An ant is at the bottom-left corner of a grid (point P) as shown below in the figure. It aims to move to the top-right corner of the grid. The ant moves only along the lines marked in the grid such that the current distance to the top-right corner strictly decreases. Which one of the following is a part of a possible trajectory of the ant during the movement?

The number of student passing or failing in an exam for a particular subject are presented in the bar chart below. Students who pass the exam cannot appear for the exam again. Students who fails the exam in the first attempt must appear for the exam in the following year. Students always pass the exam in their second attempt. The numbers of students who took the exam for the first time in the year $2^{\text {nd }}$ the year 3 respectively, are $\_\_\_\_$ .

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 $\_\_\_\_$ .