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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
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
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
Undergraduate
By
rizwanhudda
on Aug. 24, 2012 | Updated Dec. 6, 2017
Second Minimum spanning tree
Given an weighted undirected graph \( G = (V, E)\), and \(w : E \mapsto R^+\). Let T be MST i,e minimum spanning tree of graph G. Second MST is a Tree T' different from T, and its weight is less t…
Computer Science
Mathematics
Algorithms
Graph Theory
trees
0
Undergraduate
By
John Doe
on Nov. 3, 2012 | Updated Dec. 6, 2017
Direct reduction from Graph Homomorphism to SAT
The decision problem \(GraphHomo\) is defined as follows: \(GraphHomo = \{\langle G, H\rangle \mid \text{there is a graph homomorphism from G to H}\}\) Give a direct reduction from \(GraphHomo\) to …
Computer Science
Mathematics
Complexity Theory
Graph Theory
Logic
np
reduction
sat
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
Undergraduate
By
Chandra Chekuri
on July 29, 2012 | Updated Dec. 6, 2017
Simple path containing three given nodes
Let \(G=(V,E)\) be an undirected graph. Describe a linear time algorithm that given \(G\) and three distinct nodes \(u,v,w\) decides whether there is a simple path in \(G\) that contains all of them.
Computer Science
Mathematics
Algorithms
Graph Theory
linear time algorithms
0
Undergraduate
By
diego
on June 8, 2012 | Updated Dec. 6, 2017
The cube of a connected graph is hamiltonian
Prove that the vertices of any connected graph \(G\) can be listed in a cyclic order so that the distance in \(G\) of every two consecutive vertices is at most \(3\). Moreover, show that this can be …
Computer Science
Mathematics
Algorithms
Graph Theory
hamiltonian cycle
0
Undergraduate
By
diego
on June 27, 2012 | Updated Dec. 6, 2017
Unmatchable edges of bipartite graphs
Prove that the following algorithm finds the unmatchable edges of a bipartite graph \(G\) (edges that aren't in any perfect matching): find a perfect matching in \(G\), orient the unmatched edges from…
Mathematics
Graph Theory
bipartite graph
matching
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
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