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. […]
Author: Kazi Abu Rousan Where are the zeros of zeta of s? G.F.B. Riemann has made a good guess; They're all on the critical line, saith he, And their density's one over 2 p log t. Source https://www.physicsforums.com/threads/a-poem-on-the-zeta-function.16280/ If you are a person who loves to read maths related stuff then sure you have came […]
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 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 […]
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 […]