How 9 Cheenta students ranked in top 100 in ISI and CMI Entrances?

Learn More*This post contains Chennai Mathematical Institute, CMI, 2015 Objective, and Subjective Problems and Solutions. Please contribute problems and solutions in the comments.*

- For all finite word strings comprising A and B only, A string is arranged by dictionary order. eg. ABAA
- For any arbitrary string w, with another string y<w, there cannot always exist a string x, w<x<y
- There is an infinite set of strings a1,a2… such that ai<a(i+1) for all i.
- There are fewer than 50 strings less than AABBABBA

- Ten people are seated in a circle. One person contributes five hundred rupees. Every person contributes the average of the money contributed by his two neighbors.
- What is the sum contributed by all the ten?
- >5000
- < 5000
- .=5000
- Cannot say.

- 2. What is maximum contribution by an individual?
- 500
- =500
- none

- What is the sum contributed by all the ten?
- There are 4 bins and 4 balls. Let be the probability of first n balls falling into distinct bins.

Find - Let . Find
- f(2.7).
- f'(2.7)
- integral from 0 to 2.5 of f(x)dx
- value of x for which f'(x) does not exist

- In some country number plates are formed by 2 digits and 3 vowels. It is called confusing if it has both digit 0 and vowel o.
- How many such number plates exist?
- How many are not confusing

- A number is called magical if a and b are not coprime to n, a+b is also not coprime to n. For example, 2 is magical as all even numbers are not coprime to 2. Find whether the following numbers are magical
- 129
- 128
- 127
- 100

- a) In the expansion of , the term with maximum value is

b) If , where and are integers, is

- In a circle, AB be the diameter.. X is an external point. Using straight edge construct a perpendicular to AB from X
- If X is inside the circle then how can this be done

Discussion

- If X is inside the circle then how can this be done
**a**be a positive integer from set {2, 3, 4, ... 9999}. Show that there are exactly two positive integers in that set such that 10000 divides a*a-1.- Put in place of 9999. How many positive integers
**a**exists such that divides a(a-1)

Discussion

- Put in place of 9999. How many positive integers
- P(x) is a polynomial. Show that exists. Also show that the limit does not depend on the polynomial.
- We define function when x< 0; f(x) = 0 if x=0 and when x > 0 . Show that the function is continuous and differentiable. Find limit at x =0
- p,q,r any real number such that
- Show that
- Suppose . At what values (p,q, r) does f(p,q,r) maximizes and minimizes?

- Let g(n) is GCD of (2n+9) and then then find greatest value of g(n)

Cheenta is a knowledge partner of Aditya Birla Education Academy

Advanced Mathematical Science. Taught by olympians, researchers and true masters of the subject.

JOIN TRIAL