Syllabus NERIST Entrance

Engineering Entrance , NERIST

North Eastern Regional Institute of Science and Technology (NERIST) Entranc Syllabus:


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Units: Fundamental & derived units with particular reference to S.I. units-illustrations. Explanation of dimensions with examples.

Mechanics: Explanation of vector and scalar quantities with examples. Displacement as vector quality. Concepts of instantaneous velocity, acceleration. Equations of motion. Definition and explanation of Laws of motion, force, mass and weight with mathematical expressions, Universal Laws of gravitation and Projectile motion. Explanation of circular motion, Satellite motion in an orbit : Kepler's  Laws, escape velocity. Rigid body motion, moment of inertia, angular momentum, torque, Centre of mass, conservation of angular momentum. Simple harmonic  motion and its geometric representation. Derivation of its equation. Concepts of amplitude, Oscillation, time  period, frequency and phase with their mathematical expressions. Definition  and explanation of work, power and energy with mathematical relation. Problems involving potential and kinetic energies and conservation of energy. Conservative and non-conservative forces. Static and Dynamic friction.

Properties of Solids: Definition and explanation of strain, stress, elastic limit, ultimate strength, Hooke's Law and Young's modulus. Compression bending, twisting and shear. Elastic moduli and their  relations, Poisson's ratio. Concepts and examples of properties e.g. hardness, malleability, ductility, brittleness, toughness abrasion resistance, fatigue.

Properties of Liquids : Thrust of a liquid and pressure. Pressure at different depths. Pascal's Law and Hydraulic press. Buoyancy. Archimedes's Principle: definition and explanation with  illustration surface tension, viscosity, fluidity and  volatility.

Heat & Thermodynamics : Heat and temperature, Construction of  mercury thermometers. Measurement, measuring scales  and devices.

Definition and explanation of linear expansion. Area and volume expansion with mathematical relation.

Expansion of gas at constant temperature and at constant pressure. Ideal gas equation.

Measurement of specific heat capacity, relation between Cp and Cv, Isothermal and adiabatic process. Explanation of change of state of matter with change of temperature. Definition of latent heat of fusion and vaporization and  numerical examples.

Transfer of heat, Explanation  and examples of conduction, Convection and radiation processes. Thermal conductivity. Idea of black body radiation. Stefan - Boltzman Law.

Explanation of first and second laws of Thermodynamics with examples.

SOUND : Wave motion, Concept of longitudinal and transverse waves; Definition of period, frequency, wave length, amplitude and phase; Speed of sound wave; wave propagation in a medium; Doppler effect.

Properties of sound waves, Reflection, Refraction and Superposition of waves, stationary waves, beats, Vibration of Strings and Air columns, concept of resonance; Echo, Reverberation.

LIGHT : Explanation of light wave, wave front, ray, velocity of light.

Laws of reflection, reflection in different types of mirrors(plane, spherical, cylindrical, parabolic) with their geometrical drawing. Definition of image, focal length, radius of curvature, magnification with formula, numerical examples and application.

Laws of refraction, refractive index, total internal reflection, concave and convex lenses and image formation through them, formula connecting object and image distances, application in telescopes, microscopes, theodolite etc., refraction through prism.

Elementary ideas of electromagnetic waves. Wave nature of light. Young's double slit experiment and Fringe align. Single slit diffraction, polarisation.

ELECTROSTATICS :  Explanation of charge on the basis of electron theory, charging by friction, force between electric charges, concept of unit charge, electric field and electric potential, p.d. and its measurement, definition of capacitance of parallel plate capacitor, capacitors in series and  parallel. Dielectric constant.

CURRENT ELECTRICITY: Definition of emf, potential difference and current  with illustrations. Basic direct current circuits: Units of current, resistance and conductance, Ohm's Law and solution of simple problems, effect of  temperature on resistance. Series and  parallel connections of resistors. Kirchoff's  rules, their applications and examples.


Type of magnetic substances, magnetic flux, flux density, relative permeability, magnetic properties of soft iron and steel.

ELECTROMAGNETISM: Nature of magnetic field due to a straight conductor, a circular conductor and a solenoid, Fleming's  left hand and right hand rule, Effect of current flowing through two parallel conductors, Biot - Savart Law.

Electromagnetic induction: e. m. f. induced in a coil by magnet, Faradays's  law of induction, Calculation of e.m.f., Direction of induced e .m .f. Lenz's Law, Explanation of eddy current and explanation of self and 

Mutual induction, Calculation of self and mutual inductance.

Generation of alternating e.m.f. Concept of reactance :  Capacitive and inductive, Impedance. Simple a.c. circuits analysis.

MODERN PHYSICS:  Photoelectric effect, structure of atom, atoms and molecules, intermolecular forces, chemical bonding. Crystal structure  with simple examples.

Radio-activity. Explanation of fission and fusion processes.

Semiconductors: Properties and basic principles, p and n types, Action of transistors.




States of Matter: Gaseous State:  Postulates of kinetic theory of ideal gases; Derivation of kinetic equation; Derivation of Ideal gas equation. Continuity of states, Liquefaction of gases. Solid State:  Structure of solid unit cell, fcc, bcc, ccp structure of solids.

Solution and Colloidal solution: Concentration of solutions:  Mass percent, Mass fraction, Mole fraction, Molality, Normality, Molarity.  Dilute solutions: Raoult's law, its statement and explanation; Ideal and non-ideal solutions; Colligative properties: Relative lowering of vapour pressure, Elevation in boiling point, Depression in freezing point, Osmotic pressure and its determination. Determination of molecular masses based on colligative properties;  Van't Hoff  theory of dilute solutions, Van't Hoff  factor.

Colloidal solutions:  Definition, Classification, and Preparation of colloidal solutions; Properties of colloidal state: Tyndall effect, Electrophoresis, Brownian movement; Protective colloids.

Thermodynamics and Thermochemistry: First law of thermodynamics, mathematical formulation of the law, Isothermal and adiabatic changes; Relation between heat capacities at constant pressure and constant volume; Second law of thermodynamics: Carnot's cycle and derivation of an expression for efficiency of a reversible engine. Concept and physical significance of Entropy, Gibbs energy and work-function relation; Gibbs energy change and chemical spontaneity. Thermochemistry: Heats of reaction, Hess's Law of constant heat summation.

Kinetics and Chemical Equilibrium: Rate of reaction, law of mass action, velocity constant. Reversible reactions and chemical equilibrium, Equilibrium constant. Le Chatelier's principle (statement, explanation and it's industrial applications). Molecularity and Order of reaction, First and Second order of reactions,  Rate law equation and mechanism of reactions. Ionic Equilibria:  Modern Ionic theory; Modern concepts on acids and bases; Strength of acids and bases, Ionic product for water, pH scale. Common-ion effect and Solubility product,  Their applications in qualitative inorganic analysis and indicators.


Atomic Structure and Chemical Bonding: Electrons, protons and neutrons,  their charges and relative masses. The early models of the atom. Rutherford's model, Hydrogen spectra; Failure of Rutherford's model. Bohr's model of hydrogen and hydrogen like atoms; Dual nature of electrn, de-Broglie equation, Uncertainty principle.  Quantum numbers (i.e., quantum numbers and their application to electronic structure of atoms), Concept of atomic orbital, Pauli's exclusion principle, and Hund's rule, Aufbau principle.

Ionic Bonds:  Definition, factors influencing the formation of ionic compounds, Lattice energy of ionic compounds.  Covalent Bonds: Nature of covalent bond (Lewis concept), Concept of orbital overlap in bond formation, Sigma and pi bonds, Hybridization of atomic orbital (sp, sp2 sp3 hybridization), Properties of covalent compounds, Structure of simple molecules such as H2O, NH3, CH4, C2H4, C2 H2, PCI5 and SF6.   Co-ordinate covalent bonds: Lewis concept, structure of H3O+ and NH4+ ions on the basis of hybridization, Properties of co-ordinate covalent compounds.

Metallic bonds:  Bonding in metals (elementary treatment only), Insulators, Conductors and Semi-conductor, Extrinsic semi-conductors (n-type and p-type). Hydrogen bond:   Types  of hydrogen bond, Consequences of hydrogen bonding.

Periodic Properties of Elements: Mendeleef's periodic table and periodic law; Long form of periodic table, its merits and demerits. General characteristics, Properties of s-block, p-block and d-block elements. Trend of periodic properties of elements such as atomic volume, atomic radii, ionization potential, electron affinity and electronegativity in periodic table (qualitative treatment only).

Metallurgy: General principles of extraction of metals, Occurrence of metals, sources of different metals. General method of extraction of metals by pyrometallurgical process  and by electrolysis (different principles only).

Ferrous metallurgy:  Ores of iron, Metallurgy of iron and manufacture of steel. Properties of Cast iron, Wrought iron, Steel;  Effects of carbon, silicon, phosphorous, sulphur, manganese on cast iron and steel.

Non-ferrous metallurgy:  Ores of aluminium and copper, Metallurgy of aluminium and copper;  Properties and uses of Lead, Zinc, Tin and Chromium.

Alloys:  Effects of carbon and other alloying elements on the properties of steel. Composition and uses of the following alloys:  Brass, Bronze, German silver, Bell metal, Gun metal, Duralumin, Nanganin, Type metal, Nichrome and Solder.

The chemistry of some chemicals: Ammonia, Nitric acid, Sulphuric acid, Hydrochloric acid,  Hydrogen and Oxygen.


Introduction: Classification and nomenclature of organic compounds. Qualitative detection of  Nitrogen, Sulphur and Halogens.                                 

Hydrocarbons: Saturated and unsaturated aliphatic hydrocarbons. Preparation and properties with special reference to methane, ethane, ethylene, acetylene. Aromatic hydrocarbons: Preparation and properties of benzene; Structure of benzene.      Haloalkanes and Haloarenes: Preparation, properties and uses of haloalkanes and        polyhalogen derivatatives such as CHCl3,  CHI3, DDT.

Compounds with functional groups containing oxygen: General methods of preparation and properties of Alcohols and phenols, Aldehydes and ketones, Carboxylic acid and acid derivatives.

Compounds with functional groups containing nitrogen:  Preparation and properties of Nitrocompounds, Amines and Azo-compounds.


Plastics & Polymers:  Definition of a polymer; Polymerization (Addition and     condensation); Thermoplastic and thermosetting resins; Some commercially important      plastics.  Rubbers and their vulcanization.

Fuels: Definition of fuel, classification of fuels with examples; Calorific value (gross      and net). Solid Fuels: Different types of solid fuels, ignition point, Carbonization of      coal, Destructive distillation of wood (name of different products only).Liquid fuels:     Fractional distillation of crude oil (only names of different fractions, boiling ranges and      uses of different fractions); Properties of liquid fuels: Flash point, power point,      viscosity, specific gravity carbon residue; Octane and cetane number. Gaseous fuels:      Different commercial gaseous fuels with their composition and calorific value;     Manufacture of Producer gas and Water gas (principles with physico-chemical     reactions only).

Water:   Hard and soft water, Boiler feed water, Scale formation, Priming and      foaming,  Caustic embrittlement, Water softening methods, Treatment of water for     town supply and sewage disposal.

Corrosion and its protection:  Definition, Theories of corrosion, Factors affecting       rate of corrosion, Rusting of ferrous metal, Demerits of corrosion, Prevention of corrosion by various methods.

Environmental Pollution: Air and water pollution: causes and remedy.   



Algebra : Arithmetic, Geometric and Harmonic Progressions, Permutation and Combination, Binomial expansion for positive index, middle term, greatest term, binomial expansion for general index. Determinants up to third order, their properties and application to solve linear algebraic equations (Cramer's rule), concept of a matrix, types of matrices, equality of matrices, operations of addition, scalar multiplication and multiplication of matrices, determinant of a square matrix, transpose, adjoint  and inverse of a matrix, consistency and inconsistency of a system of linear equations,  solving a system of linear equations in two or three variables using inverse of a matrix.

Trigonometry : Inverse trigonometric functions, solution of inverse trigonometric equations.

Coordinate Geometry(2D) : Points and their coordinates in a plane, distance formula, area of a triangle, condition for the collinearity of three points and section formula, various forms of equations of a line, intersection of lines, angles between two lines, condition of concurrency of three lines distance of a point from a line, pair of lines, circle, tangents and normal to a circle, simple problems on parabola, ellipse and hyperbola.

Differential Calculus : Partial derivatives, maxima & minima of single & two variables, tangent and normal, curvature and derivative of arc.

Integral Calculus :  Integration of rational and irrational functions, integration of transcendental functions, definite integration, area bounded by curves, length of arc and volume of surface revolution.

Differential equation :  Differential eqs. Of first and second order of degree first & their applications.

Vector Calculus : Idea of gradient, divergence & curl, line integral, surface integral & volume integral.

Coordinate Geometry (3D) : Points and coordinates on 3-dimensional space, Distance between points, direction cosines, direction ratios, projections, equation to  a plane, angle between planes, distance of a point from a plane, angle between lines & planes, condition of co planarity of two lines, shortest distance between two lines, condition for the intersection of two lines.

Probability : Problems on probabilities, conditional probability, Baye's Theorem, Binomial & Poisson distributions.


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