’ Moivre’s theorem and its application
Permutation, Combination, Binomial Theorem for any rational index
Relationship between Binomial coefficients.
Determinant and Matrices
Properties of determinants
Types of matrices: Transpose, Adjoint and inverse of a matrix upto third order.
The solution of the simultaneous equation by matrix method.
Trigonometrical ratios, multiple and submultiple angles, solution of trigonometrical equations
Properties of triangles, Inverse circular function and its properties.
Area of trapezium
Area of Triangle
Equation of straight lines in different form
Distance of a point from a line
Equation of circle in different forms.
Definition, Algebra of vectors, Position Vector, Resolution of vector into components
Scalar and Vector product of two vectors and their application, scalar triple product and its application.
Limit and continuity of function
Derivative of standard functions
Derivative of composite functions
Differentiation of implicit functions.Differentiation of function in parametric form, Differentiation using logarithm, Differentiation of a function with respect to another function
Successive differentiation in simple cases, Maxima, minima and point of inflection
Euler’s theorem for homogeneous functions. Standard methods of integration (by parts, by substitution, by partial fraction etc.)
Definite integrals and their properties. Area bounded by curves.
Ordinary Differential Equation
Order and degree of differential equation, formation of differential equation.
The solution of first order and first degree differential equation.
Coordinate Geometry of three Dimension
Distance and Division formulae
Direction cosine and 8 direction ratio of a line condition of perpendicularity and parallelism
Equation of plane under different conditions, angle between two planes
Distance of a point from a plane General equation of a sphere, Equation of a sphere with given diameter.
Probability and Statistics
Measures of central tendency (Mean, Median, Mode)
Measures of dispersion (Mean Deviation, Standard Deviation and Variance)
Definition of probability, equally likely, Mutually exclusive and independent events.
M.I. of plane lamina like rectangle, triangle, circle, and semicircle (from 1st principle) M.I.of different engineering sections.
Frictional force, angle of friction, limiting friction, co-efficient of friction, Laws of Static Friction.
Simple problems on ladder, Body on Inclined planes with applied force parallel to the plane and horizontal, Screw Jack.
Various types of gears, Gear terminology, Velocity ratio and expression for the velocity ratio for simple gears.
Types of gear trains (simple and compound gear trains)
Simple Lifting Machine
Definition of a machine. Simple and compound lifting machines.
Mechanical Advantage (MA), Velocity Ratio (VR) and efficiency of lifting machine. Relationship between MA, VR and efficiency.
Laws of machine, Friction in machines, Friction in terms of load and friction in terms of effort.
Reversible machine and self-locking machine.
Condition of reversibility of a machine.
Velocity Ratio and efficiency of 1st , 2nd & 3rd system of pulleys; Simple and differential wheel & axle, Screw jack.
Simple Stress and Strain
Stress, strain, Tensile, compressive and shear types of stress and strain, Hooke’s Law of elasticity, Poisson’s ratio, Elastic limit, Elastics Constants (E, G & K ) relationship between E,G &K, Stressstrain curve and salient points on stress-strain curve for ductile material.
Simple problems on stress and strain in case of material with uniform cross section
Kinematics and kinetics of a particle, Principle of Dynamics:-Newton’s laws of motion, D’Alembert’s Principle and its application.
Motion of particle acted upon by a constant force.
Engineering Application of Work, Power and Energy: Work done, force-displacement diagram, Work done in 9 stretching a spring, Power, Indicated Power, Brake Power and efficiency.
Kinetic and potential energy & its application, Simple Harmonic Motion (SHM) with examples.
Free Vibration, amplitude, frequency and time period in SHM, Velocity and acceleration of particle executing SHM, application of SHM to engineering problems.
Force, Momentum and Impulse, Conservation of energy and linear momentum, Collision of elastic bodies, Co-efficient of restitution (e), Velocity after impact.
Impact of body with a fixed plane
SYLLABUS FOR LATERAL ENTRY STREAM (+3 Sc./ BSc)
Mathematics (30 Questions)
Statement, Negation, Implication, Converse, Contraposititve, Conjuction, Disjunction, Truth Table.
Different methods of proof, Principle of Mathematical induction.
Algebra of sets
Set operation, Union, Intersection, Difference, Symmetric difference, Complement, Venn diagram, Cartesian product of sets, Relation and functions, Equivalence relation, Kinds of functions and their domain and range, Composite function, Inverse of a function.
Real numbers (algebraic and order properties, rational and irrational numbers), Absolute value, Triangle inequality, AM ≥ GM, Inequalities(simple cases), Complex numbers, Algebra of complex numbers, Conjugate and square root of a complex number, Cube roots of unity, De Moivre’s theorem with simple application.
Permutations and Combinations -simple applications, Binomial theorem for positive integral index, Identities involving binomial co-efficients.
