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Author: Kazi Abu Rousan Where are the zeros of zeta of s? G.F.B. Riemann has made a good guess; They're all on the critical line, saith he, And their density's one over 2 p log t. Source https://www.physicsforums.com/threads/a-poem-on-the-zeta-function.16280/ If you are a person who loves to read maths related stuff then sure you have came […]

Problem If $\sum_{n=1}^{\infty} \frac{1}{n^2} =\frac{{\pi}^2}{6}$ then $\sum_{n=1}^{\infty} \frac{1}{(2n-1)^2}$ is equal to (A) $\frac{{\pi}^2}{24}$ (B) $\frac{{\pi}^2}{8}$ (C) $\frac{{\pi}^2}{6}$ (D) $\frac{{\pi}^2}{3}$ Hint Try to write the summation as sum of square of reciprocal of odd numbers and even numbers and take the advantage of the infinite sum Solution $\sum_{n=1}^{\infty} \frac{1}{n^2} =\frac{{\pi}^2}{6}$ $\Rightarrow \sum_{n=1}^{\infty} \frac{1}{(2n)^2} + \sum_{n=1}^{\infty} \frac{1}{(2n-1)^2}= […]

Probability theory is nothing but common sense reduced to calculation. Pierre-Simon Laplace Today we will be discussing a problem from the second chapter of A First Course in Probability(Eighth Edition) by Sheldon Ross. Let's see what the problem says: Describing the Problem The problem(prob-48) says: Given 20 people, what is the probability that among the […]

PROBLEM Let $p$ be an odd prime.Then the number of positive integers less than $2p$ and relatively prime to $2p$ is: (A)$p-2$ (B) $\frac{p+1}{2} $(C) $p-1$(D)$p+1$ SOLUTION This is a number theoretic problem .We can solve this problem in 2 different methods. Let us see them both one by one Method -1 Let us look […]

There should be no such thing as boring mathematics. Edsger W. Dijkstra In one of our previous post, we have discussed on Mandelbrot Set. That set is one of the most beautiful piece of art and mystery. At the end of that post, I have said that we can calculate the value of $\pi $ […]

Author: Kazi Abu Rousan The pure mathematician, like the musician, is a free creator of his world of ordered beauty. Bertrand Russell Today we will be discussing one of the most fascinating idea of number theory, which is very simple to understand but very complex to get into. Today we will see how to find […]

Problem Let $f$:$\mathbb{R} \rightarrow \mathbb{R}$ be a continous function such that for all$x \in \mathbb{R}$ and all $t\geq 0$ f(x)=f(ktx) where $k>1$ is a fixed constant Hint Case-1 choose any 2 arbitary nos $x,y$ using the functional relationship prove that $f(x)=f(y)$ Case-2 when $x,y$ are of opposite signs then show that $$f(x)=f(\frac{x}{2})=f(\frac{x}{4})\dots$$ use continuity to […]

PROBLEM Let $f (0,\infty)\rightarrow \mathbb{R}$ be a continous function such that for all $x \in (0,\infty)$ $f(x)=f(3x)$ Define $g(x)= \int_{x}^{3x} \frac{f(t)}{t}dt$ for $x \in (0,\infty)$ is a constant function HINT Use leibniz rule for differentiation under integral sign SOLUTION using leibniz rule for differentiation under integral sign we get $g'(x)=f(3x)-f(x)$ $\Rightarrow g'(x)=0$ [ Because f(3x)=f(x)] […]

PROBLEM Show that there are exactly $2$ numbers $a$ in the set $\{1,2,3\dots9400\}$ such that $a^2-a$ is divisible by $10000$ HINT Use Modular arithmetic and concepts of coprime numbers SOLUTION we know $10000=2^4*5^4$ In order for $10000$ to divide $a^2-a$ both $2^4$ and $5^4$ must divide $ a^2-a $ Write $a^2-a=a(a-1)$ Note that $a$ and […]

Author: Kazi Abu Rousan $\pi$ is not just a collection of random digits. $\pi$ is a journey; an experience; unless you try to see the natural poetry that exists in $\pi$, you will find it very difficult to learn. Today we will see a python code to find the value of $\pi $ up to […]

Author: Kazi Abu Rousan Pi is not merely the ubiquitous factor in high school geometry problems; it is stitched across the whole tapestry of mathematics, not just geometry’s little corner of it. $\pi$ is truly one of the most fascinating things exist in mathematics. It's not just there in geometry, but it's also there in pendulum, […]

To some extent the beauty of number theory seems to be related to the contradiction between the simplicity of the integers and the complicated structure of the primes, their building blocks. This has always attracted people. A. Knauf from "Number theory, dynamical systems and statistical mechanics"  This quote is indeed true. If you just think about the […]

Try this beautiful problem from the Pre-RMO, 2019 based on Smallest Positive Integer. You may use sequential hints to solve the problem.

Author: Kazi Abu Rousan Here there is $\pi$, there is circle. Today's blog will be a bit different. This will not discuss any formula or any proof, rather it will just contain a python program to compare a $\pi$ formula given by Leibniz and a one discovered by me (blush). How does Leibniz formula looks […]

Author: Kazi Abu Rousan Bottomless wonders spring from simple rules, which are repeated without end. Benoit Mandelbrot Today, we will be discussing the idea for making a simple Mandelbrot Set using python's Matplotlib. This blog will not show you some crazy color scheme or such. But rather the most simple thing you can make from […]

Try this beautiful problem from the Pre-RMO, 2019 based on Smallest Positive Integer. You may use sequential hints to solve the problem.

Author: Kazi Abu Rousan Mathematics is not yet ready for such problems. Paul Erdos Introduction A problem in maths which is too tempting and seems very easy but is actually a hidden demon is this Collatz Conjecture. This problems seems so easy that it you will be tempted, but remember it is infamous for eating […]

What is Mathcounts? MATHCOUNTS is a national middle school mathematics contest held in different places in the U.S. states and territories. It is established in 1983, which provides engaging mathematics programs to the US middle school students of different ability levels to grow their confidence and improve the attitudes about mathematics and problem solving. Who are the […]

reading a book written by a true master is like learning from him or her directly. It is an outstanding opportunity that none of us should miss. Here are some of those walks with the masters, that has transformed my life and the way I do mathematics. You may use this list of beautiful mathematics books to stay inspired.

What is AMC 12? American Mathematics Contest 12 (AMC 12) is the 2nd stage of the Math Olympiad Contest in the US after AMC 8 and AMC 10. The contest is in multiple-choice format and aims to develop problem-solving abilities. The difficulty of the problems dynamically varies and is based on important mathematical principles. These […]

9 Cheenta students ranked with top 100 in India and qualified for ISI and CMI Entrance. How did they achieve this? More importantly how Cheenta can help them next?

What is AMC 10? American Mathematics Contest 10 (AMC 10) is the 2nd stage of the Math Olympiad Contest in the US after AMC 8. The contest is in multiple-choice format and aims to develop problem-solving abilities. The difficulty of the problems dynamically varies and is based on important mathematical principles. These contests have lasting […]

Try this beautiful problem from the Pre-RMO, 2019 based on Smallest Positive Integer. You may use sequential hints to solve the problem.

Try this beautiful problem from the Pre-RMO, 2019 based on Smallest Positive Integer. You may use sequential hints to solve the problem.

About IIT JAM Mathematics IIT JAM Mathematics (MA) is considered one of the most sought-after master’s level competitive exams after BSc./B.Tech. Students can get direct admission into IITs and into IISC (upon clearing the interview). The IISER’s also take IIT JAM rank into account so all in all, it is a pretty important entrance if […]

About KVPY 2021 The Kishore Vaigyanik Protsahan Yojana 2021 is a National Program of Fellowship on Basic Sciences, conducted and funded by the Department of Science and Technology, Government of India. This fellowship aims to assist the students in realizing their potential at the national level and to make sure that the best scientific talent […]

Bernoulli Random Variable Story A trial is performed with probability $p$ of "success", and $X$ counts the number of successes: 1 means success (one success), 0 means failure (zero success). Definition $$X= \begin{cases}1 & \text {with probability } p \\ 0 & \text {with probability } 1-p \end{cases}$$ Example (Indicator Random Variable): Indicator Random Variable […]

This post contains the ISI M.Math 2021 Subjective Questions. It is a valuable resource for Practice if you are preparing for ISI M.Math. You can find some solutions here and try out others while discussing them in the comments below. ISI M.Math 2021 Problem 1: Let $M$ be a real $n \times n$ matrix with […]

Join the Cheenta Research Seminar on decoding Indus Vally Civilisation Inscriptions. The speaker's break through research articles are published in the prestigious Nature Group Journals.

Problem 1:  The domain of definition of $f(x)=-\log \left(x^{2}-2 x-3\right)$ is (a) $(0, \infty)$(b) $(-\infty,-1)$(c) $(-\infty,-1) \cup(3, \infty)$(d) $(-\infty,-3) \cup(1, \infty)$ Problem 2: $A B C$ is a right-angled triangle with the right angle at B. If $A B=7$ and $B C=24$, then the length of the perpendicular from $B$ to $A C$ is (a) […]

If you are preparing for Mathematics Olympiads, ISI-CMI Entrances or challenging College level entrances then this article is for you. We will describe the no short-cut approach of Cheenta Programs and how you can use them.

Let's discuss a problem from CMI Entrance Exam 2019 Problem that helps us to learn how to solve complex inequality problems using Geometry. The Problem: Count the number of roots $w$ of the equation $z^{2019} − 1 = 0$ over complex numbers that satisfy $|w + 1| ≥ 2 + √2$. The Solution: Some useful […]

Author: Kazi Abu Rousan Mathematics is the science of patterns, and nature exploits just about every pattern that there is. Ian Stewart Introduction If you are a math enthusiastic, then you must have seen many mysterious patterns of Prime numbers. They are really great but today, we will explore beautiful patterns of a special type […]

In this post, you will find ISI B.Stat B.Math 2021 Objective Paper with Problems and Solutions. This is a work in progress, so the solutions and discussions will be uploaded soon. You may share your solutions in the comments below. [Work in Progress] Problem 1 The number of ways one can express $2^{2} 3^{3} 5^{5} […]

In this post, you will find ISI B.Stat B.Math 2021 Subjective Paper with Problems and Solutions. This is a work in progress, so the solutions and discussions will be uploaded soon. You may share your solutions in the comments below. [Work in Progress] Problem 1: There are three cities each of which has exactly the […]

Let's discuss a problem from CMI Entrance Exam 2019 based on the Inscribed Angle Theorem or Central Angle Theorem and Transformation Geometry. The Problem: Let $A B C D$ be a parallelogram. Let 'O' be a point in its interior such that $\angle A D B+\angle D O C=180^{\circ}$. Show that $\angle O D C=\angle […]

Problems and Solutions of ISI MStat Entrance 2020 of Indian Statistical Institute.

In this post, we will be learning about the Rational Root Theorem Proof. It is a great tool from Algebra and is useful for the Math Olympiad Exams and ISI and CMI Entrance Exams. So, here is the starting point.... $a_{n} x^{n}+a_{n-1} x^{n-1}+\ldots+a_{2} x^{2}+a_{1} x+a_{0}$ This polynomial has certain properties. 1. The coefficients are all […]

This is a solution to a problem from American Mathematics Competition (AMC) 8 2020 Problem 18 based on Geometry. AMC 8 2018 Problem 24 In the cube $ABCDEFGH$ with opposite vertices $C$ and $E,$ $J$ and $I$ are the midpoints of edges $\overline{FB}$ and $\overline{HD},$ respectively. Let $R$ be the ratio of the area of […]

This is a solution to a problem from American Mathematics Competition (AMC) 8 2020 Problem 18 based on Geometry. AMC 8 2020 Problem 18 Rectangle $A B C D$ is inscribed in a semicircle with diameter $\overline{F E}$ as shown in the figure. Let $D A=16$, and let $F D=A E=9 .$ What is the […]

Mann Shah is a Gold Awardee in HKIMO (Hong Kong International Mathematical Olympiad), AIMO (Asia International Mathematical Olympiad), and SASMO (Singapore and Asian Schools Math Olympiad) 2021. He is a student of Class 7 and also a proud Young Achiever of Cheenta. Cheenta is happy to share the success story of Mann! Mann says, "I […]

Aryabhata is considered the "Father of Mathematics" in India. He is the first ancient Mathematician- Astronomer, whose important work includes "Aryabhatiya" and "Arya-Siddhanta". Today, let's learn 3 lessons from Aryabhata - the 𝗙𝗮𝘁𝗵𝗲𝗿 𝗼𝗳 𝗠𝗮𝘁𝗵𝗲m𝗮𝘁𝗶𝗰𝘀. 𝟭. 𝗛𝗮𝘃𝗲 𝗖𝗼𝘂𝗿𝗮𝗴𝗲 𝘁𝗼 𝗤𝘂𝗲𝘀𝘁𝗶𝗼𝗻 When eclipses were seen as something to be feared, and the concepts of "Rahu" and […]

An interesting problem based on complex numbers and their inversion. This is a Subjective Problem 89 from the Test of Mathematics Book, highly recommended for the ISI and CMI Entrance Exams. Let's check out the problem and solutions in two episodes: Useful Resources Previous Year Problems for ISI and CMI How to use invariance in […]

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This post discusses the solutions of Problems from RMO 1994 Question Paper. You may find to solution to some of these. RMO 1994 Problem 1: A leaf is torn from a paperback novel. The sum of the numbers on the remaining pages is 15000. What are the page numbers on the torn leaf. RMO 1994 Problem2: […]

This is the solution to the real analysis from ISI MStat 2020 PSB Problem 8 with designed food for thoughts on hypothesis testing and probability theory.

This is a really interesting problem in the probability theory, which enhances the intuition of independent events, conditional probability and exhaustive events.

Aaditya Dharmen Punatar is a Gold Awardee in NMTC (National Mathematics Talent Contests) and SASMO (Singapore and Asian Schools Math Olmpiad) 2021. He is a student of Class 7 from Euroschool, Airoli and also a proud Young Achiever of Cheenta. Cheenta is happy to share the succes story of Aaditya! Aaditya says, "I love solving […]

This is the solution to the real analysis from IIT JAM MS 2020 Section A Problem 1 with designed food for thoughts.

From the path of falling in love with data and chance. to an examination ISI MStat program is different and unique. We discuss that how ISI MStat program is something more than an exam. We will also discuss how to prepare for the exam.

