**Indian Statistical Institute (ISI ) Entrance Exam:**

Indian Statistical Institute (ISI) organizes an entrance exam know as ISI 2017 to screen candidates for admission in various degree programmes. ISI offers various UG, PG, PhD programme in the field of Statistics, Science & Technology. This institution has four campuses situated in Chennai, Tezpur, Delhi and Bangalore. The ISI entrance exam 2018 conducted on 14th May 2017. Here in this article we are providing information regarding ISI 2017.

**ISI Exam Pattern:**

The entrance exam has been divided into two papers i.e. paper I and paper II. Paper I will comprise of objective type questions and paper II will contain short answer type questions. Each exam pattern for M.Tech course is given below:

The exam comprises of two parts i.e. part 1 and part 2.

Part 1 - contains multiple choice or descriptive test in Mathematics at UG level.

Part2- comprise of multiple choices or descriptive test in mathematics at UG level and logical reasoning for Group A and for Group B will contain questions from Mathematics, Statistics and Physics at PG level and from Computer Science, Engineering and Technology at B.Tech level

**Courses Offered:**

**Courses Offered:**

**Degree Courses:**

**Degree Courses:**

- B Stat (Hons)
- B Math (Hons)
- MS (QE)
- M Stat
- M Math
- MS (LIS)
- MS (QMS)
- M Tech (CS)
- M Tech (QROR).

**Diploma Certificate:**

**Diploma Certificate:**

- Part-time Course in SQC
- PG Diploma in Statistical Methods & Analytics
- PG Diploma in Computer Application
- PG Diploma in Business Analytics.

**Fellowship:**

Junior/Senior Research Fellowship

**ISI Syllabus:**

**B.MATH/B.STAT**

Test Codes: UGA (Multiple-choice Type) and UGB (Short Answer Type) -

**Algebra**: Sets, operations on sets. Prime numbers, factorization of integers and divisibility. Rational and irrational numbers. Permutations and combinations, basic probability. Binomial Theorem. Logarithms. Polynomials: Remainder Theorem, Theory of quadratic equations and expressions, relations between roots and coefficients. Arithmetic and geometric progressions. Inequalities involving arithmetic, geometric & harmonic means. Complex numbers. Matrices and determinants.

**Geometry**: Plane Geometry of 2 dimensions with Cartesian and polar coordinates. Equation of a line, angle between two lines, distance from a point to a line, Concept of a Locus, Area of a triangle,Equations of circle, parabola, ellipse and hyperbola and equations of their tangents and normal, Mensuration.

**Trigonometry**: Measures of angles. Trigonometric and inverse trigonometric functions. Trigonometric identities including addition formulae, solutions of trigonometric equations. Properties of triangles. Heights and distances.

**Calculus**: Sequences - bounded sequences, monotone sequences, limit of a sequence. Functions, one-one functions, onto functions. Limits and continuity. Derivatives and methods of differentiation. The slope of a curve. Tangents and normals. Maxima and minima. Using calculus to sketch graphs of functions. Methods of integration, definite and indefinite integrals, evaluation of area using integrals.

** M.MATH:**

**M.MATH:**

- Test Code: PMB-
- Countable and uncountable sets;
- equivalence relations and partitions;
- convergence and divergence of sequence and series;
- Cauchy sequence and completeness;
- Bolzano-Weierstrass theorem;
- continuity, uniform continuity, differentiability, Taylor Expansion;
- partial and directional derivatives, Jacobians;
- integral calculus of one variable – existence of Riemann integral,
- Fundamental theorem of calculus, change of variable, improper integrals;
- elementary topological notions for metric spaces – open, closed and
- compact sets, connectedness, continuity of functions;
- sequence and series of functions;
- elements of ordinary differential equations. • Vector spaces, subspaces, basis, dimension, direct sum;
- matrices, systems of linear equations, determinants;
- diagonalization, triangular forms;
- linear transformations and their representation as matrices;
- groups, subgroups, quotient groups, homomorphisms, products,
- Lagrange’s theorem, Sylow’s theorems;
- rings, ideals, maximal ideals, prime ideals, quotient rings,
- integral domains, Chinese remainder theorem, polynomial rings, fields.
- Elementary discrete probability theory: Combinatorial probability, Conditional probability, Bayes’ Theorem. Binomial and Poisson distributions

M.STAT:

Divisibility, Congruences, Primality. Algebra of matrices. Determinant, rank and Algebra, Arithmetic, geometric and harmonic progression. Continued fractions. Elementary combinatorics: Permutations and combinations, Binomial theorem. Theory of equations. Inequalities. Complex numbers and De Moivre's theorem. Elementary set theory. Functions and relations. Elementary number theory:

**MATHEMATICS:**

TEST CODE : PSA(OBJECTIVE TYPES) & PSB(SHORT ANSWER TYPE)

Inverse of a matrix. Solutions of linear equations.

Limits and continuity of functions of one variable.

Calculus | Sequences and series: Power series, Taylor and Maclaurin series.

