### Exclusive Test Package FOR IIT-JAM

- 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 IIT-JAM

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 20 Test papers.

##### Real Analysis

TEST ID |
Syllabus |

PRT-01 |
Interior points, limit points, open sets, closed sets, Bounded sets, connected sets, compact sets, completeness of R |

PRT-02 |
Power series (of real variable),Taylor’s series, Radius and interval of convergence, term-wise differentiation and integration of power series. |

##### Sequences and Series of Real Numbers:

TEST ID |
Syllabus |

PRT-03 |
Sequence of real numbers, convergence of sequences, Cauchy sequences, subsequences, Bolzano-Weierstrass theorem. bounded and monotone sequences, convergence criteria for sequences of real numbers, |

PRT-04 |
Series of real numbers, absolute convergence, Tests of convergence for series of positive terms – comparison test, ratio test, root test; Leibniz test for convergence of alternating series |

##### Functions of One Real Variable:

TEST ID |
Syllabus |

PRT-05 |
Limit of functions, Continuity of functions, Intermediate value property |

PRT-06 |
Differentiation of functions, Rolle’s Theorem, mean value theorem, L'Hospital rule, Taylor's theorem, Maxima and Minima |

##### Functions of Two or Three Real Variables:

TEST ID |
Syllabus |

PRT-07 |
Limit of functions, Continuity of functions, Partial derivatives of functions |

PRT-08 |
Differentiability of functions, Maxima and Minima of functions |

##### Integral Calculus:

TEST ID |
Syllabus |

PRT-09: |
Integration as the inverse process of differentiation, Definite integrals and their properties, Fundamental theorem of calculus. Change of order of integration |

PRT-10 |
Double and triple integrals, Calculating surface areas and volumes using double integrals, Calculating volumes using triple integrals |

##### Differential Equations:

TEST ID |
Syllabus |

PRT-11: |
Ordinary differential equations of the first order of the formy'=f(x,y), Exact differential equations, Integrating factor, orthogonal trajectories, homogeneous differential equations, Variable separable equations, Bernoulli’s equation |

PRT-12 |
Linear differential equations of second order with constant coefficients, Method of variation of parameters, Cauchy-Euler equation |

##### Vector Calculus:

TEST ID |
Syllabus |

PRT-13 |
Scalar and vector fields, Gradient, Divergence, Curl, line integrals |

PRT-14 |
Surface integrals, Green, Stokes and Gauss theorems. |

##### Group Theory:

TEST ID |
Syllabus |

PRT-15 |
Groups, Subgroups, Abelian groups, Non-Abelian groups |

PRT-16 |
Cyclic groups, Permutation groups |

PRT-17 |
Normal subgroups, Lagrange's Theorem for finite groups, Group homomorphisms and Basic concepts of quotient groups. |

##### Linear Algebra:

TEST ID |
Syllabus |

PRT-18 |
Finite dimensional vector spaces, Linear independence of vectors, Basis, dimension |

PRT-19 |
Linear transformations, Matrix representation, Range space, Nullspace, rank-nullity theorem. Rank and inverse of a matrix, determinant |

PRT-20 |
Solutions of systems of linear equations, consistency conditions, Eigen values and eigenvectors for matrices, Cayley-Hamilton theorem |

#### Module Wise Test (MWT)

The Module Wise Test (MWT) that provides you an opportunity to assess your preparation in each Subject. There will be 9-Test papers is great revision tool that provides you an opportunity to assess your preparation and strengthen the weak areas to outperform in the actual examination.

##### Real Analysis

TEST ID |
Syllabus |

MWT-01 |
Real Analysis: Interior points, limit points, open sets, closed sets, Bounded sets, connected sets, compact sets, completeness of R.Power series (of real variable),Taylor’s series, Radius and interval of convergence, term-wise differentiation and integration of power series |

##### Real Analysis

TEST ID |
Syllabus |

MWT-01 |
Real Analysis: Interior points, limit points, open sets, closed sets, Bounded sets, connected sets, compact sets, completeness of R.Power series (of real variable),Taylor’s series, Radius and interval of convergence, term-wise differentiation and integration of power series |

##### Real Analysis

TEST ID |
Syllabus |

MWT-01 |
Real Analysis: Interior points, limit points, open sets, closed sets, Bounded sets, connected sets, compact sets, completeness of R. Power series (of real variable),Taylor’s series, Radius and interval of convergence, term-wise differentiation and integration of power series |

##### Sequences and Series of Real Numbers:

TEST ID |
Syllabus |

MWT-02 |
Sequence of real numbers, Series of real numbers, absolute convergence, Convergence of alternating series. |

##### Functions of One Real Variable:

TEST ID |
Syllabus |

MWT-03 |
Limit of functions, Continuity of functions, Intermediate value property, Differentiation of functions, Rolle’s Theorem, mean value theorem, L'Hospital rule, Taylor's theorem, Maxima and Minima. |