We have compiled all the Pdfs of the previous year's question papers and sample papers. This is a great resource for your ISI MStat Entrance Exam Preparation. ISI MStat 2020 Question Paper Pdf ISI MStat 2019 Question Paper Pdf ISI MStat 2018 Question Paper Pdf ISI MStat 2017 Question Paper Pdf ISI MStat 2016 Question […]

Arjun Gupta is an INMO Awardee and IMOTC candidate. This puts him in the top 35 students in India. Learn from this young achiever - How to Prepare for the Indian National Math Olympiad (INMO)? Cheenta is extremely proud to present this young achiever in Mathematics in our Young Achiever Seminar! The Young Achiever's Seminar […]

This is the list of answer key for ISI MStat PSA Portion. Enjoy.

Understand The Thousand Flowers Program is designed to provoke interest and curiosity in mathematics. It is particularly useful for children of age group 6 to 10 years, when they are starting out with the subject. The program wants to inspire interest and disregard intimidation. It uses a hands-on approach that freely draws from modern computational […]

How to Prepare for EGMO? Learn from the Achiever - Ananya Rajas Ranade (Silver Medal). Ananya Rajas Ranade, Silver Medalist in EGMO (European Girls Mathematics Olympiad) 2021 and a proud student of Cheenta, will be sharing with you all, how she prepared for the EGMO 2021 and how you can do it too. She will […]

Multivariate Limits and Interated Limits confuse students. This article is a detailed way to understand the relationship between the two, with a quick 30 minutes tutorial.

8 - week subscription to Cheenta Advanced Math Program for North America. Includes: One on One Class Group Class Access to Cheenta Genius App Optional Problem Solving Sessions

MLE is an important algorithm to find an estimate. Method of Moments is too. But they are often same. When are they same? What is so common between them? Let's explore.

This problem is an application of the smoothng property of expectation and variance and compares the mse of two sample survey schemes inlcuding SRSWR and SRSWOR. Let's enjoy this problem 9 of ISI MStat 2020.

Try these AMC 8 Algebra Questions and check your knowledge! AMC 8,2020 Problem 1 Luka is making lemonade to sell at a school fundraiser. His recipe requires $4$ times as much water as sugar and twice as much sugar as lemon juice. He uses $3$ cups of lemon juice. How many cups of water does […]

Math Kangaroo Competition is an International Mathematical Competition for kids of graded 1 to 12. It is also known as : "International Mathematical Kangaroo" or "Kangourou sans frontières" in French. This competition focus on the logical ability of the kids rather than their grip on learning Math formulas. Some Interesting Facts on Math Kangaroo: In […]

MLE is an important algorithm to find an estimate. Sufficiency is a good small sample property. So, how are they related? Is MLE always a function of sufficient statistic? Let's explore.

This problem is an application of the multinomial distribution, sufficiency and beautiful application of probabilistic algebraic argument. Let's enjoy this problem 6 of ISI MStat 2020.

Your Math-Mail from Cheenta Dear students,  Let the world engage in rat race. We will focus on deep and beautiful learning.  Here is a beautiful problem that we worked on this week. Suppose there are 5 points spread in 1 by 1 square field. The points can be at the corners, on the edges or […]

A beautiful geometry problem from INMO 2021 (problem 5). Learn how to use angle chasing to find center of a circle.

From the path of falling in love with data and chance. to an examination ISI MStat program is different and unique. We discuss that how ISI MStat program is something more than an exam. We will also discuss how to prepare for the exam.

Are you preparing for ISI MStat Entrance Exams? Here is the list of useful books for ISI MStat Entrance Exam based on the syllabus.

Are you ready for IIT JAM MS 2022? Check it out with a Free Diagnostic Test prepared by Cheenta Statistics & Analytics Department! Other Useful Resources for You

Let us learn about Stirling Numbers of First Kind. Watch video and try the problems related to Math Olympiad Combinatorics

Suppose $r\geq 2$ is an integer, and let $m_{1},n_{1},m_{2},n_{2} \cdots ,m_{r},n_{r}$ be $2r$ integers such that$$|m_{i}n_{j}−m_{j}n_{i}|=1$$for any two integers $i$ and $j$ satisfying $1\leq i <j <r$. Determine the maximum possible value of $r$. Solution: Let us consider the case for $r =2$. Then $|m_{1}n_{2} - m_{2}n_{1}| =1$.......(1) Let us take $m_{1} =1, n_{2} =1, m_{2} =0, n_{1} =0$. Then, clearly the condition holds for $r =2$. […]

This is a work in progress. Please come back soon for more updates. We are adding problems, solutions and discussions on INMO (Indian National Math Olympiad 2021) INMO 2021, Problem 1 Suppose $r \geq 2$ is an integer, and let $m_{1}, n_{1}, m_{2}, n_{2}, \cdots, m_{r}, n_{r}$ be $2 r$ integers such that $$|m_{i} n_{j}-m_{j} […]

Suppose we have a triangle $ABC$. Let us extend the sides $BA$ and $BC$. We will draw the incircle of this triangle. How to draw the incircle? Here is the construction. Draw any two angle bisectors, say of angle $A$ and angle $B$ Mark the intersection point $I$. Drop a perpendicular line from I to […]

This year Cheenta Statistics Department has done a survey on the scores in each of the sections along with the total score in IIT JAM MS. Here is the secret for you! We have normalized the score to understand in terms of percentage. There are three questions, we ask The general performance for the IIT […]

Here are the problems and their corresponding solutions from B.Math Hons Objective Admission Test 2008. Problem 1 : Let $a, b$ and $c$ be fixed positive real numbers. Let $u_{n}=\frac{n^{2} a}{b+n^{2} c}$ for $n \geq 1$. Then as $n$ increases, (A) $u_{n}$ increases;(B) $u_{n}$ decreases;(C) $u_{n}$ increases first and then decreases;(D) none of the above […]

Here are the problems and their corresponding solutions from B.Math Hons Objective Admission Test 2007. Problem 1 : The number of ways of going up $7$ steps if we take one or two steps at a time is (A) $19$ ;(B) $20$;(C) $21$ ;(D) $22$ . Problem 2 : Consider the surface defined by $x^{2}+2 […]

Here, you will find all the questions of ISI Entrance Paper 2011 from Indian Statistical Institute's B. Math Entrance. You will also get the solutions soon of all the previous year problems. Problem 1 : Let $a \geq 0$ be a constant such that $\sin (\sqrt{x+a})=\sin (\sqrt{x})$ for all $x \geq 0 .$ What can […]

Here, you will find all the questions of ISI Entrance Paper 2010 from Indian Statistical Institute's B. Math Entrance. You will also get the solutions soon of all the previous year problems. Problem 1: Prove that in each year, the $13$ th day of some month occurs on a Friday. Problem 2: In the accompanying […]

Here, you will find all the questions of ISI Entrance Paper 2009 from Indian Statistical Institute's B. Math Entrance. You will also get the solutions soon of all the previous year problems. Problem 1: Let $x, y, z$ be non-zero real numbers. Suppose $\alpha, \beta, \gamma$ are complex numbers such that $|\alpha|=|\beta|=|\gamma|=1 .$ If $x+y+z=0=\alpha […]

Here, you will find all the questions of ISI Entrance Paper 2008 from Indian Statistical Institute's B. Math Entrance. You will also get the solutions soon of all the previous year problems. Problem 1 : Let $f: \mathbb{R} \rightarrow \mathbb{R}$ be a continuous function. Suppose $$f(x)=\frac{1}{t} \int_{0}^{t}(f(x+y)-f(y)) d y$$ for all $x \in \mathbb{R}$ and […]

This post discusses the solutions to the problems from IIT JAM Mathematical Statistics (MS) 2021 Question Paper - Set C. You can find solutions in video or written form. Note: This post is getting updated. Stay tuned for solutions, videos, and more. IIT JAM Mathematical Statistics (MS) 2021 Problems & Solutions (Set C) Problem 1 […]

In 2021, Cheenta is proud to introduce 5-days-a-week problem solving sessions for Math Olympiad and ISI Entrance.

This post discusses the solutions to the problems from IIT JAM Mathematical Statistics (MS) 2021 Question Paper - Set A. You can find solutions in video or written form. Note: This post is getting updated. Stay tuned for solutions, videos, and more. IIT JAM Mathematical Statistics (MS) 2021 Problems & Solutions (Set A) Problem 1 […]

This post discusses the solutions to the problems from IIT JAM Mathematical Statistics (MS) 2021 Question Paper - Set B. You can find solutions in video or written form. Note: This post is getting updated. Stay tuned for solutions, videos, and more. IIT JAM Mathematical Statistics (MS) 2021 Problems & Solutions (Set B) Problem 1 […]

Here, you will find all the questions of ISI Entrance Paper 2014 from Indian Statistical Institute's B.Stat Entrance. You will also get the solutions soon of all the previous year problems. Problem 1: The system of inequalities$$a-b^{2} \geq \frac{1}{4}, b-c^{2} \geq \frac{1}{4}, c-d^{2} \geq \frac{1}{4}, d-a^{2} \geq \frac{1}{4} \quad \text { has }$$(A) no solutions(B) […]

Here, you will find all the questions of ISI Entrance Paper 2013 from Indian Statistical Institute's B.Stat Entrance. You will also get the solutions soon of all the previous year problems. Problem 1: Let $i=\sqrt{-1}$ and $S=\{i+i^{2}+\cdots+i^{n}: n \geq 1\} .$ The number of distinct real numbers in the set $S$ is (A) 1(B) 2(C) […]

Complex numbers and geometry are very closely related. We consider a problem from I.S.I. Entrance that uses this geometric character complex numbers.

Try a beautiful problem from complex numbers and geometry. It is from I.S.I. Entrance. We have created sequential hints to make this mathematical journey enjoyable!

This is a Test of Mathematics Solution Subjective 188 (from ISI Entrance). The book, Test of Mathematics at 10+2 Level is Published by East West Press. This problem book is indispensable for the preparation of I.S.I. B.Stat and B.Math Entrance. Problem Consider the squares of an $ 8 X 8 $ chessboard filled with the […]

This is a Test of Mathematics Solution Subjective 181 (from ISI Entrance). The book, Test of Mathematics at 10+2 Level is Published by East West Press. This problem book is indispensable for the preparation of I.S.I. B.Stat and B.Math Entrance. Also visit: I.S.I. & C.M.I. Entrance Course of Cheenta Problem Suppose that one moves along […]

This is a Test of Mathematics Solution Subjective 177 (from ISI Entrance). The book, Test of Mathematics at 10+2 Level is Published by East West Press. This problem book is indispensable for the preparation of I.S.I. B.Stat and B.Math Entrance. Also visit: I.S.I. & C.M.I. Entrance Course of Cheenta Problem  There are 1000 doors $ […]

This is a Test of Mathematics Solution Subjective 176 (from ISI Entrance). The book, Test of Mathematics at 10+2 Level is Published by East West Press. This problem book is indispensable for the preparation of I.S.I. B.Stat and B.Math Entrance. Also visit: I.S.I. & C.M.I. Entrance Course of Cheenta Problem Suppose that P(x) is a […]

This is a Test of Mathematics Solution Subjective 175 (from ISI Entrance). The book, Test of Mathematics at 10+2 Level is Published by East West Press. This problem book is indispensable for the preparation of I.S.I. B.Stat and B.Math Entrance. Also visit: I.S.I. & C.M.I. Entrance Course of Cheenta Problem  Let \(\text{P(x)}=x^n+a_{n-1}x^{n-1}+a_{n-2}x^{n-2}+\dots+a_{1}x+a_{0}\) be a polynomial […]

This is a Test of Mathematics Solution Subjective 170 (from ISI Entrance). The book, Test of Mathematics at 10+2 Level is Published by East West Press. This problem book is indispensable for the preparation of I.S.I. B.Stat and B.Math Entrance. Also visit: I.S.I. & C.M.I. Entrance Course of Cheenta Problem Let \({C_n}\) be an infinite […]

This is a Test of Mathematics Solution Subjective 166 (from ISI Entrance). The book, Test of Mathematics at 10+2 Level is Published by East West Press. This problem book is indispensable for the preparation of I.S.I. B.Stat and B.Math Entrance. Also visit: I.S.I. & C.M.I. Entrance Course of Cheenta Problem A cow is grazing with […]

This is a Test of Mathematics Solution Subjective 157 (from ISI Entrance). The book, Test of Mathematics at 10+2 Level is Published by East West Press. This problem book is indispensable for the preparation of I.S.I. B.Stat and B.Math Entrance. Also visit: I.S.I. & C.M.I. Entrance Course of Cheenta Problem Evaluate $ \mathbf {\displaystyle \lim_{n […]

This is a Test of Mathematics Solution Subjective 155 (from ISI Entrance). The book, Test of Mathematics at 10+2 Level is Published by East West Press. This problem book is indispensable for the preparation of I.S.I. B.Stat and B.Math Entrance. Also visit: I.S.I. & C.M.I. Entrance Course of Cheenta Problem   Evaluate: $ \lim_{n\to\infty} (\frac{1}{n+1}+\frac{1}{n+2}+\frac{1}{n+3}+...+\frac{1}{n+n})$ […]

This is a Test of Mathematics Solution Subjective 150 (from ISI Entrance). The book, Test of Mathematics at 10+2 Level is Published by East West Press. This problem book is indispensable for the preparation of I.S.I. B.Stat and B.Math Entrance. Also visit: I.S.I. & C.M.I. Entrance Course of Cheenta Problem Find the maximum among $ […]

This is a Test of Mathematics Solution Subjective 144 (from ISI Entrance). The book, Test of Mathematics at 10+2 Level is Published by East West Press. This problem book is indispensable for the preparation of I.S.I. B.Stat and B.Math Entrance. Also visit: I.S.I. & C.M.I. Entrance Course of Cheenta   Problem Suppose $ f(x)$ is […]

This is a Test of Mathematics Solution Subjective 127 (from ISI Entrance). The book, Test of Mathematics at 10+2 Level is Published by East West Press. This problem book is indispensable for the preparation of I.S.I. B.Stat and B.Math Entrance. Problem Find all (x, y) such that sin x + sin y = sin (x+y) […]

This is a Test of Mathematics Solution Subjective 126 (from ISI Entrance). The book, Test of Mathematics at 10+2 Level is Published by East West Press. This problem book is indispensable for the preparation of I.S.I. B.Stat and B.Math Entrance. Problem  Sketch, on plain paper, the regions represented, on the plane by the following: (i) […]

This is a Test of Mathematics Solution Subjective 125  (from ISI Entrance). The book, Test of Mathematics at 10+2 Level is Published by East West Press. This problem book is indispensable for the preparation of I.S.I. B.Stat and B.Math Entrance. Problem  Let $ f: \mathcal{N} to \mathcal{N} $ be the function defined by f(0) = […]

