# Indian Statistical Institute, ISI BStat & BMath 2019 Solutions & Discussions

## ISI BMath & BSTAT 2019 Subjective Questions UGB along with hints and solutions and discussions

**Indian Statistical Institute,ISI BMATH/BSTAT 2021 All UGA Objective Solutions: Click Here**

**Problem 1.**

Prove that the positive integers that cannot be written as a sum of consecutive positive integers, with are of the form for some

### Topic: Number Theory

Difficulty level: High

**Indian Statistical Institute, ISI Subjective BStat & BMath 2019 Problem 1 UGB Solution & Discussion Video:**

**Problem 2.**

Let be defined by

- Show that has exactly one point of discontinuity.
- Evaluate at its point of discontinuity.

### Topic: Calculus: Limits and Continuity

Difficulty Level: Medium

**Indian Statistical Institute, ISI Subjective BStat & BMath 2019 Problem 2 UGB Solution & Discussion Video:**

**Problem 3.**

Let If then draw a sketch of

Justify your answer.

### Topic: Complex Numbers

Difficulty Level: High

**Indian Statistical Institute, ISI Subjective BStat & BMath 2019 Problem 3 UGB Solution & Discussion Video:**

**Problem 4.**

Let be a twice differentiable function such that

Show that there exist such that for all

### Topic: Calculus: Differentiation, Definite Integral

Difficulty Level: Medium

**Indian Statistical Institute, ISI Subjective BStat & BMath 2019 Problem 4 UGB Solution & Discussion Video:**

**Problem 5.**

A subset of the plane is called if given two points and in the line segment joining and is containted in A quadrilateral is called convex if the region enclosed by the edges of the quadrilateral is a convex set.

Show that given a convex quadrilateral of area 1, there is a rectangle of area such that can be drawn inside

### Topic: Geometry: Construction

Difficulty Level: Very Easy

**Indian Statistical Institute, ISI Subjective BStat & BMath 2019 Problem 5 UGB Solution & Discussion Video:**

**Problem 6.**

For all natural numbers let

- Show that for

- Hence or otherwise, evaluate the limit

### Topic: Trigonometry

Difficulty Level: Medium

**Indian Statistical Institute, ISI Subjective BStat & BMath 2019 Problem 6 UGB Solution & Discussion Video:**

**Problem 7.**

Let be a polynomial with integer coefficients. Define

and

If there exists a natural number such that then prove that either or

### Topic: Geometry: Polynomials

Difficulty Level: Hard

**Indian Statistical Institute, ISI Subjective BStat & BMath 2019 Problem 7 UGB Solution & Discussion Video:**

**Problem 8.**

Consider the following subsets of the plane:

and

Given any two points and of the plane, their distance is defined by

Show that there exists a unique choice of points and such that

If there is any typing error please do let us know by commenting here.

Thank you

Fractions

Like!! I blog frequently and I really thank you for your content. The article has truly peaked my interest.

Thank you.

Hello sir thanks for making YouTube videos for isi b math solution.

I am preparing for isi b math can you tell how much complex numbers and matrices and determinants should we practice and till what level.

Thank you for your help.

You are welcome Jatin. For complex numbers try to follow the book “Complex Numbers from A to …Z

Book by Dorin Andrica and Titu Andreescu” and for matrices and determinants just study the basic properties.

Sir how much probability and coordinate geometry weigh in isi b math exam how much to practice.

You can expect around two questions from probability and coordinate geometry each. Try to follow “Coordinate Geometry.

Book by S. L. Loney” and for probability, you can check this out, “https://projects.iq.harvard.edu/stat110/youtube”.

How much to practice depends on you. If you are not confident enough to solve any problem on a particular topic, then do keep practicing.

Thank you sir

sir I have solved Q1 by contradiction Q3 in another way and Q8 in another way..but I am not sure that my solutions are right or wrong.. what should I do..and also I found recent ISI subjective polynomial problems hard but I am able to solve other past paper polynomial problems with ease …what should I do??

Okay, you can type your solutions here in the comment box. If you are finding them hard then don’t worry about it, even I find them hard sometimes, just keep on practicing for polynomials practice from Problem solving strategies.

Sir do you provide doubt solving sessions in isi and cmi entrance exam course

We provide personal one to one classes for doubt clearing.

sir , in an hour i was able to solve only 3 questions , kindly suggest how to gain approach to crack the solutions for the hard questions and where should i study induction from

Three questions in an hour are considered to be good. You can still try to do better. There is no such algorithm or formula to get the problems done. You have to practice as much as possible. For mathematical induction you can follow this notes: https://cseweb.ucsd.edu/classes/sp14/cse20-a/InductionNotes.pdf

Sir, this website is great.

I am somewhat weak in pure euclidean geometry… is that a cause for concern for isi?

If you are fine with the other topics then it shouldn’t be a concern.