## P. G. ENTRANCE EXAMS

#### GATE

These are the entrance exams of POST GRADUATE COURSES (P.G.)

Graduate Aptitude Test in Engineering (GATE ) is an all India examination that primarily tests the comprehensive understanding of the candidate in various undergraduate subjects in Engineering/Technology/Architecture and post-graduate level subjects in Science. The GATE score of a candidate reflects a relative performance level in a particular subject in then (this) exam across several years. The score is used for admissions to post-graduate programs (e.g. M.E., M.Tech, direct Ph.D.) in Indian institutes of higher education with financial assistance provided by MHRD and other Government agencies. The score may also be used by Public and Private Sector Undertakings for employment screening purposes. The information in this brochure is mainly categorized into Pre-Examination (Eligibility, Application submission, Examination Centers, etc.), Examination (Syllabus, Pattern, Marks/Score, Model Question Papers, etc.) & Post-Examination (Answers, Results, Scorecard, etc.) sections.

## ABOUT GATE

The Indian Institute of Science (IISc) and seven Indian Institutes of Technology (IITs at Bombay, Delhi, Guwahati, Kanpur, Kharagpur , Madras and Roorkee) jointly administer the conduct of GATE. The operations related to GATE in each of the 8 zones are managed by a zonal GATE Office at the IITs or IISc. The Organizing Institute (OI) is responsible for the end-to-end process and coordination amongst the administering Institutes.The Organizing Institute for GATE is IISc Banglore.

## BASIC FEATURES OF GATE

- Examinations for all the 22 papers will be conducted by an ONLINE Computer Based Test (CBT). The online examination paper will contain some questions for which numerical answers must be keyed in by the candidate using the virtual keypad. Rest of the questions shall be of Multiple Choice Question (MCQ) type.
- Biometric information (Photograph and Fingerprints) for randomly selected candidates may be captured before the start of the examination.
- GATE examinations will be held during forenoon and afternoon sessions on alternate weekends (Saturday and Sunday). Examination for some of the papers in GATE will be held in multiple sessions. Exact details regarding complete examination schedule will be notified at a later date.
- For GATE the entire process of filling up of application form, uploading of certificates/documents, etc., will be online and the candidates should not send any hard copy of their application form/documents, etc., to any of the IIT/IISc zonal GATE office.
- The payment of application fees would be online through different modes like net banking, debit/credit card, e-challan, etc.
- The admit cards for GATE would be available through the online process only. Candidates can download their admit card from GATE website. No hard copy of admit cards will be posted to the candidates.

## GENERAL INFORMATION ON GATE

**Application Process:** For GATE all information related to the candidates will be available in a single GATE Online Application Processing System (GOAPS). Candidates have to register and fill the application via ONLINE mode ONLY by accessing the zonal GATE websites of IISc and any of the seven IITs. The photograph and signature of the applicant must be uploaded during the online application. Please note that all necessary certificates, such as, degree certificate/certificate from the Principal and the category certificate, if any are also to be uploaded. Please note that application forms are not available for sale anywhere else.

**Downloadable Admit Card:** Admit cards will NOT be sent by e-mail/post, they can ONLY be downloaded from the zonal GATE websites tentatively. The candidate has to bring the printed admit card to the test center along with at least one original (not photocopied/scanned copy) and valid (not expired) photo identification. It may be noted that one of the following photo identifications is ONLY permitted: Driving license, Passport, PAN Card, Voter ID, Aadhaar UID, College ID, Employee identification card, or a notarized affidavit with Photo, Signature, Date of Birth and Residential Address. The details of this ID proof have to be given while filling the online application.

**Numerical Answer Type Questions:** The question paper for GATE will consist of questions of both multiple-choice type and numerical answer type. For multiple choice type questions, candidates have to choose the answer from the given choices. For numerical answer type questions, choices will not be given. Candidates have to enter a number as the answer using a virtual keypad.

## IMPORTANT DATES RELATED TO GATE

GATE Online Application Processing System (GOAPS) Website Opens | 1ST Week of September (00.00 Hrs) |
---|---|

Last Date for Submission of Online Application through Website | 2ND Week of October |

Last Date for Request for Change in the Choice of City | Last Week of November |

Availability of Admit Card on the Online Application Interface for printing | 3RD Week of December |

GATE Online Examination | Last Week of January Or First Week of February |

Announcement of Results on the Online Application Website | 3RD Week of March |

## APPLICATION FEE PAYMENT OPTIONS

The application fee and various payment options are shown in Table below. The application fee is non-refundable. All charges given below are in Indian Rupees.

Candidate Category | Mode | Application Fee in * |
---|---|---|

Male (General/OBC) | Online Net Banking | 1500 |

e-challan | 1500 | |

Women (All Categories) | Online Net Banking | 750 |

e-challan | 750 | |

Other (General/OBC-NCL) | Online Net Banking | 1500 |

e-challan | 1500 | |

SC/ST/PwD | Online Net Banking | 750 |

e-challan | 750 |

## Syllabus/ Books

#### LINEAR ALGEBRA

Finite dimensional vector spaces; Linear transformations and their matrix representations, rank; systems of linear equations, eigen values and eigen vectors, minimal polynomial, Cayley-Hamilton Theroem, diagonalisation, Hermitian, Skew-Hermitian and unitary matrices; Finite dimensional inner product spaces, Gram-Schmidt orthonormalization process, self-adjoint operators.

