Categories

## IIT JAM Stat Mock Test Toppers

We are really happy with the performance of our students and thus, we have initiated to name the Toppers of IIT JAM Stat Mock Test. These toppers are named in this leader board according to their performance in IIT JAM Stat Mock Tests.

So, here goes the list:

 Mock Test name Topper’s name and their scores IIT JAM Mock Test 1 (Full) 1. Somyadipta Ghosh – 88.5%2. Mainack Paul – 83.7%3. Abhradiptaa Ghosh – 78.7%4. Prabirkumar Das – 71.2%5. Debepsita Mukherjee – 68% IIT JAM Mock Test 2 (Full) 1. Somyadipta Ghosh – 74.2%2. Mainack Paul – 68.2%3. Prabirkumar Das – 58.6%4. Saikat Kar – 57.6%5. Debepsita Mukherjee – 49.7% IIT JAM Mathematics Mock Test 1 1. Bidisha Ghosh – 51.4%2. Mainack Paul – 51%3. Somyadipta Ghosh – 50.3% IIT JAM Mathematics Mock Test 2 1. Abhradiptaa Ghosh – 57.8%2. Debepsita Mukherjee – 54.7%3. Srija Mukherjee – 52.5% IIT JAM Statistics Mock Test 1 1. Somyadipta Ghosh – 68%2. Mainack Paul – 64%3. Debepsita Mukherjee – 56%4. Srija Mukherjee – 52%5. Abhradiptaa Ghosh – 52% IIT JAM Statistics Mock Test 2 1. Somyadipta Ghosh – 56.7%2. Mainack Paul – 56.7% IIT JAM Probability Mock Test 1 1. Mainack Paul – 80%2. Anis Pakrashi – 76.7%3. Somyadipta Ghosh – 76.7%4. Prabirkumar Das – 73.3% IIT JAM Probability Mock Test 2 1. Abhradiptaa Ghosh – 80%2. Mainack Paul – 76%3. Srija Mukherjee – 76%4. Anis Pakrashi – 68%5. Prabirkumar Das – 68%

These Mock Tests are part of our Cheenta Statistics Bronze Learning Path. You can learn more about it here.

## Pigeonhole Principle

“The Pigeonhole principle” ~ Students who have never heard may think that it is a joke. Pigeonhole Principle is one of the simplest but most useful ideas in mathematics. Let’s learn the Pigeonhole Principle with some applications.

## Pigeonhole Principle Definition:

In Mathematics, the pigeonhole principle states that if we must put N + 1 or more pigeons into N Pigeon Holes, then some pigeonholes must contain two or more pigeons.

### Pigeonhole Principle Example:

If Kn+ 1 (where k is a positive integer) pigeons are distributed among n holes than some hole contains at least k + 1 pigeons.

### Applications of Pigeonhole Principle:

This principle is applicable in many fields like Number Theory, Probability, Algorithms, Geometry, etc.

## Problems:

### Problem 1

A bag contains beads of two colours: black and white. What is the smallest number of beads which must be drawn from bag, without looking so that among these beads, two are of the same colour?

Solution: We can draw three beads from bags. If there were no more than one bead of each colour among these, then there would be no more than two beads altogether. This is obvious and contradicts the fact that we have chosen there beads. On the other hand, it is clear that choosing two beads is not enough. Here the beads play the role of pigeons, and the colours (black and white) play the role of pigeonhole.

### Problem 2

Find the minimum number of students in a class such that three of them are born in the same month?

Solution: Number of month n =12

According to the given condition,

K+1 = 3

K = 2

M = kn +1 = 2*12 + 1 = 25.

### Problem 3

Show that from any three integers, one can always chose two so that $a^3$b – a$b^3$ is divisible by 10.

Solution: We can factories the term $a^3$b – a$b^3$ = ab(a + b)(a – b), which is always even, irrespective of the pair of integers we choose.

If one of three integers from the above factors is in the form of 5k, which is a multiple of 5, then our result is proved.

