Part I Problem 1 Let \(XZ\) be a diameter of circle \(\omega\). Let Y be a point on \(XZ\) such that \(XY=7\) and \(YZ=1\). Let W be a point on \(\omega\) such that \(WY\) is perpendicular to \(XZ\). What is the square of the length of the line segment \(WY\) ? (a) 7(b) 8(c) 10(d) […]
PART I Problem 1 Answer: A Problem 2 Answer: D Problem 3 Answer: D Problem 4 Answer: A Problem 5 Answer: D Problem 6 Answer: D Problem 7 Answer: D Problem 8 Answer: C Problem 9 Answer: B Problem 10 For positive real numbers a and b, the minimum value of\( \left18 a+\frac{1}{3 b}\right\left3 b+\frac{1}{8 […]
Problem 1 Let $\mathbb{N}$ be the set of all positive integers and $S=\left\{(a, b, c, d) \in \mathbb{N}^4: a^2+b^2+c^2=d^2\right\}$. Find the largest positive integer $m$ such that $m$ divides $a b c d$ for all $(a, b, c, d) \in S$. Solution Notice that $(2, 2, 1, 3)\in S\Rightarrow m$ is a divisor of $12 […]
Try this ISI BStat - BMath Entrance 2023, Problem no. 2 with hints and final solution.
In the math world, a unique challenge emerges, combining algebra and number theory. The goal: show that specific equation solutions aren't simple fractions. We reveal a key insight about b² - 4ac: it's always a distinct odd perfect square. Using "parity check," No matter the numbers, the left side remains even, while the right side stays odd. The result: these solutions differ from simple fractions, highlighting math's power in problem-solving.
In 2023, the following Cheenta students are successful for Indian Statistical Institute's B.Stat Entrance and Chennai Mathematical Institute's B.Sc. Math Entrance. They ranked within the first 100 in the entire country in these entrances. Most of these students attended the problem solving workshops regularly, which happen 5 times every week. CMI B.Sc. Math Entrance I.S.I. […]
The leaders in the IOQM, ISI Entrance, American Math Competitions and Math Kangaroo mock contests in Cheenta
Please use the following form to contribute problems of CMI BSc Math Entrance 2023. We will work on the solutions. Also come back to this page to see the updates on Problems and Solutions of CMI BSc Math Entrance 2023. B1. Let \( n \) be an odd positive number greater than 1. We have […]
Questions, Solutions and discussions on ISI BStat-BMath Entrance 2023.
Question 1 What is \(100(100-3)-(100 \cdot 100-3)\) ? (a) \(-20,000\) (b) \(-10,000\) (c) -297 (d) -6 (e) 0 Question 2 Makayla attended two meetings during her 9 -hour work day. The first meeting took 45 minutes and the second meeting took twice as long. What percent of her work day was spent attending meetings? (a) […]
Question 1 What is \[ \frac{2+4+6}{1+3+5}-\frac{1+3+5}{2+4+6}? \] (a) \(-1\) (b) \(\frac{5}{36}\) (c) \(\frac{7}{12}\) (d) \(\frac{147}{60}\) (e) \(\frac{43}{3}\) Question 2 Josanna's test scores to date are \(90,80,70,60,\) and 85. Her goal is to raise her test average at least 3 points with her next test. What is the minimum test score she would need to accomplish […]
Question 1 Each third-grade classroom at Pearl Creek Elementary has 18 students and 2 pet rabbits. How many more students than rabbits are there in all 4 of the third-grade classrooms? (a) 48 (b) 56 (c) 64 (d) 72 (e) 80 Question 2 A circle of radius 5 is inscribed in a rectangle as shown. […]
Question 1 What is \[ \frac{2+4+6}{1+3+5}-\frac{1+3+5}{2+4+6}? \] (a) \(-1\) (b) \(\frac{5}{36}\) (c) \(\frac{7}{12}\) (d) \(\frac{49}{20}\) (e) \(\frac{43}{3}\) Question 2 Mr.\ Green measures his rectangular garden by walking two of the sides and finds that it is 15 steps by 20 steps. Each of Mr.\ Green's steps is 2 feet long. Mr.\ Green expects half a […]
Question 1 Leah has 13 coins, all of which are pennies and nickels. If she had one more nickel than she has now, then she would have the same number of pennies and nickels. In cents, how much are Leah's coins worth? (a) 33 (b) 35 (c) 37 (d) 39 (e) 41 Question 2 What […]
Question 1 What is the value of $$ \frac{2 a^{-1}+\frac{a^{-1}}{2}}{a} $$ when $a=\frac{1}{2}$ ? (a) 1 (b) 2 (c) $\frac{5}{2}$ (d) 10 (e) 20 Question 2 If $n \circlearrowleft m=n^{3} m^{2}$, what is $\frac{294}{49^{2}}$ ? (a) $\frac{1}{4}$ (b) $\frac{1}{2}$ (c) 1 (d) 2 (e) 4 Question 3 Let $x=-2016$. What is the value of $|||x|-x|-|x||-x$ […]
Question 1 What is the value of \(2-(-2)^{-2}\)? (a) \(-2\) (b) \(\frac{1}{16}\) (c) \(\frac{7}{4}\) (d) \(\frac{9}{4}\) (e) \(6\) Question 2 Marie does three equally time-consuming tasks in a row without taking breaks. She begins the first task at 1:00 PM and finishes the second task at 2:40 PM. When does she finish the third task? […]
