### General Information

- About GATE

Graduate Aptitude Test in Engineering (GATE) is an examination conducted jointly by the Indian Institute of Science (IISc), Bangalore and the seven Indian Institutes of Technology (at Bombay, Delhi, Guwahati, Kanpur, Kharagpur, Madras and Roorkee) on behalf of the National Coordination Board (NCB)-GATE, Department of Higher Education, Ministry of Human Resource Development (MHRD), Government of India. Qualifying in GATE is a mandatory requirement for seeking admission and/or financial assistance to: (i) Master’s programs and direct Doctoral programs in Engineering/Technology/Architecture and (ii) Doctoral programs in relevant branches of Science, in the institutions supported by the MHRD and other Government agencies. Even in some colleges and institutions, which admit students without MHRD scholarship/assistantship, the GATE qualification is mandatory. Further, many Public Sector Undertakings (PSUs) have been using the GATE score in their recruitment process.

**Scholarship/Assistantship for Post-graduate Programs**

To avail the financial assistance (scholarship/assistantship), the candidate must first secure the admission to a program in one of the central government supported institutes, by a procedure that could vary from institute to institute. Depending upon the norms adopted by a specific institute or department of the institute, a candidate may be admitted directly into a course based on**: **his/her performance in GATE only; **or **based on his/her performance in GATE **and **an admission test/interview conducted by the department to which he/she has applied **and/or **the candidate’s academic record. In the test/interview based selection procedure, as per the MHRD guidelines, a minimum of 70% weightage will be given to the performance in GATE and the remaining will be given to the candidate’s performance in test/interview and/or academic record. However, the admitting institutes could prescribe a minimum passing marks in the test/interview. Candidates are advised to seek the complete details of the admission procedures and the availability of MHRD scholarship/assistantship from the corresponding admitting institutions.

The criteria for postgraduate admission with scholarship/assistantship could be different for different institutions. The management of the post-graduate scholarship/assistantship is also the responsibility of the admitting institution. Similarly, reservation of the seats for different categories will be as per the policies and norms of the admitting institution and the Government of India rules. The admitting institute may also specify the number of candidates who will be provided financial assistance (scholarship), if admission is secured. Qualification in GATE is also a minimum requirement to apply for various fellowships awarded by many Government organizations.

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**Use of GATE score for Employment:**

In the past, several Public Sector Undertakings (PSUs) have used GATE scores to shortlist the candidates for employment. A few such organizations are:

- Bharat Heavy Electricals Limited (BHEL),
- Gas Authority of India Limited (GAIL),
- Hindustan Aeronautics Limited (HAL),
- Indian Oil Corporation Limited (IOCL),
- National Thermal Power Corporation (NTPC),
- Nuclear Power Corporation of India Limited (NPCIL),
- Oil and Natural Gas Corporation (ONGC) and
- Power Grid Corporation of India.

Direct recruitment to Group A level posts in Central government, i.e., Senior Field Officer (Tele), Senior Research Officer (Crypto) and Senior Research Officer (S&T) in Cabinet Secretariat, Government of India, is now being carried out on the basis of GATE score. The details of the scheme of recruitment are normally published in National Newspapers/Employment News by the concerned authority. Some other Government of India Organizations have also expressed their interest to utilize GATE 2018 score for their recruitment purpose.

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**Pre-Examination Related Information:**

GATE 2018 examination for all the papers will be conducted in an **ONLINE **Computer Based Test (CBT) mode where the candidates will be shown the questions on a computer screen.

A Virtual Scientific Calculator will be available on the computer screen during the examination. Candidates have to use the same during the examination. Personal calculators, wristwatches, mobile phones or any other electronic devices are **NOT allowed **inside the examination hall. Candidates should not bring any charts/tables/papers into the examination hall. GATE officials will not be responsible for the safe-keep of the candidates’ personal belongings. Scribble pads will be provided to the candidates for any rough work. The candidate has to write his/her name and registration number on the scribble pad before he/she starts using it. The scribble pad must be returned to the invigilator at the end of the examination.

