AMU Engineering Exam Syllabus

Aligarh Muslim University (AMU) is a public university founded by the central government of India which was established by Sir Syed Ahmed Khan as Madrasatul Uloom Musalmanan-e-Hind in 1875 which later became Mohammedan Anglo-Oriental College (MAO College). This was designed to train Muslims for government service in India and prepare them for advanced training in British universities. Then Mohammedan Anglo-Oriental College became Aligarh Muslim University in 1920. Main campus of AMU is located in the city of Aligarh in India. There are two fully functioning off-campus centers located in the cities of Malappuram and Murshidabad. AMU was recently ranked 9 among the top 10 Indian institutions by the Times Higher Education India. Alumni of the university are popularly known as Aligarians. Given below AMU engineering exam syllabus

AMU Engineering Entrance Syllabus

Pattern of Exam:- AMU organize engineering exam in 2 parts that is paper-1 and paper-2. Part- 2 is compulsory to attend for all those candidates who desire to take admission in architecture courses along with paper-1. Paper-2 is designed to test the aptitude of the candidates in architecture field. Paper-1 is for students who desire to get into B.tech program. Questions will be asked from Physics, Chemistry and Biology. and all are MCQ type. The cut off marks depends on a number of factors like- Total candidates appeared, no. of candidates cleared, level of difficulty of paper, availability of seats, reservation of seats for various section.

AMU Engineering Exam Syllabus:-

 Physics

• Physical World and Measurement- It consists of basic topics or the fundamental topics of measurement.  It include topics- Physics – scope and excitement, nature of physical laws; Physics, Technology and society. Need for measurement : Units of measurement; systems of units; SI units, fundamental and derived units, Length, mass  and time measurements; accuracy  and  precision  of  measuring  instruments,  errors   in   measurement; significant figures. Dimensions of physical quantities, dimensional analysis and its applications.

• Kinematics- Mechanics branch that deals with motion of objects without refering the forces that causes the motion. It include topics :- Frame of reference, Motion in a straight line : Position-time graph, speed and velocity,  Uniform and  non-uniform  motion,  average  speed  and  instantaneous veolocity.  Uniformly  accelerated  motion,  velocity-time,  position-time  graphs, relations for uniformly accelerated motion (graphical treatment). Elementary concepts of differentiation and integration for describing motion. Scalar and vector quantities : Position and displacement vectors, general vectors and notation, equality of vectors, multiplication of vectors  by a real number; addition and subtraction of vectors.  Relative velocity.Unit vector; Resolution of a vector in a plane-rectangular components.  Motion in a plane.  Cases of uniform velocity and uniform acceleration – projectile motion. Uniform circulation motion.

• Laws of Motion- The physical law which plays a role in foundation of classical mechnaics. It include topics:-  Intuitive concepts of force.  Inertia, Newton’s first law of motion; momentum and Newton’s second law of  motion;  impulse; Newton’s third law of motion. Law of conservation of linear momentum and its applications.Equilibrium of concurrent forces, static and kinetic friction, laws of friction, rolling friction. Dynamics of  uniform circular motion: Centripetal force, examples of circular motion (vehicle on level circular road, vehicle on banked road).

• Work, Energy and Power- Work will be called as force when it acts on a body and that bosy causes displacment in the direction of force. Energy can only be calculated from its state and it cannot be measured as its a extensive property of physical system. Power is energy consumed/unit time. It inculde topics :- Scalar product of vectors. Work done by a constant force and a variable force;kinetic energy, work-energy theorem, power.Notion of potential energy, potential energy of a spring, conservative forces : conservation  of   mechanical  energy  (kinetic   and  potential   energies);  non- conservative forces : elastic and inelastic collisions in one and two dimensions.

•  Motion of System of Particles and Rigid Body- It analyse the movement of systems of interlinked bodies. It include topics-  Centre of mass of a two-particle system, momentum conversation and centre of mass motion. Centre of mass of a rigid body; centre of mass of uniform rod.Vector  product  of  vectors;  moment  of  a  force,  torque,  angular  momentum, conservation of angular momentum with some examples.Equilibrium of rigid bodies, rigid body rotation and equiations of rotational motion. Comparison  of  linear  and  rotational  motions;  moment  of  inertia,  radius  of gyration.Values of  moments  of  inertia  for  simple  geometrical  objects  (no  derivation). Statement of parallel and perpendicular axes theorems and their applications.

