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 -> […]
The BStat and BMath Entrance of ISI Entrance is ‘different’ from IIT JEE or other engineering entrances. It tests creativity and ingenuity of the problem solver that requires more than mechanical application of formulae. Many of these problems are inspired from erstwhile Soviet Union math contests and other math olympiads. The entrance has two sections: […]
NMTC 2010 Primary Stage 1 Question 1 $\mathrm{n}, \mathrm{a}$ are natural numbers each greater than 1 . If $a+a+a+a+\ldots+a=2010$, and there are $n$ terms on the left hand side, then the number of ordered pairs $(a, n)$ is NMTC 2019 Primary Stage 1 Question 10 Sum of the odd numbers from 1 to 2019 both […]
NMTC 2019 Stage 1 Sub junior Question 10 How many positive integers smaller than 400 can you get as a sum of eleven consecutive positive integers? NMTC 2019 Stage 1 Sub junior Question 11 Let $x, y$ and $z$ be positive real numbers and let $x \geq y \geq z$ so that $x+y+z=20.1$. Which of […]
NMTC 2010 Primary Stage 1 Question 1 $\mathrm{n}, \mathrm{a}$ are natural numbers each greater than 1 . If $a+a+a+a+\ldots+a=2010$, and there are $n$ terms on the left hand side, then the number of ordered pairs $(a, n)$ is NMTC 2019 Inter Stage 1 Question 17 The number of times the digit occurs in the result […]
NMTC 2019 Stage 1 Inter Question 5 The area of the curve enclosed by $|x-2 \sqrt{2}|+|y-\sqrt{5}|=2$ is : (A) 16(B) 12(C) 8(D) 4 NMTC 2019 Inter Stage 1 Question 11 In a rectangle $A B C D$, point $E$ lies on $B C$ such that $\frac{B E}{E C}=2$ and point $F$ lies on $C D$ […]
Try these AMC 10 Geometry Questions and check your knowledge! Two right circular cones with vertices facing down as shown in the figure below contains the same amount of liquid. The radii of the tops of the liquid surfaces are $3$ cm and $6$ cm. Into each cone is dropped a spherical marble of radius […]
Author: Kazi Abu Rousan C is hard but fast But you need to be on guard to last. Python is easy but slow But you can use it to glow. But if you have julia Beautiful rhythms will flow. ---Me Julia is a high-level, high-performance, dynamic programming language. Most of you guys have heard or […]
Dear student, In the past few years several Cheenta students reached the top 300 universities in the world. These universities include Oxford, UCLA, NUS, MIT and University of Edinburgh. We have gradually shaped a success pathway for students that works in the long run. This pathway can be useful for you as well.There two components of this success path: Component 1: Performance […]
Author: Kazi Abu Rousan There are some problems in number theory which are very important not only because they came in exams but also they hide much richer intuition inside them. Today, we will be seeing one of such problems. Sources: B.Stat. (Hons.) and B.Math. (Hons.) I.S.I Admission Test 2012 problem-2. B.Stat. (Hons.) and B.Math. […]
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 One can holds 12 ounces of soda. What is the minimum number of cans to provide a gallon (128 ounces) of soda? (a) 7 (b) 8 (c) 9 (d) 10 (e) 11 Question 2 Four coins are picked out of a piggy bank that contains a collection of pennies, nickels, dimes, and quarters. […]
Question 1 A bakery owner turns on his doughnut machine at 8:30 AM. At 11:10 AM the machine has completed one third of the day's job. At what time will the doughnut machine complete the job? (a) 1:50 PM (b) 3:00 PM (c) 3:30 PM (d) 4:30 PM (e) 5:50 PM Question 2 A square […]
Question 1 What is the value of \(\left(2^{0}-1+5^{2}+0\right)^{-1}\times 5\)? (a) \(-125\) (b) \(-120\) (c) \(\frac{1}{5}\) (d) \(\frac{5}{24}\) (e) \(25\) Question 2 A box contains a collection of triangular and square tiles. There are 25 tiles in the box, containing 84 edges total. How many square tiles are there in the box? (a) 3 (b) 5 […]
Question 1 What is the value of \(\frac{11!-10!}{9!}\)? (a) 99 (b) 100 (c) 110 (d) 121 (e) 132 Question 2 For what value of \(x\) does \(10^{x}\cdot 100^{2x}=1000^{5}\)? (a) 1 (b) 2 (c) 3 (d) 4 (e) 5 Question 3 For every dollar Ben spent on bagels, David spent 25 cents less. Ben paid \($12.50\) […]
Question 1 A taxi ride costs \($1.50\) plus \($0.25\) per mile traveled. How much does a 5-mile taxi ride cost? (a) \($2.25\) (b) \($2.50\) (c) \($2.75\) (d) \($3.00\) (e) \($3.25\) Question 2 Alice is making a batch of cookies and needs \(2\frac{1}{2}\) cups of sugar. Unfortunately, her measuring cup holds only \(\frac{1}{4}\) cup of sugar. […]
Question 1 Cagney can frost a cupcake every 20 seconds and Lacey can frost a cupcake every 30 seconds. Working together, how many cupcakes can they frost in 5 minutes? (a) 10 (b) 15 (c) 20 (d) 25 (e) 30 Question 2 A square with side length 8 is cut in half, creating two congruent […]
Question 1 A cell phone plan costs \($20\) each month, plus \($0.05\) per text message sent, plus \($0.10\) for each minute used over 30 hours. In January Michelle sent 100 text messages and talked for 30.5 hours. How much did she have to pay? (a) \($24.00\) (b) \($24.50\) (c) \($25.50\) (d) \($28.00\) (e) \($30.00\) Question […]
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 […]
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. […]