### Book Recommendations:

- Linear Algebra –Serg Lang
- Linear Algebra -Kenneth M Hoffman Ray Kunze (PHI Publication)
- Linear Algebra -Vivek Sahai, Vikas Bist (Narosa Publication)

## COMPLEX ANALYSIS

Algebra of complex numbers, the complex plane, polynomials, power series, transcendental functions such as exponential, trigonometric and hyperbolic functions. Analytic functions, Cauchy-Riemann equations. Contour integral, Cauchy's theorem, Cauchy's integral formula, Liouville's theorem, Maximum modulus principle, Schwarz lemma, Open mapping theorem. Taylor series, Laurent series, calculus of residues. Conformal mappings, Mobius transformations.

- Complex Variables -H.S. Kasana(PHI Publication )
- Complex Analysis -S Ponnusamy(Narosa Publication)
- Complex Analysis -R.V. Churchill(Tata McGraw - Hill Publication)

**Real Analysis:** Sequences and series of functions, uniform convergence, power series, Fourier series, functions of several variables, maxima, minima; Riemann integration, multiple integrals, line, surface and volume integrals, theorems of Green, Stokes and Gauss; metric spaces, completeness, Weierstrass approximation theorem, compactness; Lebesgue measure, measurable functions; Lebesgue integral, Fatou's lemma, dominated convergence theorem.

- Principle of Mathematical Analysis -S.L. Gupta, N.R. Gupta(Pearson Publication)
- Real Analysis -Robert G Bartle(Wiley Publication)
- Real Analysis -M.D. Raisinghania(S. Chand Publication)

**Ordinary Differential Equations:** First order ordinary differential equations, existence and uniqueness theorems, 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; Legendre and Bessel functions and their orthogonality.

## Topology

- Introduction to topology and modern analysis - G.F. Simmons
- Metric Spaces – Pawan K. Jain, Khalil Ahmad (Pearson Publication).
- Topology of Metric Spaces - S.Kumaresan
- Topology - K. D. Joshi

## ORDINARY DIFFERENTIAL EQUATIONS (ODE)

Existence and uniqueness of solutions of initial value problems for first order ordinary differential equations, singular solutions of first order ODE , system of first order ODE. General theory of homogenous and non-homogeneous linear ODEs, variation of parameters, Sturm-Liouville boundary value problem, Green's function.

- Differential Equations -Earl Codington (PHI Publication )
- Ordinary Differential Equations -MD Rai Singhania ( S.Chand Publication )
- Differential Equations -Shepley L. Ross (Wiley Publication )

**Algebra:** Normal subgroups and homomorphism theorems, automorphisms; Group actions, Sylow's theorems and their applications; Euclidean domains, Principle ideal domains and unique factorization domains. Prime ideals and maximal ideals in commutative rings; Fields, finite fields.

- A First Course In Abstract Algebra - John B. Fraleigh
- Contemporary Abstract Algebra -Joseph A. Gallian (Narosa Publication )
- Modren Algebra -Surjeet Singh and Qazi Zameeruddin (Vikas Publication)

**Functional Analysis:** Banach spaces, Hahn-Banach extension theorem, open mapping and closed graph theorems, principle of uniform boundedness; Hilbert spaces, orthonormal bases, Riesz representation theorem, bounded linear operators.

## Functional Analysis by Rudin

**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, Gauss 51 Legendre quadrature, method of undetermined parameters; least square polynomial approximation; numerical solution of systems of linear equations: direct methods (Gauss elimination, LU decomposition); iterative methods (Jacobi and Gauss-Seidel); matrix eigenvalue problems: power method, numerical solution of ordinary differential equations: initial value problems: Taylor series methods, Euler's method, Runge-Kutta methods.

- Numerical Analysis - R.K. Jain, S.R.K. Iyengar (New Age Publication)

**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 and diffusion equations in two variables; Fourier series and Fourier transform and Laplace transform methods of solutions for the above equations.

- Partial Differential Equations -T. Amaranath(Narosa Publication )
- Introduction To Partial Differential Equations - K. Sankara Rao(PHI Publication)

**Mechanics:** Virtual work, Lagrange's equations for holonomic systems, Hamiltonian equations.

**Topology:** Basic concepts of topology, product topology, connectedness, compactness, countability and separation axioms, Urysohn's Lemma.

## Topology -

- Introduction to topology and modern analysis - G.F. Simmons
- Metric Spaces –Pawan K. Jain, Khalil Ahmad (Pearson Publication).

Probability and Statistics: Probability space, conditional probability, Bayes theorem, independence, Random variables, joint and conditional distributions, standard probability distributions and their properties, expectation, conditional expectation, moments; Weak and strong law of large numbers, central limit theorem; Sampling distributions, UMVU estimators, maximum likelihood estimators, Testing of hypotheses, standard parametric tests based on normal, X2 , t, F – distributions; Linear regression; Interval estimation.

- Probablity and statistics-S. C. Gupta and V. K. Kapoor (S.Chand Publication )