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# Type of Questions in GATE EXAM

The GATE examination shall be of 3 hours duration with a maximum of 100 marks. The question paper for GATE 2020 will consist of questions of both multiple-choice type and numerical answer type. For multiple choice type questions, candidates must choose the answer from the given choices. For numerical answer type questions, candidates have to enter a number as the answer using a virtual keypad.

# GATE 2020 Metallurgical Engineering Syllabus

Section 1: Engineering Mathematics
Linear Algebra: Matrices and Determinants, Systems of linear equations, Eigen values and Eigen vectors.

Calculus: Limit, continuity and differentiability; Partial derivatives; Maxima and minima; Sequences and series; Test for convergence; Fourier series.

Vector Calculus: Gradient; Divergence and Curl; Line, Surface and volume integrals; Stokes, Gauss and Green’s theorems.

Differential Equations: Linear and non-linear first order ODEs; Higher order linear ODEs with constant coefficients; Cauchy’s and Euler’s equations; Laplace transforms; PDEs –Laplace, one dimensional heat and wave equations

Probability and Statistics: Definitions of probability and sampling theorems, conditional probability, Mean, median, mode and standard deviation; Random variables; Poisson, normal and binomial distributions; Correlation and regression analysis

Numerical Methods: Solutions of linear and non-linear (Bisection, Secant, Newton-Raphson methods) algebraic equations; integration by trapezoidal and Simpson’s rule; single and multi-step methods for differential equations

Section 2: Thermodynamics and Rate Processes
Laws of thermodynamics, activity, equilibrium constant, applications to metallurgical systems, solutions, phase equilibria, Ellingham and phase stability diagrams, thermodynamics of surfaces, interfaces and defects, adsorption and segregation;

Basic kinetic laws, order of reactions, rate constants and rate limiting steps; principles of electro chemistry- single electrode potential, electrochemical cells and polarizations, aqueous corrosion and protection of metals, galvanic corrosion, crevice corrosion, pitting corrosion, intergranular corrosion, selective leaching, oxidation and high temperature corrosion – characterization and control

Heat transfer – conduction, convection and heat transfer coefficient relations, radiation, mass transfer – diffusion and Fick’s laws, mass transfer coefficients; momentum transfer – concepts of viscosity, shell balances, Bernoulli’s equation, friction factors.

Section 3: Extractive Metallurgy
Minerals of economic importance, comminution techniques, size classification, flotation, gravity and other methods of mineral processing; agglomeration, pyro-, hydro-, and electro-metallurgical processes; material and energy balances

Principles and processes for the extraction of non-ferrous metals – aluminium, copper, zinc, lead, magnesium, nickel, titanium and other rare metals

Iron Making – principles, role structure and properties of slags, metallurgical coke, blast furnace, direct reduction processes

Primary and secondary steel making, ladle metallurgy operations including deoxidation, desulphurization, sulphide shape control, inert gas rinsing and vacuum reactors; secondary refining processes including AOD, VAD, VOD, VAR and ESR; ingot and continuous casting; stainless steel making, furnaces and refractories

Section 4: Physical Metallurgy
Crystal structure and bonding characteristics of metals, alloys, ceramics and polymers, structure of surfaces and interfaces, nano-crystalline and amorphous structures

Solid solutions; solidification; phase transformation and binary phase diagrams; principles of heat treatment of steels, cast iron and aluminium alloys; surface treatments; recovery, recrystallization and grain growth; structure and properties of industrially important ferrous and non-ferrous alloys

Elements of X-ray and electron diffraction; principles of optical, scanning and transmission electron microscopy; industrial ceramics, polymers and composites; introduction to electronic basis of thermal, optical, electrical and magnetic properties of materials; introduction to electronic and opto-electronic materials.

Section 5: Mechanical Metallurgy
Elasticity, yield criteria and plasticity; defects in crystals;

Elements of dislocation theory – types of dislocations, slip and twinning, source and multiplication of dislocations, stress fields around dislocations, partial dislocations, dislocation interactions and reactions; strengthening mechanisms

Tensile, fatigue and creep behaviour; superplasticity; fracture – Griffith theory, basic concepts of linear elastic and elastoplastic fracture mechanics, ductile to brittle transition, fracture toughness; failure analysis

mechanical testing – tension, compression, torsion, hardness, impact, creep, fatigue, fracture toughness and formability.

