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Wiley Acing the GATE Engineering Mathematics and General Aptitude is intended to be the complete
book for those aspiring to compete in the Graduate Aptitude Test in Engineering (GATE) in various engineering
disciplines, including Electronics and Communication, Electrical, Mechanical, Computer Science, Civil, Chemical and
Instrumentation, comprehensively covering all topics as prescribed in the syllabus in terms of study material and an
elaborate question bank. There are host of salient features offered by the book as compared to the content of the other
books already published for the same purpose. Some of the important ones include the following.
One of the notable features of the book includes presentation of study material in simple and lucid language
and in small sections while retaining focus on alignment of the material in accordance with the
requirements of GATE examination. While it is important for a book that has to cover a wide range of topics in
Engineering Mathematics, General Aptitude including Verbal Ability and Numerical Ability to be precise in the treat-
ment of different topics, the present book achieves that goal without compromising completeness. The study material
and also the question bank have all the three important `C’ qualities, Conciseness, Completeness and Correctness, for
communicating effectively with the examinees.
Another important feature of the book is its comprehensive question bank. The question bank is organized in
three different categories, namely the Solved Examples, Practice Exercise and Solved GATE Previous Years’ Questions.
Solved Examples contain a large number of questions of varying complexity. Each question in this category is followed
by its solution. Under Practice Exercise, again there are a large number of multiple choice questions. The answers to
these questions are given at the end of the section. Each of the answers is supported by an explanation unlike other
books where solutions to only selected questions are given. The third category contains questions from previous GATE
examinations from 2003 onwards. Each question is followed by a complete solution.
Briefly outlining the length and breadth of the material presented in the book, it is divided into two broad sections,
namely Engineering Mathematics and General Aptitude. Section on General Aptitude is further divided into two
sections covering Verbal Ability and Numerical Ability.
Engineering Mathematics is covered in eleven different chapters. These include Linear Algebra covering impor-
tant topics such as matrix algebra, systems of linear equations, and eigenvalues and eigenvectors; Calculus covering
important topics such as functions of single variable, limit, continuity and differentiability, mean value theorem, defi-
nite and improper integrals, partial derivatives, maxima and minima, gradient, divergence and curl, directional deriva-
tives, line, surface and volume integrals, Stokes’ theorem, Gauss theorem and Green’s theorem, and Fourier series;
Differential Equations covering linear and non-linear differential equations, Cauchy’s and Euler’s equations, Laplace
transforms, partial differentiation, solutions of one-dimensional heat and wave equations, Laplace equation, and method
of variation of parameters; Complex Variables covering analytic functions, Cauchy’s integral theorem, and Taylor and
Laurent series; Probability and Statistics covering conditional probability, random variables, discrete and continuous
distributions, Poisson, normal, uniform, exponential and binomial distributions, correlation and regression analyses,
residue theorem, and solution integrals; Numerical Methods covering numerical solutions of linear and non-linear alge-
braic equations, integration by trapezoidal and Simpson’s rules, single and multi-step methods for differential equa-
tions, numerical solutions of non-linear algebraic equations by secant, bisection, Runge—Kutta and Newton—Raphson
methods; Mathematical Logic including first-order logic and proportional logic; Set Theory and Algebra including
sets, relations, functions and groups, partial orders, lattice, and Boolean algebra; Combinatory covering permutations
and combinations, counting, summation, generating functions, recurrence relations, and asymptotics; Graph Theory
covering connectivity and spanning trees, cut vertices and edges, covering and matching, independent sets, colouring,
planarity, and isomorphism; and Transform Theory covering Fourier transform, Laplace transform and z-transform.
General Aptitude comprises two sub-sections namely Verbal Ability and Numerical Ability. Important topics
covered under Verbal Ability include English grammar, synonyms, antonyms, sentence completion, verbal analogies,
word groups, and critical reasoning and verbal deduction. Under Numerical Ability, important topics covered include
basic arithmetic, algebra, and reasoning and data interpretation. Under Basic Arithmetic, we have discussed number
system; percentage; profit and loss; simple interest and compound interest; time and work; average, mixture and
allegation; ratio, proportion and variation; and speed, distance and time. Under Algebra, we have discussed permu-
tation and combination; progression; probability; set theory; and surds, indices and logarithm. The topics covered
under Reasoning and Interpretation are cubes and dices, line graph, tables, blood relationship, bar diagram, pie chart,
puzzles, and analytical reasoning.
The Graduate Admission Test in Engineering (GATE) is an All-India level competitive examination for
engineering graduates aspiring to pursue Master’s or Ph.D. programs in India. The examination evaluates the exam-
inees in General Aptitude, Engineering Mathematics and the subject discipline. Though majority of questions is asked
from the subject discipline; there are sizable number of questions set from Engineering Mathematics and General
Aptitude. It is an examination where close to ten lakh students appear every year. The level of competition is therefore
very fierce. While admission to a top institute for the Master’s programme continues to be the most important reason
for working hard to secure a good score in the GATE examination; another great reason to appear and handsomely
qualify GATE examination is that many Public Sector Undertakings (PSUs) are and probably in future almost all
will be recruiting through GATE examination. And it is quite likely that even big private sector companies may start
considering GATE seriously for their recruitment as GATE score can give a bigger clue about who they are recruiting.
The examination today is highly competitive and the GATE score plays an important role. This only reiterates the
need to have a book that prepares examinees not only to qualify the GATE examination by getting a score just above
the threshold but also enabling them to achieve a competitive score. In a competition that is as fierce as the GATE is,
a high score in Engineering Mathematics and General Aptitude section can be a great asset.
The present book is written with the objective of fulfilling this requirement. The effort is intended to offer to the
large section of GATE aspirants a self-study and do-it-yourself book providing comprehensive and step-by-step treat-
ment of each and every aspect of the examination in terms of concise but complete study material and an exhaustive
set of questions with solutions. The authors would eagerly look forward to the feedback from the readers through pub-
lishers to help them make the book better.