**Understanding the Methodology of CI Classes for IIT-JAM Preparation**

CI Classes is a renowned coaching institute that specializes in preparing students for the prestigious IIT-JAM examination. With their systematic approach and experienced faculty, CI Classes has established itself as a trusted name in the field of IIT-JAM preparation. In this article, we will explore the methodology employed by CI Classes to ensure effective learning for IIT-JAM aspirants.

**Strategies used by CI Classes to Ensure Effective Learning for IIT-JAM**** Exam Coaching**

: One of the key strategies employed by CI Classes is the creation of comprehensive study materials. These materials are designed to cover the entire syllabus of the IIT-JAM examination and are structured in a way that facilitates easy understanding and retention of concepts. The study materials provided by CI Classes include detailed notes, solved examples, and practice questions, which help students build a strong foundation and develop problem-solving skills.**Comprehensive Study Materials**: CI Classes understands the importance of regular assessments in tracking students’ progress and identifying areas of improvement. To ensure effective learning, they conduct regular mock tests that simulate the actual IIT-JAM examination. These tests help students familiarize themselves with the exam pattern and time management, and also provide an opportunity to assess their strengths and weaknesses. The faculty at CI Classes then provides personalized feedback and guidance to students to help them improve their performance.*Regular Mock Tests and Assessments*: CI Classes believes in providing personalized attention to each student to cater to their individual needs. They conduct regular doubt clearing sessions, where students can seek clarification on any topic or concept. The faculty at CI Classes are highly experienced and are always available to guide and mentor students. This personalized attention ensures that students are able to overcome their doubts and difficulties, and stay motivated throughout their IIT-JAM preparation journey.*Doubt Clearing Sessions and Personalized Attention*

CI Classes’ methodology for IIT-JAM preparation focuses on providing comprehensive study materials, regular mock tests, and personalized attention to students. By employing these key strategies, CI Classes ensures effective learning and equips students with the necessary skills and knowledge to excel in the IIT-JAM examination. If you are aspiring to crack IIT-JAM, enrolling in CI Classes can be a wise decision that will pave the way for your success.

**Exam Pattern**

## IIT-JAM

CI Classes **IIT JAM coaching **delivers the complete syllabus of IIT JAM Mathematics or Physics in the shortest span of time. Our **IIT JAM Mathematics offline & online coaching** syllabus is designed to deliver as much information as possible in the shortest amount of time. With us, you will get access to: real one on one classes (both in online and offline mode), Interactive quizzes and tests, MCQs and unsolved questions with detailed solutions, live class sessions with your personal mentors.

We strive to develop both the conceptual and analytical capabilities of students with our **best online coaching for IIT jam mathematics** **& Physics**.

For students to win a competition, effective guidance is the primary requirement. We help students to build a strong foundation in Physics & mathematics.

Our unique method of teaching helps students to get better grades and perform well in competitive exams like IIT-JEE, JRF-NET, CAT, MAT, etc… Our commitment to excellence and perfection in imparting quality education is reflected in excellent results in the **IIT JAM Mathematics & Physics**

We provide equal attention for every student at CICIIT, helping them achieve their goals. Students are always motivated by our faculty to achieve their goals, as they continually guide them in the right direction. Students will be introduced to each topic from the very basics to the most advanced level. Students joins from all over India at CICIIT for **JAM Mathematics & Physics Entrance exam preparation**

Whenever students do not understand any topic, our teachers repeat that topic to ensure students are understanding the topic.

CICIIT also known as one of the best **IIT JAM ****Mathematics & Physics**

Joint Admission test for IIT JAM Mathematics today and get relevant study materials, assignments and question booklets.

## Special **Features of our Classes**

IIT-JAM Mathematics & Physics Classroom/Live Classes with three options are available.