• Gravitation :- Its a natural phenomenon because of which all physical bodies attract each other. It includes :-  Keplar’s laws of planetary motion. The Universal law of gravitation. Acceleration dues to gravity and its variation with altitude and depth.Gravitational potential energy;  gravitational potential,  Escape Velocity, Orbital Velocity of a satellite, Geo-stationary satellites.

• Properties of Bulk Matter :- It include topics related to the properties of matter  that can exist in different forms. Elastic behaviour, Stress-strain relationship, Hooke’s law, Young’s modulus, bulk modulus, shear, modulus of rigidity. Pressure due to a fluid column; Pascal’s law and its applications (hydraulic lift and hydraulic brakes). Effect of gravity on fluid pressure. Viscosity,  Stokes’  law,  terminal  velocity,  Reynold’s  number,  streamline  and turbulent flow, Bernoulli’s theorem and its applications.Surface energy and surface tension, angle of  contact, application of surface tension ideas to drops, bubbles and capillary rise. Heat, temperature, thermal expansion; specific heat-calorimetry; change of state- latent   heat. Heat   transfer-conduction,  convection  and   radition,   thermal conductivity, Newton’s law of cooling.

• Thermodynamics- Branch of natural science that is concerned with heat and its relation to energy & work. It include topics :- Thermal    equilibrium    and    definition    of    temperature    (zeroth     law    of thermodynamics). Heat, work and internal energy.  First law of thermodynamics.Second law of thermodynamics :  reversible and irreversible processes.  Heat engines and refrigerators.

• Behaviour of Perfect Gas and Kinetic Theory- It include topics related to kinetic theory and perfect gas behaviour- Equation of state of perfect gas, work done on compressing a gas. Kinetic theory of gases-assumptions, concept of pressure. Kinetic energy and temperature;  rms   speed  of   gas   molecules;  degrees  of freedom, law of equipartition  of  energy  (statement  only)  and  application  to  specific  heats  of gases; concept of mean free path, Avogadro’s number.

• Oscillations and Waves- Repetitive variation mainly in time called oscillation. Wave is the disturbance that travels through space & matter. It include topics :-  Periodic motion-period, frequency, displacement as a function of time. Periodic functions.  Simple harmonic motion (S.H.M.) and its equation; oscillations of a spring  –  restoring  force  and  force  constant;  energy  in S.H.M.  –  kinetic  and potential energies’ simple pendulum – derivation of expression for its time period’ free, forced and damped oscillations(qualitative ideas only), resonance. Wave  motion,  Longitudinal  and  transverse  waves,  speed  of  wave  motion. Displacement  relation  for  a  progressive  wave.     Principle  of  superposition  of waves,  reflection  of  waves,  standing  waves  in   strings  and  organ   pipes, fundamental mode and harmonics, Beats, Doppler effect.

• Electrostatics- It deals with the phenomena & properties of slow moving electric charges  without any acceleration. It include topics-  Electric charges, Conservation of charge, Coulomb’s low-force between two point charges forces between multiple charges, superposition principle and continuous charge distribution.Electric field, electric field due to a point charge, electric field lines’ electric dipole electric field due to a dipole torque on a dipole in uniform electric field. Electric flux, statement of gauss’s theorem and its applications to find field due to infinitely long straight wire  uniformly charges infinite plane sheet and uniformly charged tin spherical shell (field inside and outside).Electric potential difference, electric potential due to a point charge, a dipole and system of charge; equipotential surfaces, electrical potential energy of a system of two point charges and of electric dipole in an electrostatic field.Conductors and insulators free charges and bound charges inside a conductor. Dielectrics and electric polarization, capacitors and capacitance, combination of capacitors in series and in parallel, capacitance of a parallel plate capacitor with and without dielectric medium between the plates, energy stored in a capacitor. Van de Graaff generator.

• Current Electricity- Flow of electric charges and it includes topics-  Electric current flow of electric chargers in a metallic conductor drift velocity, mobility and their relation with  electric current; Ohm’s electrical resistance, V-I characterstics  (linear  and  non-linear),  electrical  energy  and  power,  electrical resistivity and conductivity.  Carbon resistors colour code for carbon resistors; series  and  parallel   combinations  of  resistors;   temperature  dependence of resistance.Internal resistance of a cell, potential difference and emf of a cell combination of cells in series and in parallel.Kirchhoff’s laws and simple applications. Wheatstone bridge and metre bridge. Potentiometer – principle and its applications to measure potential difference and for comparing emf of two cells; measurement of internal resistance of a cell.