Section 6: Manufacturing Processes
Metal casting – patterns and moulds including mould design involving feeding, gating and risering, melting, casting practices in sand casting, permanent mould casting, investment casting and shell moulding, casting defects and repair;

Hot, warm and cold working of metals; Metal forming – fundamentals of metal forming processes of rolling, forging, extrusion, wire drawing and sheet metal forming, defects in forming

Metal joining – soldering, brazing and welding, common welding processes of shielded metal arc welding, gas metal arc welding, gas tungsten arc welding and submerged arc welding; Welding metallurgy, problems associated with welding of steels and aluminium alloys, defects in welded joints

Powder metallurgy – production of powders, compaction and sintering

NDT using dye-penetrant, ultrasonic, radiography, eddy current, acoustic emission and magnetic particle methods.

# GATE 2020 Chemical Engineering Syllabus

Section 1: Engineering Mathematics
Linear Algebra: Matrix algebra, Systems of linear equations, Eigen values and Eigen vectors

Calculus: Functions of single variable, Limit, continuity and differentiability, Taylor series, Mean value theorems, Evaluation of definite and improper integrals, Partial derivatives, Total derivative, Maxima and minima

Vector Calculus: Gradient, Divergence and Curl, Vector identities, Directional derivatives, Line, Surface and Volume integrals, Stokes, Gauss and Green’s theorems

Differential Equations: First order equations (linear and nonlinear), Higher order linear differential equations with constant coefficients, Cauchy’s and Euler’s equations, Initial and boundary value problems, Laplace transforms, Solutions of one dimensional heat and wave equations and Laplace equation

Complex Variables: Complex number, polar form of complex number, triangle inequality

Probability and Statistics: Definitions of probability and sampling theorems, Conditional probability, Mean, median, mode and standard deviation, Random variables, Poisson, Normal and Binomial distributions, Linear regression analysis

Numerical Methods: Numerical solutions of linear and non-linear algebraic equations. Integration by trapezoidal and Simpson’s rule. Single and multi-step methods for numerical solution of differential equations

Section 2: Process Calculations and Thermodynamics
Steady and unsteady state mass and energy balances including multiphase, multi- component, reacting and non-reacting systems. Use of tie components; recycle, bypass and purge calculations; Gibb’s phase rule and degree of freedom analysis

First and Second laws of thermodynamics. Applications of first law to close and open systems. Second law and Entropy. Thermodynamic properties of pure substances: Equation of State and residual properties, properties of mixtures: partial molar properties, fugacity, excess properties and activity coefficients; phase equilibria: predicting VLE of systems; chemical reaction equilibrium

Section 3: Fluid Mechanics and Mechanical Operations
Fluid statics, Newtonian and non-Newtonian fluids, shell-balances including differential form of Bernoulli equation and energy balance, Macroscopic friction factors, dimensional analysis and similitude, flow through pipeline systems, flow meters, pumps and compressors, elementary boundary layer theory, flow past immersed bodies including packed and fluidized beds, Turbulent flow: fluctuating
velocity, universal velocity profile and pressure drop

Particle size and shape, particle size distribution, size reduction and classification of solid particles; free and hindered settling; centrifuge and cyclones; thickening and classification, filtration, agitation and mixing; conveying of solids

Section 4: Heat Transfer
Steady and unsteady heat conduction, convection and radiation, thermal boundary layer and heat transfer coefficients, boiling, condensation and evaporation; types of heat exchangers and evaporators and their process calculations. Design of double pipe, shell and tube heat exchangers, and single and multiple effect evaporators

Section 5: Mass Transfer
Fick’s laws, molecular diffusion in fluids, mass transfer coefficients, film, penetration and surface renewal theories; momentum, heat and mass transfer analogies; stage-wise and continuous contacting and stage efficiencies; HTU & NTU concepts; design and operation of equipment for distillation, absorption, leaching, liquid-liquid extraction, drying, humidification, dehumidification and adsorption.

Section 6: Chemical Reaction Engineering
Theories of reaction rates; kinetics of homogeneous reactions, interpretation of kinetic data, single and multiple reactions in ideal reactors, non-ideal reactors; residence time distribution, single parameter model; non-isothermal reactors; kinetics of heterogeneous catalytic reactions; diffusion effects in catalysis.

Section 7: Instrumentation and Process Control
Measurement of process variables; sensors, transducers and their dynamics, process modeling and linearization, transfer functions and dynamic responses of various systems, systems with inverse response, process reaction curve, controller modes (P, PI, and PID); control valves; analysis of closed loop systems including stability, frequency response, controller tuning, cascade and feed forward control.