**Option 1**. 4-5 days (Monday to Friday) a week,

**Option 2**. Weekend ,

- Entire syllabus of IIT JAM Mathematics or physics will be covered twice with revision
- Professors online/Offline Note will be provided.
- JAM Mathematics or Physics will be given Daily Practice Paper (DPP) for each class.
- IIT JAM Mathematics or Physics Online Test will be conducted.
- 10 to 12 Mock Test for IIT JAM Mathematics or Physics entire (Full Syllabus. IIT JAM Mathematics or Physics Exam Pattern: 120 Questions)
- Questions, Answers, Discussion of all questions of IIT JAM Mathematics or Physics Test Paper after the Test conducted.
- Online/Classroom Interactive Classes with Best Lecturers where student can clear any kind of doubt by asking questions in-between the Classes.
- Notes will be provided time to time on regular basis.
- Online/Classroom Test Series will be provided with detailed analysis.

**Syllabus**

**Maths**

**Real Analysis** **Sequences and Series of Real Numbers:** Convergence of sequences, bounded and monotone sequences, Cauchy sequences, Bolzano-Weierstrass theorem, absolute convergence, tests of convergence for series – comparison test, ratio test, root test; Power series (of one real variable), radius and interval of convergence, term-wise differentiation and integration of power series.

**Functions of One Real Variable: **Limit, continuity, intermediate value property, differentiation, Rolle’s Theorem, mean value theorem, L’Hospital rule, Taylor’s theorem, Taylor’s series, maxima and minima, Riemann integration (definite integrals and their properties), fundamental theorem of calculus.

**Multivariable Calculus and Differential Equations****Functions of Two or Three Real Variables:** : Limit, continuity, partial derivatives, total derivative, maxima and minima.

**Integral Calculus:** Double and triple integrals, change of order of integration, calculating surface areas and volumes using double integrals, calculating volumes using triple integrals.

**Differential Equations:** Bernoulli’s equation, exact differential equations, integrating factors, orthogonal trajectories, homogeneous differential equations, method of separation of variables, linear differential equations of second order with constant coefficients, method of variation of parameters, Cauchy-Euler equation.

**Linear Algebra and Algebra:****Matrices:** Systems of linear equations, rank, nullity, rank-nullity theorem, inverse, determinant, eigenvalues, eigenvectors.

**Finite Dimensional Vector Spaces: **Linear independence of vectors, basis, dimension, linear transformations, matrix representation, range space, null space, rank-nullity theorem.

**Groups:** Cyclic groups, abelian groups, non-abelian groups, permutation groups, normal subgroups, quotient groups, Lagrange’s theorem for finite groups, group homomorphisms.**MATHEMATICAL STATISTICS (MS)**

The Mathematical Statistics (MS) Test Paper comprises following topics of Mathematics (about 30% weight) and Statistics (about 70% weight).

**Mathematics****Sequences and Series of real numbers: **Sequences of real numbers, their convergence, and limits. Cauchy sequences and their convergence. Monotonic sequences and their limits. Limits of standard sequences. Infinite series and its convergence, and divergence. Convergence of series with non-negative terms. Tests for convergence and divergence of a series. Comparison test, limit comparison test, D’Alembert’s ratio test, Cauchy’s 𝑛 𝑡ℎ root test, Cauchy’s condensation test and integral test. Absolute convergence of series. Leibnitz’s test for the convergence of alternating series. Conditional convergence. Convergence of power series and radius of convergence.

**Differential Calculus of one and two real variables:** Limits of functions of one real variable. Continuity and differentiability of functions of one real variable. Properties of continuous and differentiable functions of one real variable. Rolle’s theorem and Lagrange’s mean value theorems. Higher order derivatives, Lebnitz’s rule and its applications. Taylor’s theorem with Lagrange’s and Cauchy’s form of remainders. Taylor’s and Maclaurin’s series of standard functions. Indeterminate forms and L’ Hospital’s rule. Maxima and minima of functions of one real variable, critical points, local maxima and minima, global maxima and minima, and point of inflection. Limits of functions of two real variables. Continuity and differentiability of functions of two real variables. Properties of continuous and differentiable functions of two real variables. Partial differentiation and total differentiation. Lebnitz’s rule for successive differentiation. Maxima and minima of functions of two real variables. Critical points, Hessian matrix, and saddle points. Constrained optimization techniques (with Lagrange multiplier).

**Integral Calculus:** Fundamental theorems of integral calculus (single integral). Lebnitz’s rule and its applications. Differentiation under integral sign. Improper integrals. Beta and Gamma integrals: properties and relationship between them. Double integrals. Change of order of integration. Transformation of variables. Applications of definite integrals. Arc lengths, areas and volumes.

**Matrices and Determinants: **Vector spaces with real field. Subspaces and sum of subspaces. Span of a set. Linear dependence and independence. Dimension and basis. Algebra of matrices. Standard matrices (Symmetric and Skew Symmetric matrices, Hermitian and Skew Hermitian matrices, Orthogonal and Unitary matrices, Idempotent and Nilpotent matrices). Definition, properties and applications of determinants. Evaluation of determinants using transformations. Determinant of product of matrices. Singular and nonsingular matrices and their properties. Trace of a matrix. Adjoint and inverse of a matrix and related properties. Rank of a matrix, row-rank, column-rank, standard theorems on ranks, rank of the sum and the product of two matrices. Row reduction and echelon forms. Partitioning of matrices and simple properties. Consistent and inconsistent system of linear equations. Properties of solutions of system of linear equations. Use of determinants in solution to the system of linear equations. Cramer’s rule. Characteristic roots and Characteristic vectors. Properties of characteristic roots and vectors. Cayley Hamilton theorem.

**Statistics** **Probability: **Random Experiments. Sample Space and Algebra of Events (Event space). Relative frequency and Axiomatic definitions of probability. Properties of probability function. Addition theorem of probability function (inclusion exclusion principle). Geometric probability. Boole’s and Bonferroni’s inequalities. Conditional probability and Multiplication rule. Theorem of total probability and Bayes’ theorem. Pairwise and mutual independence of events.

**Univariate Distributions:** Definition of random variables. Cumulative distribution function (c.d.f.) of a random variable. Discrete and Continuous random variables. Probability mass function (p.m.f.) and Probability density function (p.d.f.) of a random variable. Distribution (c.d.f., p.m.f., p.d.f.) of a function of a random variable using transformation of variable and Jacobian method. Mathematical expectation and moments. Mean, Median, Mode, Variance, Standard deviation, Coefficient of variation, Quantiles, Quartiles, Coefficient of Variation, and measures of Skewness and Kurtosis of a probability distribution. Moment generating function (m.g.f.), its properties and uniqueness. Markov and Chebyshev inequalities and their applications.

**Standard Univariate Distributions:** Degenerate, Bernoulli, Binomial, Negative binomial, Geometric, Poisson, Hypergeometric, Uniform, Exponential, Double exponential, Gamma, Beta (of first and second type), Normal and Cauchy distributions, their properties, interrelations, and limiting (approximation) cases.

**Multivariate Distributions: **Definition of random vectors. Joint and marginal c.d.f.s of a random vector. Discrete and continuous type random vectors. Joint and marginal p.m.f., joint and marginal p.d.f.. Conditional c.d.f., conditional p.m.f. and conditional p.d.f.. Independence of random variables. Distribution of functions of random vectors using transformation of variables and Jacobian method. Mathematical expectation of functions of random vectors. Joint moments, Covariance and Correlation. Joint moment generating function and its properties. Uniqueness of joint m.g.f. and its applications. Conditional moments, conditional expectations and conditional variance. Additive properties of Binomial, Poisson, Negative Binomial, Gamma and Normal Distributions using their m.g.f.

**Standard Multivariate Distributions: **Multinomial distribution as a generalization of binomial distribution and its properties (moments, correlation, marginal distributions, additive property). Bivariate normal distribution, its marginal and conditional distributions and related properties.

