### APPLIED MATHEMATICS DIPLOMA ENGG CET SYLLABUS 2012

APPLIED MATHEMATICS

Max Marks : 40 Marks

ALGEBRA

DETERMINANTS.                                                                                                  1 X 2 = 2M

Definition, Order, Expansion of 2nd & 3rd order Determinants by means of examples. Problems on finding unknown quantity in a 2nd & 3rd determinant using expansion. Solving simultaneous linear equations by determinant method ( Cramer’s rule).

MATRICES.                                                                                                             1 X 3 = 3M

Determinant value of a square matrix. Singular and non singular matrices. Minor and co factor of an element of a matrix. Adjoint of a matrix. Inverse of a matrix. Characteristics equations of a square matrix and its roots, problems.

BINOMIAL THEOREM.                                                                                          1 X 2 = 2M

Meaning of nCr and its value. Binomial theorem for (x + a)n, where n is a positive integer. Expansion. Finding constant term, co-efficient of xn, particular term and middle term(s).

VECTOR ALGEBRA.                                                                                             1 X 3 = 3M

Definition of vector. Magnitude of a vector. Position vector. Addition and subtraction of vector. Product of vectors, scalar and vector product. Geometrical meaning of scalar and vector product. Applications of dot(scalar) and cross(vector) product: Projection of a vector on another vector. Area of parallelogram and area of triangle. Work done by a force and moment of force, problems

TRIGONOMETRY

TRIGONOMETRIC RATIOS OF AN ACUTE ANGLE.                                    1 X 2 = 2M

Defination of Trigonometric ratios in terms of sides of a triangle for an acute angle. Trigonometric identities. Trigonometric ratios of standard angles: The numerical value of trigonometric ratios of standard angles like 00, 300, 450, 600 and 900, problems

ALLIED ANGLES.                                                                                                 1 X 2 = 2M

Angle of any magnitude, sign of the trigonometric ratios. Meaning of allied angles. Trigonometric ratios of allied angles in terms of θ. Complimentary angles and relation between trigonometric ratios of complimentary angles, problems.

COMPOUND ANGLES.                                                                                        1 X 2 = 2M

Recall Sin( A + B) and Cos(A + B). Find Tan( A + B) using      Sin( A + B) and Cos(A + B). Write the formulae for Sin( A - B), Cos(A - B) and tan( A - B), problems.

Write ratios of multiple angles of 2A and 3A and sub multiple angle formulae, problems.

TRANSFORMATION FORMULAE.                                                                   1 X 1 = 1M

Express sum or difference of Sine and Cosine of an angles in to product form. Express product of Sine and Cosine of angles in to sum or difference form, simple problems.

INVERSE TRIGONOMETRIC FUNCTIONS.                                                   1 X 1 = 1M

Definition. Principle values of inverse trigonometric functions. Results like sin-1x + cos-1x =Л/2 = tan-1x + cot-1x = cosec-1x + sec-1x, tan-1x + tan-1y = tan-1 [(x+y)/(1-xy)] etc., problems.

ANALYTICAL GEOMETRY

BASIC CONCEPTS OF ANALYTICAL GEOMETRY.                                               1 X 3 = 3M

Defination of a point in a plane, Specification of a point using co-ordinate system. Points on X-axis and Y-axis. Distance formula. Section formulae. Co-ordinate of a point which divide the line internally and externally in the given ratio. Mid point formula. Centroid, area of a triangle and collinear points, problems.

STRAIGHT LINES.                                                                                                            1 X 3 = 3M

Inclination of a line with horizontal line and its slope. Intercept of a straight line. Slope of a line parallel to X-axis and Y-axis. Conditions for two lines to be parallel and perpendicular.  Equations of straight lines y = mx + c,  y – y1 = m (x – x1 ),  y – y1 = (y2 – y1 / x2 – x1 ) (x – x1 ), (x / a ) + (y / b) = 1. Equation of lines through a point and parallel or perpendicular to a given line. Angle between two lines, problems.