• Magnetic Effects of Current and Magnetism :- It deals with the magnetic effects when magnets exert forces on other magnets. It include topics :-  Concept of magnetic field, Oersted’s experiment. Biot-Savart law and its application to current carrying circular loop.Ampere’s law and its applications to infinitely long straight wire, straight and toroidal solenoids.Force on a moving charge in uniform magnetic and electric fields.  Cyclotron. Force on a current – carrying  conductor in a uniform magnetic field. Force between  two  parallel  current  –  carrying  conductors  –  definition  of  ampere.Torque experienced by a current loop in uniform magnetic field; moving coil galvanometer – its current sensitivity and conversion to ammeter and voltmeter. Current loop as a magnetic dipole and its magnetic dipole moment.      Magnetic dipole, moment of a revolving electron, magnetic field intensity due to a magnetic dipole (bar magnet) along its  axis and perpendicular to its axis.   Torque on magnetic dipole (bar magnet) in a  uniform magnetic field; bar magnet as an equivalent solenoid magnetic field line;   Earth’s  magnetic field and magnetic elements  pars  –  dia  –  and  ferro  –  magnetic  substances,  with  examples. Electromagnets and factors of affection their strengths.  Permanent magnets.

• Electromagnetic Induction and Alternating Currents- When a conductor is exposed to varying magnetic field than there is a generation of potential difference across it. It include topics :- Electromagnetic Induction;  Faraday’s law, Induced emf and current; Lenz’s law, Eddy current self and mutual inductance. Need for displacement current.Alternating  currents,  peak  and  rms  value  of  alternating;  current  /  voltage, reactance and impedance;LC oscillations (qualitative treatment only), LCR series circuit, resonance, power in ac circuits wattles current.AC generator and transformer.

• Electromagnetic Waves:- Energy radiated or absorbed by charged particles which exhibit wave behaviour. It include topics:- Displacement  current,  current  Electromagnetic  wave  and  their  characteristics(qualitative ideas only) Transverse nature of electromagnetic waves. Electromagnetic spectrum (radio waves, microwaves infrared, visible ultraviolet, x-rays gamma rays) including elementary facts about their uses.

• Optics:- It refers to behaviour and properties of light as well as its interaction with matter. It include topics :-  Reflection of light spherical mirror, mirror formula refraction of light, total internal reflection  and  its  applications,  optical  fibres  refraction  at  spherical  surfaces, lenses thin lens formula lens maker’s Formula.  Magnification power of a lens, combination of thin lenses in contract.  Refraction and dispersion of light through a prism.Scattering of light – blue colour of the sky and reddish appearance of the sun at sunrise and sunset.Optical instruments : Human eye, image formation and accommodation, correct of  eye  defects  (myopia,  hypermetropia,  presbyopia  and  astigmatism)  using lenses.  Microscopes and astronomical Telescopes (reflecting and refraction) and their magnifying powers.Waves optics : Wave front and Huygens principle reflection and refraction of plane wave at a plane surface using wave fronts.  Proof of laws of reflection and refraction using Huygen’s principle, Interference, Young’s double slit experiment and expression for fringe width coherent sources and sustained interference of light.  Diffraction due to a single slit, width of central maximum.  Resolving power of microscopes and astronomical telescopes. Polarization, plane polarized light; Brewster’s law.  Uses of plane polarized light and polaroids.

• Dual Nature of Matter and Radiation:- It include the following topics :- Dual  nature   of   Radiation  Photoelectric,  Hertz   and  Lenard’s  observations; Einstein’s Photoelectric equation – particle nature of light.Master  waves  –  wave  nature  of  particles,  de  Broglie  relation.  DAvission  – General experiment.

• Atoms & Nuclei :- Atom is the basic unit of matter. It includes-  Alpha – particle scattering experiment, Rutherford’s model of atom; Bohr model, energy levels hydrogen spectrum.Composition and size of nucleus, atomic masses, isotopes, isobars; isotones. Radioactivity – alpha, beta  and  gamma particles / rays and their properties; radioactive decay law Mass-energy relation, mass defect;  binding energy per nucleon and its variation with mass number, nuclear fission, nuclear reactor, nuclear fusion.

• Electronic Devices: The components that help in digital information processing. It include topics :-  Semiconductors;  semiconductor  diode  I  –  V,  characteristics  in  forward  and reverse bias, diode as a rectifier; I – V characteristics of LED, photodiode, solar cell and Zener diode : Zener diode as a voltage regulator. Junction transistor, transistor action characteristics of a transistor; transistor as an amplifier (common emitter configuration) and oscillator.  Logic gages (OR, AND,  NOT NAND and NOR ).  Transistor as a switch.

