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# OJEE Syllabus – Odisha Joint entrance exam syllabus

OJEE Syllabus – Odisha Joint entrance exam syllabus – This three part entrance test for engineering students is meant for those students from diploma who want direct admission into this degree course.Hence they will have to give in the test in engineering subjects of first year like Engineering mechanics, Applied Mathematics and Basic Electricity and Electronics among other subjects.

## OJEE Syllabus – Odisha Joint entrance exam syllabus

### (A) BASIC ELECTRICAL ENGINEERING (40 Questions)

Fundamentals: Concept of Source and Load, Ohm’s Law, Concept of resistance, Series and
Parallel DC circuits, Kirchhoff’s Laws, Faraday’s Laws of Electromagnetic Induction, Fleming’s
Left Hand Rule and Right Hand Rule.
AC Theory: Generation of alternating emf, Difference between DC and AC, Amplitude, Cycle, Time
period, Frequency, Phase, Phase Angle, Phase Difference, Instantaneous value, RMS value,
Average value, 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, 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.
Measuring Instruments: Introduction to measuring instruments, 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.
Storage Devices: Introduction to storage devices and their types. Charging, Discharging and

### (B) MATHEMATICS (40 Questions)

Algebra: 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. Crammer’s Rule, Types of matrices,
Transpose, Adjoint and inverse of a matrix upto third order. Solution of simultaneous equation by
matrix method.
Trigonometry: Trigonometrical ratios, multiple and submultiple angles, solution of trigonometrical
equations, Properties of triangles, Inverse circular function and its properties.
Analytical Geometry: Distance formula, Division formula, 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.
Vector Algebra: 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.
Calculus: 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, Partial
derivative, 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. Solution of first order and first degree differential equation.
Coordinate Geometry of three Dimension: Distance and Division formulae, Direction cosine and
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. Addition theorem of probability.

### (C) ENGINEERING MECHANICS (40 Questions)

Force and Moments
Force and its effects, Classification of forces, Principle of Transmissibility, Principle of
Superposition, Action and Reaction, Tension and Compression, Free Body Diagram.
Co-planer concurrent forces: Resultant of forces, Equilibrium of forces and equilibrant,
Parallelogram law of forces and determination of the resultant of two concurrent forces,
Components and resolve parts of a force, Principle of resolution of a force and any number of
forces, Analytical determination of resultant of number of concurrent forces, Lami’s Theorem,
Triangle law of forces and polygon law of forces. Coplanar non-concurrent forces: Moment of a
force, Statement and prove of Varignon’s theorem, Conditions of equilibrium, Determination of
resultant of two like and unlike parallel forces, Couple and its moment, Various types of supports
with their reactions, Simple problems on coplanar non concurrent forces with the help of free body
diagram.
Center of Gravity and Moment of Inertia
Centroid and Center of Gravity(C.G.), Expression for C.G. of straight line (uniform rod),triangle,
rectangle,circular,semicircular lamina. Expression for C.G. of solids like hemisphere and cone
(Expression only). Different types of engineering sections (symmetrical and non-symmetrical built
up sections). Location of the C.G. of the above sections. Definition Moment of Inertia(M.I.) of plain
figure as second moment of area. Perpendicular axes theorem, parallel axis theorem. M.I. of plane
lamina like rectangle, triangle, circle, and semicircle (from 1st principle) M.I.of different engineering
sections.
Friction
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.
Gear Drive
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.
Dynamics 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 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.