If none of the integers are a multiple of 5 then the chosen integers should be in the form of (5k)+-(1) and (5k)+-(2) respectively.

Clearly, two of these three numbers in the above factors from the given expression should lie in one of the above two from, which follows by the virtue of this principle.

These two integers are the ones such that their sum and difference is always divisible by 5. Hence, our result is proved.

### Problem 4

If n is a positive integer not divisible by 2 or 5 then n has a multiple made up of 1’s.

Watch the solution:

Categories

## Mathematics Summer Camps in India One Should Explore

Mathematics Summer Camps help students to feel the richness of Mathematics. These summer mathematics programme in India instills the love for Mathematics in students. In this post, we are going to discuss the Mathematics Summer Camps in India for School and College Students. Here we go:

## 1. Programs in Mathematics for Young Scientists – PROMYS India

PROMYS India is a challenging six-week summer program for Mathematics aspirants. This program is held at Ashoka University in Sonepat, Haryana. Secondary and higher secondary students can participate in the camp, i.e., students from Grades 9 – 12 or equivalent are eligible for PROMYS.

In response to Global Covid 19 Pandemic, the launch of PROMYS India has been shifted from 2020 to 2021.

## 2. Epsilon India

Epsilon Camp is designed for those who are not only exceptionally or profoundly gifted but who also love Mathematics. Students in the age group of 9 through 13 are eligible for this camp. This camp is useful for students to get an early start in Mathematics.

Due to Covid 19, the Epsilon Camp is going to held online in May 2021. The exact dates for the registration will be provided during January, 2021.

## 3. IMSc summer camp

If a bachelors and masters student is interested in research in the areas of Theoretical Physics, Mathematics, Theoretical Computer Science and Computational Biology, he/she can visit the IMSc institute in the summer vacation. IMSc accepts students through the summer program organized by the joint Indian Academies of Science too.

Students currently in their pre-final or final year of BSc/BE/BTech or first year MSc/ME/MTech or equivalent with a good academic record are encouraged to apply through IMSc’s formal application process.

Due to the prevailing situation regarding COVID-19 Summer Student Programme 2020 is CANCELLED for Mathematics.

To know more, visit: https://www.imsc.res.in/summer_research_programme

## 4. Visiting Students’ Research Programme (VSRP)

Visiting Students’ Research Programme (VSRP) is conducted by Tata Institute of Fundamental Research (TIFR). TIFR is one of the best place for mathematics research within India.

The date for VSRP, 2021 is not announced yet.

To know more, visit: https://www.tifr.res.in/~vsrp/

## 5. Summer Program in Mathematics (SPIM)

Harish Chandra Research Institute (HRI), an autonomous institute, located in Prayagraj, Uttar Pradesh, conducts the Summer Program in Mathematics (SPIM). SPIM introduces basic mathematics at Master’s level in an interesting way to the highly motivated undergraduates or first year post graduates from various colleges/universities.

The programme involves a three-week in-depth lectures on Algebra (Group Theory, Field Theory and Galois Theory), Analysis (Measure Theory, Basic Complex Analysis) and Topology (Set Topology up to homotopy theory) in the summer of every year.

The important dates for SPIM 2021 are not announced yet. You can check the official website during February or March, 2021 for information of the registration dates.

## 6. MathILY

MathILY is an in-depth five-week residential summer program for mathematically excellent secondary students. It is held through internet and promise to offer you maximized mathematical marvelousness.

The important dates for MathILY 2021 are not announced yet. The tentative months are June – August, 2021.

Here is the link to the offficial website: http://www.mathily.org/

## 7. Stanford University Mathematics Camp (SUMaC)

Stanford University Mathematics Camp (SUMaC) is a 3-week online program to engage you in deep exploration of mathematics and develop as a mathematician. High school junior and senior students from around the world are eligible for this program.

It generally occurs in the month of June and July. The dates for 2021 is not available yet.

