Post Number:#1 by BdMO
» Fri Jan 28, 2011 10:14 pm Dhaka Divisional
Mathematical Olympiad 2011 : Secondary
 In a box there are 50
gold rings of 10 different sizes and 75
silver rings of 12 different sizes. The size
of a gold ring might be the same as that of a silver ring. What is the
minimum number of rings one need to pick up to be sure of having at
least two rings different both in size and material?
viewtopic.php?f=41&t=472
 A
is the product of seven odd prime numbers. AB
is a perfect even square. What is the minimum number of prime factors
of B?
viewtopic.php?f=41&t=473
 x–25
and yx–4 .
Find the minimum and maximum values of xy.
viewtopic.php?f=41&t=474
a+b+c+d+e= a−2b+c−2d+e= a+b−3c+d−3e= −4a+b+c−4d+e= a−5b+c+d−5e= 1 2 3 4 5 উপরের
সমীকরণগুলো থেকে a এর মান বের কর। Find a
from the above set of equations. viewtopic.php?f=41&t=475
 Find
the range of the function
Here,
x
represents the minimum integer greater than x and 2x
represents the maximum integer less than x. viewtopic.php?f=41&t=476  The
diagonal AB
in quadrilateral ADBC
bisects the angle CBD.
DB and DA are
tangent to the circumcircle of triangle ABC
at points A and B. The perimeter
of triangle ABC
is 20
and perimeter of triangle ABD
is 12.
Find the length of BD.
viewtopic.php?f=41&t=477  A
six headed monster has 120 children. He wants to
give a different name to each of his children. The names will consist of
3
English letters and one letter can be used more than once in a single
name. What is the minimum number of letters the monster must use?
viewtopic.php?f=41&t=478  A
palindrome, such as 83438,
is a number that remains the same when its digits are reversed. N
is a six digit palindrome which is divisible by 6. The
number obtained by eliminating its leftmost and rightmost digits is
divisible by 4. How many possible values
of N
are possible?
viewtopic.php?f=41&t=479  x
is a positive integer so that 2x
and x2 leaves
same remainder when divided by 3. There
are many possible values for x. What
will be the remainder when the sum of the first 2011
values of x is divided by 1000?
viewtopic.php?f=41&t=480  For
three non empty finite sets ABC
the following relations hold:
B(C–A)= BC= ABCN
(N
is the set of natural numbers) Given that A=1234C=3456
and no element of B is greater than the largest
element of C how many possible options are
there for B? viewtopic.php?f=41&t=481