**Limit Theorems: **Convergence in probability, convergence in distribution and their inter relations. Weak law of large numbers and Central Limit Theorem (i.i.d. case) and their applications.

**Sampling Distributions: ** Definitions of random sample, parameter and statistic. Sampling distribution of a statistic.

**Order Statistics:** Definition and distribution of the 𝑟 𝑡ℎ order statistic (d.f. and p.d.f. for i.i.d. case for continuous distributions). Distribution (c.d.f., p.m.f., p.d.f.) of smallest and largest order statistics (i.i.d. case for discrete as well as continuous distributions).

**Central Chi-square distribution:** Definition and derivation of p.d.f. of central 𝜒2 distribution with 𝑛 degrees of freedom (d.f.) using m.g.f.. Properties of central 𝜒2 distribution, additive property and limiting form of central 𝜒2 distribution.

**Central Student’s 𝒕-distribution:** Definition and derivation of p.d.f. of Central Student’s 𝑡-distribution with 𝑛 d.f., Properties and limiting form of central 𝑡-distribution.** **

**Snedecor’s Central 𝑭-distribution:** Definition and derivation of p.d.f. of Snedecor’s Central 𝐹-distribution with (𝑚, 𝑛) d.f.. Properties of Central 𝐹-distribution, distribution of the reciprocal of 𝐹- distribution. Relationship between 𝑡, 𝐹 and 𝜒2 distributions.

**Estimation: **Unbiasedness. Sufficiency of a statistic. Factorization theorem. Complete statistic. Consistency and relative efficiency of estimators. Uniformly Minimum variance unbiased estimator (UMVUE). RaoBlackwell and Lehmann-Scheffe theorems and their applications. Cramer-Rao inequality and UMVUEs.

**Methods of Estimation: **Method of moments, method of maximum likelihood, invariance of maximum likelihood estimators. Least squares estimation and its applications in simple linear regression models. Confidence intervals and confidence coefficient. Confidence intervals for the parameters of univariate normal, two independent normal, and exponential distributions.

**Testing of Hypotheses: ** Null and alternative hypotheses (simple and composite), Type-I and Type-II errors. Critical region. Level of significance, size and power of a test, p-value. Most powerful critical regions and most powerful (MP) tests. Uniformly most powerful (UMP) tests. Neyman Pearson Lemma (without proof) and its applications to construction of MP and UMP tests for parameter of single parameter parametric families. Likelihood ratio tests for parameters of univariate normal distribution.

**Physics**

**Mathematical Methods**: Calculus of single and multiple variables, partial derivatives, Jacobian,

imperfect and perfect differentials, Taylor expansion, Fourier series. Vector algebra, Vector Calculus,

Multiple integrals, Divergence theorem, Green’s theorem, Stokes’ theorem. First order equations and

linear second order differential equations with constant coefficients. Matrices and determinants, Algebra

of complex numbers.**Mechanics and General Properties of Matter**: Newton’s laws of motion and applications, Velocity and acceleration in Cartesian, polar and cylindrical coordinate systems, uniformly rotating frame, centrifugal

and Coriolis forces, Motion under a central force, Kepler’s laws, Gravitational Law and field, Conservative and non-conservative forces. System of particles, Center of mass, equation of motion of

the CM, conservation of linear and angular momentum, conservation of energy, variable mass systems.

Elastic and inelastic collisions. Rigid body motion, fixed axis rotations, rotation and translation, moments

of Inertia and products of Inertia, parallel and perpendicular axes theorem. Principal moments and axes.

Kinematics of moving fluids, equation of continuity, Euler’s equation, Bernoulli’s theorem.**Oscillations, Waves and Optics**: Differential equation for simple harmonic oscillator and its general

solution. Superposition of two or more simple harmonic oscillators. Lissajous figures. Damped and

forced oscillators, resonance. Wave equation, traveling and standing waves in one-dimension. Energy

density and energy transmission in waves. Group velocity and phase velocity. Sound waves in media.