Here is the link to the official website: https://sumac.spcs.stanford.edu/sumac-online

## 8. Summer School for Women in Mathematics and Statistics

Summer School for Women in Mathematics and Statistics (by TIFR) is intended for women students studying in first year B.A/B.Sc./B.E./B.Tech. or equivalent degree and having Mathematics as one of the major subjects/courses.

The program date for 2021 is not announced yet. Although the tentative month for registration is February or March, 2021.

Here is the link to the official website: https://www.icts.res.in/program/swms2019

## 9. Bose Maths Olympiad – Summer

Cheenta also powers an online Maths Olympiad Program called Bose Maths Olympiad. This Olympiad occurs thrice a year – Spring, Summer and Winter.

The Program consist of written test followed by training camps. After these stages, the students are instructed to form teams to participate in the team round. This team round is kept to instill the team spirit among students.

After evaluating the performance of the students in all these rounds, the results are announced and scholarships are provided to some brilliant students.

The Summer Camp registration will be announced around March, 2021.

These 9 Mathematics summer camps are worth attending for the mathematical enthusiasts in India. Participating in such camps provide memorable experience and long-lasting learning to the students.

Hope this helps you.

Categories

## How to use Vectors and Carpet Theorem in Geometry 1?

Here is a video solution for a Problem based on using Vectors and Carpet Theorem in Geometry 1? This problem is helpful for Math Olympiad, ISI & CMI Entrance, and other math contests. Watch and Learn!

Here goes the question…

Given ABCD is a quadrilateral and P and Q are 2 points on AB and CD respectively, such that AP/AB = CQ/CD. Show that: in the figure below, the area of the green part = the white part.

We will recommend you to try the problem yourself.

Done?

Let’s see the solution in the video below:

Categories

## Mahalanobis National Statistics Competition

Mahalanobis National Statistics Competition = MNStatC

organized by Cheenta Statistics Department

with exciting cash prizes.

## What is MNStatC?

Mahalanobis National Statistics Competition (MNStatC) is a national level statistics competition, aimed at undergraduate students as well as masters, Ph.D. students, and data analytics, and ML professionals. MNStatC plans to test your core mathematics, probability, and statistics (theoretical + applied) skills.

#### MNStatC aims

• to engage the data lovers to explore the beauty of data through effective problem-solving.
• to enhance the mathematics, probability, and statistics skills for data analytics and machine learning professionals and equip them for the interviews.
• to let the undergraduate, masters, and Ph.D. students to taste a flavor of out of the box statistics using the same knowledge they learned in their colleges.
• to build a community and team of authentic and serious data lovers, who plan to change the world through their data-driven minds.
• to raise awareness of the importance of core statistics, probability, and mathematics in the rising field of Data Science, ML, and AI.

## Exam Date and Time

The Exam will be live on 15th November 2020 and end on 30th November.

You can give the exam and enjoy the problems at your own time.

## Registration Time and Fee

The Registration will be over by 10th November 2020.

The Registration Fee is Rs 101 for undergraduate students.

The Registration Fee is Rs 241 for masters, Ph.D. students, and data analytics, and ML professionals.

## Syllabus

The syllabus is the undergraduate statistics syllabus of a statistics course at an Indian University/College.

#### Mathematics

• High School Mathematics (10+2 Level)
• One Variable Calculus
• Multiple Variable Calculus
• Linear Algebra

#### Probability

###### (Reference: Mathematical Statistics and Data Analysis by John.A.Rice Chapters 1- 6)
• Probability Space
• Conditional Probability, Independence, Bayes Theorem
• Random Variables, Moments, MGF, Characteristic Function
• Distribution Function, Density
• Discrete, Continuous, and Mixed Random Variables
• Various Probability Distributions and their relationships
• Joint, Marginal and Conditional Distributions
• Functions of Joint Distributions
• Order Statistics and Sampling Distributions
• Limit Theorems

#### Statistics

###### (Reference: Mathematical Statistics and Data Analysis by John.A.Rice Chapters 7 – 14)
• Parametric Estimation Theory*
• Basic Non-Parametric Estimation Theory
• Testing of Hypothesis*
• Simple and Multiple Linear Regression*
• Analysis of Variance*
• Basic Categorical Data Analysis
• Basic Bayesian Inference

* = important

#### Programming Skills

Skill in any mathematical/statistical computational software is a plus. You must take the help of your coding skills to quickly compute stuff.

