simplify the following equation
$$ (1-{1\over3})(1-{1\over4})(1-{1\over5})......(1-{1\over n})$$

If $$ \sqrt {x^2+y^2}=25$$, and y=2x, find x. 

The ratio of two unequal sides of a rectangle is 1 : 2. If its perimeter is 24 cm, then the length of diagonal in cm is:

If x – y + z = 15, xyz = -216 and xz – xy – yz = 18, then the value of $$ {x^3}-{y^3}+{z^3}=$$

If 0.4 m + 0.8 n = 2.2 and 0.8 m + 0.4 n = 1.4, then the value of $$ {m^2}+{n^2}$$ is equal to 

If $$ {x^2} -4x-1 $$ then the value of $$ {{x^6} -{x^4}+{x^2}-1}\over {x^3}$$ will be

If $$ m+{1\over m-2}=0$$ then the value of $$ (m-2)^{12}+{1\over{(m-2)}^{12}} $$ is.

$$ {x+{1\over{x}}}$$, then the value of $$ {x^2}+{1\over{x^2}}$$ is