HARD
IOQM - PRMO and RMO
IMPORTANT
Earn 100
Find the largest positive integer such that the number of integers in the set which are divisible by is equal to the number of integers which are divisible by or (or both).
50% studentsanswered this correctly
Important Questions on Combinatorics
HARD
IOQM - PRMO and RMO
IMPORTANT
Consider a permutation of We say the -tuple is flawless if for all the sequence is not an arithmetic progression (in that order). Find the number of flawless -tuples.
HARD
IOQM - PRMO and RMO
IMPORTANT
Ari chooses balls at random from balls numbered to If the probability that no two of the drawn balls have consecutive numbers equals the probability of exactly one pair of consecutive numbers in the chosen balls, find
HARD
IOQM - PRMO and RMO
IMPORTANT
Five persons wearing badges with numbers are seated on chairs around a circular table. In how many ways can they be seated so that no two persons whose badges have consecutive numbers are seated next to each other? (Two arrangements obtained by rotation around the table are considered different.)
MEDIUM
IOQM - PRMO and RMO
IMPORTANT
In how many ways can a pair of parallel diagonals of a regular polygon of sides be selected?
HARD
IOQM - PRMO and RMO
IMPORTANT
There are several tea cups in the kitchen, some with handles and the others without handles. The number of ways of selecting two cups without a handle and three with a handle is exactly What is the maximum possible number of cups in the kitchen?
HARD
IOQM - PRMO and RMO
IMPORTANT
If is the number of triangles of different shapes (i.e. not similar) whose angle are all integers (in degrees), what is
EASY
IOQM - PRMO and RMO
IMPORTANT
What is the number of ways in which one can choose unit squares from a chessboard such that no two chosen squares have a side in common?
HARD
IOQM - PRMO and RMO
IMPORTANT
What is the number of ways in which one can colour the squares of a chessboard with colours red and blue such that each row as well as each column has exactly two red squares and two blue squares?
