GATE RA Conquest Book

Compiled and Signed @ 2026JUL23IST © CC BY-NC-ND 4.0

Conquer GATE RA 2027 by mastering total 0 concepts of this book

available through website, downloadable PDF, or scannable QR code link.

The knowledge of all things is possible.

Leonardo da Vinci

Common Section

Engineering Mathematics: (i) Linear Algebra: Matrices, transpose, determinant, rank, eigenvalues and eigenvec-

tors, trace, adjoint, solutions to system of linear equations. (ii) Calculus: Functions of a single variable, limit, continuity,

normal distributions, hypothesis testing, Probability Density Function (PDF), Cumulative Distribution Function (CDF).

(v) Numerical Methods: Solutions of linear algebraic equations, solutions of non-linear algebraic equations, integration by

trapezoidal and Simpson’s rules, finite differences, explicit single and multi-step methods for differential equations.

Basics of Mechatronics: (i) Network Elements: Ideal voltage and current sources, dependent sources, R, L, C,

M elements. Network Solution Methods: Kirchoff’s laws (KCL, KVL), Node and Mesh analysis. Network Theorems:

Thevenin’s theorem, Norton’s theorem, Superposition, Maximum Power Transfer theorem. Transient and AC Networks:

Transient response of DC and AC networks, sinusoidal steady-state analysis, resonance, two-port networks, balanced three-

phase circuits, complex power, power factor in AC circuits. (ii) Digital Circuits: Boolean algebra. Combinational Circuits:

multiplexers, encoders, decoders. Sequential Circuits: sequential circuits, flip-flops, counters. (iii) Sensors: Resistive sen-

sors, capacitive sensors, inductive sensors, piezoelectric sensors, Hall effect sensors, associated signal conditioning circuits.

functions, arrays, dictionary, strings, recursion. (vii) Data Structures: Stack, queue, linked list, binary search tree, binary

heap, graph.

Principles of Rob otics and Automation: Robotic Classification: serial and parallel manipulators, geometrical

configuration, Links and joints, Coordinate systems and degrees-of-freedom, Rotation matrices in 2D and 3D, homoge-

neous transformations, forward kinematics. Robot Applications: point-to-point and continuous path control, types of

end-effectors, robot accuracy and repeatability. Computer Integrated Manufacturing: Automation in Manufacturing, Pro-

grammable Logic Controllers (PLCs) in manufacturing, Automated material handling systems, Automated storage and

retrieval systems, Automated identification, detection and capture systems, computer numerical control, Basics of single

and multi-axis positioning systems, Basics of concurrent design and manufacturing planning for automation.

Electrical Engineering

Signals and Systems: Representation of continuous and discrete time signals, shifting and scaling properties, linear

time-invariant and causal systems, Fourier series representation of continuous and discrete time periodic signals, Shannon’s

sampling theorem, Definitions and properties of Fourier Transform, Laplace Transform, Z transform, R.M.S. value, average

value calculation.

Control Systems: Mathematical modeling and representation of systems, feedback principle, transfer function, Block

diagrams, Signal flow graphs, Transient and Steady-state analysis of linear time-invariant systems. Stability analysis using:

Routh-Hurwitz, Nyquist criteria, Bode plots, Root Loci, Lag compensators, Lead compensators, Lead-Lag compensators,

P, PI and PID controllers.

Mechanical Engineering

Mechanics of Materials: Stress and strain, elastic constants, Poisson’s ratio, Mohr’s circle for plane stress and plane

Machine Design and Computer Integrated Manufacturing: Design for static and dynamic loading, failure the-

ories, fatigue strength, the S-N diagram, principles of the design of machine elements such as, bolted, riveted and welded

joints, shafts, rolling and sliding contact bearings, brakes, clutches, springs, Basic concepts of Computer Aided Design

(CAD)/Computer Aided Manufacturing (CAM) and their integration tools, additive manufacturing.

PYQs: —

Bibliography: My Tastefully Curated Sources of Learning

1 Engineering Mathematics

Mathematics is the language in which God

has written the universe.

Galileo Galilei

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1.4 rank

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1.5 eigenvalues and eigenvectors

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1.6 trace

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1.7 adjoint

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1.8 solutions to system of linear equations

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1.12 differentiability

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1.13 mean value theorems

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1.14 indeterminate forms

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1.15 evaluation of definite and improper integrals

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1.16 double and triple integrals

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1.20 maxima and minima

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1.21 gradient

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1.22 divergence and curl

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1.23 vector identities

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1.24 First-order equations (linear and nonlinear)

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1.28 Laplace transforms

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1.29 solutions of heat, wave, and Laplace’s equations

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1.30 Fourier series

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1.31 Axioms of probability

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1.32 conditional probability

1.34 median

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1.37 random variables

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1.38 expectation

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1.39 binomial

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1.40 Poisson

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1.41 normal distributions

2 Basics of Mechatronics

2.16 power factor in AC circuits

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2.20 decoders

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2.21 sequential circuits

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2.22 flip-flops

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2.23 counters

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2.24 Resistive sensors

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2.28 Hall effect sensors

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2.29 associated signal conditioning circuits

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2.30 displacement

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2.31 linear

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2.32 angular

2.34 acceleration

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2.38 Pressure

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2.39 Principles of operation

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2.40 performance

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2.41 torque-speed characteristics

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2.42 hydraulic actuators

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2.46 servo motors

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2.47 Free-body diagrams

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2.48 equilibrium

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2.49 friction and its applications

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2.50 rolling friction

2.52 trusses and frames

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2.56 operators

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2.57 expressions

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2.58 conditional statements (if, elif, else, case)

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2.59 looping statements (while, for)

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2.60 loop control statements (break and continue)

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2.64 strings

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2.65 recursion

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2.66 Stack

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2.67 queue

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2.68 linked list

2.70 binary heap

7 Mechanics of Materials

7.1 Stress and strain

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7.2 elastic constants

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7.3 Poisson’s ratio

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7.4 Mohr’s circle for plane stress and plane strain

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7.5 thin cylinders

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7.9 concept of shear centre

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7.10 deflection of beams

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7.11 torsion of circular shafts

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7.12 Euler’s theory of columns

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7.13 Castigliano’s theorems

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7.16 testing of materials with universal testing machine

8 Kinematics and Dynamics

Dynamics is the study of forces and

motion—the heartbeat of every machine.

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8.4 dynamic analysis of linkages

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8.5 gears and gear trains

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8.6 balancing of reciprocating and rotating masses

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8.7 gyroscope

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8.8 free and forced vibration of single degree of freedom systems

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8.12 critical speeds of shafts

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9 Machine Design and Computer Integrated Manufacturing

Design is not just what it looks like and feels

like. Design is how it works.

9.2 failure theories

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9.3 fatigue strength

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9.4 the S-N diagram

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9.5 principles of the design of machine elements

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9.6 bolted joints

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9.10 rolling contact bearings

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9.11 sliding contact bearings

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9.12 brakes

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9.13 clutches

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9.14 springs

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9.16 additive manufacturing

more than the meals I have eaten; even so,

they have made me.

Ralph Waldo Emerson