This is a Test of Mathematics Solution Subjective 124 (from ISI Entrance). The book, Test of Mathematics at 10+2 Level is Published by East West Press. This problem book is indispensable for the preparation of I.S.I. B.Stat and B.Math Entrance. Problem  Sketch on plain paper, the graph of $ y = \frac {x^2 + 1} […]

This is a subjective problem from TOMATO based on Graphing integer value function. Problem: Graphing integer value function Let [x] denote the largest integer (positive, negative or zero) less than or equal to x. Let $y= f(x) = [x] + \sqrt{x - [x]} ,s=2 $ be defined for all real numbers x. (i) Sketch on […]

This is a Test of Mathematics Solution Subjective 116 (from ISI Entrance). The book, Test of Mathematics at 10+2 Level is Published by East West Press. This problem book is indispensable for the preparation of I.S.I. B.Stat and B.Math Entrance. Problem If A, B, C are the angles of a triangle, then show that $ […]

This is a Test of Mathematics Solution Subjective 115 (from ISI Entrance). The book, Test of Mathematics at 10+2 Level is Published by East West Press. This problem book is indispensable for the preparation of I.S.I. B.Stat and B.Math Entrance. Problem If $\displaystyle { \frac{\sin^4 x }{a} + \frac{\cos^4 x }{b} = \frac{1}{a+b} }$ , […]

This is a Test of Mathematics Solution Subjective 113 (from ISI Entrance). The book, Test of Mathematics at 10+2 Level is Published by East West Press. This problem book is indispensable for the preparation of I.S.I. B.Stat and B.Math Entrance. Problem: Find the vertices of the two right angles triangles, each having area 18 and […]

This is a Test of Mathematics Solution Subjective 110 (from ISI Entrance). The book, Test of Mathematics at 10+2 Level is Published by East West Press. This problem book is indispensable for the preparation of I.S.I. B.Stat and B.Math Entrance. Also visit: I.S.I. & C.M.I. Entrance Course of Cheenta Problem: : Let ABCD be a […]

This is a Test of Mathematics Solution Subjective 107 (from ISI Entrance). The book, Test of Mathematics at 10+2 Level is Published by East West Press. This problem book is indispensable for the preparation of I.S.I. B.Stat and B.Math Entrance. Also visit: I.S.I. & C.M.I. Entrance Course of Cheenta Problem: If a, b and c […]

This is a Test of Mathematics Solution Subjective 90 (from ISI Entrance). The book, Test of Mathematics at 10+2 Level is Published by East West Press. This problem book is indispensable for the preparation of I.S.I. B.Stat and B.Math Entrance. Also visit: I.S.I. & C.M.I. Entrance Course of Cheenta Problem: : Draw the region of […]

This is a Test of Mathematics Solution Subjective 88 (from ISI Entrance). The book, Test of Mathematics at 10+2 Level is Published by East West Press. This problem book is indispensable for the preparation of I.S.I. B.Stat and B.Math Entrance. Also visit: I.S.I. & C.M.I. Entrance Course of Cheenta Problem: A pair of complex numbers […]

This is a Test of Mathematics Solution Subjective 84 (from ISI Entrance). The book, Test of Mathematics at 10+2 Level is Published by East West Press. This problem book is indispensable for the preparation of I.S.I. B.Stat and B.Math Entrance. Problem Show that there is exactly one value of \(x\) that satisfies the equation: \(2 […]

This is a Test of Mathematics Solution Subjective 83 (from ISI Entrance). The book, Test of Mathematics at 10+2 Level is Published by East West Press. This problem book is indispensable for the preparation of I.S.I. B.Stat and B.Math Entrance. Problem If a and b are positive real numbers such that a + b = […]

This is a Test of Mathematics Solution Subjective 82 (from ISI Entrance). The book, Test of Mathematics at 10+2 Level is Published by East West Press. This problem book is indispensable for the preparation of I.S.I. B.Stat and B.Math Entrance. Also visit: I.S.I. & C.M.I. Entrance Course of Cheenta Problem Let a, b, c, d […]

This is a Test of Mathematics Solution Subjective 81 (from ISI Entrance). The book, Test of Mathematics at 10+2 Level is Published by East West Press. This problem book is indispensable for the preparation of I.S.I. B.Stat and B.Math Entrance. Also visit: I.S.I. & C.M.I. Entrance Course of Cheenta Problem Find all possible real numbers […]

This is a Test of Mathematics Solution Subjective 79 (from ISI Entrance). The book, Test of Mathematics at 10+2 Level is Published by East West Press. This problem book is indispensable for the preparation of I.S.I. B.Stat and B.Math Entrance. Also visit: I.S.I. & C.M.I. Entrance Course of Cheenta Problem Let $ {{\theta}_1}$, $ {{\theta}_2}$, […]

This is a Test of Mathematics Solution Subjective 78 (from ISI Entrance). The book, Test of Mathematics at 10+2 Level is Published by East West Press. This problem book is indispensable for the preparation of I.S.I. B.Stat and B.Math Entrance. Also visit: I.S.I. & C.M.I. Entrance Course of Cheenta Problem For real numbers $ {x}$, […]

This is a Test of Mathematics Solution Subjective 77 (from ISI Entrance). The book, Test of Mathematics at 10+2 Level is Published by East West Press. This problem book is indispensable for the preparation of I.S.I. B.Stat and B.Math Entrance. Problem For $ {x > 0}$, show that $ {\displaystyle{\frac{x^n - 1}{x - 1}}{\ge}{n{x^{\frac{n - […]

This is a Test of Mathematics Solution Subjective 76 (from ISI Entrance). The book, Test of Mathematics at 10+2 Level is Published by East West Press. This problem book is indispensable for the preparation of I.S.I. B.Stat and B.Math Entrance. Problem Find the set of all values of $ {m}$ such that $ {\displaystyle {y} […]

This is a Test of Mathematics Solution Subjective 75 (from ISI Entrance). The book, Test of Mathematics at 10+2 Level is Published by East West Press. This problem book is indispensable for the preparation of I.S.I. B.Stat and B.Math Entrance. Also visit: I.S.I. & C.M.I. Entrance Course of Cheenta Problem Show that there is at […]

This is a Test of Mathematics Solution Subjective 74 (from ISI Entrance). The book, Test of Mathematics at 10+2 Level is Published by East West Press. This problem book is indispensable for the preparation of I.S.I. B.Stat and B.Math Entrance. Also visit: I.S.I. & C.M.I. Entrance Course of Cheenta Problem The sum of squares of […]

This is a Test of Mathematics Solution Subjective 73 (from ISI Entrance). The book, Test of Mathematics at 10+2 Level is Published by East West Press. This problem book is indispensable for the preparation of I.S.I. B.Stat and B.Math Entrance. Also visit: I.S.I. & C.M.I. Entrance Course of Cheenta Problem Consider the equation $ {x^3 […]

This is a Test of Mathematics Solution Subjective 72 (from ISI Entrance). The book, Test of Mathematics at 10+2 Level is Published by East West Press. This problem book is indispensable for the preparation of I.S.I. B.Stat and B.Math Entrance. Also visit: I.S.I. & C.M.I. Entrance Course of Cheenta Problem If $ {\displaystyle{\alpha}, {\beta}, {\gamma}} […]

This is a Test of Mathematics Solution Subjective 71 (from ISI Entrance). The book, Test of Mathematics at 10+2 Level is Published by East West Press. This problem book is indispensable for the preparation of I.S.I. B.Stat and B.Math Entrance. Also visit: I.S.I. & C.M.I. Entrance Course of Cheenta Problem Consider the following simultaneous equations […]

This is a Test of Mathematics Solution Subjective 58 (from ISI Entrance). The book, Test of Mathematics at 10+2 Level is Published by East West Press. This problem book is indispensable for the preparation of I.S.I. B.Stat and B.Math Entrance. Also visit: I.S.I. & C.M.I. Entrance Course of Cheenta Problem In a certain game, 30 […]

This is a Test of Mathematics Solution Subjective 57 (from ISI Entrance). The book, Test of Mathematics at 10+2 Level is Published by East West Press. This problem book is indispensable for the preparation of I.S.I. B.Stat and B.Math Entrance. Also visit: I.S.I. & C.M.I. Entrance Course of Cheenta Problem How many 6-letter words can […]

This is a Test of Mathematics Solution Subjective 70 (from ISI Entrance). The book, Test of Mathematics at 10+2 Level is Published by East West Press. This problem book is indispensable for the preparation of I.S.I. B.Stat and B.Math Entrance. Also visit: I.S.I. & C.M.I. Entrance Course of Cheenta Problem Suppose that all roots of […]

This is a Test of Mathematics Solution Subjective 69 (from ISI Entrance). The book, Test of Mathematics at 10+2 Level is Published by East West Press. This problem book is indispensable for the preparation of I.S.I. B.Stat and B.Math Entrance. Also visit: I.S.I. & C.M.I. Entrance Course of Cheenta Problem Suppose that the three equations […]

This is a Test of Mathematics Solution Subjective 67 (from ISI Entrance). The book, Test of Mathematics at 10+2 Level is Published by East West Press. This problem book is indispensable for the preparation of I.S.I. B.Stat and B.Math Entrance. Also visit: I.S.I. & C.M.I. Entrance Course of Cheenta Problem Describe the set of all […]

This is a Test of Mathematics Solution Subjective 66 (from ISI Entrance). The book, Test of Mathematics at 10+2 Level is Published by East West Press. This problem book is indispensable for the preparation of I.S.I. B.Stat and B.Math Entrance. Also visit: I.S.I. & C.M.I. Entrance Course of Cheenta Problem If c is a real […]

This is a Test of Mathematics Solution Subjective 65 (from ISI Entrance). The book, Test of Mathematics at 10+2 Level is Published by East West Press. This problem book is indispensable for the preparation of I.S.I. B.Stat and B.Math Entrance. Problem Show that for all real x, the expression $ {ax^2} $ + bx + […]

This is a Test of Mathematics Solution Subjective 64 (from ISI Entrance). The book, Test of Mathematics at 10+2 Level is Published by East-West Press. This problem book is indispensable for the preparation of I.S.I. B.Stat and B.Math Entrance. Also visit: I.S.I. & C.M.I. Entrance Course of Cheenta Problem If f(x) is a real-valued function […]

This is a Test of Mathematics Solution Subjective 63 (from ISI Entrance). The book, Test of Mathematics at 10+2 Level is Published by East West Press. This problem book is indispensable for the preparation of I.S.I. B.Stat and B.Math Entrance. Also visit: I.S.I. & C.M.I. Entrance Course of Cheenta Problem If any one pair among […]

This is a Test of Mathematics Solution Subjective 62 (from ISI Entrance). The book, Test of Mathematics at 10+2 Level is Published by East West Press. This problem book is indispensable for the preparation of I.S.I. B.Stat and B.Math Entrance. Also visit: I.S.I. & C.M.I. Entrance Course of Cheenta Problem Consider the system of equations […]

This is a Test of Mathematics Solution Subjective 61 (from ISI Entrance). The book, Test of Mathematics at 10+2 Level is Published by East West Press. This problem book is indispensable for the preparation of I.S.I. B.Stat and B.Math Entrance. Also visit: I.S.I. & C.M.I. Entrance Course of Cheenta Problem Solve $ {{6x}^{2}} $ - […]

This is a Test of Mathematics Solution Subjective 60 (from ISI Entrance). The book, Test of Mathematics at 10+2 Level is Published by East West Press. This problem book is indispensable for the preparation of I.S.I. B.Stat and B.Math Entrance. Also visit: I.S.I. & C.M.I. Entrance Course of Cheenta Problem Consider the set S of […]

This is a Test of Mathematics Solution Subjective 59 (from ISI Entrance). The book, Test of Mathematics at 10+2 Level is Published by East West Press. This problem book is indispensable for the preparation of I.S.I. B.Stat and B.Math Entrance. Also visit: I.S.I. & C.M.I. Entrance Course of Cheenta Problem Consider the set of point […]

This is a Test of Mathematics Solution Subjective 116 (from ISI Entrance). The book, Test of Mathematics at 10+2 Level is Published by East West Press. This problem book is indispensable for the preparation of I.S.I. B.Stat and B.Math Entrance. Problem If A, B, C are the angles of a triangle, then show that $ […]

This is a Test of Mathematics Solution Subjective 55 (from ISI Entrance). The book, Test of Mathematics at 10+2 Level is Published by East West Press. This problem book is indispensable for the preparation of I.S.I. B.Stat and B.Math Entrance. Also visit: I.S.I. & C.M.I. Entrance Course of Cheenta Problem For a finite set A, […]

This is a Test of Mathematics Solution Subjective 50 (from ISI Entrance). The book, Test of Mathematics at 10+2 Level is Published by East West Press. This problem book is indispensable for the preparation of I.S.I. B.Stat and B.Math Entrance. Also visit: I.S.I. & C.M.I. Entrance Course of Cheenta Problem All the permutation of the […]

This is a Test of Mathematics Solution Subjective 49 (from ISI Entrance). The book, Test of Mathematics at 10+2 Level is Published by East West Press. This problem book is indispensable for the preparation of I.S.I. B.Stat and B.Math Entrance. Also visit: I.S.I. & C.M.I. Entrance Course of Cheenta Problem: \(x\) red balls, \(y\) black balls,\(z\) […]

This is a Test of Mathematics Solution Subjective 48 (from ISI Entrance). The book, Test of Mathematics at 10+2 Level is Published by East West Press. This problem book is indispensable for the preparation of I.S.I. B.Stat and B.Math Entrance. Also visit: I.S.I. & C.M.I. Entrance Course of Cheenta Problem Find the different number of […]

This is a Test of Mathematics Solution Subjective 43 (from ISI Entrance). The book, Test of Mathematics at 10+2 Level is Published by East West Press. This problem book is indispensable for the preparation of I.S.I. B.Stat and B.Math Entrance. Also visit: I.S.I. & C.M.I. Entrance Course of Cheenta Problem Show that the equation $ […]

Test of Mathematics Solution Subjective 38 (from ISI Entrance). The book, Test of Mathematics at 10+2 Level is Published by East West Press. This problem book is indispensable for the preparation of I.S.I. B.Stat and B.Math Entrance. Also see: Cheenta I.S.I. & C.M.I. Entrance Course Problem Show that if a prime number p is divided […]

Test of Mathematics Solution Subjective 37 (from ISI Entrance). The book, Test of Mathematics at 10+2 Level is Published by East West Press. This problem book is indispensable for the preparation of I.S.I. B.Stat and B.Math Entrance. Also see: Cheenta I.S.I. & C.M.I. Entrance Course Problem Supposed p is a prime Number such that (p-1)/4 […]