**Examination Duration**

All the papers of the GATE 2018 examination will be for 3 hours duration and they consist of 65 questions for a total of 100 marks. Since the examination is an ONLINE computer based test, at the end of the stipulated time (3-hours), computer will automatically close the screen inhibiting any further action. Candidates will be permitted to occupy their allotted seats 40 minutes before the scheduled start of the examination. Candidates can login and start reading the instructions 20 minutes before the start of examination. Candidate will NOT be permitted to enter the examination hall after 09:30 hours in the forenoon session and after 14:30 hours in the afternoon session. Candidates will NOT be permitted to leave the examination hall before the end of the examination.

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**Important Dates**

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Events | Date(s) |

Registration and Application | September, 01^{st} Week |

Last Date for Submission | October, 1^{st} Week |

Last Date for Requesting Change of Examination | November, 2^{nd} Week |

Admit Card availability | January 1^{st} week |

GATE Examination | February 1^{st} week |

Announcement of the Results | March 3^{rd} Week |

**Eligibility Criteria for GATE (No age limit)**

**Qualifying Degree**

- Sc./ M.A./MCA or equivalent, Master’s degree in any branch of Science/ Mathematics/ Statistics/ Computer Applications or equivalent, Currently in the final year or already completed, Year of Qualification not later than Current Year .

- Guide Lines

**Pattern of Questions**

GATE would contain questions of two different types in all the papers:

**Multiple Choice Questions **(MCQ) carrying **1 **or **2 **marks each in all the papers and sections.These questions are objective in nature, and each will have a choice of four answers, out of which the candidate has to select (mark) the correct answer.

**Negative Marking for Wrong Answers:** For a wrong answer chosen in a MCQ, there will be negative marking. For **1-mark **MCQ, **1/3 **mark will be deducted for a wrong answer. Likewise , for **2-mark **MCQ, **2/3 **mark will be deducted for a wrong answer.

**Numerical Answer Type (NAT)** Questions carrying 1 or 2 marks each in all the papers and sections. For these questions, the answer is a signed real number, which needs to be entered by the candidate using the virtual numeric keypad on the monitor (keyboard of the computer will be disabled). No choices will be shown for these type of questions. The answer can be a number such as 10 or -10 (an integer only). The answer may be in decimals as well, for example, 10.1 (one decimal) or 10.01 (two decimals) or -10.001 (three decimals). These questions will be mentioned with, up to which decimal places, the candidates need to make an answer. Also, an appropriate range will be considered while evaluating the numerical answer type questions so that the candidate is not penalized due to the usual round-off errors. Wherever required and possible, it is better to give NAT answer up to a maximum of three decimal places

**Negative Marking for Wrong Answers:** **There is NO negative marking for a wrong answer in NAT questions.**

Marking Scheme – Marks and Questions Distribution:

There will be a total of **65 **questions carrying **100 **marks, out of which **10 **questions carrying a total of **15 **marks will be on General Aptitude (GA), which is intended t test the Language and Analytical Skills

**General Aptitude (GA) Questions:** GA questions carry a total of **15 marks**. The GA section includes **5 **questions carrying **1-mark **each (sub-total **5 marks**) and **5 **questions carrying **2-marks **each (subtotal **10 marks**).

**Mathematical Science: ** These Section Containing 55 questions carry a total of ** 85 marks**. Consists of **25 **questions carrying **1-mark **each (sub-total **25 marks **and some of these may be numerical answer type questions) and consists of **30 **questions carrying **2-marks **each (sub-total **60 marks **and some of these may be numerical answer type questions).

**Exam Analysis**

**Syllabi :**

**Linear Algebra**- Finite dimensional vector spaces;
- Linear transformations and their matrix representations, rank;
- Systems of linear equations,
- Eigenvalues and eigenvectors, minimal polynomial, Cayley-Hamilton Theorem,
**Diagonalization, Jordan-canonical form,****Hermitian, Skew- Hermitian and unitary matrices;****Finite dimensional inner product spaces, Gram-Schmidt orthonormalization process, self-adjoint operators,****Definite forms.**

**Complex Analysis**- Analytic functions,
- Complex integration: Cauchy’s integral theorem and formula;
- Liouville’s theorem, maximum modulus principle; Zeros and singularities;
- Taylor and Laurent’s series; residue theorem and applications for evaluating real integrals.
- Conformal mappings, bilinear transformations;

**Real Analysis****:**- Riemann integration,
- Sequences and series of functions, uniform convergence,
- Power series, Fourier series,
- Functions of several variables, maxima, minima;
- Multiple integrals, line, surface and volume integrals,
- Theorems of Green, Stokes and Gauss;
- Metric spaces, compactness, completeness,
- Weierstrass approximation theorem;
- Lebesgue measure, measurable functions; Lebesgue integral,
- Fatou’s lemma, dominated convergence theorem.