CALCULUS

LIMITS.                                                                                                                     1 X 2 = 2M

Variables and Constants. Definition of function. Concept of x tends to ‘a’. Definition of limit of a function. Problems on limit of a function by factorization, rationalization when x tend to ‘0’, when x tend to ‘∞’ and x tend to ‘a’. Algebraic and Trigonometric limits, problems.

DIFFERENTIAL CALCULUS.                                                                            1 X 4 = 4M

List of standard derivatives. Rules of differentiation: Sum, product and quotient of functions. Derivatives of function of a function(Chain rule). Derivatives of inverse Trigonometric functions, Hyperbolic functions and inverse of hyperbolic functions, Implicit functions, Parametric functions. Logarithmic differentiation. Successive differentiation up to second order, problems.

APPLICATIONS OF DIFFERENTIATION.                                                      1 X 2 = 2M

Geometrical meaning of derivative. Equation of tangent and normal to the curve y = f(x) at a given point. Derivative as a rate measure. Maxima and minima of a function, problems

INTEGRAL CALCULUS.                                                                                     1 X 3 = 3M

Definition of Integration. List of standard integrals. Rules of integration (only statement)

Integration by substitution method. Integration by parts. Rule of integration by parts, problems.

DEFINITE INTEGRALS.                                                                                      1 X 2 = 2M

Definition of Definite integral. Theorems on definite integrals, problems.

APPLICATIONS OF DEFINITE INTEGRALS.                                                           1 X 1= 1M

Find area, volume and r m s value of a function, problems.

DIFFERENTIAL EQUATIONS.                                                                           1 X 2 = 2M

Definition, example, order and degree of differential equation with examples. Formation of differential equation by eliminating arbitrary constants up to second order. Solution of D E of first degree and first order by variable separable method. Linear equations and its solution.

### DIPLOMA MECHANICAL ENGINEERING CET SYLLABUS 2012

Group code: ME              MECHANICAL ENGINEERING                     Marks: 100

1          Basic Management Skills

Team, Group, Team Building, Production and Productivity, Product Design and its Stages, Types of Production, Functions of Production, Planning and Control Department, Purchasing and its Procedure, Stores Management, Logistics, Inventory Control, Total Productive Maintenance-Concept and Techniques, Quality, Inspection-Types, Total Quality management-Concept and Tools, I.S.O 9000,Quality Standards, Accident and its Prevention

15 Marks

2          Manufacturing Technology

Lathe, Drilling, Milling, Shaping, Grinding,(Types of Machines , Operations, Tools And Accessories ); NC & CNC Machines ( Comparison, advantages and disadvantages); Electric Discharge Machining(EDM), Ultrasonic Machining(USM), Abrasive Jet Machining(AJM) , Laser Beam Machining(LBM), Electro Chemical Machining(ECM), Electron Beam Machining(EBM); Casting, Molding Sands, Patterns, Casting Processes, Special Casting Techniques; Welding Techniques -Arc Welding, Gas Welding, TIG, MIG, Resistance Welding, EBW, LBW, Plasma Arc Welding; Forging, Rolling, Extrusion; Sheet Metal Operation-Shearing, Blanking, Punching, Trimming, Drawing, Embossing.

20 Marks

3          Thermal Engineering

Basic terms and Concepts, Perfect Gas Laws, Zeroth Law, First and Second Laws of Thermodynamics, , Thermodynamic Processes Perfect Gases; Air Standard Cycles, Air Compressors; SI & CI-Engine(Two stroke & Four stroke), Compression Ratio, Valve Timing Diagram,  Lubrication and cooling; Fuels-types-Calorific Value of Fuel.

15 Marks

4          Theory of Machines

Basic Kinematics of Machines, Transmission of power-Belt drive, Rope drive, Chain drives, Gear drives, Gear trains, Balancing of rotating masses in the same plane, Cams and Followers-Classification, Friction, Types of Friction, Laws of Friction, Brakes, Clutches and Dynamometers.

15 Marks

5          Strength of Materials and Engineering Mechanics

Simple Stress and Strain, Types of Stresses, Hooks Law, Modulus of Elasticity, Modulus of Rigidity, Poisons Ratio, Relations between three Elastic Constants, Temperature Stresses,  Bending Moment, Shear Forces, BMD and SFD diagrams for Cantilever, Simply Supported Beams with Point Load and Uniformly Distributed Load.