Test of Mathematics Solution Subjective 36 (from ISI Entrance). The book, Test of Mathematics at 10+2 Level is Published by East West Press. This problem book is indispensable for the preparation of I.S.I. B.Stat and B.Math Entrance. Also see: Cheenta I.S.I. & C.M.I. Entrance Course Problem Let $ a_1 , a_2 , ... , a_n […]

Test of Mathematics Solution Subjective 33 (from ISI Entrance). The book, Test of Mathematics at 10+2 Level is Published by East West Press. This problem book is indispensable for the preparation of I.S.I. B.Stat and B.Math Entrance. Also see: Cheenta I.S.I. & C.M.I. Entrance Course Problem Let \(k\) be a fixed odd positive integer. Find […]

Test of Mathematics Solution Subjective 32 (from ISI Entrance). The book, Test of Mathematics at 10+2 Level is Published by East West Press. This problem book is indispensable for the preparation of I.S.I. B.Stat and B.Math Entrance. Also see: Cheenta I.S.I. & C.M.I. Entrance Course Problem Show that the number 11...1 with $ 3^n $ […]

This is a Test of Mathematics Solution (from ISI Entrance). The book, Test of Mathematics at 10+2 Level is Published by East West Press. This problem book is indispensable for the preparation of I.S.I. B.Stat and B.Math Entrance. Also see: Cheenta I.S.I. & C.M.I. Entrance Course   Problem If the coefficients of a quadratic equation […]

This is a Test of Mathematics Solution Subjective 56 (from ISI Entrance). The book, Test of Mathematics at 10+2 Level is Published by East West Press. This problem book is indispensable for the preparation of I.S.I. B.Stat and B.Math Entrance. Also visit: I.S.I. & C.M.I. Entrance Course of Cheenta Problem  Show that the number of […]

This is a Test of Mathematics Solution of Subjective 42 (from ISI Entrance). The book, Test of Mathematics at 10+2 Level is Published by East West Press. This problem book is indispensable for the preparation of I.S.I. B.Stat and B.Math Entrance. Also Visit: I.S.I & CMI Entrance Course of Cheenta Problem Let f(x) be a […]

Here, you will find all the questions of ISI Entrance Paper 2011 from Indian Statistical Institute's B.Stat Entrance. You will also get the solutions soon of all the previous year problems. Group A Problem 1: The limit $$\lim _{x \rightarrow 0} \frac{1-\cos \left(\sin ^{2} \alpha x\right)}{x}$$ (A) equals $1$;(B) equals $\alpha$;(C) equals $0$ ;(D) does […]

Here, you will find all the questions of ISI Entrance Paper 2010 from Indian Statistical Institute's B.Stat Entrance. You will also get the solutions soon of all the previous year problems. Problem 1: There are 8 balls numbered $1,2, \ldots, 8$ and 8 boxes numbered $1,2, \ldots, 8$. The number of ways one can put […]

Here, you will find all the questions of ISI Entrance Paper 2015 from Indian Statistical Institute's B.Stat Entrance. You will also get the solutions soon of all the previous year problems. Problem 1: Let $\mathbb{C}$ denote the set of complex numbers and $S=\{z \in \mathbb{C} \mid \bar{z}=z^{2}\},$ where $\bar{z}$ denotes the complex conjugate of $z […]

This is a Test of Mathematics Solution Subjective 46 (from ISI Entrance). The book, Test of Mathematics at 10+2 Level is Published by East West Press. This problem book is indispensable for the preparation of I.S.I. B.Stat and B.Math Entrance. Also visit: I.S.I. & C.M.I. Entrance Course of Cheenta Problem A function \(f\) from set \(A\) into set […]

Here, you will find all the questions of ISI Entrance Paper 2016 from Indian Statistical Institute's B.Stat Entrance. You will also get the solutions soon of all the previous year problems. Problem 1: The largest integer $n$ for which $n+5$ divides $n^{5}+5$ is(A) 3115(B) 3120(C) 3125(D) 3130 . Problem 2: Let $p, q$ be primes […]

Here, you will find all the questions of ISI Entrance Paper 2009 from Indian Statistical Institute's B.Stat Entrance. You will also get the solutions soon of all the previous year problems. Group A Problem 1: If $k$ times the sum of the first $n$ natural numbers is equal to the sum of the squares of […]

Here, you will find all the questions of ISI Entrance Paper 2007 from Indian Statistical Institute's B.Stat Entrance. You will also get the solutions soon of all the previous year problems. Problem 1: Let $C$ be the circle $x^{2}+y^{2}+4 x+6 y+9=0$. The point $(-1,-2)$ is(A) inside $C$ but not the centre of $C$;(B) outside $C$;(C) […]

Here, you will find all the questions of ISI Entrance Paper 2007 from Indian Statistical Institute's B.Stat Entrance. You will also get the solutions soon of all the previous year problems. Problem 1: Let $x$ be an irrational number. If $a, b, c$ and $d$ are rational numbers such that $\frac{a x+b}{cx+d}$ is a rational […]

This post contains problems from Indian National Mathematics Olympiad, INMO 2015. Try them and share your solution in the comments. INMO 2015, Problem 1 Let $A B C$ be a right-angled triangle with $\angle B=90^{\circ} .$ Let $B D$ be the altitude from $B$ on to $A C .$ Let $P, Q$ and $I$ be […]

This post will provide you all the PRMO (Pre-Regional Mathematics Olympiad) 2012 Set A problems and solutions. You may find some solutions with hints too. There are 20 questions in the question paper and question carries 5 marks. Time Duration: 2 hours PRMO 2012 Set A, Problem 1: Rama was asked by her teacher to […]

This post will provide you all the PRMO (Pre-Regional Mathematics Olympiad) 2013 Set A problems and solutions. You may find some solutions with hints too. There are 20 questions in the question paper and question carries 5 marks. Time Duration: 2 hours PRMO 2013 Set A, Problem 1: What is the smallest positive integer $k$ […]

This post will provide you all the PRMO (Pre-Regional Mathematics Olympiad) 2015 Set B problems and solutions. You may find some solutions with hints too. PRMO 2015 Set B, Problem 1: A man walks a certain distance and rides back in $3 \frac{3}{4}$ hours; he could ride both ways in $2 \frac{1}{2}$ hours. How many […]

This post will provide you all the PRMO (Pre-Regional Mathematics Olympiad) 2014 problems and solutions. You may find some solutions with hints too. PRMO 2014, Problem 1: A natural number $k$ is such that $k^{2}<2014<(k+1)^{2}$. What is the largest prime factor of $k ?$ PRMO 2014, Problem 2: The first term of a sequence is […]

This post is getting updated. Stay tuned for solutions, videos and more. IOQM 2021 - Problem 1 Let $ABCD$ be a trapezium in which $AB \parallel CD$ and $AB=3CD$. Let $E$ be the midpoint of the diagonal $BD$. If $[ABCD]= n \times [CDE] $, what is the value of $n$ ? (Here $[\Gamma]$ denotes the […]

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: These […]

“The Pigeonhole principle” ~ Students who have never heard may think that it is a joke. The 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 Discrete Mathematics, the pigeonhole principle states that if we must put N + […]

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 […]

What is National Mathematics Talent Contest ? The National Mathematics Talent Contest or NMTC is a national-level mathematics contest conducted by the Association of Mathematics Teachers of India (AMTI). Aim of the contest: To find and encourage students who have the ability for original and creative thinking, preparedness to tackle unknown and non-routine problems having a general mathematical ability […]

Bose Olympiad Senior is suitable for kids in Grade 8 and above. There are two levels of this olympiad: Prelims Mains Curriculum Number Theory Combinatorics Algebra Polynomials Complex Numbers Inequality Geometry Number Theory The following topics in number theory are useful for the Senior round: Bezout’s Theorem and Euclidean Algorithm Theory of congruence Number Theoretic […]

Bose Olympiad Intermediate is suitable for kids in Grade 5, 6, and 7. There are three stages of this olympiad: Research Project Round Individual Round Team Round Curriculum Elementary Number Theory Counting Principles Algebra Geometry Number Theory The following topics in number theory are useful for the Intermediate round: Primes and Composites Arithmetic of Remainders […]

Bose Olympiad Junior is suitable for kids in Grade 1, 2, 3 and 4. There are two levels of this Olympiad: Prelims Mains Curriculum Arithmetic Geometry Mathematical Puzzles Arithmetic Basic skills of addition, subtraction and multiplication and division will be sufficient for attending arithmetic problems. Fundamental ideas about place-value system and ratios could be useful […]

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 […]

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 […]

Dear parent, One of the key contributions of modern mathematics is its tryst with infinity. As parents and teachers we can initiate thought provoking communication with our children using infinity. Consider the following set: N = {1, 2, 3, … } Notice that N contains infinitely many elements. Take a subset of N that consists […]

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 […]

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 this beautiful Problem on Trigonometry from PRMO -2018.You may use sequential hints to solve the problem.

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 […]

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: Some Useful Links: How to Construct Rational Numbers? […]

Parity in Mathematics is a term which we use to express if a given integer is even or odd. It basically depends on the remainder when we divide a number by 2. Parity can be divided into two categories - 1. Even Parity 2. Odd Parity Even Parity : If we divide any number by 2 […]

Try this Integer Problem from Number theory from PRMO 2018, Question 16 You may use sequential hints to solve the problem.

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: Some […]

Try this beautiful Problem on Trigonometry from PRMO -2018.You may use sequential hints to solve the problem.

Here is a video solution for ISI Entrance Number Theory Problems based on Sum of 8 fourth powers. Watch and Learn! Can you show that the sum of 8 fourth powers of integers never adds up to 1993? How can you solve this fourth-degree diophantine equation? Let's see in the video below: Some Useful Links: […]

Try this beautiful Problem on Trigonometry from PRMO -2018.You may use sequential hints to solve the problem.

Try this good numbers Problem from Number theory from PRMO 2018, Question 22 You may use sequential hints to solve the problem.

Try this Integer Problem from Number theory from PRMO 2018, Question 30 You may use sequential hints to solve the problem.

Try this Integer Problem from Number theory from PRMO 2018, Question 19 You may use sequential hints to solve the problem.

Try this beautiful Problem on Combinatorics from PRMO -2018.You may use sequential hints to solve the problem.

Try this beautiful Problem on Trigonometry from PRMO -2018.You may use sequential hints to solve the problem.

Try this beautiful Problem on geometry based on circle from AMC 10A, 2018. Problem-15. You may use sequential hints to solve the problem.

Try this beautiful Problem on Probability from AMC 10A, 2014. Problem-17, You may use sequential hints to solve the problem.

Try this beautiful Problem on Co-ordinate geometry from AMC 10A, 2018. Problem-21, You may use sequential hints to solve the problem.

Try this beautiful Problem on Algebra from AMC 10A, 2018. Problem-14, You may use sequential hints to solve the problem.

Try this beautiful Problem on triangle from AMC 10A, 2018. Problem-16. You may use sequential hints to solve the problem.

Try this beautiful Problem on triangle from AMC 10A, 2018. Problem-13. You may use sequential hints to solve the problem.

Try this beautiful Problem on Combinatorics from PRMO -2018.You may use sequential hints to solve the problem.

Try this beautiful Problem on triangle from AMC 10A, 2018. Problem-23. You may use sequential hints to solve the problem.

Try this beautiful Problem on Geometry on Circle from AMC 10B, 2016. Problem-20. You may use sequential hints to solve the problem.

Try this beautiful Problem on Probability from AMC 10A, 2017. Problem-18, You may use sequential hints to solve the problem.

Try this beautiful Problem on Geometry on Rectangle from AMC 10A, 2010. Problem-19. You may use sequential hints to solve the problem.

Problems and Solutions of ISI MStat Entrance 2020 of Indian Statistical Institute.

Try this beautiful Problem on Geometry on cube from AMC 10A, 2010. Problem-20. You may use sequential hints to solve the problem.

Problems and Solutions of ISI BStat and BMath Entrance 2020 of Indian Statistical Institute.

Try this beautiful Problem on Geometry from AMC 10A, 2019.Problem-13. You may use sequential hints to solve the problem.

Try this beautiful Problem on Geometry from PRMO -2018.You may use sequential hints to solve the problem.

Try this beautiful Problem on Algebra from AMC 10A, 2019. Problem-15, You may use sequential hints to solve the problem.

Try this beautiful Problem on Algebra from AMC 10A, 2019. Problem-24, You may use sequential hints to solve the problem.

This is a problem from the ISI MStat Entrance Examination,2016 making us realize the beautiful connection between exponential and geometric distribution and a smooth application of Central Limit Theorem.

Try this beautiful Problem on Algebra from AMC 10A, 2015. Problem-15. You may use sequential hints to solve the problem.

IOQM 2021-2022 Announcement by HBCSE Day and Date: Sunday, January 9, 2022 Venue: Designated IOQM Centres Type of exam: Three hour paper and pen exam with responses to be written on OMR sheet. The IOQM will have 30 questions with each question having an integer answer in the range 00-99. The syllabus and standard of this […]

Try this beautiful Problem on Rectangle and triangle from AMC 10A, 2015. Problem-24. You may use sequential hints to solve the problem.

This is a very simple and regular sample problem from ISI MStat PSB 2009 Problem 8. It It is based on testing the nature of the mean of Exponential distribution. Give it a Try it !

Try this beautiful Problem on Rectangle and triangle from AMC 10A, 2014. Problem-23. You may use sequential hints to solve the problem.

How can you roll a dice by tossing a coin? Can you use your probability knowledge? Use your conditioning skills.

Try this beautiful Problem on Probability from AMC 10A, 2010. Problem-23. You may use sequential hints to solve the problem.

Try this beautiful Problem on Number theory based on Triangle and Circle from AMC 10A, 2010. Problem-22. You may use sequential hints to solve the problem.

Try this beautiful Problem on Triangle and Circle from AMC 10A, 2017. Problem-22. You may use sequential hints to solve the problem.

Listen to a frequentist's carping over Bayesian school of thinking!

The International Youth Mathematics Challenge, IYMC is a large scale competition reaching across borders to compete nationally and internationally. This competition enables students from all countries to prove their mathematical skills and creativity to win awards, cash prizes, and global recognition. Eligibility Criteria To participate in the International Youth Mathematics Challenge, IYMC a participant needs […]

In this post we will be discussing mainly about, naive Bayes Theorem, and how Laplace, developed the same idea as Bayes, independently and his law of succession goes.