##### Functions of Two or Three Real Variables:

TEST ID |
Syllabus |

MWT-04 |
Limit of functions, Continuity of functions, Partial derivatives of functions, Differentiability of functions, Maxima and Minima of functions |

##### Integral Calculus:

TEST ID |
Syllabus |

MWT-05 |
Integration as the inverse process of differentiation, Definite integrals and their properties, Fundamental theorem of calculus. Change of order of integration, Double and triple integrals, Calculating surface areas and volumes using double integrals, Calculating volumes using triple integrals. |

##### Differential Equations:

TEST ID |
Syllabus |

MWT-06 |
Ordinary differential equations of the first order of the formy'=f(x,y), Exact differential equations, Integrating factor, orthogonal trajectories, homogeneous differential equations, Variable separable equations,Bernoulli’s equation, Linear differential equations of second order with constant coefficients, Method of variation of parameters, Cauchy-Euler equation. |

##### Vector Calculus:

TEST ID |
Syllabus |

MWT-07 |
Scalar and vector fields, Gradient, Divergence, Curl, line integrals, Surface integrals, Green, Stokes and Gauss theorems. |

##### Group Theory:

TEST ID |
Syllabus |

MWT-08 |
Group Theory: Groups, Subgroups, Abelian groups, Non-Abelian groups, Cyclic groups, Permutation groups, Normal subgroups, Lagrange's Theorem for finite groups, Group homomorphisms and Basic concepts of quotient groups. |

##### Linear Algebra:

TEST ID |
Syllabus |

MWT-09 |
Finite dimensional vector spaces, Linear independence of vectors, Basis, dimension, Linear transformations, Matrix representation, Range space, Nullspace, rank-nullity theorem. Rank and inverse of a matrix, determinant, Solutions of systems of linear equations, consistency conditions, Eigen values and eigenvectors for matrices, Cayley-Hamilton theorem |

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

IIT-JAM 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 |
Section-C |

EPT-01 | 30- Multiple Choice Questions (MCQ) | 10-Multiple Select Questions (MSQ) | 20-Numerical Answer Type (NAT) questions |

EPT-02 | 30- Multiple Choice Questions (MCQ) | 10-Multiple Select Questions (MSQ) | 20-Numerical Answer Type (NAT) questions |

EPT-03 | 30- Multiple Choice Questions (MCQ) | 10-Multiple Select Questions (MSQ) | 20-Numerical Answer Type (NAT) questions |

EPT-04 | 30- Multiple Choice Questions (MCQ) | 10-Multiple Select Questions (MSQ) | 20-Numerical Answer Type (NAT) questions |

Section Based Test Package (CBTP) is an opportunity to assess your preparation and strengthen the weak areas to outperform in the actual examination. This Test package consisting of 20 Question Papers

#### Section Based Test Package (CBTP)

Section Based Test Package (CBTP) is an opportunity to assess your preparation and strengthen the weak areas to outperform in the actual examination. This Test package consisting of 20 Question Papers

##### Real Analysis

TEST ID | Syllabus |

PRT-01 | Interior points, limit points, open sets, closed sets, Bounded sets, connected sets, compact sets, completeness of R |

PRT-02 | Power series (of real variable),Taylor’s series, Radius and interval of convergence, term-wise differentiation and integration of power series. |

##### Sequences and Series of Real Numbers:

TEST ID | Syllabus |

PRT-03 | Sequence of real numbers, convergence of sequences, Cauchy sequences, subsequences, Bolzano-Weierstrass theorem. bounded and monotone sequences, convergence criteria for sequences of real numbers, |

PRT-04 | Series of real numbers, absolute convergence, Tests of convergence for series of positive terms – comparison test, ratio test, root test; Leibniz test for convergence of alternating series |

##### Functions of One Real Variable:

TEST ID | Syllabus |

PRT-05 | Limit of functions, Continuity of functions, Intermediate value property |

PRT-06 | Differentiation of functions, Rolle’s Theorem, mean value theorem, L'Hospital rule, Taylor's theorem, Maxima and Minima |

##### Functions of Two or Three Real Variables:

TEST ID | Syllabus |

PRT-07 | Limit of functions, Continuity of functions, Partial derivatives of functions |

PRT-08 | Differentiability of functions, Maxima and Minima of functions |

##### Integral Calculus:

TEST ID | Syllabus |

PRT-09: | Integration as the inverse process of differentiation, Definite integrals and their properties, Fundamental theorem of calculus. Change of order of integration |

PRT-10 | Double and triple integrals, Calculating surface areas and volumes using double integrals, Calculating volumes using triple integrals |

##### Differential Equations:

TEST ID | Syllabus |

PRT-11: | Ordinary differential equations of the first order of the formy'=f(x,y), Exact differential equations, Integrating factor, orthogonal trajectories, homogeneous differential equations, Variable separable equations, Bernoulli’s equation |

PRT-12 | Linear differential equations of second order with constant coefficients, Method of variation of parameters, Cauchy-Euler equation |

