### Exclusive Test Package for GATE

The objective of Test Series is to provide aspirant the smartest way to prepare for the exam with the newest trends in Entrance Exam Preparation. Our Online test Series is a great revision tool that provides you an opportunity to assess your preparation and strengthen the weak areas to outperform in the actual examination. This Test Package Contained Improve Your Skill By Joining Gurukulam Institute of Mathematic Test Packages for GATE

#### NET JRF Previous Year Question Papers

#### Subject Wise Test (SWT)

Subject Wise Test Package (SWTP): is that provides you an opportunity to assess your preparation in each section of your whole course. This Test package consisting of 11-Question papers

##### Linear Algebra:

TEST ID | Syllabus |

SWT-01 | Linear Algebra: Finite dimensional vector spaces; Linear transformations,Systems of linear equations, Eigenvalues and eigenvectors, Diagonalization, Jordan-canonical form, Hermitian, Skew- Hermitian and unitary matrices; Finite dimensional inner product spaces, Definite forms. |

##### Complex Analysis:

TEST ID | Syllabus |

SWT-02 | 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:

TEST ID | Syllabus |

SWT-03 | Real Analysis: Riemann integration, Sequences and series of functions, Power series, Fourier series,Functions of several variables, maxima, minima; Integral Calculus , Vector Calculus Metric spaces Lebesgue measure, Lebesgue integral |

##### Ordinary Differential Equations:

TEST ID | Syllabus |

SWT-04 | 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:

TEST ID | Syllabus |

SWT-05 | 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:

TEST ID | Syllabus |

SWT-06 | 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:

TEST ID | Syllabus |

SWT-07 | Numerical Analysis: Numerical solution of algebraic and transcendental equations: Interpolation: Numerical differentiation; Numerical integration: Numerical solution of systems of linear equations: Numerical solution of ordinary differential equations |

##### Partial Differential Equations:

TEST ID | Syllabus |

SWT-08 | 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:

TEST ID | Syllabus |

SWT-09 | Topology: Basic concepts of topology, Bases, subbases, subspace topology, Order topology, product topology, Connectedness, compactness, Countability and separation axioms, Urysohn’s Lemma. distributions; Simple linear regression. |

##### Probability and Statistics:

TEST ID | Syllabus |

SWT-10 | Probability and Statistics: Conditional probability, Bayes theorem, Joint and conditional distributions, Standard probability distributions and their properties Discrete distributions Continuous distributions 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 Simple linear regression. |

##### Linear programming:

TEST ID | Syllabus |

SWT-11 | 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. |

##### Exam Pattern Test Package (EPTP)

GATE Exam is on its way. You have with plenty of study books, and Solved previous years papers, got all expert references. Still you might be confused to figure out what to study and what not! In such strenuous situations, you need to analysis your performance and wish to know about the important topics and questions that have higher weightage and are more likely to be asked in the exam. Exam Pattern Test Papers & Practice Sets fulfill all your requirements!

TEST ID | SECTION-A | SECTION -B |

EPT-01 | General Aptitudes | 55-MCQuestions |

EPT-02 | General Aptitudes | 55-MCQuestions |

EPT-03 | General Aptitudes | 55-MCQuestions |

EPT-0$ | General Aptitudes | 55-MCQuestions |