Try this beautiful Problem based on Interior Point of a Triangle from PRMO -2017, Problem-24. You may use sequential hints to solve the problem.

Try this beautiful Problem on Side of a Quadrilateral from AMC 10A, 2009. Problem-12. You may use sequential hints to solve the problem.

Try this beautiful Problem based on Linear Equations, Algebra AMC 10A, 2015, Problem-16. You may use sequential hints to solve the problem.

Try this beautiful Problem on Geometry: quadrilateral from AMC 10A, 2009. Problem-12. You may use sequential hints to solve the problem.

This is a very simple and regular sample problem from ISI MStat PSB 2009 Problem 8. It It is based on testing the nature of the mean of Exponential distribution. Give it a Try it !

This is a very beautiful sample problem from ISI MStat PSB 2009 Problem 4. It is based on the idea of Polar Transformations, but need a good deal of observation o realize that. Give it a Try it !

This is a very beautiful sample problem from ISI MStat PSB 2008 Problem 7 based on finding the distribution of a random variable. Let's give it a try !!

This is a very beautiful sample problem from ISI MStat PSB 2008 Problem 2 based on definite integral as the limit of the Riemann sum . Let's give it a try !!

This is a very beautiful sample problem from ISI MStat PSB 2008 Problem 3 based on Functional equation . Let's give it a try !!

This is a very beautiful sample problem from ISI MStat PSB 2009 Problem 6. It is based on the idea of Restricted Maximum Likelihood Estimators, and Mean Squared Errors. Give it a Try it !

This is a very simple but beautiful sample problem from ISI MStat PSB 2009 Problem 3. It is based on recognizing density function and then using CLT. Try it !

This is a very simple sample problem from ISI MStat PSB 2009 Problem 1. It is based on basic properties of Nilpotent Matrices and Skew-symmetric Matrices. Try it !

This post discusses how judgements can be quantified to probabilities, and how the degree of beliefs can be structured with respect to the available evidences in decoding uncertainty leading towards Bayesian Thinking.

Let's learn how to calculate the geometric mean. This is a concept video useful for Mathematics Olympiad and ISI and CMI Entrance. Watch and Learn: Read and Learn: What is the Geometric mean of two numbers a and b & how to calculate it? Suppose a and b are positive numbers then their geometric mean […]

Try this beautiful Problem on Geometry: Circular arc from AMC 10A, 2012. Problem-18. You may use sequential hints to solve the problem.

This explores the unsung sector of probability : "Nonconglomerability" and its effects on conditional probability. This also emphasizes the idea of how important is the idea countable additivity or extending finite addivity to infinite sets.

Try this beautiful Problem on geometry from AMC 10A, 2012. You may use sequential hints to solve the problem.

This is a very subtle sample problem from ISI MStat PSB 2006 Problem 2. After seeing this problem, one may think of using Lagrange Multipliers, but one can just find easier and beautiful way, if one is really keen to find one. Can you!

This is a very beautiful sample problem from ISI MStat PSB 2007 Problem 6 based on counting principle . Let's give it a try !!

This is a very subtle sample problem from ISI MStat PSB 2005 Problem 3. Given that one knows the property of orthogonal matrices its just a counting problem. Give it a thought!

This is a very beautiful sample problem from ISI MStat PSB 2006 Problem 6 based on counting principle . Let's give it a try !!

This is a very beautiful sample problem from ISI MStat PSB 2006 Problem 5 based on use of binomial distribution . Let's give it a try !!

This is a very beautiful sample problem from ISI MStat PSB 2006 Problem 1 based on Inverse of a matrix. Let's give it a try !!

Try this beautiful Problem from Geometry based on the area of the trapezium from PRMO 2017, Question 30. You may use sequential hints to solve the problem.

This is a very beautiful sample problem from ISI MStat PSB 2007 Problem 2 based on Rank of a matrix. Let's give it a try !!

This is a very beautiful sample problem from ISI MStat PSB 2007 Problem 1 based on Determinant and Eigen values and Eigen vectors . Let's give it a try !!

This is a very beautiful sample problem from ISI MStat PSB 2007 Problem 4 based on use of Newton Leibniz theorem . Let's give it a try !!

This is a very beautiful sample problem from ISI MStat PSB 2007 Problem 3 based on use of L'hospital Rule . Let's give it a try !!

This is a very beautiful sample problem from ISI MStat PSB 2005 Problem 1. It is based on some basic properties of upper triangular matrix and diagonal matrix, only if you use them carefully. Give it a thought!

Try this beautiful problem from Geometry: Problem on Circle and Triangle from AMC-10A (2016) Problem 21. You may use sequential hints to solve the problem.

This post discusses how judgements can be quantified to probabilities, and how the degree of beliefs can be structured with respect to the available evidences in decoding uncertainty leading towards Bayesian Thinking.

Try this beautiful problem from Algebra based on least possible number.AMC-10A, 2019. You may use sequential hints to solve the problem

Try this beautiful problem from the Pre-RMO, 2018 based on the Nearest value. You may use sequential hints to solve the problem.

This post discusses about the history of frequentism and how it was an unperturbed concept till the advent of Bayes. It sheds some light on the trending debate of frequentism vs bayesian thinking.

This is a very simple sample problem from ISI MStat PSB 2014 Problem 4. It is based on order statistics, but generally due to one's ignorance towards order statistics, one misses the subtleties . Be Careful !

This is a very beautiful sample problem from ISI MStat PSB 2009 Problem 2 based on Convergence of a sequence. Let's give it a try !!

This is a very beautiful sample problem from ISI MStat PSB 2012 Problem 6 based on Conditional probability . Let's give it a try !!

This is a very beautiful sample problem from ISI MStat PSB 2013 Problem 3 based on Counting principle . Let's give it a try !!

This is a very beautiful sample problem from ISI MStat PSB 2013 Problem 8 based on finding the distribution of a random variable. Let's give it a try !!

This is a very beautiful sample problem from ISI MStat PSB 2009 Problem 5 based on finding the distribution of a random variable. Let's give it a try !!

This is our 6th post in our ongoing probability series. In this post, we deliberate about the famous Bertrand's Paradox, Buffon's Needle Problem and Geometric Probability through barycentres.

This is our 5th post in the Cheenta Probability Series. This article teaches how to mathematically estimate the length of an earphone wire by it's picture.

This is a very simple sample problem from ISI MStat PSB 2018 Problem 9. It is mainly based on estimation of ordinary least square estimates and Likelihood estimates of regression parameters. Try it!

Try this beautiful problem from the American Invitational Mathematics Examination II, AIME II, 2015 based on Sequence and permutations.

This is our 4th post in the Cheenta Probability Series. This article deals with mainly the physics involved in coin tossing, and based on such problems how it effects the chances of the outcome of coin toss , and how it reveals the true nature of uncertainty !!

This is a very beautiful sample problem from ISI MStat PSB 2004 Problem 7 based on finding the distribution of a random variable. Let's give it a try !!

Try this beautiful problem number 1 from the American Invitational Mathematics Examination, AIME, 2012 based on Numbers of positive integers.

This is a very simple and beautiful sample problem from ISI MStat PSB 2013 Problem 7. It is mainly based on simple hypothesis testing of normal variables where it is just modified with a bernoulli random variable. Try it!

We are really happy with the performance of our students and thus, we have initiated to name the Toppers of the month in Cheenta. The names of the toppers will be updated every month to keep the healthy competition alive in Cheenta. These toppers are named in this leader board according to their performance in […]

Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1999 based on the number of points and planes.

This is a very beautiful sample problem from ISI MStat PSB 2004 Problem 4 based on finding probability using a uniform distribution. Let's give it a try !!

This is a very beautiful sample problem from ISI MStat PSB 2005 Problem 2 based on finding probability using binomial distribution. Let's give it a try !!

This is another blog of the Cheenta Probability Series. Let's give a formal definition of statistical regularity to bring some seriousness into account. **10 min read** “The Law of Statistical Regularity formulated in the mathematical theory of probability lays down that a moderately large number of items chosen at random from a very large group […]

This is a very simple and beautiful sample problem from ISI MStat PSB 2013 Problem 9. It is mainly based on geometric distribution and its expectation . Try it!

Try this beautiful problem number 2 from the American Invitational Mathematics Examination I, AIME I, 2012 based on Arithmetic Sequence Problem.

Try this beautiful Problem on Graph Coordinates from co-ordinate geometry from AMC 10A, 2015. You may use sequential hints to solve the problem.

Try this beautiful problem from the Pre-RMO, 2018 based on Digits of number. You may use sequential hints to solve the problem.

Try this beautiful problem from the Pre-RMO, 2018 based on the Smallest value. You may use sequential hints to solve the problem.

This is a very beautiful sample problem from ISI MStat PSB 2012 Problem 9, It's about restricted MLEs, how restricted MLEs are different from the unrestricted ones, if you miss delicacies you may miss the differences too . Try it! But be careful.

This is a very beautiful sample problem from ISI MStat PSB 2013 Problem 2 based on use of Sandwich Theorem . Let's give it a try !!

This is a very beautiful sample problem from ISI MStat PSB 2014 Problem 2 based on the use and properties of a function. Let's give it a try !!

Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1987 based on Length and Triangle.

This is a very beautiful sample problem from ISI MStat PSB 2012 Problem 3 based on finding the distribution of a random variable . Let's give it a try !!

Try this Integer Problem from Algebra from PRMO 2017, Question 1 You may use sequential hints to solve the problem.

Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1987 based on Algebra and Positive Integer.

Cheenta Statistics Department has been preparing quality mock tests for the passionate students appearing for ISI M.Stat.This post contains the leaderboard for all the ISI MStat Mock Tests to appreciate the achiever's performance in the mock test. Full Mock Test 1 Serial No. Name of the Student Score 1. Pratik Lakhani 108/120 2. Niranjan Dey […]

This is a very elegant sample problem from ISI MStat PSB 2010 Problem 10, based on properties of uniform, and its behavior when modified. Try it!

Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1987 based on Distance and Spheres.

Try this beautiful problem from the American Invitational Mathematics Examination, AIME, 2015 based on Arithmetic Mean. You may use sequential hints.

Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 2012 based on Distance Time. You may use sequential hints.

This is our 2nd post on Cheenta Probability series, where we discuss mainly with two gambling problems, solved collaboratively by two great mathematcians Blaise Pascal and Pierre de Fermat, who ended up defining the idea of fairness of a game.

This blog series is aimed towards Undergraduates in Statistics who want to savour probability theory in a different form altogether. We are pretty curious to collaborate and interact with probability theory enthusiasts. It would be great if they enlighten us with their insights too.

Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 2000 based on Algebra and Combination.

Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 2000 based on Algebraic Equation.

This is a very beautiful sample problem from ISI MStat PSB 2014 Problem 1 based on Vector space and Eigen values and Eigen vectors . Let's give it a try !!

Try this beautiful problem from the American Invitational Mathematics Examination, AIME, 2000 based on Sequence and fraction.

Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 2000 based on Arithmetic and geometric mean with Algebra.

This is a very simple sample problem from ISI MStat PSB 2012 Problem 10. It's a very basic problem but very important and regular problem for statistics students, using one of the most beautiful theorem in Point Estimation. Try it!

Try this beautiful problem from the American Invitational Mathematics Examination, AIME I, 2000 based on Logarithms and Equations.

Try this beautiful problem from the American Invitational Mathematics Examination, AIME I, 1996 based on Finding the smallest positive Integer.

This is a very beautiful sample problem from ISI MStat PSB 2010 Problem 1 based on Matrix multiplication and Eigenvalues and Eigenvectors.

This is a very simple sample problem from ISI MStat PSB 2006 Problem 9. It's based on point estimation and finding consistent estimator and a minimum variance unbiased estimator and recognizing the subtle relation between the two types. Go for it!

Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1996 based on Amplitude and Complex numbers.

Try this beautiful problem from the American Invitational Mathematics Examination, AIME, 1996 based on Roots of Equation and Vieta's formula.

This is a very beautiful sample problem from ISI MStat PSB 2013 Problem 10. It's based mainly on counting and following the norms stated in the problem itself. Be careful while thinking !

Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1992 based on Tetrahedron Problem.

Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1995 based on Triangle and integers.

This is a simple and elegant sample problem from ISI MStat PSB 2005 Problem 5. It's based the mixture of Discrete and Continuous Uniform Distribution, the simplicity in the problem actually fools us, and we miss subtle happenings. Be careful while thinking !

This is a very beautiful sample problem from ISI MStat PSB 2012 Problem 2 based on solving polynomials using calculus . Let's give it a try !!

This is an interesting problem which tests the student's knowledge on how he visualizes the normal distribution in higher dimensions.

Try this problem from Singapore Mathematics Olympiad, SMO, 2018 based on Functional Equation. You may use sequential hints if required.

This is a very beautiful sample problem from ISI MStat PSB 2012 Problem 5 based on the Application of Central Limit Theorem.

Try this beautiful problem from Algebra: Arithmetic sequence from AMC 10A, 2015, Problem. You may use sequential hints to solve the problem.

Try this beautiful problem from the American Invitational Mathematics Examination, AIME, 2000 based on Sequence and the greatest integer.

Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 2011 based on Rectangles and sides.

Try this beautiful problem from Mensuration: Problem based on Cylinder from AMC 10A, 2015. You may use sequential hints to solve the problem.

Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1999 based on Series and sum.

Try this beautiful problem from Algebra, based on the Cubic Equation problem from AMC-10A, 2010. You may use sequential hints to solve the problem.

Try this beautiful problem from Geometry based on Median of numbers from AMC 10A, 2020. You may use sequential hints to solve the problem.

Try this beautiful problem from the American Invitational Mathematics Examination, AIME, 1998, Problem 1, based on LCM and Integers.

This is a very beautiful sample problem from ISI MStat PSB 2007 Problem 7. It's a very simple problem, which very much rely on conditioning and if you don't take it seriously, you will make thing complicated. Fun to think, go for it !!

Try this beautiful Pen & Note Books Problem from Algebra from PRMO 2017, Question 8. You may use sequential hints to solve the problem.

Try this beautiful Rectangle Problem from Geometry from PRMO 2017, Question 13. You may use sequential hints to solve the problem.

Try this beautiful Problem on Fraction from Algebra from AMC 10A, 2015. You may use sequential hints to solve the problem.

Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1993 based on Integers. Use sequential hints if required.

Try this beautiful problem from the American Invitational Mathematics Examination, AIME, 1996, Question 2, based on Greatest Positive Integer.

Are you preparing for ISI MStat Entrance Exams? Here is the list of useful books for ISI MStat Entrance Exam based on the syllabus.

Try this beautiful problem from the PRMO II, 2019, Question 26, based on Distance travelled. You may use sequential hints to solve the problem.

