How to Prepare for Chennai Mathematical Institute, CMI? Learn from Vemparala Bhuvan who got into the CMI Entrance 2022.
How to Prepare for Chennai Mathematical Institute, CMI? Learn from Vemparala Bhuvan 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.
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 A point mass m moves in a straight line under a retardation $k v^{2}$ [where $k$ is a positive constant and $v$ is the instantaneous velocity]. The initial velocity of the point mass is $u$. The displacement of the point mass at time t is (a) $\frac{1}{k} \ln (1+k u t)$ (b) $\frac{1}{k} […]
During Week 11 of the Teacher Training Program, the trainees participated in an assessment covering three essential areas: Literacy, Numeracy, and Digital Literacy. The purpose of the assessment was to evaluate their knowledge, practical understanding, and ability to apply the skills acquired during the training. The activities included reading and writing tasks, numeracy exercises, and […]
Question 1 Let $\alpha$ and $\beta$ be the roots of $x^{2}-5 x+3=0$ with $\alpha>\beta$. If $a_{n}=\alpha^{n}-\beta^{n}$ for $n \geq 1$ then the value of $\frac{3 a_{6}+a_{8}}{a_{7}}$ is (a) 2 (b) 3 (c) 4 (d) 5 Question 2 The number of triples $(x, y, z)$ such that any one of these numbers is added to the […]
Question 1 A tiny ball of mass $m$ is initially at rest at height $H$ above a cake of uniform thickness $h$. At some moment the particle falls freely, touches the cake surface and then penetrates in it at such a constant rate that its speed becomes zero on just reaching the ground (bottom of […]
Question 1 A target of ${ }^{7} \mathrm{Li}$ is bombarded with a proton beam of current $10^{-4}$ ampere for 1 hour to produce ${ }^{7} \mathrm{Be}$ of activity $1.8 \times 10^{8}$ disintegrations per second. Assuming that bombarding of 1000 protons produces one ${ }^{7} \mathrm{Be}$ radioactive nucleus, the half-life of ${ }^{7} \mathrm{Be}$ is estimated […]
Question 1 An air filled parallel plate capacitor, with plate area $A$ and plate separation $d$, is connected to a battery of emf $V$ volt having negligible internal resistance. One of the plates of the capacitor vibrates with amplitude ' $a$ ' ( $a \ll d$ ) and angular frequency $\omega$. If the instantaneous current […]
Question 1 Rod AB of radius 2 r is joined with rod BC of radius r . They are of same material and are of same length. The combination carries a current I. Choose the correct statement. (a) $V_{A B}=4 V_{B C}$ (b) Current per unit in AB and BC are equal (c) Resistance of […]
Question 1 Gravitational collapse is the contraction of an astronomical object under its own gravity. This draws the matter inwards towards the centre of gravity. A neutron star is an example of the collapsed core of a giant star. A certain neutron star of radius 10 km is of mass $1.5 M_{\odot}$. The acceleration due […]
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 […]