Doppler Effect. Fermat’s Principle. General theory of image formation. Thick lens, thin lens and lens

combinations. Interference of light, optical path retardation. Fraunhofer diffraction. Rayleigh criterion

and resolving power. Diffraction gratings. Polarization: linear, circular and elliptic polarization. Double

refraction and optical rotation.**Electricity and Magnetism**: Coulomb’s law, Gauss’s law. Electric field and potential. Electrostatic

boundary conditions, Solution of Laplace’s equation for simple cases. Conductors, capacitors,

dielectrics, dielectric polarization, volume and surface charges, electrostatic energy. Biot-Savart law,

Ampere’s law, Faraday’s law of electromagnetic induction, Self and mutual inductance. Alternating

currents. Simple DC and AC circuits with R, L and C components. Displacement current, Maxwell’s

equations and plane electromagnetic waves, Poynting’s theorem, reflection and refraction at a dielectric

interface, transmission and reflection coefficients (normal incidence only). Lorentz Force and motion of

charged particles in electric and magnetic fields.**Kinetic Theory, Thermodynamics**: Elements of Kinetic theory of gases. Velocity distribution and

Equipartition of energy. Specific heat of Mono-, di- and tri-atomic gases. Ideal gas, van-der-Waals gas and equation of state. Mean free path. Laws of thermodynamics. Zeroth law and concept of thermal equilibrium. First law and its consequences. Isothermal and adiabatic processes. Reversible,

irreversible and quasi-static processes. Second law and entropy. Carnot cycle. Maxwell’s

thermodynamic relations and simple applications. Thermodynamic potentials and their applications.

Phase transitions and Clausius-Clapeyron equation. Ideas of ensembles, Maxwell-Boltzmann, Fermi Dirac and Bose-Einstein distributions.**Modern Physics**: Inertial frames and Galilean invariance. Postulates of special relativity. Lorentz

transformations. Length contraction, time dilation. Relativistic velocity addition theorem, mass energy

equivalence. Blackbody radiation, photoelectric effect, Compton effect, Bohr’s atomic model, X-rays.

Wave-particle duality, Uncertainty principle, the superposition principle, calculation of expectation

values, Schrödinger equation and its solution for one, two and three dimensional boxes. Solution of

Schrödinger equation for the one dimensional harmonic oscillator. Reflection and transmission at a step

potential, Pauli exclusion principle. Structure of atomic nucleus, mass and binding energy. Radioactivity

and its applications. Laws of radioactive decay.**Solid State Physics, Devices and Electronics**: Crystal structure, Bravais lattices and basis. Miller indices.

X-ray diffraction and Bragg’s law; Intrinsic and extrinsic semiconductors, variation of resistivity with temperature. Fermi level. p-n junction diode, I-V characteristics, Zener diode and its applications, BJT:

characteristics in CB, CE, CC modes. Single stage amplifier, two stage R-C coupled amplifiers. Simple Oscillators: Barkhausen condition, sinusoidal oscillators. OPAMP and applications: Inverting and noninverting amplifier. Boolean algebra: Binary number systems; conversion from one system to another system;

binary addition and subtraction. Logic Gates AND, OR, NOT, NAND, NOR exclusive OR; Truth tables;

combination of gates; de Morgan’s theorem

## Our JAM Courses

## Regular Weekday Classes

## for 6 or 12 Months Course for

## Mathematics & Physics** **

**Regular Weekday C**ourse

Physics & Mathematics

**Monday to Friday CLASSES – WEEKDAY COURSES – Six Month or One year**

*Highlights*

**Aim** – Brush up basics followed by higher level concepts and final exam preparation

**Classes**– 4-5 days/week. Only classroom or online but pure live classes **(no recorded classes)**

**Duration & Time **– 5 Hours per day (with self practice sessions), 4/5 days a week teaching plus tests**Level** – Higher level concepts with lot of practice questions**Tests** – Respective class wise & higher level Pattern. 30 plus Mock Tests**Feedback** – Personalized Performance