Try this beautiful problem from the PRMO II, 2019 based on the Sum of Digits base 10. You may use sequential hints to solve the problem.

This is a very beautiful sample problem from ISI MStat PSB 2008 Problem 8. It's a very simple problem, based on bivariate normal distribution, which again teaches us that observing the right thing makes a seemingly laborious problem beautiful . Fun to think, go for it !!

Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1992 based on Digits and Rationals.

Try this beautiful Problem from Geometry based on Circle from PRMO 2017, Question 27. You may use sequential hints to solve the problem.

Try this beautiful Problem based on Chords in a Circle, Geometry from PRMO 2017, Question 26. You may use sequential hints to solve the problem.

Try this beautiful problem from Geometry: Side of Square from AMC-10A (2013) Problem 3. You may use sequential hints to solve the problem.

Try this beautiful problem from Algebra based on Counting Days from AMC-10A (2013), Problem 17. You may use sequential hints to solve the problem.

This is a very beautiful sample problem from ISI MStat PSB 2004 Problem 6. It's a very simple problem, and its simplicity is its beauty . Fun to think, go for it !!

This is a very beautiful sample problem from ISI MStat PSB 2004 Problem 1. Games are best ways to understand the the role of chances in life, solving these kind of problems always indulges me to think and think more on the uncertainties associated with the system. Think it over !!

Try this beautiful problem from Combinatorics based on Chosing Program from AMC-10A (2013), Problem 7. You may use sequential hints to solve the problem.

Try this beautiful problem from Algebra, based on Order Pair problem from AMC-10B, 2012. You may use sequential hints to solve the problem

This is a sample problem from ISI MStat PSB 2013 Problem 5 based on the simple random sampling model, finding the unbiased estimates of the population size.

Try this beautiful problem from the Pre-RMO, 2017, Question 23, based on Solving Equation. You may use sequential hints to solve the problem.

Try this beautiful problem from the Pre-RMO, 2017, Question 23, based on Solving Equation. You may use sequential hints to solve the problem.

Try this beautiful problem from the Pre-RMO, 2017, Question 23, based on Solving Equation. You may use sequential hints to solve the problem.

This is a sample problem from ISI MStat PSB 2013 Problem 4. It is based on the simple linear regression model, finding the estimates, and MSEs.

This is ISI MStat PSB 2011 Problem 1, based on patterns in matrices and determinants, and using a special kind of determinant decomposition. Try this out!

Try this beautiful problem from Geometry: The area of triangle AMC-10, 2009. You may use sequential hints to solve the problem

Try this beautiful problem from Geometry: Side Length of Rectangle from AMC-10, 2009. You may use sequential hints to solve the problem

Try this beautiful problem from the Pre-RMO II 2019, based on Missing Integers. You may use sequential hints to solve the problem.

This is a another beautiful sample problem from ISI MStat PSB 2014 Problem 9. It is based on testing simple hypothesis, but reveals and uses a very cute property of Geometric distribution, which I prefer calling sister to Loss of memory . Give it a try !

This is a really beautiful sample problem from ISI MStat PSB 2008 Problem 10. Its based on testing simple, hypothesis. According to, this problem teaches me how observation, makes life simple. Go for it!

Try this beautiful problem from the Pre-RMO, 2017 based on Roots and coefficients of equations. You may use sequential hints to solve the problem.

Try this beautiful problem from the Pre-RMO, 2017 based on Number of ways. You may use sequential hints to solve the problem.

Try this beautiful problem from the Pre-RMO, 2017 based on Number of ways of arrangement. You may use sequential hints to solve the problem.

This is a beautiful sample problem from ISI MStat 2010 PSB Problem 2. This is based how one can find the number of isosceles triangles with sides of integer length one can construct, using simple counting principles . We provide detailed solution with prerequisites mentioned explicitly.

Try this beautiful problem from the Pre-RMO, 2017 based on Real Numbers and Integers. You may use sequential hints to solve the problem.

Try this beautiful problem from the Pre-RMO, 2017 based on Roots of Equation. You may use sequential hints to solve the problem.

Try this beautiful problem from Geometry:Squarefrom AMC-10A (2008) You may use sequential hints to solve the problem.

Try this beautiful problem from Geometry:Squarefrom AMC-10A (2008) You may use sequential hints to solve the problem.

Try this beautiful problem from Geometry: Circle from AMC-10A (2006) You may use sequential hints to solve the problem.

Try this beautiful problem from Geometry: Circle from AMC-10A (2006) You may use sequential hints to solve the problem.

Try this beautiful problem from Geometry based on Centroid. You may use sequential hints to solve the problem

Try this beautiful problem from Geometry - AMC-10 B (2013), Problem-16 based triangle. You may use sequential hints to solve the problem.

Try this beautiful problem from Number system, based on digits problem from AMC-10A, 2007. You may use sequential hints to solve the problem

Try this beautiful problem from algebra, based on Sum of reciprocals in quadratic equation from AMC-10A, 2003. You may use sequential hints.

Try this beautiful problem from the Pre-RMO, 2017 based on Non-Parallel lines. You may use sequential hints to solve the problem.

Try this beautiful problem from the Pre-RMO, 2017, Question 23, based on Solving Equation. You may use sequential hints to solve the problem.

Try this beautiful problem from Geometry: Area of Trapezium from AMC-10A, 2018. You may use sequential hints to solve the problem.

Try this beautiful problem from algebra, based on equation from AMC-10A, 2007. Problem-20,You may use sequential hints to solve the problem

Try this beautiful Problem from Algebra based on Pen & Note Books from PRMO 2019, Question 16. You may use sequential hints to solve the problem.

Try this beautiful problem from algebra, based on the quadratic equation from AMC-10A, 2003. You may use sequential hints to solve the problem.

Try this TOMATO Objective Problem from I.S.I. B.Stat Entrance based on Sum of divisors and Integers. You may use sequential hints to solve the problem.

Open Mock Test Pre Regional Maths Olympiad (PRMO), India.

Try this beautiful problem from Number theory based on sum of digits from PRMO 2016. You may use sequential hints to solve the problem.

Try this TOMATO problem from I.S.I. B.Stat Entrance Objective Problem based on Divisibility and Integers. You may use sequential hints to solve the problem.

This concept of independence, conditional probability and information contained always fascinated me. I have thus shared some thoughts upon this.

Try this beautiful Integer-based Problem from Algebra from PRMO 2018, Question 20. You may use sequential hints to solve the problem.

Try this beautiful problem from Algebra, based on Sum of two digit numbers from PRMO 2016. You may use sequential hints to solve the problem.

Try this beautiful problem from the Pre-Regional Mathematics Olympiad, PRMO, 2014, based on finding side of Triangle. You may use sequential hints.

Try this problem from I.S.I. B.Stat Entrance Objective Problem from TOMATO based on Sets and Probability. You may use sequential hints to solve the problem.

Problem - Number Series ( B.Stat Objective Problem ) We are going to discuss about Number Series from B.Stat Objective Problem . A student studying the weather for d days observed that(i) it rained on 7 days morning or afternoon, (ii) when it rained in the afternoon it was clear in the morning, (iii) there […]

Try this problem from I.S.I. B.Stat Entrance Objective Problem from TOMATO based on Numbers and Group. You may use sequential hints to solve the problem.

Try this TOMATO problem from I.S.I. B.Stat Entrance Objective Problem based on Number of Factors. You may use sequential hints to solve the problem.

Try this TOMATO problem from I.S.I. B.Stat Entrance Objective based on Combinatorics and Integers. You may use sequential hints to solve the problem.

Try this TOMATO problem from I.S.I. B.Stat Entrance Objective Problem based on Number of divisors and Integer. You may use sequential hints.

Try this TOMATO problem from I.S.I. B.Stat Entrance Objective based on Greatest Integer and remainder. You may use sequential hints.

Try this beautiful problem from Geometry: The area of a trapezoid from AMC-8 (2003). You may use sequential hints to solve the problem.

Try this beautiful problem from Prime number from TOMATO useful for ISI BStat Entrance. You may use sequential hints to solve the problem.

Try this beautiful Hundred Integers problem on Number system from TOMATO useful for ISI B.Stat Entrance. You may use sequential hints to solve the problem.

Try this beautiful problem from AMC 8, 2003, problem no-22 based on Largest area. You may use sequential hints to solve the problem.

This is the problem from ISI MStat 2019 PSA Problem 15. First, try it yourself and then go through the sequential hints we provide.

This is a problem from ISI MStat 2019 PSA Problem no. 14. First, try the problem yourself, then go through the sequential hints we provide.

This is a problem from ISI MStat 2015 PSA Problem 17. First, try the problem yourself, then go through the sequential hints we provide.

This is a beautiful problem from ISI MSTAT 2016 PSA problem 9 based on Equation of a circle . We provide sequential hints so that you can try .

This is a beautiful problem from ISI MSTAT 2015 PSA problem 18 based on complex number . We provide sequential hints so that you can try .

This is a beautiful problem from ISI MSTAT 2019 problem 12 based on finding the domain of the function .We provide sequential hints so that you can try .

Try this TOMATO problem from I.S.I. B.Stat Entrance Objective Problem based on Number of points. You may use sequential hints.

Try this TOMATO Objective Problem from I.S.I. B.Stat Entrance based on Number of divisors and Integers. You may use sequential hints to solve the problem.

Try this TOMATO problem from I.S.I. B.Stat Entrance Objective Problem based on Surface area. You may use sequential hints.

Try this beautiful problem from Geometry, based on Cube from AMC-10A, 2007. You may use sequential hints to solve the problem

Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 2012 based on Angles and Triangles.

Try this problem from Geometry: Ratios of the areas of Triangle and Quadrilateral from AMC-10A, 2005 You may use sequential hints to solve the problem.

Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 2012 based on Digits and Numbers.

Try this beautiful problem from Geometry based on Try this beautiful problem from Algebra based on Largest Common Divisor . from PRMO 2014. You may use sequential hints to solve the problem.

Try this beautiful problem from Algebra based on AP GP from AMC-10A, 2004. You may use sequential hints to solve the problem.

Try this beautiful problem from ALGEBRA: Greatest Common Divisor AMC-10A, 2018. You may use sequential hints to solve the problem

Try this beautiful problem from Geometry:Area of Octagon.AMC-10A, 2005. You may use sequential hints to solve the problem

Try this beautiful problem from Prime number from TOMATO useful for ISI B.Stat Entrance.You may use sequential hints to solve the problem.

This is a beautiful problem from ISI MSAT 2019 PSA problem 16 based on Area bounded by the curve .We provide sequential hints so that you can try .

This is a beautiful problem from ISI MSAT 2018 PSA problem 11 based on Sequence . We provide sequential hints so that you can try .

This is a beautiful problem from ISI MSAT 2018 PSA problem 8 based on limit . We provide sequential hints so that you can try .

This is a beautiful problem from ISI MSAT 2018 PSA problem 10 based on Dirichlet Function. We provide sequential hints so that you can try .

This is a beautiful problem from ISI MSAT 2018 PSA problem 7 based on Continuous Funtion. We provide sequential hints so that you can try .

This is a beautiful problem from ISI MSAT 2018 PSA problem 12 based on Sequence of positive numbers. We provide sequential hints so that you can try .

Try this TOMATO problem from I.S.I. B.Stat Entrance Objective Problem based on a derivative of Function. You may use sequential hints to solve the problem.

This is a beautiful problem from ISI MSAT 2018 PSA problem 13 based on basic counting principles . We provide sequential hints so that you can try .

This is a beautiful problem from ISI MStat 2018 PSA problem 13 based on basic probability of functions. We provide sequential hints so that you can try .

Try this problem from ISI MStat 2018 PSA Problem 14 based on all possible colorings. We provide sequential hints to help you solve the problem.

This is a beautiful problem from ISI MSTAT 2019 PSA problem 11 based on basic counting principles . We provide sequential hints so that you can try .

This is a beautiful problem from ISI MSTAT 2019 PSA problem 6 based on basic counting principles . We provide sequential hints so that you can try .

Try this beautiful problem from Geometry based on lengths of the rectangle from AMC-10A, 2009. You may use sequential hints to solve the problem.

Try this beautiful problem from AMC 10A, 2003 based on Probability in Divisibility. You may use sequential hints to solve the problem.

This is a beautiful problem from ISI MSTAT 2019 PSA problem 4 based on basic counting principles . We provide sequential hints so that you can try .

Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1988 based on function. You may use sequential hints.

Try this beautiful problem from the Pre-RMO, 2017, Question 23, based on Solving Equation. You may use sequential hints to solve the problem.

Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1988 based on Fibonacci sequence.

This is a beautiful problem from ISI Mstat 2019 PSA problem 17 based on limit of a function. We provide sequential hints so that you can try this .

This problem is a very easy and cute problem of probability from ISI MStat 2019 PSA Problem 18.

Try this beautiful problem from the Pre-RMO, 2017, Question 23, based on Solving Equation. You may use sequential hints to solve the problem.

Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1988, Question 14, based on Reflection.

This is a beautiful sample problem from ISI MStat 2018 PSB Problem 1. This is based on finding the real solution of a system of homogeneous equations . We provide detailed solution with prerequisites mentioned explicitly.

Try this beautiful Number Theory problem from PRMO, 2019, problem-18, based on Ordered Pairs. You may use sequential hints to solve the problem.

Try this beautiful Geometry problem from PRMO, 2019, problem-23, based on finding the maximum area. You may use sequential hints to solve the problem.

Try this beautiful problem from Geometry based on Rectangle Pattern from AMC-10A, 2016, Problem 10. You may use sequential hints to solve the problem.

Try this beautiful problem from Geometry: Ratio of area of Circles from AMC-10A, 2009, Problem 21. You may use sequential hints to solve the problem.

Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1988, Question 11, based on Complex plane.

Try this I.S.I. B.Stat Entrance Objective Problem from TOMATO based on a derivative of Function. You may use sequential hints to solve the problem.

This is a problem involving BLUE for regression coefficients and MLE of a regression coefficient for a particular case of the regressors.

From the path of falling in love with data and chance. to an examination ISI MStat program is different and unique. We discuss that how ISI MStat program is something more than an exam. We will also discuss how to prepare for the exam.

This is a beautiful problem from ISI MStat 2015 PSB . We provide detailed solution with prerequisite mentioned explicitly .

Try this TOMATO problem from I.S.I. B.Stat Entrance Objective Problem based on a derivative of Function. You may use sequential hints to solve the problem.

Try this beautiful problem based on Probability in game from AMC-10A, 2005. You may use sequential hints to solve the problem.