Section 8: Plant Design and Economics
Principles of process economics and cost estimation including depreciation and total annualized cost, cost indices, rate of return, payback period, discounted cash flow, optimization in process design and sizing of chemical engineering equipments such as compressors, heat exchangers, multistage contactors.

Section 9: Chemical Technology
Inorganic chemical industries (sulfuric acid, phosphoric acid, chlor-alkali industry), fertilizers (Ammonia, Urea, SSP and TSP); natural products industries (Pulp and Paper, Sugar, Oil, and Fats); petroleum refining and petrochemicals; polymerization industries (polyethylene, polypropylene, PVC
and polyester synthetic fibers).

# Eligibility Criteria For GATE 2020

 Qualifying Degree Qualifying Degree/Examination (Descriptive) Degree Status Year of qualification not later than- B.E./ B.Tech./ B.Pharm. Bachelor’s degree in Engineering/ Technology (4 years after 10+2 or 3 years after B.Sc./Diploma in Engineering/ Technology) and those who are in the final year of such programs Currently in the final year or already completed 2019 B.Sc. (Research)/ B.S. Bachelor’s degree in Science (Post-Diploma/ 4 years after 10+2) Currently in the 4th year or already completed 2019 Int. M.E/ M.Tech (Post-B.Sc.) Post-BSc Integrated Master’s degree programs in Engineering / Technology (Four year program) Currently in the 2nd/3rd/4th year or already completed 2021 Int. M.E./ M.Tech or Dual Degree (after Diploma or 10+2) Integrated Master’s degree program or Dual Degree program in Engineering / Technology (Five year program) Currently in the 4th/5th year or already completed 2020 Int. M.Sc/ Int. B.S.-M.S. Integrated M.Sc. or Five year integrated B. S./M. S. program Currently in the final year or already completed 2019 Professional Society Examination (equivalent to B.E./ B.Tech./ B.Arch.) B.E./B.Tech./B.Arch. equivalent examinations of Professional Societies, recognized by MHRD/UPSC/AICTE (e.g., AMIE by Institution of EngineersIndia, AMICE by the Institute of Civil Engineers-India) Completed section A or equivalent of such professional courses NA

# GATE Information Brochure # GATE Virtual Calculator

How to use virtual scientific calculator and how it works # EXAMPLE 1: Simple Arithmetic: Simply follow the sequence

To evaluate: 50 + 45 x 3
Enter as follows: 50, +, 45, *, 3, =
To evaluate: 50 x 45-2
Enter as follows: 50, *, 45, -, 2, =
To evaluate: 25 x (5+5)
Enter as follows: 25, *, (, 5, +, 5, ), =

# EXAMPLE 2: To evaluate function(value), enter value followed by function

To evaluate: 2 + log(20) x 5
Enter as follows: 20, log, *, 5, +, 2, =
To evaluate: log(30) x 5 – 7
Enter as follows: 30, log,*, 5, -, 7, =
To evaluate: In(25) x 2 + 5
Enter as follows: 25, In, *, 2, +, 5, =
To evaluate: 5 + In(25) x 2
Enter as follows: 25, In, *, 2, +, 5,=

# EXAMPLE 3: sin(Degree), cos(Degree), tan(Degree):

Select Deg
To evaluate: sin(45) or cos(45) or tan(45)
Enter as follows: 45, sin or cos or tan
To evaluate: tan(45) x 5 + 2
Enter as follows: 45, tan, *, 5, +, 2, =

# EXAMPLE 4: yroot() value:

To evaluate: 4th root of 5
Enter as follows: 5, y√x, 4, =

# EXAMPLE 5:cube() value:

To evaluate: 563 x 6+8
Enter as follows:56, X3, *, 6, +, 8, =

# EXAMPLE 6: π value:

To evaluate: 5 π
Enter as follows: 5, *, π

# EXAMPLE 7: cuberoot():

To evaluate: cube root(3)
Enter as follows: 3,3√

# EXAMPLE 8: square root:

To evaluate: square root(4)
Enter as follows: 4,√

# EXAMPLE 9: factorial (nỊ)

To evaluate: factorial(5)
Enter as follows: 5,
nỊ To evaluate: factorial(6)*5-2
Enter as follows: 6, nỊ, *, 5, -, 2, =

# EXAMPLE 10: exponential (ex)

To evaluate: e0
Enter as follows: 0, ex

# EXAMPLE 11: 10x

To evaluate: 102.5
Enter as follows: 2.5, 10x To evaluate: 10-0.509
Enter as follows: 10, ^, 0.509, +/-, =
To evaluate: 10-2
Enter as follows: 10, ^, 2, +/-, =