Coordinate geometry | Straight lines, circles, parabolas, ellipses and hyperbolas.

Eigenvalues and eigenvectors of matrices. Simple properties of a group.Di

erentiationfunctions of one variable with applications. De

and integration ofnite integrals. Maxima and minima.

Functions of several variables - limits, continuity, di

erentiabilityand their applications. Ordinary linear

. Double integralsdi

erential equations.

Elementary discrete probability theory | Combinatorial probability, Conditional probability, Bayes theorem. Binomial and Poisson distributions.

Syllabus for Mathematics:

Combinatorics; Elements of set theory. Permutations and combinations.

Binomial and multinomial theorem. Theory of equations. Inequalities.

Linear Algebra: Vectors and vector spaces. Matrices. Determinants. Solution of linear equations. Trigonometry. Co-ordinate geometry.

Complex Numbers: Geometry of complex numbers and De Moivres theorem.

Calculus: Convergence of sequences and series. Functions. Limits and continuity of functions of one or more variables. Power series. Diﬀerentiation.

Leibnitz formula. Applications of diﬀerential calculus, maxima and minima.

Taylor’s theorem. Diﬀerentiation of functions of several variables. Indeﬁnite

integral. Fundamental theorem of calculus. Riemann integration and properties. Improper integrals. Double and multiple integrals and applications.

**Descriptive Statistics**: Descriptive statistical measures. Contingency tables and measures of association. Product moment and

types of correlation. Partial and multiple

as CRD, RBD, LSD and their analyses. Elements of factorial designs. Conventional sampling techniques (SRSWR/SRSWOR) including stratiﬁcation. Ratio and regression methods of estimation.correlation. Simple and multiple linear regression.

Statistical Inference: Elementary theory of estimation (unbiasedness, minimum variance, suﬃciency). Methods of estimation (maximum likelihood method, method of moments). Tests of hypotheses

(basic concepts and simple applications of Neyman-Pearson Lemma).

Conﬁdence intervals. Inference related to regression. ANOVA. Elements of nonparametric inference.

Design of Experiments and Sample Surveys: Basic designs suchother

limit theorem.

moment generating functions. Standard univariate discrete and continuous distributions. Joint probability distributions. Multinomial distribution. Bivariate normal and multivariate normal distributions. Sampling distributions of statistics. Weak law of large numbers. Central

and independence. Random variables and expectations. Moments and

and probability. Combinatorial probability. Conditional probability

Probability and Sampling Distributions: Notions of sample space

Syllabus for Statistics and Probability

**MSQE**:

Syllabus for(Mathematics), 2017

**Algebra**: Binomial Theorem, AP, GP, Series, Permutations and Combinations, Theory of Polynomial Equations. Linear Algebra: Vector spaces, linear transformations, matrix representations and elementary operations, systems of linear equations.

**Calculus**: Functions, Limits, Continuity, Differentiation of functions of one or more variables. Unconstrained Optimization, Definite and Indefinite Integrals: Integration by parts and integration by substitution. Convexity and quasi-convexity. Constrainedoptimization of functions of not more than two variables. The implicit function theorem, homogeneous and homothetic functions. Elementary Statistics: Elementary probability theory, measures of central tendency, dispersion, correlation and regression, probability distributions, standard distributions-Binomial and Normal.

**Syllabus for(Economics), 2017 Microeconomic**s: Theory of consumer behaviour, theory of production, market structure under perfect competition, monopoly, price discrimination, duopoly with Cournot and Bertrand competition, public goods, externalities, general equilibrium, welfare economics. Macroeconomics: National income accounting, simple Keynesian Model of income determination and the multiplier, IS-LM Model, models of aggregate demand and aggregate supply, money, banking and inflation, Phillips Curve, elementary open-economy macroeconomics, Harrod-Domar, Solow, and optimal growth models.

**How to Prepare for ISI Admission Test:**

- Practice previous years question papers.
- For better preparation, it is necessary for you to be in good health. So along side of preparation also maintain your health.
- Follow the syllabus as prescribed by the ISI.
- Gather information about exam pattern and syllabus.
- Make the effective time table and start preparation accordingly.

**FACILITIES AVAILABLE AT SOURAV SIR’S CLASSES**

- COACHING CLASSES (ONLINE & OFFLINE)
- STUDY MATERIALS
- DOUBT CLEARING CLASSES
- PERIODICAL MOCK TEST
- PRACTICE PAPER
- STUDY MATERIALS ARE AVAILABLE FOR ISI

**ISIB.MATH/B.STAT**

STUDY MATERIAL FOR ISI B STAT / B MATH ENTRANCE + MODEL PAPERS + TOMATO SOLUTION+ PREVIOUS YEAR SOLUTION+ TEST OF MATHEMATICS AT THE 10+2 LEVEL SOLVED COMPLETE B.STAT B.MATH BOOK1- KIT NOTES PACKAGE BSTAT BMATH

**ISI M.STAT**

**ISI MSQMS**

**ISI M.TECH**

**ISI M.MATH**

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