Try this beautiful problem based on Discontinuity from TOMATO 730 useful for ISI B.Stat Entrance. You may use sequential hints to solve the problem.

Try this beautiful problem from algebra, based on Quadratic equation from AMC-10A, 2005. You may use sequential hints to solve the problem.

Try this beautiful problem from the Pre-RMO, 2019 based on Covex Cyclic Quadrilateral. You may use sequential hints to solve the problem.

Try this beautiful problem from the Pre-RMO, 2017 based on Sides of Quadrilateral. You may use sequential hints to solve the problem.

Try this beautiful problem from PRMO, 2019, problem-19, based on the Ratio of the areas. You may use sequential hints to solve the problem.

Try this beautiful problem from Geometry: Area of the inner square AMC-10A, 2005, Problem-8. You may use sequential hints to solve the problem.

Try this beautiful problem from Geometry: Ratios of the areas of Triangle and Quadrilateral from AMC-10A. You may use sequential hints to solve the problem.

Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1990 based on real numbers. Use sequential hints if required.

Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1990 based on Digits and Integers.

This is a beautiful problem from ISI MStat 2016 PSB (sample) Problem 1 based on area bounded by the curves. We provide a detailed solution with the prerequisites mentioned explicitly.

Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1990 based on Complex numbers and Sets.

Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1990 based on Consecutive Positive Integers.

Try this TOMATO problem from I.S.I. B.Stat Entrance Objective Problem based on a derivative of Function. You may use sequential hints to solve the problem.

Try this beautiful Logarithm Problem From Singapore Mathematics Olympiad, SMO, 2011 (Problem 7). You may use sequential hints to solve the problem.

Try this beautiful problem from the Pre-RMO, 2017 based on Sides of Quadrilateral. You may use sequential hints to solve the problem.

This is a beautiful problem from ISI MStat 2016 PSB (sample) based on Vectorspace . It uses several concepts to solve it . We provide detailed solution with prerequisites mentioned explicitly .

Try this beautiful problem from Geometry based on pentagon and square pattern from AMC-10A, 2001. You may use sequential hints to solve the problem.

Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1990 based on Fair Coin Problem.

Try this beautiful problem based on calculas from TOMATO 728 useful for ISI B.Stat Entrance. You may use sequential hints to solve the problem.

Try this beautiful problem based on Real valued function from TOMATO 690 useful for ISI B.Stat Entrance. You may use sequential hints to solve the problem.

Try this beautiful problem from algebra, based on Sum of the numbers from AMC-10A, 2001. You may use sequential hints to solve the problem.

Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1990 based on combinatorics in Tournament.

This is a beautiful sample problem from ISI MStat 2016 PSB Problem 2.This is based on application of continuity and integration .

Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1990 based on Ordered pair. You may use sequential hints.

Try this beautiful problem from Geometry: circular cylinder from AMC-10A, 2001. You may use sequential hints to solve the problem.

Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1990 based on combinatorics in Tournament.

Try this TOMATO problem from I.S.I. B.Stat Entrance Objective Problem based on derivative of Function. You may use sequential hints to solve the problem.

Try this beautiful problem from Geometry: Area of region from AMC-10A, 2007, Problem-24. You may use sequential hints to solve the problem.

Try this beautiful problem from algebra, based on algebraic equations from AMC-10A, 2001. You may use sequential hints to solve the problem.

This is a beautiful problem from ISI MStat 2017 PSB based on matrices . We provide details solution with the prerequisites mentioned explicilty.

Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1990 based on Head Tail Problem.

Try this beautiful problem based on expansion from TOMATO 102 useful for ISI B.Stat Entrance. You may use sequential hints to solve the problem.

Try this beautiful problem from the Pre-RMO, 2019 based on the Diameter of a circle. You may use sequential hints to solve the problem.

Try this beautiful problem from the Pre-RMO, 2019 based on natural numbers. You may use sequential hints to solve the problem.

Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1990 based on Interior Angle.

Try this TOMATO problem from I.S.I. B.Stat Entrance Objective Problem based on Surface area. You may use sequential hints.

This is a beautiful problem ISI MStat 2016 (sample) PSB based on order statistics . We provide detailed solution with the prerequisites mentioned explicitly.

Try this beautiful problem from algebra, based on Sum of the digits from AMC-10A, 2007. You may use sequential hints to solve the problem

Try this beautiful problem based on Integers and Divisors from TOMATO useful for ISI B.Stat Entrance. You may use sequential hints to solve the problem.

Try this beautiful problem from Geometry:Radius of a circle.AMC-10A, 2003. You may use sequential hints to solve the problem

Try this beautiful problem from Geometry based on medians of triangle from PRMO 2018. You may use sequential hints to solve the problem.

Try this beautiful sum of Co-ordinates based on co-ordinate Geometry from AMC-10A, 2014. You may use sequential hints to solve the problem.

Try this beautiful problem from Geometry based on Hexagon from AMC-10A, 2014. You may use sequential hints to solve the problem

This is a beautiful problem from ISI MStat 2016 (sample ) PSB Problem 1. This is based on finding the minimum value of a function subjected to the restriction .

Try this beautiful problem from the Pre-RMO, 2019 based on the Diameter of a circle. You may use sequential hints to solve the problem.

Try this beautiful problem from Algebra based on positive integers from PRMO 2019. You may use sequential hints to solve the problem.

Try this beautiful problem from Singapore Mathematical Olympiad, SMO, 2010 - Problem 7 based on the combination of equations.

Try this beautiful problem from PRMO, 2019, problem-17, based on Largest Possible Value Problem. You may use sequential hints to solve the problem.

Try this beautiful problem from TOMATO useful for ISI B.Stat Entrance based on Sign change. You may use sequential hints to solve the problem.

Try this beautiful problem from TOMATO useful for ISI B.Stat Entrance based on Calculus. You may use sequential hints to solve the problem.

Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1990 based on combinatorics in Tournament.

Try this TOMATO problem from I.S.I. B.Stat Entrance Objective Problem based on Maximum and Minimum Element. You may use sequential hints.

Try this TOMATO problem from I.S.I. B.Stat Entrance Objective Problem based on function. You may use sequential hints to solve the problem.

Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1990 based on Interior Angle.

Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1990 based on Smallest positive Integer.

Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1990 based on Proper divisors.

Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1990 based on Algebraic value.

Try this beautiful problem from Probability based on dice from AMC-10A, 2011. You may use sequential hints to solve the problem

Try this beautiful problem from Geometry: Area of Region in a Circle from AMC-10A, 2011, Problem -18. You may use sequential hints to solve the problem.

Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1990 based on Positive solution.

Try this beautiful problem from Algebra based smallest positive value from PRMO 2019. You may use sequential hints to solve the problem.

Try this beautiful problem from combinatorics based on Regular Polygon from PRMO 2019. You may use sequential hints to solve the problem.

Try this beautiful problem from the Pre-RMO, 2019 based on Greatest Integer. You may use sequential hints to solve the problem.

Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1996 based on Parallelogram Problem.

Try this beautiful problem from PRMO, 2019, problem-12, based on Integer Problem. You may use sequential hints to solve the problem.

Try this beautiful problem from TOMATO useful for ISI B.Stat Entrance based on Graph in Calculus. You may use sequential hints to solve the problem.

Try this TOMATO problem from I.S.I. B.Stat Entrance Objective Problem based on Set of real numbers. You may use sequential hints.

Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1995 based on Right Rectangular Prism.

This is a problem from ISI MStat 2016 sample paper which tests the student's ability to write a model and then test the equality of parameters in it using appropriate statistics.

Try this beautiful problem from Geometry: Sectors in Circle from AMC-10A, 2012. You may use sequential hints to solve the problem

Try this beautiful problem from Algebra: Sum of whole numbers from AMC-10A, 2012. You may use sequential hints to solve the problem

Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1995 based on Pyramid with Square base.

Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1995 based on Repeatedly Flipping a Fair Coin.

Try this beautiful problem from the Pre-RMO, 2019 based on Sum of digits. You may use sequential hints to solve the problem.

Try this TOMATO problem from I.S.I. B.Stat Entrance Objective Problem based on Number of roots. You may use sequential hints.

Try this beautiful problem from Singapore Mathematics Olympiad, SMO, 2009 based on Trigonometry Simplification. You may use sequential hints.

Try this TOMATO problem from I.S.I. B.Stat Entrance Objective Problem based on Periodic Function. You may use sequential hints.

Try this beautiful problem from the Pre-RMO, 2019 based on Sum of digits. You may use sequential hints to solve the problem.

Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1993 based on Smallest positive Integer.

Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1993 based on Equation of X and Y.

Try this beautiful problem from Geometry: Area of quadrilateral from AMC-10A, 2020. You may use sequential hints to solve the problem.

Try this beautiful problem from Geometry:Tetrahedron box from AMC-10A, 2011. You may use sequential hints to solve the problem

Try this beautiful problem from PRMO, 2018 based on Algebra: Inequality You may use sequential hints to solve the problem.

Try this TOMATO problem from I.S.I. B.Stat Entrance Objective Problem based on Periodic Function. You may use sequential hints.

Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1992 based on Largest Area of Triangle.

Try this beautiful problem from PRMO, 2019, problem-4, based on Geometry: Direction & Angles. You may use sequential hints to solve the problem.

Try this beautiful problem from TOMATO useful for ISI B.Stat Entrance based on Negative & Positive Roots. You may use sequential hints to solve the problem.

Try this beautiful problem from TOMATO useful for ISI B.Stat Entrance based on Calculus. You may use sequential hints to solve the problem.

Try this TOMATO problem from I.S.I. B.Stat Entrance Objective Problem based on Equations and Roots. You may use sequential hints.

Try this beautiful Geometry Problem on Equilateral Triangle from AMC-10A, 2010.You may use sequential hints to solve the problem.

Try this beautiful problem from Geometry:cubical box from AMC-10A, 2010. You may use sequential hints to solve the problem

Try this beautiful problem from TOMATO useful for ISI B.Stat Entrance based on Graphs in Calculus. You may use sequential hints to solve the problem.

Try this beautiful problem from Algebra:Roots of cubic equation from AMC-10A, 2010. You may use sequential hints to solve the problem

This is a problem from ISI MStat Examination 2016. This primarily tests the student's knowledge in finding confidence intervals and using the Central Limit Theorem as an useful approximation tool.

Try this beautiful problem from the Pre-RMO, 2017 based on GP and 2-digit number. You may use sequential hints to solve the problem.

Try this beautiful problem from PRMO, 2018 based on Geometry. You may use sequential hints to solve the problem.

Try this beautiful problem from TOMATO useful for ISI B.Stat Entrance based on Quadratic Equation. You may use sequential hints to solve the problem.

Try this beautiful problem from Geometry: Hexagon from AMC-10A, 2010. You may use sequential hints to solve the problem.

Try this beautiful problem from the Pre-RMO, 2017 based on Altitudes of triangle. You may use sequential hints to solve the problem.

Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1992 based on Digits and Rationals.

Try this beautiful problem from Algebra, based on Sum of digits from AMC-10A, 2020. You may use sequential hints to solve the problem

Try this beautiful problem from Number theory based on Integer from AMC-10A, 2020. You may use sequential hints to solve the problem.

Try this beautiful problem from the Pre-RMO, 2017 based on Average and Integers. You may use sequential hints to solve the problem.

Try this beautiful problem from Singapore Mathematics Olympiad, SMO, 2012 based on Probability. You may use sequential hints to solve the problem.

Try this TOMATO problem from I.S.I. B.Stat Entrance Objective Problem based on Equations and Roots. You may use sequential hints.

Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1992 based on Row of Pascal Triangle.

This is a problem from the ISI MStat 2017 Entrance Examination and tests how good are your skills in modelling a life testing experiment using exponential distribution.

This is a problem from the ISI MStat Entrance Examination,2019 involving the MLE of the population size and investigating its unbiasedness.

This is a problem from ISI MStat 2017 PSB Problem 3, where we use the basics of Bijection principle and Vandermone's identity to solve this problem.

Try this beautiful problem from Pre-Regional Mathematics Olympiad, PRMO, 2017 based on Time & Work. You may use sequential hints to solve the problem.

Try this beautiful problem from TOMATO useful for ISI B.Stat Entrance based on balls. You may use sequential hints to solve the problem.

Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1992 based on Digits and Order.

Try this TOMATO problem from I.S.I. B.Stat Entrance Objective Problem based on Sets and Integers. You may use sequential hints.

Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1992 based on Ratio and Inequalities.

Try this beautiful problem from the Pre-RMO, 2017 based on Geometric Progression. You may use sequential hints to solve the problem.

This problem is an easy application of the basic algorithmic ideas to approach a combinatorics problem using permutation and combination and basic counting principles. Enjoy this problem 3 from ISI MStat 2018 PSB.

Try this beautiful problem from Geometry: Area of Trapezoid from AMC-10A, 2002. You may use sequential hints to solve the problem.

Try this beautiful problem from AMC-10A, 2004 based on ratio of two triangles.You may use sequential hints to solve the problem.

Try this beautiful problem from Algebra on Quadratic equation from AMC-10A, 2002. You may use sequential hints to solve the problem.

Try this TOMATO problem from I.S.I. B.Stat Entrance Objective Problem based on Arbitrary Arrangement. You may use sequential hints.

Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1994 based on Remainders and Functions.

Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1992 based on Rational Numbers.

This problem is a simple application of the sequential definition of continuity from ISI MStat 2015 PSB Problem 1.

This is a problem from ISI MStat Examination,2019. This tests one's familiarity with the simple and multiple linear regression model and estimation of model parameters and is based on the Invariant Regression Coefficient.

This is a problem from the ISI MStat Entrance Examination, 2019. This primarily tests one's familiarity with size, power of a test and whether he/she is able to condition an event properly.

Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1994 based on Points of Equilateral triangle.

Try this beautiful problem from Algebra based on real numbers from PRMO 2017. You may use sequential hints to solve the problem.

Try this beautiful problem from the Pre-RMO, 2017 based on ratio and proportion. You may use sequential hints to solve the problem.

Try this beautiful problem from Number Theory based on largest possible value from AMC-10A, 2004. You may use sequential hints to solve the problem.

Try this beautiful problem from AMC 10A, 2004 based on Mensuration: Cylinder. You may use sequential hints to solve the problem.

Try this beautiful problem from AMC-10A, 2004 based on Triangle. You may use sequential hints to solve the problem.

This problem is an easy application in calculus using the basic ideas of curve sketching. This is the problem 1 from ISI MStat 2019 PSB.

This is a problem from ISI MStat Examination,2018.
It involves construction of a most powerful test of size alpha using Neyman Pearson Lemma. The aim is to find its critical region in terms of quantiles of a standard distribution.

