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Crease of a square paper
A square sheet of paper ABCD is so
folded that B falls on the mid-point of M of CD. Prove that the crease
will divide BC in the ratio 5:3.
Discussion:
Assuming
the side of the square is ‘s’. Let a part of the crease be ‘x’ (hence
the remaining part is ‘s-x’). We apply Pythagoras Theorem we solve for
x:
implies 
and 
Hence the ratio is 5:3.
Standard
Discussion:
Assuming
the side of the square is ‘s’. Let a part of the crease be ‘x’ (hence
the remaining part is ‘s-x’). We apply Pythagoras Theorem we solve for
x: implies and Hence the ratio is 5:3.
is divided by 1990.
digit (from the left) are 1.If N is divisible by 13, find the 
and AB subtends 1350 at the center of the circle. Find the maximum possible area of ABCD.
and 
be two sets of prime numbers such that 
and 
. Suppose 
and 
. Prove that 30 divides 
.
n∈N of functions as 
, 
, for 
. Prove that each 
is a polynomial with integer coefficients.
be a function satisfying 
, 
and
,
for all x , 
simultaneously.
and 
, find the set of all integers n such that 
.