**Ordinary Differential Equations**- First order ordinary differential equations,
- Existence and uniqueness theorems for initial value problems,
- Systems of linear first order ordinary differential equations,
- Linear ordinary differential equations of higher order with constant coefficients;
- Linear second order ordinary differential equations with variable coefficients;
- Method of Laplace transforms for solving ordinary differential equations,
- Series solutions (power series, Frobenius method);
- Legendre and Bessel functions and their orthogonal properties.

**Algebra**- Groups, subgroups, cyclic groups and permutation groups,
- normal subgroups, Quotient groups and
- Homomorphism theorems, automorphisms;
- Sylow’s theorems and their applications;
- Rings, ideals, prime and maximal ideals, quotient rings,
- Unique factorization domains, Principle ideal domains, Euclidean domains, polynomial
- Rings and irreducibility criteria;
- Fields, finite fields, field extensions.

**Functional Analysis**- Normed linear spaces,
- Banach spaces, Hahn-Banach extension theorem,
- Open mapping and closed graph theorems,
- Principle of uniform boundedness;
- Inner-product spaces, Hilbert spaces, orthonormal bases,
- Riesz representation theorem, bounded linear operators.

**Numerical Analysis**- Numerical solution of algebraic and transcendental equations:
- Bisection, secant method,
- Newton-Raphson method,
- Fixed point iteration;

- Interpolation:
- Error of polynomial interpolation,
- Lagrange, Newton interpolations;
- Numerical differentiation;
- Numerical integration:
- Trapezoidal and Simpson rules;

- Numerical solution of systems of linear equations:
- Direct methods (Gauss elimination, LU decomposition);
- Iterative methods (Jacobi and Gauss-Seidel);

- Numerical solution of ordinary differential equations:
- initial value problems:
- Euler’s method,
- Runge-Kutta methods of order 2.

**Partial Differential Equations**- Linear and quasilinear first order partial differential equations,
- Method of characteristics;
- Second order linear equations in two variables and their classification;
- Cauchy, Dirichlet and Neumann problems;
- Solutions of Laplace, wave in two dimensional Cartesian coordinates,
- Interior and exterior Dirichlet problems in polar coordinates;
- Separation of variables method for solving wave and diffusion equations in one space variable;
- Fourier series and Fourier transform and
- Laplace transforms methods of solutions for the above equations.

**Topology**- Basic concepts of topology,
- Bases, subbases, subspace topology,
- Order topology, product topology,
- Connectedness, compactness,
- Countability and separation axioms,
- Urysohn’s Lemma.

**Probability and Statistics**- Probability space, conditional probability, Bayes theorem,
- Independence, Random variables, joint and conditional distributions,
- Standard probability distributions and their properties
- Discrete
- uniform,
- Binomial, Poisson,
- Geometric,
- Negative binomial,
- Normal,
- Exponential,
- Gamma,

- Continuous
- uniform,
- Bivariate
- Normal,
- Multinomial,

- Expectation, conditional expectation, moments;
- Weak and strong law of large numbers,
- Central limit theorem;
- Sampling distributions, UMVU estimators,
- Maximum likelihood estimators;
- Interval estimation;
- Testing of hypotheses, standard parametric tests based on normal distributions;
- Simple linear regression.

- Discrete
**Linear programming**- Linear programming problem and its formulation,
- Convex sets and their properties,
- Graphical method,
- Basic feasible solution, Infeasible and unbounded LPP’s, alternate optima
- Simplex method, big-M and two phase methods;
- Dual problem and duality theorems,
- Dual simplex method
- Application in post optimality analysis;
- Balanced and unbalanced transportation problems,
- Vogel’s approximation method for solving transportation problems;
- Hungarian method for solving assignment problems.

- Numerical solution of algebraic and transcendental equations:

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