How to Prepare for Chennai Mathematical Institute, CMI? Learn from Ryan Hota who got into the CMI Entrance 2022.
How to Prepare for Chennai Mathematical Institute, CMI? Learn from Ryan Hota who got into the CMI Entrance 2022.
How to Prepare for Chennai Mathematical Institute, CMI? Learn from Shravani Parulekar who got into the CMI Entrance 2022.
Try this beautiful Subjective Matrix Problem appeared in ISI Entrance - 2018. You may use sequential hints to solve it.
Try this beautiful Subjective Sequence Problem appeared in ISI Entrance - 2015 problem 8. You may use sequential hints to solve it.
Try this beautiful Subjective Calculus Problem appeared in ISI Entrance 2019 Problem 2. You may use sequential hints to solve it.
Try this beautiful Objective Sequence Problem appeared in ISI Entrance 2018 Problem 8. You may use sequential hints to solve it.
This collection of problems and solutions from CMI Entrance 2022 is a work in progress. If you remember the problems, let us know in the comment section. Part A (indicate if each statement is true or false) Problem A1 Let $a_0 , a_1, a_2…..$ be an arithmetic progression such that $a_0$ and $a_1$ are positive […]
Try this beautiful Objective Limit Problem appeared in ISI Entrance - 2021. You may use sequential hints to solve it.
Try this beautiful Subjective Problem 5 from Polynomials appeared in ISI Entrance - 2021. You may use sequential hints to solve it.
This is a work in progress. Please come back for the solutions. You can also suggest your solutions in the comment section Objective Section Answer Key Problem 1 -> A Problem 7 -> C 13. Problem 19 -> B Problem 25 -> C Problem 2 -> D 8. Problem 14 -> C Problem 20 -> […]
Question 1 Sandwiches at Joe's Fast Food cost \($3\) each and sodas cost \($ 2\) each. How many dollars will it cost to purchase 5 sandwiches and 8 sodas? (a) 31 (b) 32 (c) 33 (d) 34 (e) 35 Question 2 Define \(x \otimes y=x^{3}-y\). What is \(h \otimes(h \otimes h)\) ? (a) \(-h\) (b) […]
Question 1 What is $10 \cdot\left(\frac{1}{2}+\frac{1}{5}+\frac{1}{10}\right)^{-1}$ ? (a) 3 (b) 8 (c) $\frac{25}{2}$ (d) $\frac{170}{3}$ (e) 170 Question 2 Roy's cat eats $\frac{1}{3}$ of a can of cat food every morning and $\frac{1}{4}$ of a can of cat food every evening. Before feeding his cat on Monday morning, Roy opened a box containing 6 cans […]
Question 1 What is the value of $9901 \cdot 101-99 \cdot 10101$ ? (a) 1 (b) 20 (c) 200 (d) 202 (e) 2020 Question 2 A model used to estimate the time it will take to hike to the top of the mountain on a trail is of the form $T=a L+b G$, where $a$ […]
Question 1 What is the value of $$ 3+\frac{1}{3+\frac{1}{3+\frac{1}{3}} ?} $$ (a) $\frac{31}{10}$ (b) $\frac{49}{15}$ (c) $\frac{33}{10}$ (d) $\frac{109}{33}$ (e) $\frac{15}{4}$ Question 2 Mike cycled 15 laps in 57 minutes. Assume he cycled at a constant speed throughout. Approximately how many laps did he complete in the first 27 minutes? (a) 5 (b) 7 (c) […]
Question 1 What is the value of $$ \left(2^{2}-2\right)-\left(3^{2}-3\right)+\left(4^{2}-4\right) ? $$ (a) 1 (b) 2 (c) 5 (d) 8 (e) 12 Question 2 Portia's high school has 3 times as many students as Lara's high school. The two high schools have a total of 2600 students. How many students does Portia's high school have? (a) […]
Question 1 What value of $\boldsymbol{x}$ satisfies $$ x-\frac{3}{4}=\frac{5}{12}-\frac{1}{3} ? $$ (a) $-\frac{2}{3}$ (b) $\frac{7}{36}$ (c) $\frac{7}{12}$ (d) $\frac{2}{3}$ (e) $\frac{5}{6}$ Question 2 The numbers $3,5,7, a$ and $b$ have an average (arithmetic mean) of 15 . What is the average of $a$ and $b$ ? (a) 0 (b) 15 (c) 30 (d) 45 (e) […]
Question 1 Cities $A$ and $B$ are 45 miles apart. Alice and Barbara start biking from $A$ and $B$ at speeds of 18 mph and 12 mph , respectively. How far away from city $A$ will they be when they meet? (a) 20 (b) 24 (c) 25 (d) 26 (e) 27 Question 2 The weight […]
Question 1 What is the value of \[ 2^{\left(0^{\left(1^{9}\right)}\right)}+\left(\left(2^{0}\right)^{1}\right)^{9}? \] (a) 0 (b) 1 (c) 2 (d) 3 (e) 4 Question 2 What is the hundreds digit of \((20!-15!)\)? (a) 0 (b) 1 (c) 2 (d) 4 (e) 5 Question 3 Ana and Bonita were born on the same date in different years, \(n\) years […]
Question 1 What is the value of $$ \left(\left((2+1)^{-1}+1\right)^{-1}+1\right)^{-1}+1 ? $$ (a) $\frac{5}{8}$ (b) $\frac{11}{7}$ (c) $\frac{8}{5}$ (d) $\frac{18}{11}$ (e) $\frac{15}{8}$ Question 2 Liliane has $50 %$ more soda than Jacqueline, and Alice has $25 %$ more soda than Jacqueline. What is the relationship between the amounts of soda that Liliane and Alica have? (a) […]
Question 1 Mary's top book shelf holds five books with the following widths, in centimeters: \(6, \frac{1}{2}, 1,2.5\), and 10. What is the average book width, in centimeters? (a) 1 (b) 2 (c) 3 (d) 4 (e) 5 Question 2 Four identical squares and one rectangle are placed together to form one large square as […]
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 […]
In 2026, the following Cheenta students have been successful for Indian Statistical Institute's M.Stat Entrance. They ranked within the first 50 in the entire country in these entrances. I.S.I. M.Stat Entrance
In 2026, the following Cheenta students have been successful for Indian Statistical Institute's B.Stat Entrance and Chennai Mathematical Institute's B.Sc. Math Entrance. They ranked within the first 200 in the entire country in these entrances. Most of these students attended the problem solving workshops regularly, which happen 5 days every week. CMI B.Sc. Math Entrance […]
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 […]
Week 28 of the Hundred Miles Project got underway on Sunday with a focused and purposeful energy. The session served primarily as a baseline assessment across all three learning modules, establishing the starting points against which each learner's growth will be measured in the weeks ahead through the Learning Velocity Indicator — a new assessment […]
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 […]
The session opened with the Literacy module, in which all learners were assessed using a structured oral and written reading tool to determine their current levels, which were duly recorded in the assessment tick sheet. The group responded to the activity with genuine enthusiasm, and the facilitators noted that every learner showed a willingness to […]