Determinants and matrices
Determinants of third order, Minors and cofactors,
Properties of determinants, Matrices upto third order, Types of matrices, algebra of matrix, adjoint and inverse of matrix
Application of determinants and matrices to the solution of linear equations (in three unknowns).
Compound angles, Multiple and Submultiple angles, Solution of trigonometric equations, Properties of triangles, Inverse circular function, Sum and product of sine and cosine functions.
Co-ordinate geometry of two dimensions
Straight lines, Pairs of straight lines
Circles, Equations of tangents and normals to a circle
Equations of parabola, Ellipse and hyperbola in simple forms, their tangents and normals.
Condition of tangency
Rectangular and Conjugate hyperbolas.
Coordinate geometry of three dimensions
Distance and Division formulae, Direction cosines and direction ratios, Projection, Angle between two planes, Angle between a line and a plane.
Distance of a point from a line and a plane.
Equation of a sphere – general equation, Equation of sphere when end points of diameter are given.
Roots of a quadratic polynomial, Factorisation of quadratic polynomials, Maximum and minimum values of quadratic polynomials for all real values of the variable, sign of the quadratic polynomial for all real values of the variable, Solution of quadratic inequations.
Sequence and Series
Definition, Infinite geometric series, Arithmetic-geometric series, Exponential and Logarithmic series.
Fundamentals, Dot and cross product of two vectors, Scalar triple product and vector triple product, Simple application of different products.
Concept of limit, Continuity of functions, Derivative of standard Algebraic and Transcendental functions
Derivative of composite functions, functions in parametric form, Implicit differentiation
Partial differentiation, Application of Euler’s theorem
Derivative as a rate measure, Increasing and decreasing functions, Maxima and Minima, Indeterminate forms
Geometrical application of derivatives such as finding tangents and normals to plane curves.
Standard methods of integration (substitution, by parts, by partial fraction, etc)
Integration of rational, irrational functions and trigonometric functions
Definite integrals and 10 properties of definite integrals, Areas under plane curves.
Definition, order, degree of a differential equation, General and particular solution of a differential equation
Formation of a differential equation
The solution of differential equations by the method of separation of variables
Homogeneous differential equations of first order and first degree, Linear differential equations of the form dy/dx +p(x)y = q(x), Solutions of differential equations of the form d2 y/dx2 =f(x)
Probability and statistics
Average (mean, median and mode).
Dispersion (standard deviation and variance), Definition of probability, Mutually exclusive events, Independent events, Compound events, Conditional probability, Addition theorem.
Decimal, binary, octal, hexadecimal numbers and their conversion.
+3 Sc. / B.Sc. Physics (15 Questions)
laws of motion, motion in a uniform field, components of velocity and acceleration in different coordinate systems.
Motion under a central force, Kepler’s law, Gravitational law and field.
Potential due to a spherical body, Gauss and Poisson equations for gravitational self-energy.
System of particles, center of mass, equation of motion, conservation of linear and angular momenta, conservation of energy, elastic and inelastic collisions.
Rigid body motion, rotational motion, moment of inertia and their products.
Harmonic oscillations, kinetic and potential energy, examples of simple harmonic oscillations, spring and mass system, simple and compound pendulum, torsional pendulum.
Superposition of two simple harmonic motions of the same frequency along the same line, interference, superposition of two mutually perpendicular simple harmonic vibrations of the same frequency, Lissajous figures, case of different frequencies
Motion of charged particles in electric and magnetic fields
E as an accelerating field, electron gun, case of discharge tube, linear accelerator, E as deflecting field-CRO, sensitivity.
Properties of Matter: Elasticity, small deformations, Hooke’s law, elastic constants for an isotropic solid, beams supported at both the ends, cantilever, torsion of a cylinder, bending moments and shearing forces.
Bernoulli’s theorem, viscous fluids, streamline and turbulent flow.
Capillarity, tube of flow, Reynold’s number, Stokes law.
Surface tension and surface energy, molecular interpretation of surface tension, pressure across a curved liquid surface, angle of contact and wetting.
Coulomb’s law (in vacuum) expressed in vector forms, calculation of E for simple distributions of charge at rest, dipole and quadrupole fields Work done on a charge in an electrostatic field expressed as a line integral, conservative nature of the electrostatic field.
Electric potential , E = -dV/dx, Torque on a dipole in a uniform electric field and its energy, flux of the electric field, Gauss’ law and its application for finding E for symmetric charge distributions, Gaussian pillbox, fields at the surface of a conductor.
Screening of electric field by a conductor.
Capacitors, electrostatic energy, force per unit area of the surface of a conductor in an electric field.
Steady current, Current density vector J, non-steady currents and continuity equation, Kirchoff’s law and analysis of multi-loop circuits, rise and decay of current in LR and CR circuits, decay constants, transients in LCR circuits, AC circuits, Complex numbers and their applications in solving AC circuit problems, complex impedance and reactance, series and parallel resonance, Q factor, power consumed by an AC circuit, power factor.