##### Vector Calculus:

TEST ID | Syllabus |

PRT-13 | Scalar and vector fields, Gradient, Divergence, Curl, line integrals |

PRT-14 | Surface integrals, Green, Stokes and Gauss theorems. |

##### Group Theory:

TEST ID | Syllabus |

PRT-15 | Groups, Subgroups, Abelian groups, Non-Abelian groups |

PRT-16 | Cyclic groups, Permutation groups |

PRT-17 | Normal subgroups, Lagrange's Theorem for finite groups, Group homomorphisms and Basic concepts of quotient groups. |

##### Linear Algebra:

TEST ID | Syllabus |

PRT-18 | Finite dimensional vector spaces, Linear independence of vectors, Basis, dimension |

PRT-19 | Linear transformations, Matrix representation, Range space, Nullspace, rank-nullity theorem. Rank and inverse of a matrix, determinant |

PRT-20 | Solutions of systems of linear equations, consistency conditions, Eigen values and eigenvectors for matrices, Cayley-Hamilton theorem |

The Module Wise Test (MWT) that provides you an opportunity to assess your preparation in each Subject. There will be 9-Test papers is great revision tool that provides you an opportunity to assess your preparation and strengthen the weak areas to outperform in the actual examination.

##### Real Analysis

TEST ID | Syllabus |

MWT-01 | Real Analysis: Interior points, limit points, open sets, closed sets, Bounded sets, connected sets, compact sets, completeness of R.Power series (of real variable),Taylor’s series, Radius and interval of convergence, term-wise differentiation and integration of power series |

##### Real Analysis

TEST ID | Syllabus |

MWT-01 |

##### Real Analysis

TEST ID | Syllabus |

MWT-01 | Real Analysis: Interior points, limit points, open sets, closed sets, Bounded sets, connected sets, compact sets, completeness of R. Power series (of real variable),Taylor’s series, Radius and interval of convergence, term-wise differentiation and integration of power series |

##### Sequences and Series of Real Numbers:

TEST ID | Syllabus |

MWT-02 | Sequence of real numbers, Series of real numbers, absolute convergence, Convergence of alternating series. |

##### Functions of One Real Variable:

TEST ID | Syllabus |

MWT-03 | Limit of functions, Continuity of functions, Intermediate value property, Differentiation of functions, Rolle’s Theorem, mean value theorem, L'Hospital rule, Taylor's theorem, Maxima and Minima. |

##### Functions of Two or Three Real Variables:

TEST ID | Syllabus |

MWT-04 | Limit of functions, Continuity of functions, Partial derivatives of functions, Differentiability of functions, Maxima and Minima of functions |

##### Integral Calculus:

TEST ID | Syllabus |

MWT-05 | Integration as the inverse process of differentiation, Definite integrals and their properties, Fundamental theorem of calculus. Change of order of integration, Double and triple integrals, Calculating surface areas and volumes using double integrals, Calculating volumes using triple integrals. |

##### Differential Equations:

TEST ID | Syllabus |

MWT-06 | Ordinary differential equations of the first order of the formy'=f(x,y), Exact differential equations, Integrating factor, orthogonal trajectories, homogeneous differential equations, Variable separable equations,Bernoulli’s equation, Linear differential equations of second order with constant coefficients, Method of variation of parameters, Cauchy-Euler equation. |

##### Vector Calculus:

TEST ID | Syllabus |

MWT-07 | Scalar and vector fields, Gradient, Divergence, Curl, line integrals, Surface integrals, Green, Stokes and Gauss theorems. |

##### Group Theory:

TEST ID | Syllabus |

MWT-08 | Group Theory: Groups, Subgroups, Abelian groups, Non-Abelian groups, Cyclic groups, Permutation groups, Normal subgroups, Lagrange's Theorem for finite groups, Group homomorphisms and Basic concepts of quotient groups. |

##### Linear Algebra:

TEST ID | Syllabus |

MWT-09 | Finite dimensional vector spaces, Linear independence of vectors, Basis, dimension, Linear transformations, Matrix representation, Range space, Nullspace, rank-nullity theorem. Rank and inverse of a matrix, determinant, Solutions of systems of linear equations, consistency conditions, Eigen values and eigenvectors for matrices, Cayley-Hamilton theorem |

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

IIT-JAM 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 | Section-C |

EPT-01 | 30- Multiple Choice Questions (MCQ) | 10-Multiple Select Questions (MSQ) | 20-Numerical Answer Type (NAT) questions |

EPT-02 | 30- Multiple Choice Questions (MCQ) | 10-Multiple Select Questions (MSQ) | 20-Numerical Answer Type (NAT) questions |

EPT-03 | 30- Multiple Choice Questions (MCQ) | 10-Multiple Select Questions (MSQ) | 20-Numerical Answer Type (NAT) questions |

EPT-04 | 30- Multiple Choice Questions (MCQ) | 10-Multiple Select Questions (MSQ) | 20-Numerical Answer Type (NAT) questions |