### Exclusive Test Package FOR NET/JRF

- 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 PackagesFOR NET JRF

Course Based (TP) Course Based Test Package (CBTP) 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 consisting of 30 Question Papers

#### Performance Review Package (PRP)

The Performance Review Test that provides you an opportunity to assess your preparation in each section of your whole course. There will be 25 Test papers.

##### Real Analysis

TEST ID |
Syllabus |

PRT-01 |
Countable and uncountable sets, Point Set Topology, Sequences and series, convergence |

PRT-02 |
Limit and Continuity, Uniform continuity, Differentiability |

PRT-03 |
Riemann integral, Improper Integrals, Functions of bounded variation, Sequences and series of functions, Functions of several variables |

##### Linear Algebra

TEST ID |
Syllabus |

PRT-04 |
Vector spaces, subspaces, Basis, dimension, linear transformations, Algebra of matrices ,Linear equations, Eigen values, Eigen spaces , |

PRT-05 |
Diagonal forms, Canonical forms, triangular forms, Jordan forms, Inner product spaces, Quadratic forms |

##### Complex Analysis:

TEST ID |
Syllabus |

PRT-06 |
Introduction complex analysis , Analytic functions, Cauchy-Riemann equations. Contour integral, Cauchy’s theorem, Cauchy’s integral formula, |

PRT-07 |
Liouville’s theorem, Maximum modulus principle, Schwarz lemma, Open mapping theorem. Taylor series, Laurent series, Calculus of residues. Conformal mappings, Mobius transformations. |

##### Modern Algebra:

TEST ID |
Syllabus |

PRT-08 |
Fundamental of arithmetic ,Groups, subgroups, Cyclic groups, Permutation groups, |

PRT-09 |
Class equations, Normal subgroups, quotient groups, Homomorphisms, Cayley’s theorem, Sylow theorems. |

PRT-10 |
Rings, Sub ring ,ideals, quotient rings, Prime and maximal ideals, Unique factorization domain, principal ideal domain, Euclidean domain. |

PRT-11 |
Polynomial rings and irreducibility criteria. Fields, finite fields, field extensions, Galois Theory. |

##### Ordinary Differential Equations (ODEs):

TEST ID |
Syllabus |

PRT-13: |
General theory of homogenous and non-homogeneous linear ODEs, Existence and uniqueness, |

PRT-14 |
System of first order ODEs, Sturm-Liouville boundary value problem, Singular solutions of first order ODEs, |

##### Partial Differential Equations (PDEs):

TEST ID |
Syllabus |

PRT-15: |
Lagrange and Charpit methods for solving first order PDEs, Cauchy problem for first order PDEs. General solution of higher order PDEs with constant coefficients, |

PRT-16 |
Classification of second order PDEs, Method of separation of variables for Laplace, Heat and Wave equations. Green’s function. |

##### Numerical Analysis:

TEST ID |
Syllabus |

PRT-17 |
Numerical solutions of algebraic equations, Rate of convergence, Solution of systems of linear algebraic equations using Gauss elimination and Gauss-Seidel methods, Finite differences, Lagrange, Hermite and spline interpolation, |

PRT-18 |
Numerical differentiation and integration, Numerical solutions of ODEs using Picard, Euler, modified Euler and Runge-Kutta methods. |

##### Calculus of Variations:

TEST ID |
Syllabus |

PRT-19 |
Variation of a functional, Euler-Lagrange equation, Necessary and sufficient conditions for extrema. Variational methods for boundary value problems in ordinary and partial differential equations. |

##### Linear Integral Equations:

TEST ID |
Syllabus |

PRT-20 |
Linear integral equation of the first and second kind of Fredholm and Volterra type, Solutions with separable kernels. Characteristic numbers and eigenfunctions, Resolvent kernel. |

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 20 question papers

##### Real Analysis

TEST ID | Syllabus |

PRT-01 | Countable and uncountable sets, Point Set Topology, Sequences and series, convergence |

PRT-02 | Limit and Continuity, Uniform continuity, Differentiability |

PRT-03 | Riemann integral, Improper Integrals, Functions of bounded variation, Sequences and series of functions, Functions of several variables |

##### Linear Algebra

TEST ID | Syllabus |

PRT-04 | Vector spaces, subspaces, Basis, dimension, linear transformations, Algebra of matrices ,Linear equations, Eigen values, Eigen spaces , |