15 Marks

6          Material Science

Mechanical Properties of Metal, Manufacturing, Properties & Uses of Pig Iron Cast Iron & Steel, Properties & Uses of Copper, Aluminum, Lead, Zinc, Tin, Cobalt & Nickel, Iron-Carbon Equilibrium Diagram, Heat Treatment of Steel, Alloys of Steel.                                                                                                                                                                                                                                                                                                                                            10 Marks

7      Engineering Drawing

Basics of Drawing, Conventions, Types, Dimensioning, Surface finish symbols, Projections-Orthographic and Isometric.

10 Mark

### APPLIED SCIENCE DIPLOMA ENGINEERING CET SYLLABUS

APPLIED SCIENCE

Max. Marks: 40

UNIT-I: UNITS, DIMENSIONS AND MEASUREMENT:

Physical quantities, Systems of units, Advantages of SI, Dimensions, Dimensional formula and its Applications, Principle of  Vernier, its usage, Principle of Screw guage, its usage-Problems.

1x4=4 marks

UNIT –II: BASICS OF DYNAMICS:

Equations of motion, Newton’s laws of motion, Force , Inertia, Momentum, Law of conservation of momentum, Simple problems. Friction, Advantages and disadvantages.

1x4=4 marks

UNIT-III: BASICS OF STATICS:

Scalars, Vectors,  Resultant, Equilibrium, Resolution of Vectors. Laws of  Vectors (Parallelogram law, Triangle law, Lami’s theorem, Polygon law) Simple problems.

Co-planar parallel Forces, Moment of Force, Couple, Moment of Couple, Parallel Forces, Conditions of Equilibrium, Simple problems.

1x5=5 marks

UNIT-IV: PROPERTIES OF SOLIDS AND LIQUIDS:

Plasticity and Elasticity, Types of Stress and Strain, Hooke’s Law,Types of modulii of elasticity, Compressibility, Poisson’s ratio, Factor of safety, simple problems.

Liquid pressure, Cohesive and Adhesive forces, Angle of contact, Surface Tension and its Application, Capillarity and its Applications, Viscosity and its Applications, simple problems.

1x6= marks

UNIT-V: HEAT AND PROPERTIES OF GASES:

Heat and Temperature, Specific Heat, Heat Capacity, Specific heats of gases, Cp    and Cv  relation between them, Gas laws-Boyle’s law, Charle’s law ,absolute scale of temperature, Perfect gas equation, simple problems.

1x3=3 marks

Continued…

Page 2

UNIT-VI: WAVE MOTION:

Basic definitions of vibratory motion, SHM, Wave motion, Types of waves, Stationary Waves and its Characteristics, Resonance, Beats and its applications, Velocity of sound in gas, affecting factors, Laws of transverse vibrations of stretched string, Acoustics of building-Echo, Reverberation, simple problems.

1x7=7 marks

UNIT-VII: PHYSICAL OPTICS:

Introduction to theories of light- Newton’s corpuscular theory, Huygen’s wave theory

Maxwell’s electromagnetic theory, Planck’s quantum theory.

Interference- Theory of interference, Expression for amplitude and intensity of resultant wave, conditions for constructive and destructive interference, expression for path difference and fringe width, simple problems on fringe width and path difference.

Diffraction- Fresnel’s diffraction, Fraunhoffer’s  diffraction, difference between interference and diffraction, Resolving power, expression for resolving power of microscope and telescope.

Polarisation-Plane of vibration, plane of polarization, methods of producing plane polarized light, Brewster’s  law.

1x5= 5 marks

UNIT-VIII: MODERN PHYSICS:

Electron emission-Thermionic emission, Photoelectric emission, Field emission and secondary emission, Experimental  results of photoelectric effect, Einstein’s photoelectric equation, Photoelectric cell and its applications, scattering of light, coherent scattering and incoherent scattering, Raman effect-applications

Laser-Principle, necessary conditions, properties and applications of laser,