Question 1 Mary thought of a positive two-digit number. She multiplied it by 3 and added 11. Then she switched the digits of the result, obtaining a number between 71 and 75, inclusive. What was Mary's number? (a) 11 (b) 12 (c) 13 (d) 14 (e) 15 Question 2 Sofia ran 5 laps around the […]
Question 1 Kate bakes 20 -inch by 18 -inch pan of cornbread. The cornbread is cut into pieces that measure 2 inches by 2 inches. How many pieces of cornbread does the pan contain? (a) 90 (b) 100 (c) 180 (d) 200 (e) 360 Question 2 Sam drove 96 miles in 90 minutes. His average […]
Question 1 What is the value of $$ 1-(-2)-3-(-4)-5-(-6) ? $$ (a) -20 (b) -3 (c) 3 (d) 5 (e) 21 Question 2 Carl has 5 cubes each having side length 1 , and Kate has 5 cubes each having side length 2 . What is the total volume of these 10 cubes? (a) 24 […]
Cheenta recently hosted the final round of the Sharygin Geometrical Olympiad 2026 at its Kolkata center, spread across two days — 31st July and 1st August, from 12 PM to 4 PM each day. Students sat across the table from a panel of jurors and defended their geometric proofs the old-fashioned way: pen, paper, and […]
Week 15 of the Hundred Miles Project saw learners continue steadily through this stage's assessment paper, even as the week's embroidery class had to be cancelled after the instructor was unable to arrive due to inclement weather. In the Literacy module, participants read a short passage about a community that came together after a flood, […]
Week 14 of the Hundred Miles Project carried a steady, focused energy, as learners worked through this stage's assessment paper across all three modules alongside the week's embroidery class. In the Literacy module, participants read a short passage about a young woman who struggles with reading for weeks before finally reading a full story aloud […]
Question 1 Consider the process of the melting of a spherical ball of ice originally at 0° Assuming that the heat is being absorbed uniformly through the surface and the rate of absorption is proportional to the instantaneous surface area. Which of the following is true for the radius (r) of the ice ball at […]
On Week 13 of the Teacher Training Program, trainees took part enthusiastically in a thorough evaluation spanning three key domains: Literacy, Numeracy, and Digital Literacy. This assessment aimed to measure their grasp, comprehension, and hands-on application of the material studied throughout the training. Every trainee finished the evaluation with diligence and eagerness, showcasing their dedication […]
চিত্রে একটি দুই ডিজিটের স্কোরবোর্ড দেখানো হয়েছে; যেটাতে কিছু টিউব লাইট জ্বালিয়ে স্কোর নির্দেশ করা হয়। যদি সকল ১৪টি টিউব লাইট জ্বালিয়ে দেওয়া হয়, তাহলে নির্দেশিত স্কোর দাঁড়ায় '৮৮'। (a) যদি ৪, ৯, ১১, ১২ ও ১৩ নং টিউব-লাইট OFF এবং বাকিগুলো ON রাখা হয়, তবে নির্দেশিত স্কোর কত ?(b) যদি স্কোরবোর্ডে ১৩ দেখাতে হয়, […]
What happens when elementary school mathematics leaves the textbook and enters the garden, the night sky, and embroidered cloth? We share three open-ended problems for grades 1 to 6, each built on two levers, discovery and creation, and each ending with an invitation to invent a definition.
During Week 12 of the Teacher Training Program, the trainees actively participated in a comprehensive assessment covering three important areas: Literacy, Numeracy, and Digital Literacy. The assessment was designed to evaluate their knowledge, understanding, and practical application of the concepts learned during the training. All participants completed the assessment with dedication and enthusiasm, demonstrating their […]
Question 1 Two wave pulses I and II have the same wavelength. They are travelling in the directions as shown by the single headed arrows. The resultant sketch of the two wave pulses at some instant of time when $P$ coincides with $R$ is ____ . Question 2 The equivalent resistance of two resistances in […]
Semiconductors sit at the heart of nearly every modern technology, and this minicourse traces the full arc from materials to finished chips. It opens with inorganic semiconductor devices, laying out the physics of diodes, transistors, and junctions that have powered electronics for decades. Organic semiconductor devices follow, exploring how carbon-based materials enable flexible, low-cost alternatives […]