PRT-05 | Diagonal forms, Canonical forms, triangular forms, Jordan forms, Inner product spaces, Quadratic forms |

##### Complex Analysis:

TEST ID | Syllabus |

PRT-06 | Introduction complex analysis , Analytic functions, Cauchy-Riemann equations. Contour integral, Cauchy’s theorem, Cauchy’s integral formula, |

PRT-07 | Liouville’s theorem, Maximum modulus principle, Schwarz lemma, Open mapping theorem. Taylor series, Laurent series, Calculus of residues. Conformal mappings, Mobius transformations. |

##### Modern Algebra:

TEST ID | Syllabus |

PRT-08 | Fundamental of arithmetic ,Groups, subgroups, Cyclic groups, Permutation groups, |

PRT-09 | Class equations, Normal subgroups, quotient groups, Homomorphisms, Cayley’s theorem, Sylow theorems. |

PRT-10 | Rings, Sub ring ,ideals, quotient rings, Prime and maximal ideals, Unique factorization domain, principal ideal domain, Euclidean domain. |

PRT-11 | Polynomial rings and irreducibility criteria. Fields, finite fields, field extensions, Galois Theory. |

##### Ordinary Differential Equations (ODEs):

TEST ID | Syllabus |

PRT-13: | General theory of homogenous and non-homogeneous linear ODEs, Existence and uniqueness, |

PRT-14 | System of first order ODEs, Sturm-Liouville boundary value problem, Singular solutions of first order ODEs, |

##### Partial Differential Equations (PDEs):

TEST ID | Syllabus |

PRT-15: | Lagrange and Charpit methods for solving first order PDEs, Cauchy problem for first order PDEs. General solution of higher order PDEs with constant coefficients, |

PRT-16 | Classification of second order PDEs, Method of separation of variables for Laplace, Heat and Wave equations. Green’s function. |

##### Numerical Analysis:

TEST ID | Syllabus |

PRT-17 | Numerical solutions of algebraic equations, Rate of convergence, Solution of systems of linear algebraic equations using Gauss elimination and Gauss-Seidel methods, Finite differences, Lagrange, Hermite and spline interpolation, |

PRT-18 | Numerical differentiation and integration, Numerical solutions of ODEs using Picard, Euler, modified Euler and Runge-Kutta methods. |

##### Calculus of Variations:

TEST ID | Syllabus |

PRT-19 | Variation of a functional, Euler-Lagrange equation, Necessary and sufficient conditions for extrema. Variational methods for boundary value problems in ordinary and partial differential equations. |

##### Linear Integral Equations:

TEST ID | Syllabus |

PRT-20 | Linear integral equation of the first and second kind of Fredholm and Volterra type, Solutions with separable kernels. Characteristic numbers and eigenfunctions, Resolvent kernel. |

EXAM HABIT PACKAGE (EHP) : Know about the important topics and questions that have higher weightage and are more likely to be asked in the exam. There will be 10-Test papers.

##### Module Wise Test Series

TEST ID | Syllabus |

MWT-01 | Analysis, Topology |

MWT-02 | Linear Algebra |

MWT-03 | Ordinary Differential Equations (ODEs),Partial Differential Equations (PDEs) |

MWT-04 | Complex Analysis |

MWT-05 | Numerical Analysis, Calculus of Variations, Linear Integral Equations |

MWT-06 | Algebra,L.P.P |

MWT-07 | Classical Mechanics, Descriptive Statistics, exploratory data analysis |

##### Exam Pattern Test(EPT)

CSIR NET/JRF 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 | Syllabus |

EPT-01 | As Per Exam Pattern (PART-A,PART-B,PART-C) |

EPT-02 | As Per Exam Pattern (PART-A,PART-B,PART-C) |

EPT-03 | As Per Exam Pattern (PART-A,PART-B,PART-C) |

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

CSIR NET/JRF 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 | PART-A | PART-B | PART-C |

EPT-01 | General Aptitudes | 40-MCQ Questions | 60-MSQ Questions |

EPT-02 | General Aptitudes | 40-MCQ Questions | 60-MSQ Questions |

EPT-03 | General Aptitudes | 40-MCQ Questions | 60-MSQ Questions |