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 $\_\_\_\_$ .

The importance of sleep is often overlooked by students when they are preparing for exams. Research has consistently shown that sleep deprivation greatly reduces the ability to recall the material learnt. Hence, cutting down on sleep to study longer hours can be counterproductive.

Which one of the following statements is the CORRECT inference from the above passage?