## Competition Pattern

You have to solve a total of 18 multiple choice and numerical problems in 2 hours.

• Mathematics (3 problems)
• Probability Theory (6 problems)
• Theoretical Statistics (6 problems)
• Applied Statistics (3 problems)

You can take the help of any book or resources or person during the competition.

## Exciting Cash Prizes and Discussion Session

#### 1. Undergraduate Students (current position)

1st Cash Prize: Rs 1000

2nd Cash Prize: Rs 400

3rd Cash Prize: Rs 200

#### 2. Masters, Ph.D. students, and Data Analytics Professionals (current position)

1st Cash Prize: Rs 1200

2nd Cash Prize: Rs 600

3rd Cash Prize: Rs 400

Terms and Conditions Apply* (read at the bottom of the page)

## Demo Competition

Go to Mahalanobis National Statistics Competition.

You will find a Demo Competition over there.

Click on it and enjoy the demo problems.

## Register now

Terms and Conditions Apply*

During prize collection, if you cannot share the proper proof of your college id card or office id card with your name in the application, we will be moving on to the next deserving candidate for the prize.

This is to stop the insurgence of various intelligent scam applicants.

Example: Suppose, you are not an undergraduate and you decide to enroll in the undergraduate exam and you become first in the undergraduate category. We will ask for proof that you are an undergraduate. If you are an undergraduate passout, you belong to the masters’ group. If you cannot provide the proof, we will give the cash prize to the next candidate.

Categories

## Carpet Strategy in Geometry | Watch and Learn

Here is a video solution for a Problem based on Carpet Strategy in Geometry. This problem is helpful for Math Olympiad, ISI & CMI Entrance, and other math contests. Watch and Learn!

Here goes the question…

Suppose ABCD is a square and X is a point on BC such that AX and DX are joined to form a triangle AXD. Similarly, there is a point Y on AB such that DY and CY are joined to form the triangle DYC. Compare the area of the triangles to the area of the square.

We will recommend you to try the problem yourself.

Done?

Let’s see the solution in the video below:

Categories

## Bijection Principle Problem | ISI Entrance TOMATO Obj 22

Here is a video solution for a Problem based on Bijection Principle. This is an Objective question 22 from TOMATO for ISI Entrance. Watch and Learn!

Here goes the question…

Given that: x+y+z=10, where x, y and z are natural numbers. How many such solutions are possible for this equation?

We will recommend you to try the problem yourself.

Done?

Let’s see the solution in the video below:

Categories

## What is the Area of Quadrilateral? | AMC 12 2018 | Problem 13

Here is a video solution for a Problem based on finding the area of a quadrilateral. This question is from American Mathematics Competition, AMC 12, 2018. Watch and Learn!

Here goes the question…

Connect the centroids of the four triangles in a square. Can you find the area of the quadrilateral?

We will recommend you to try the problem yourself.

Done?

Let’s see the solution in the video below:

Categories

## Solving Weird Equations using Inequality | TOMATO Problem 78

Here is a video solution for ISI Entrance Number Theory Problems based on solving weird equations using Inequality. Watch and Learn!

Here goes the question…

Solve: 2 \cos ^{2}\left(x^{3}+x\right)=2^{x}+2^{-x}

We will recommend you to try the problem yourself.

Done?

Let’s see the proof in the video below:

Categories

## AM-GM Inequality Problem | ISI Entrance

Here is a video solution for ISI Entrance Number Theory Problems based on AM-GM Inequality Problem. Watch and Learn!

Here goes the question…

a, b, c, d are positive real numbers. Prove that: (1+a)(1+b)(1+c)(1+d) <= 16.

We will recommend you to try the problem yourself.

Done?

Let’s see the proof in the video below: