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 What is the difference between the sum of the first 2003 even counting numbers and the sum of the first 2003 odd counting numbers? (a) 0 (b) 1 (c) 2 (d) 2003 (e) 4006 Question 2 Members of the Rockham Soccer League buy socks and T-shirts. Socks cost \($ 4\) per pair and […]
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 The axes of a coordinate system $\mathrm{S}_{2}$ are inclined at an angle $\theta$ to those of another coordinate system $\mathrm{S}_{1}$. The origins of both the systems are coinciding. A particle $\mathrm{P}_{1}$ at rest in system $\mathrm{S}_{1}$, starts from point ($-2,0$) and travels along positive direction of $\mathrm{X}_{1}$ axis with uniform acceleration of $1.25 […]
Question 1 A student, intending to catch a bus on the bus stand, finds that the bus starts and accelerates away from him/her with uniform acceleration $a=2 m s^{-2}$ when he is 16 m far from the bus. He runs fast enough with a uniform speed so as just to catch the bus. The minimum […]
Question 1 A particle of mass 0.3 kg starts moving from rest, in one dimension, under a force that delivers constant power $\mathrm{P}=1.5$ watt. The kinetic energy of the particle will be $\mathrm{KE}=15$ Joule after a time of (a) 5 S (b) 10 S (c) 12 S (d) 15 S Question 2 A trolley of […]
Question 1 Select the correct order of dielectric constant, refractive index and intermolecular forces for water $\left(\mathrm{H}_{2} \mathrm{O}\right)$ and heavy water $\left(\mathrm{D}_{2} \mathrm{O}\right)$ at 293 K respectively among those given below (i) Dielectric constant $-\mathrm{H}_{2} \mathrm{O}>\mathrm{D}_{2} \mathrm{O}$ (ii) Dielectric constant $-\mathrm{D}_{2} \mathrm{O}>\mathrm{H}_{2} \mathrm{O}$ (iii) Refractive index $-\mathrm{H}_{2} \mathrm{O}>\mathrm{D}_{2} \mathrm{O}$ (iv) Refractive index $-\mathrm{D}_{2} \mathrm{O}>\mathrm{H}_{2} \mathrm{O}$ […]
Question 1 The magnitude of electrostatic force between two tiny spherical balls carrying charge $\mathrm{q}_{1}$ and $\mathrm{q}_{2}$ separated by a distance r in free space is given by $\mathrm{F}=\mathrm{K} \frac{\mathrm{q}_{1} \mathrm{q}_{2}}{\mathrm{r}^{2}}$ where the constant $\mathrm{K}=9 \times 10^{9}$ in SI units Two tiny spherical balls of carbon $\left({ }_{6}^{12} \mathrm{C}\right)$ weighing 1 g each are kept […]
Question 1 Which of the following graphs is correct for a particle moving in a circle of radius $r$ at a speed of v (where ' $a$ ' is magnitude of acceleration) ? Question 2 Electronic configuration of $\mathrm{Na}^{+}$ is $(2,8)$ and that of sodium element is $(2,8,1)$. Choose the correct statements. (i) $\quad \mathrm{Na}^{+}{ […]
Today marked the 8th week of our assessment program. We were introduced to Mr. Rony Basak, who joined us as the Project Coordinator from this week onwards. The day began with an introductory session where Mr. Basak greeted the students and interacted with them to establish a comfortable and friendly environment. Following the introduction, we […]
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 […]