Force on a moving charge, Lorentz force equation and definition of B, force on a straight conductor carrying current in a uniform magnetic field, torque on a current loop, magnetic dipole moment, Biot and Savart’s law, calculation of B in simple geometric situations, Ampere’s law ∇∇.B=0, ∇×B,= µ0J, field due to a magnetic dipole.
Electromagnetic induction, Faraday’s law, electromotive force e=σ.E.dr, 11 Integral and differential forms of Faraday’s law, mutual and self inductance, transformers, energy in a static magnetic field, Maxwell’s displacement current, Maxwell’s equations, electromagnetic field, energy density
The wave equation satisfied by E and B, plane electromagnetic waves in vacuum, Poynting’s vector
Kinetic theory of Matter
Real gas: Van der Waals gas, equation of state, nature of Van der Waals forces, comparison with experimental P-V curves.
The critical constants, distinction between gaseous and vapour state, Joule expansion of ideal gas, and of a Vander Waals gas, Joule coefficient, estimates of J-T cooling.
Blackbody radiation: energy distribution in blackbody spectrum.
Planck’s quantum postulates, Planck’s law.
Interpretation of behaviour of specific heats of gases at low temperature.
Kinetic Theory of Gases
Maxwellian distribution of speeds in an ideal gas: distribution of speeds and of velocities, distinction between mean, rms and most probable speed values.
The principle of superpositions, Interference of a light, double-slit interference, coherence requirement for the sources, optical path retardation, lateral shift of fringes, Localized fringes: thin films, Michelson interferometer,
Fraunhofer diffraction : Diffraction of a single slit, the intensity distribution, diffraction at a circular aperture and a circular disc.
Diffraction gratings: Diffraction at N parallel slits, intensity distribution, plane diffraction grating, polarization of transverse waves, plane, circular and elliptically polarized light.
Polarization by reflection and refraction. Double reflection and optical rotation: Refraction, in uniaxial crystals, its electromagnetic theory.
Phase retardation plates, double image prism, rotation of plane of polarized light, origin of optical rotation in liquids and in crystals.
Origin of the quantum theory: failure of classical physics to explain the phenomena such as blackbody spectrum, photoelectric effect, Ritz combination principle in spectra, stability of an atom, Planck’s radiation law, Einstein’s explanation of photoelectric effect, Bohr’s quantization of angular momentum and its applications to hydrogen atom, limitations of Bohr’s theory.
Wave-particle duality and uncertainty principle: de Broglie’s hypothesis for matter waves, the concept of wave and group velocities, evidence for diffraction and interference of particles, experimental demonstration of matter waves.
The consequence of de Broglie’s concepts; quantization in hydrogen atom; quantized energy levels of a particle in a box, wave packets, Heisenberg’s uncertainty relation for p and x, its extension to energy and time.
The consequence of the uncertainty relation: gamma-ray microscope, diffraction at a slit, particle in a box, position of the electron in a Bohr orbit.
Quantum Mechanics: Schrodinger’s equation. Postulatory basis of quantum mechanics, operators, expectation values, transition probabilities, applications to particle in a one dimensional box, harmonic oscillator, reflection at a step potential, transmission across a potential barrier
Continuous X-ray spectrum and its dependence on voltage, Characteristics X-rays.
Moseley’s law, Raman effect, Stokes and anti-Stocks lines, fission and fusion (concepts), energy production in stars by p-p and carbon cycles (concepts).
Solid State Physics
X-ray diffraction, Bragg’s law.
Atomic magnetic moment, magnetic susceptibility, Dia-Para-, and Ferromagnetism, Ferromagnetic domains, Hysteresis.
Energy bands, energy gap, metals, insulators, semiconductors.
Solid State Devices
Semiconductors – Instrinsic semiconductors, electrons and holes, Fermi level. Temperature dependence of electron and hole concentrations. Doping: impurity states, n and p type semiconductors.
Power supply: diode as a circuit element, load line concept, rectification, ripple factor, Zener diode, voltage stabilization, IC voltage regulation, characteristics of a transistor in CB, CE and CC mode.
Field effect transistors
JFET volt-ampere curves, biasing JFET, RC coupled amplifier, gain, frequency response, input and output impedance
+3 Sc. / B.Sc Chemistry (15 Questions)
Definition of thermodynamic terms, systems, surroundings etc.
Types of systems, intensive and extensive properties, state and path functions and their differentials, thermodynamic processes, concept of heat and work.
