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High School
By
True IITJEE
on May 27, 2014 | Updated Jan. 3, 2018
JEE-Main 2013 Mathematics 31
The circle passing through \((1, −2)\) and touching the axis of \(x\) at \((3, 0)\) also passes through the point
Mathematics
Geometry
circle
jee
jee main
2
High School
By
Shiva Kintali
on Aug. 28, 2013 | Updated Jan. 4, 2018
7 points inside a hexagon
Consider a hexagon \(H\) with side length 1. Given any 7 points inside \(H\), show that at least two points are separated by a distance of at most 1.
Puzzles
Puzzles
geometry puzzle
pigeonhole principle
3
High School
By
True IMO
on Nov. 14, 2016 | Updated Jan. 4, 2018
International Mathematical Olympiad 2016 Problem 5
The equation \((x-1)(x-2)(x-3)...(x-2016) = (x-1)(x-2)(x-3)...(x-2016)\) is written on a board, with 2016 linear factors on each side. What is the least possible value of \(k\) for which it is p…
Mathematics
Combinatorics
imo
imo 2016
polynomials
2
High School
By
Shiva Kintali
on June 24, 2012 | Updated Dec. 6, 2017
Toggling 100 doors
There are 100 doors numbered 1 to 100 in a row. There are 100 people. The first person opens all the doors. The second person closes all the even-numbered doors. The third person changes the state of…
Puzzles
Puzzles
interview question
math puzzle
1
High School
By
True IMO
on July 1, 2017 | Updated Jan. 4, 2018
International Mathematical Olympiad 2015 Problem 2
Determine all triples of positive integers such that each of the numbers is a power of 2.
Mathematics
Algebra
imo
imo 2015
0
High School
By
True IITJEE
on Jan. 16, 2017 | Updated Jan. 3, 2018
JEE Advanced 2016 Paper 1 Mathematics Question 42
Consider a pyramid OPQRS located in the first octant \(( x \geq 0, y \geq 0, z \geq 0 )\) with O as origin, and OP and OR along the x-axis and the y-axis, respectively. The base OPQR of the pyramid is…
Mathematics
Geometry
Trigonometry
jee
jee 2016
jee advanced
jee mathematics
pyramid
2
High School
By
True IMO
on July 21, 2016 | Updated Jan. 4, 2018
International Mathematical Olympiad 2016 Problem 3
Let \(P = A_1, A_2 \dots A_k\) be a convex polygon on the plane. The vertices \(P = A_1, A_2 \dots A_k\) have integral coordinates and lie on a circle. Let \(S\) be the area of \(P\). An odd positive …
Mathematics
Geometry
imo
imo 2016
polygon
0
High School
By
Shiva Kintali
on Jan. 5, 2018
Euler's proof of the Basel problem
The Basel Problem asks for the precise sum of the following infinite series: …
Mathematics
Mathematical Analysis
infinite series
1
High School
By
True IITJEE
on May 29, 2014 | Updated Jan. 3, 2018
JEE-Main 2013 Mathematics 35
All the students of a class performed poorly in Mathematics. The teacher decided to give grace marks of 10 to each of the students. Which of the following statistical measures will not change even aft…
Mathematics
Mathematics
jee
jee main
statistics
variance
1
High School
By
True IITJEE
on May 29, 2014 | Updated Jan. 3, 2018
JEE-Advanced 2013 Mathematics 55
A rectangular sheet of fixed perimeter with sides having their lengths in the ratio 8 : 15 is converted into an open rectangular box by folding after removing squares of equal area from all four corne…
Mathematics
Mathematics
volume
1
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3
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