Problem 1 . A shop sells two kind of products A and B. One day a salesman sold both A and B at the same price, $2100$ to a customer. Suppose A makes a profit of 20% and B makes a loss of 20%. Then the deal
(A) make a profit of $70$; (B) make a loss of $70$;(C) make a profit of $175$; (D) make a loss of $70$.
Problem 2 . Let f and g be functions such that for all real numbers x and y $g(f(x+y))$ = $f(x)$ + $(x+y)g(y)$...
Find the value of $g(0)$ + $g(1)$ + ... + $g(2013)$
Problem 3 . Each chocolate costs 1 dollar, each licorice stick costs 50 cents and each lolly costs 40 cents. How many different combinations of these three items cost a total of 10 dollars.
Problem 4 . Let $A= {1, 2, 3, 4, 5, 6}$. Find the number of distinct functions f: A → A such that $f(f(f(n))) = n$ for all $n ∈ A$.
Problem 5 . Find the number of triangles whose sides are formed by the sides of the diagonals of a regular heptagon (7 sided polygon). (Note: the vertices of the triangle need not be vertices of the heptagon).
Problem 6 . Six seats are arranged in a circular table. Each seat is to be painted in red, blue or green such that any two adjacent seats have different colors. How many ways are there to paint the seats?
Problem 7 . ΔABC is an equilateral triangle with side length 30. Fold the triangle so that A touches a point X on BC. If BX = 6, find the value of k, where √k is the length of the crease obtained from folding.
Problem 8 . As shown in the figure below, circles C1 and C2 of radius 360 are tangent to each other, and both tangent to the straight line l. If the circle C3 is tangent to C1 , C2 and l, and circle C4 is tangent to C1 , C3 and l, find the radius of C4 .
Problem 9 . Set {x} = x - ⌊x⌋, where ⌊x⌋ denotes the largest integer less than or equal to x. Find the number of real solutions to the equation {x} + {x2 } = 1 , |x| ≤ 10.
Problem 10 . Find the value of \( ( \frac {3 + \sqrt 17 }{2} )^6 \).
Problem 11 . A regular dodecagon (12 sided polygon) is inscribed in a circle of radius 10. Find it's area.
Problem 12 . to be continued...
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
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In 2025, 8 students from Cheenta Academy cracked the prestigious Regional Math Olympiad. In this post, we will share some of their success stories and learning strategies. The Regional Mathematics Olympiad (RMO) and the Indian National Mathematics Olympiad (INMO) are two most important mathematics contests in India.These two contests are for the students who are […]
Cheenta Academy proudly celebrates the success of 27 current and former students who qualified for the Indian Olympiad Qualifier in Mathematics (IOQM) 2025, advancing to the next stage — RMO. This accomplishment highlights their perseverance and Cheenta’s ongoing mission to nurture mathematical excellence and research-oriented learning.
2. for all real numbers x and y g(f(x+y)) = f(x) + (x+y)g(y)putting y=-x, g(f(0))=f(x) for all x.for any y, choose x such that x+y=1, g(f(1))=f(x)+g(y)f(0)=f(1)=g(f(0))g(f(1))=g(f(0)), giving g(y)=0hence the sum=0
3.10c+5r+4y=100this means y=0,5when y=0, 2c+r=20, giving 11 sets of valueswhen y=5, 2c+r=16, giving 9 sets of valuestotal 20.
4. for an element n ∈ A, either f(n)=n or f(n)=b, f(b)=c, f(c)=n, b,c,n being all distinct (like a triangle whose sides have a 0 vector sum).so, total no. of f's= 1+[6p3/3]+[6p3/3*2]=1+40+80=121
I think all the options in the 1st question are wrong. The correct answer should be that the deal makes a loss of $175.CPa + 0.2CPa = SPa = $2100CPb - .2CPb = SPb = $2100=> CPa = $2100/1.2 = $1750and CPb = $2100/0.8 = $2625so, Total CPdeal = $4375and Total SPdeal = $4200So, Total LOSS = $175 (as SPdeal<CPdeal)