First law of thermodynamics, statement, definition of internal energy, enthalpy, heat capacity, heat capacity at constant volume, constant pressure and their relation, Joule’s law, Joule-Thomson coefficient and inversion temperature, calculation of w, q, U, H, for the expansion of ideal gases under isothermal and adiabatic conditions for reversible processes, Work done in irreversible process.
standard state, standard enthalpy of formation, Hess’s law of heat of summation and its application, heat of reaction at constant pressure and constant volume, enthalpy of neutralization, bond dissociation energy and its calculation from thermochemical data, temperature dependence of enthalpy.
Equilibrium constant and free energy.
Derivation of law of mass action (Study of homogeneous and heterogeneous equilibria).
Le chaterlier’s principle.
Phase equilibrium: Statement and meaning of the terms – phase, component and degree of freedom, derivation of Gibbs phase rule, phase equilibrium of one component system – water and sulphur system
Electrical transport-conduction in metals and in electrolyte solution, specific conductance and equivalent conductance, measurement of equivalent conductance, variation of equivalent and specific conductance with dilution, migration of ions and Kohlrausch law, Arrhenius theory of electrolytic dissociation and its limitations, weak and strong electrolytes, Ostawald’s dilution law, its uses and limitations.
Application of conductivity measurements, determination of degree of dissociation, determination of Ka of acids, Determination of solubility product of a sparingly soluble salt, conductometric titration
Types of reversible electrodes- gas metal ion, meta-metal ion, metalinsoluble salt-anion and redox electrodes.
Electrode reactions, Nernst equation, derivation of cell EMF and single electrode potential, standard hydrogen electrodes-reference electrodes, standard electrode potentials, sign conventions, electrochemical series and its significant, EMF of a cell and its measurements.
Computation of cell EMF, concentration of cell with and without transport, liquid junction potential, definition of H, and Ka, determination of H using hydrogen electrode, buffers-mechanism of buffer action, Henderson equation.
Hydrolysis of salts (quantitative treatment), determination of H, Ka, Kw and Kh by emf methods
Idea of de Broglie matter waves, Heisenberg uncertainty principle, atomic orbitals, Schrodinger wave equation (Mathematical derivations excluded) significance of quantum numbers, shapes of s,p,d orbitals.
Aufbau and Pauli exclusion principles, Hund’s multiplicity rule.
Electronic configurations of the elements.
Atomic and ionic radii, ionization enthalpy and electron – gain enthalpy, electronegativity-definition, methods of determination or evaluation, trends in periodic table and applications in predicting and explaining the chemical behavior.
Covalent Bond – valence bond theory and its limitations, directional characteristics of covalent bond, various types of hybridization and shapes of simple inorganic molecules and ions.
Valence shell electron pair repulsion, (VSEPR) theory of NH3 , H3O+, SF4, CIF3, ICl2 and H2O.
MO theory, homonuclear and heteronuclear (CO and NO) diatomic molecules.
Comparative study, diagonal relationships, salient features of hydrides, 13 solvation and complexation tendencies including their function in biosystems
Comparative study (including diagonal relationship) of groups 13-17 elements, compounds like hydrides, oxides, oxyacids and halides of groups 13-16, hydrides of boron-diborane, borazine, borohydrides, fullerenes, carbides, fluorocarbons, silicates (structural principle), basic properties of halogens, interhalogen compounds
Chemistry of Noble Gases
Chemical properties of the noble gases, chemistry of xenon, structure and bonding in xenon compounds (fluorides and oxides), Chemistry of elements of first transition series.
Characteristic properties of d-block elements.
Properties of the elements of the first transition series, their binary compounds and complexes illustrating relative stability of their oxidation states, coordination number and geometry
Werner’s coordination theory and its experimental verification, effective atomic number concept, chelates, nomenclature of coordination compounds, isomerism in coordination compounds (4 and 6 only) valence bond theory of transition metal complexes
Acids and Bases
Arrhenius, Bronsted-Lowry, Lewis concepts of acids and bases
Structure, bonding and mechanism of Organic reactions
Inductive effect, resonance, steric effect, influence of these effects on acidity, basicity and dipole moments, reactive intermediate- carbocations, carbanions, free-radicals and carbenes – formation, stability and structure, types and mechanism of organic reactions- SN1 , SN2, SE1, SE2 , E1, E2, AdE, AdN
Stereochemistry of Organic compounds
Concept of isomerism, types of isomerism, optical isomerism, elements of symmetry, molecular chirality, enantiomers, stereogenic center, optical activity, properties of enantiomers, chiral and achiral molecules with two stereogenic centers, diastereomers, meso compounds, relative and absolute configuration, sequence rules, D-L, R-S, systems of nomenclature, geometric isomerism, determination of configuration of geometric isomers, E-Z system of nomenclature, conformational isomerism, conformational analysis of ethane and n-butane, conformations of cyclohexanes, axial and equatorial bonds, difference between conformation and configurations.
OJEE Exam Pattern 2020
Look into the subjects and no. of questions asked from the subjects in two different lateral entry.