• Communication Systems :- Various systems that help in communication which include following topics :-  Elements of a communication system (block diagram only); bandwidth of signals (speech, TV and digital data); bandwidth of transmission medium.  Propagation of electromagnetic waves in the atmosphere, sky and space  wave propagation. Need of modulation.  Production and detection of an amplitude-modulate waves.

 1. Some Basic concepts of Chemistry, Structure of Atom, Classification of elements and periodicity in properties, Chemical bonding and molecular structure.

2. States of matter : Gases and liquids, Solid State, Solutions.

3. Thermodynamics.

4. Equilibrium, Redox reactions, Electrochemistry.

5. Chemical Kinetics, Surface Chemistry.

6. Hydrogen, General principles and process of isolation of elements, Studies of s & p-d and f – block elements, Coordination compounds.

7. Organic   Chemistry  :    Some   basic   principles   and   Techniques,   Hydrocarbons. Haloalkanes and Haloarenes, alcohols, phenols and Ethers.

8. Aldehydes, Ketones and Carboxylic acids.

9. Organic compounds containing nitrogen.

10. Biomolecules, Polymers, Chemistry in everyday life.

11. Environmental Chemistry.

Note : Text Books of Chemistry Class XI and Class XII NCERT Publication, latest edition will be the best to prepare for exam.

UNIT – I : SETS AND FUNCTIONS

1.  Sets      

• Sets and their representations. Empty set. Finite & Infinite sets. Equal sets. Subsets.Subsets of the set of real numbers especially Intervals (with notations). Power set. Universal  set. Venn diagrams. Union and Intersection of sets.    Difference of sets. Complement of a set.

2.  Relations & Functions

• Orders pairs, Cartesian product of sets.  Number of elements in the Cartesian product of two finite sets.  Cartesian product of the reals with itself (upto R x R x R). Definition of relation, pictorial diagrams, domain, codomain and range of a relation.  Function as a special kind of relation from one set to another.  Pictorial representation of a function, domain, co-domain and range of a function.  Real valued function of the real variable, domain and range of these functions,  constant,  identity,  polynomial,  rational  modulus,  signum  and  greatest  integer functions with their graphs, Sum, difference, product and quotients of functions.

3.  Trignometric functions :

• Positive  and  negative  angles.     Measuring  angles  in  radians  and  in  degrees  and conversion from one measure to another. Definition of trigonometric functions with the help of unit circle.  Truth of the identity sin2  x + cos2  x = 1 for all x. Signs of trigonometric functions and sketch of their graphs.  Identities related to sin 2 x, cos 2 x, tan 2 x, sin 3 x, cos 3 x and tan 3 x. General solution of trigonometric equiations of the type sin = sin

1.  Principle of Mathematical Induction

• Process of the proof by induction, motivating the application of the method by looking at natural  numbers   as  the  least  inductive  subset  of  real  numbers.The  principle  of mathematical induction and simple applications.

2.  Complex numbers & Quadratic Equations :-

• Need for complex numbers, especially1 , to be motivated by inability to solve every quadratic equation. Brief description of algebraic properties of complex numbers. Argand plane and polar representation of complex numbers.  Statement of Fundamental Theorem of Algebra, Solution of quadratic equations in the complex number system.

3.  Linear Inequalities

• Linear  inequalities,  Algebraic  solutions  of  linear  inequalities  in  one  variable  and  their representation on the number line. Graphical solution of linear inequalities in two variables. Solution of system mof linear inequalities in two variables graphically.

4.  Permutation & Combination

• Fundamental  principle  of  counting. Factorial  n  (n1)  Permutations  and  combinations, derivation of formulae and their connections, simple applications.

5.  Binomial theorem

• History, statement and proof of the binomial theorem for positive integral indices.  Pascal’s triangle, General and middle term in binomial expansion, simple applications.

6.  Sequence & Series

• Sequence and Series, Arithmetic progression (A > P), arithmetic mean (A.M.) Geometric progression (G.P., General term of a G.P., sum of n terms of a G.P., geometric mean (G >M), relation between A.M. and G.M. Sum to a terms of the special series

UNIT III :  COORDINATE GEOMETRY :

 1.  Straight Lines

• Brief recall of 2 D from earlier classes. Slope of a line and angel between two lines.  Various forms of equations of a line : parallel to axes, point-slope form, slope intercept form, two point form, intercepts form  and normal form. General equation of a line.  Distance of a point from a line.

