For the following questions answer them individually
If x and y are natural numbers such that $$(\frac{1}{x})^\frac{1}{y}=0.\overline{3}$$, then the value of XY is
The sum of the squares of two consecutive natural numbers is 61. The numbers are
The sum of digits of a natural number $$(10^{n}-1)$$ is 4707, where n is a natural number. The value of n is
The last digit in the decimal representation of $$(\frac{1}{5})^{2000}$$ is
If $$\log 2 = 0.3010$$, then the number of digits in $$4^{50}$$ is
If $$\log \frac{a^{2}}{b}+\log \frac{b}{a^{2}}=\log(a+b)$$, then
$$\frac{1}{\log_a^b}\times\frac{1}{\log_c^b}\times\frac{1}{\log_a^c}$$ is equal to
The ratio of the areas of a square and a square on its diagonal is
The volume of the largest possible cube that can be inscribed in a hollow spherical ball of radius r cm is