Which one of the following numbers is exactly divisible by $\left(11^{13}+1\right) ?$

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In the figure shown above, each inside square is formed by joining the mid points of the sides of the next larger square. The area of the smallest square (shaded) as shown, in $\mathrm{cm}^2$ is

Let $X$ is a continuous random variable denoting the temperature measured. The range of temperature is $[0,100]$ degree Celsius and let the probability density function of $X$ be $f(x)=0.01$ for $0 \leq X \leq 100$. The mean of $X$ is $\_\_\_\_$ .