In a trapezium, ABCD, with AB
parallel to CD. If M is the midpoint of
line segment AD and P is a point on
line BC such that MP is perpendicular
to BC. Show that, we need only the
lengths of line segments MP and BC
to calculate the area ABCD.
A rectangular cardboard is 8cm long
and 6cm wide. What is the least
number of beads you can arrange on
the board such that there are at least
two of the beads that are less than
(√(10))cm apart.
Let N be the greatest multiple of 36 all
of whose digits are even and no two of
whose digits are the same. Find the
remainder when N is divided by 1000.
Let K be the product of all factors
(b−a) (not necessarily distinct)
where a and b are integers satisfying
1≤a≤b≤10. Find the greatest
integer n such that 2^n divides K.