This problem is a cute application of joint distribution and conditional probability. This is the problem 5 from ISI MStat 2018 PSB.

Try this TOMATO problem from I.S.I. B.Stat Entrance Objective Problem based on Binomial Expression. You may use sequential hints to solve the problem.

Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1994 based on Right angled triangle.

Try this TOMATO problem from I.S.I. B.Stat Entrance Objective Problem based on Perfect square and Positive Integer. You may use sequential hints.

Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1994 based on Complex roots and equations.

Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1994 based on Length and Inequalities.

Try this beautiful problem from the Pre-RMO, 2017 based on Trigonometry & natural numbers. You may use sequential hints to solve the problem.

Try this beautiful problem from TOMATO useful for ISI B.Stat Entrance from Integer based on divisibility. You may use sequential hints.

Try this beautiful problem from Probability: positive factors AMC-10A, 2003. You may use sequential hints to solve the problem

Try this beautiful problem from AMC 10A, 2007 based on Numbers on cube. You may use sequential hints to solve the problem.

Try this beautiful problem from TOMATO useful for ISI B.Stat Entrance based on Pairs of Positive Integer. You may use sequential hints.

Try this beautiful problem from TOMATO useful for ISI B.Stat Entrance based on Quadratic equation You may use sequential hints.

This problem is an application of the non negative integer solution and the symmetry argument. This is from ISI MStat 2015 PSB Problem 4.

This problem is a beautiful application of the probability theory and cauchy functional equation. This is from ISI MStat 2019 PSB problem 4.

Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1995 based on GCD and Ordered pair.

Try this problem from ISI MSQMS 2018 which involves the concept of Inequality. You can use the sequential hints provided to solve the problem.

Try this beautiful problem from the Pre-RMO, 2017 based on Integers and Inequality. You may use sequential hints to solve the problem.

Try this beautiful problem from Singapore Mathematics Olympiad, SMO, 2011 based on Permutation. You may use sequential hints to solve the problem.

Try this beautiful problem from AMC-10A, 2009 based on Diamond Pattern. You may use sequential hints to solve the problem.

Try this TOMATO problem from I.S.I. B.Stat Entrance Objective Problem based on Problem on Digits. You may use sequential hints to solve the problem.

Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1999 based on Squares and Triangles.

Try this beautiful problem from the Pre-RMO, 2017 based on Series Problem. You may use sequential hints to solve the problem.

Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1997 based on Trigonometry and greatest integer.

Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1995 based on Trigonometry and positive integers.

This post verifies central limit theorem with the help of simulation in R for distributions of bernoulli, uniform and poisson.

This problem is a beautiful problem connecting linear algebra, geometry and data. Go ahead and dwelve into the glorious connection.

Try this TOMATO problem from I.S.I. B.Stat Entrance Objective Problem based on Arrangement in a Ring. You may use sequential hints to solve the problem.

Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1997 based on Odd and Even integers.

Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1997 based on Two and Three-digit numbers.

Try this beautiful problem from the Pre-RMO, 2017 based on Geometric Progression and Integers. You may use sequential hints to solve the problem.

Try this TOMATO problem from I.S.I. B.Stat Entrance Objective Problem based on number of triangles in a Polygon. You may use sequential hints.

Try this problem from ISI MSQMS 2015 which involves the concept of Integral Inequality and real analysis. You can use the sequential hints provided to solve the problem.

Try this beautiful problem from TOMATO useful for ISI B.Stat Entrance based on Sitting Arrangement. You may use sequential hints.

Try this beautiful problem from Probability in Dice from AMC-10A, 2009. You may use sequential hints to solve the problem.

Try this beautiful problem from Singapore Mathematics Olympiad, SMO, 2008 based on Trigonometry. You may use sequential hints to solve the problem.

Try this problem from the Singapore Mathematics Olympiad, SMO, 2010 based on the application of the Pythagoras Theorem. You may use sequential hints.

This problem is an extension of the bijection princple idea used in counting the number of subsets of a set. This is ISI MStat 2014 Sample Paper PSB Problem 3.

Try this problem from ISI MSQMS 2017 which involves the concept of Inequality. You can use the sequential hints provided to solve the problem.

Try this beautiful problem from Probability based on divisibility from AMC-10A, 2003. You may use sequential hints to solve the problem.

Try this beautiful problem from Pre-Regional Mathematics Olympiad, PRMO, 2018 based on Triangles. You may use sequential hints to solve the problem.

Try this beautiful Problem from Singapore Mathematics Olympiad, 2012 based on Functional Equations. You may use sequential hints to solve the problem.

Try this beautiful Problem from Singapore Mathematics Olympiad, SMO, 2008 based on Trigonometry. You may use sequential hints to solve the problem.

Try this beautiful problem from Pattern based on Triangle from AMC-10A, 2003. You may use sequential hints to solve the problem

Try this beautiful problem from Number theory based on divisibility from AMC-10A, 2003. You may use sequential hints to solve the problem.

Try this beautiful problem from Inequation from TOMATO useful for ISI B.Stat Entrance based on condition checking.You may use sequential hints.

This problem is called the Elchanan Mossel's Dice Paradox. The problem has a paradoxical nature, but there is always a way out. This ISI MStat 2018 PSB Problem 6.

Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 2011 based on Rectangles and sides.

Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1999 based on Function of Complex numbers.

Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1999 based on Squares and Triangles.

Try this TOMATO problem from I.S.I. B.Stat Entrance Objective Problem based on Logic True-False Reasoning. You may use sequential hints.

This problem is a beautiful and simple application of bijection principle to count how we can select the number of non consecutive integers in combinatorics from Problem 3 of ISI MStat 2019 PSB.

This is an interesting problem from conditional probability and bernoulli random variable mixture, which gives a sweet and sour taste to the Problem 4 of ISI MStat 2016 PSB.

Try this TOMATO problem from I.S.I. B.Stat Entrance Objective Problem based on Series and Integers. You may use sequential hints.

Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1999 based on A Parallelogram and a Line.

Try this beautiful problem from the Pre-RMO, 2019 based on Triangle and Integer. You may use sequential hints to solve the problem.

Try this TOMATO problem from I.S.I. B.Stat Entrance Objective Problem based on Combination of Sequence. You may use sequential hints.

This problem is a very basic and cute application of set theory, venn diagram and and am gm inequality to solve the ISI MStat 2016 PSB Problem 3.

Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1999 based on Smallest prime.

Try this beautiful problem from the Pre-RMO, 2019 based on Area of Triangle and Integer. You may use sequential hints to solve the problem.

Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 2008 based on Cones and circle.

Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 2001 based on Incentre and Triangle.

This problem is a beautiful example when the maximum likelihood estimator is same as the method of moments estimator. Infact, we have proposed a general problem, is when exactly, they are equal? This is from ISI MStat 2016 PSB Problem 7, Stay Tuned.

Try this beautiful problem based on the combinatorics from TOMATO useful for ISI B.Stat Entrance. You may use sequential hints to solve the problem.

Try this beautiful problem from Geometry: Octahedron AMC-10A, 2006. You may use sequential hints to solve the problem

Try this beautiful problem from Probability in Coordinates from AMC-10A, 2003. You may use sequential hints to solve the problem.

Try this beautiful problem from Pre-Regional Mathematics Olympiad, PRMO, 2012 based on Triangle You may use sequential hints to solve the problem.

Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1999 based on Triangle and Trigonometry.

Try this beautiful problem from Singapore Mathematics Olympiad, SMO, 2013 based on HCF. You may use sequential hints to solve the problem.

Try this beautiful problem from Singapore Mathematics Olympiad based on area of triangle. You may use sequential hints to solve the problem.

Try this TOMATO problem from I.S.I. B.Stat Entrance Objective Problem based on Integers and remainders. You may use sequential hints to solve the problem.

Try this beautiful problem from American Invitational Mathematics Examination, AIME, 1999 based on Probability in Games. You may use sequential hints.

Try this beautiful problem from the American Invitational Mathematics Examination, AIME, 2000 based on Least Positive Integer.

Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 2015 based on Theory of Equations.

Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 2019 based on Equations and Complex numbers.

This problem is an interesting application of the moment generating function of normal random variable to see how the correlation behaves under monotone function. This is the problem 6 from ISI MStat 2016 PSB.

Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 2015 from Geometry based on Area of Equilateral Triangle.

Try this beautiful problem from the American Invitational Mathematics Examination, AIME, 2015 based on Probability. You may use sequential hints.

Try this beautiful problem from American Invitational Mathematics Examination, AIME, 2009 based on Probability of tossing a coin.

Try this beautiful problem from the American Invitational Mathematics Examination, AIME, 2010 based on Probability of divisors.

Try this beautiful problem from the American Invitational Mathematics Examination, AIME, 2009 based on Equations with a number of variables.

Try this problem from I.S.I. B.Stat Entrance Objective Problem based on Logic and Group. You may use sequential hints to solve the problem.

Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 2009 based on Coordinate Geometry.

Try this beautiful problem from the American Invitational Mathematics Examination, AIME, 2010 based on Exponents and Equations.

Try this beautiful problem from the Pre-RMO, 2019 based on Two Arrangements. You may use sequential hints to solve the problem.

Try this beautiful problem from the American Invitational Mathematics Examination, AIME, 2012 based on Arrangement of Digits. You may use sequential hints.

Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 2012 based on Complex Numbers and prime.

Try this beautiful problem from American Invitational Mathematics Examination I, AIME I, 2009 based on geometric sequence. Use hints to solve the problem.

This problem from ISI MStat 2016 PSB is a beautiful application of basic counting principles, symmetry and double counting principles in combinatorics.

This problem is a regression problem, where we use the ordinary least square methods, to estimate the parameters in a restricted case scenario. This is ISI MStat 2017 PSB Problem 7.

Try this problem of TIFR GS-2010 using your concepts of number theory and congruence based on natural numbers. You may use the sequential hints provided.

Try this problem from ISI-MSQMS 2018 which involves the concept of Real numbers, sequence and series and Definite integral. You can use the sequential hints

Try this beautiful problem from Singapore Mathematics Olympiad, SMO, 2010 based on functional equation. You may use sequential hints.

Try this problem from ISI MSQMS 2018 which involves the concept of Inequality. You can use the sequential hints provided to solve the problem.

Try this problem from ISI MSQMS 2018 which involves the concept of Inequality and Combinatorics. You can use the sequential hints provided.

Try this beautiful problem from the Pre-RMO, 2019 based on Trigonometry Problem. You may use sequential hints to solve the problem.

This problem is a beautiful and elegant probability based on elementary problem on how to effectively choose the key to a lock. This gives a simulation environment to the problem 6 of ISI MStat 2017 PSB.

Try this beautiful problem from Algebra based on quadratic equation from PRMO 2016. You may use sequential hints to solve the problem.

Try this beautiful problem based on the remainder from TOMATO useful for ISI B.Stat Entrance. You may use sequential hints to solve the problem.

Try this TOMATO problem from I.S.I. B.Stat Entrance Objective Problem based on Logic True-False Reasoning. You may use sequential hints.

Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 2009 based on Triangles and sides.

Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 2011 based on Rectangles and sides.

Try this problem of TIFR GS-2010 using your concepts of number theory based on Positive Integers. You may use the sequential hints provided.

This is a beautiful problem from ISI MStat 2018 problem 2, which uses the cutae little ideas of telescopic sum and partial fractions.

Try this beautiful problem from Geometry: Triangle from AMC-10B, 2011, Problem-9. You may use sequential hints to solve the problem.

Try this beautiful problem from Geometry: Area of triangle from AMC-10A, 2009, Problem-10. You may use sequential hints to solve the problem.

Try this beautiful problem from algebra, based on Arithmetic Progression from AMC-10B, 2004. You may use sequential hints to solve the problem

Try this beautiful problem from Geometry:Area of Trapezium.AMC-10A, 2018. You may use sequential hints to solve the problem

Try this problem from TIFR GS-2010 which involves the concept of cyclic group. You can use the sequential hints provided to solve the problem.

Try this beautiful problem from PRMO, 2016 based on Triangle You may use sequential hints to solve the problem.

The solution plays with eigen values and vectors to solve this cute and easy problem in Linear Algebra from the ISI MStat 2015 problem 3.

Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 2007 based on Sequence and Integers.

Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 2001 based on Patterns and Integers.

Try this beautiful problem from the Pre-RMO, 2018 based on Centroids and Area. You may use sequential hints to solve the problem.

Try this TOMATO problem from I.S.I. B.Stat Entrance Objective Problem based on Logic and Integers. You may use sequential hints to solve the problem.

Try this problem of TIFR GS-2010 from Real analysis, Differentiantiation and Maxima, and Minima. Try with the sequential hints provided.

Try this beautiful problem from Singapore Mathematics Olympiad, SMO, 2009 based on Centroid of Triangle. You may use sequential hints to solve the problem.

Try this beautiful problem from the Pre-RMO, 2019 based on Rectangle and Squares. You may use sequential hints to solve the problem.

This cute little problem gives us the wisdom that when we minimize two functions at single point uniquely , then their sum is also minimized at the same point. This is applied to calculate the least square estimates of two group regression from ISI MStat 2016 Problem 7.

This problem from ISI MStat 2016 is an application of the ideas of indicator and independent variables and covariance of two summative random variables.

This ISI MStat 2016 problem is an application of the ideas of tracing the trace and Eigen values of a matrix and using a cute sum of squares identity.

Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 2011 based on Planes and distance.

Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1985 based on GCD and Sequence.

Try this TOMATO problem from I.S.I. B.Stat Entrance Objective Problem based on Equations and roots. You may use sequential hints.

Try this beautiful problem from the Pre-RMO, 2017 based on GCD and Primes. You may use sequential hints to solve the problem.

Try this TOMATO problem from I.S.I. B.Stat Entrance Objective Problem based on Integer and Divisibility. You may use sequential hints.

Try this beautiful problem from Singapore Mathematics Problem, SMO, 2012 based on Series. You may use sequential hints to solve the problem.

Try this beautiful problem from the American Invitational Mathematics Examination, AIME, 1984 based on Function and symmetry. You may use sequential hints.

Try this beautiful problem from Singapore Mathematics Olympiad, SMO, 2012 based on Prime numbers. You may use sequential hints to solve the problem.

Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 2008 based on Logic and speed.

Try this TOMATO problem from I.S.I. B.Stat Entrance Objective Problem based on Logic True-False Reasoning. You may use sequential hints.

Try this beautiful problem from Geometry based on Triangle from PRMO 2018. You may use sequential hints to solve the problem.

Try this beautiful problem from Algebra based on LCM from AMC-8, 2016. You may use sequential hints to solve the problem.