 3.  Introduction to 3D Geometry

• Coordinate axes and coordinate planes in three dimensions.    Coordinatoes of a point. Distance between two points and section formula.

UNIT IV :  CALCULUS

1.  Limits & Derivatives

• Derivative introduced as rate of change both as that of distance function and geometrically, intuitive idea of  limit. Definition of derivative, relate it to slope of tangent of the curve, derivative of sum, difference, product and quotient of functions. Derivatives of polynomial and trigonometric functions.

UNIT V : MATHEMATICAL REASONING

1.  Mathematical Reasoning

• Mathematically acceptable statements.    Connecting words / phrases – consolidating the understanding of “if and only if (necessary and sufficient) condition”, implies”, and/ or”, implied by,   “and”, “or”, “three exists” and their use through variety of examples related to real life and mathematics. Validating the statements involving the connecting words – difference between contradiction, converse and contrapositive.

2.  Probability

• Random experiments : Outcomes, sample, spaces (set representation).  Events : occurrence of events, `not’, `and’ and `or’ events, exhaustive events, mutually exclusive events Axiomatic (set theoretic) probability, connections with the theories of earlier classes.  Probability of an event,  Probability of `not’, `and’ and `or’ events.

Following text books are recommended for preparation:-

(1)  Mathematics Part I – Textbook for Class XI, NCERT Publication. (2) Mathematics Part II – Textbook for Class XI, NCERT Publication.

UNIT – I  RELATIONS AND FUNCTIONS

1. Relations and Functions :

• Types of relations : reflexive, symmetric, transitive and equivalence relations.  One to one  and  onto   functions,  composite  functions,  inverse  of  a  function.Binary operations.

2. Inverse Trigonometric Functions :

• Defintion, range, domain, principal value branches, Graphs of inverse trigonometric functions.  Elementary properties of inverse trigonometric functions.

UNIT II :  ALGEBRA

1. Matrices :

• Concept, notation, order, equality, types of matrices, zero matrix, transpose of a matrix,  symmetric and kew symmetric matrices.  Addition, multiplication and scalar multiplication  of  matrices,  simple  properties  of  edition,  multiplication  and  scalar multiplication.  Non commutativity of multiplication of matrices and existence of non zero matrices whose product is the zero matrix (restrict to square matrices of order
• Concept of elementary row and column operations.  Invertible matrices and proof of the uniqueness of inverse, if it exists. (Here all matrices will have real entries).

2.  Determinants :

• Determinant of a square matrix (upto 3 x 3 matrices), properties of determinants, minors, cofactors and  applications of determinants in finding the area of a triangle. A joint and inverse of a square matrix.  Consistency, inconsistency and number of solutions of system of linear equations  by examples, solving system of linear equations in two or three variables (having unique solution) using inverse of a matrix.

UNIT III  : CALCULUS

1.  Continuity and Differentiability :

• Continuity and Differentiability, derivative of composite functions, chain rule, derivative of inverse  trigonometric functions, derivative of implicit function.   Concept of exponential and logarithmic functions and their derivative.  Logarithmic differentiation.  Derivative of functions expressed in  parametric forms.    Second order derivatives.    Rolle’s and Lagrange’s Mean Value Theorems (without proof) and their geometric interoperations.

2.  Applications of Derivatives :

• Applications of derivatives : rate of change, increasing / decreasing functions, tangets and normals, approximation, maxima and minima (first derivative test motivated geometrically and second  derivative  test  given  as  a  provable  tool)..  Simple  problems  (that  illustrate  basic principles and understanding of the subject as well as real life situations).

3. Integrals

• Integration as inverse process of differentiation.    Integration of a variety of functions by substitution, by partial fractions and by parts, only simple integrals of the type : To be evaluated. Define integrals as a limit of sum, Fundamental Theorem of calculus (without proof). Basic properties of definite integrals and evaluation of definite integrals.

• Applications in findings the area under simple curves, especially lines, areas of circles / parabolas / ellipse (in standard form only), area between the two above said curves (the region should be clearly identifiable).

5. Differential Equations :

• Definition, order and degree, general and particular solutions of a differential equation. Formation of differential equation whose general solution is given. Solution of differential equations by method of separation of variables,  homogeneous differential equations of first order and first degree. Solutions of linear differential equations of the type :dy    py dxq , where p and q are functions of x.

4 Responses to AMU Engineering Exam Syllabus

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