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 You and five friends need to raise \($ 1500\) in donations for a charity, dividing the fundraising equally. How many dollars will each of you need to raise? (a) 250 (b) 300 (c) 1500 (d) 7500 (e) 9000 Question 2 For any three real numbers \(a, b\), and \(c\), with \(b \neq c\), […]
Question 1 While eating out, Mike and Joe each tipped their server 2 dollars. Mike tipped \(10 %\) of his bill and Joe tipped \(20 %\) of his bill. What was the difference, in dollars between their bills? (a) 2 (b) 4 (c) 5 (d) 10 (e) 20 Question 2 For each pair of real […]
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 […]
During Week 9 of the Teacher Training Program, participants engaged in a comprehensive assessment focused on three key areas: Literacy, Numeracy, and Digital Literacy. The assessment was designed to evaluate the trainees’ understanding and application of essential teaching competencies developed throughout the training sessions. Participants completed a variety of tasks that measured their reading, writing, […]
Today marked the 10th week of the assessment program. The attendance of the trainees was comparatively low, with only seven students present for the session. Susmita was absent today. Abantika Ma'am was in charge of supervising and coordinating the day's activities. Additionally, our class was shifted to the meeting room on the first floor, where […]
Question 1 Alicia had two containers. The first was $\frac{\mathbf{5}}{\mathbf{6}}$ full of water and the second was empty. She poured all the water from the first container into the second container, at which point the second container was $\frac{\mathbf{3}}{\mathbf{4}}$ full of water. What is the ratio of the volume of the first container to the […]
Question 1 Isabella's house has 3 bedrooms. Each bedroom is 12 feet long, 10 feet wide, and 8 feet high. Isabella must paint the walls of all the bedrooms. Doorways and windows, which will not be painted, occupy 60 square feet in each bedroom. How many square feet of walls must be painted? (a) 678 […]
Question 1 A basketball player made 5 baskets during a game. Each basket was worth either 2 or 3 points. How many different numbers could represent the total points scored by the player? (a) 2 (b) 3 (c) 4 (d) 5 (e) 6 Question 2 A \(4 \times 4\) block of calendar dates is shown. […]
Question 1 Each morning of her five-day workweek, Jane bought either a 50 -cent muffin or a 75 -cent bagel. Her total cost for the week was a whole number of dollars. How many bagels did she buy? (a) 1 (b) 2 (c) 3 (d) 4 (e) 5 Question 2 Which of the following is […]
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 […]