Weight of a person can be expressed as a function of their age. The function usually varies from person to person. Suppose this function is identical for two brothers, and it monotonically increases till the age of 50 years and then it monotonically decreases. Let $a_1$ and $a_2$ (in years) denote the ages of the brothers and $a_1 < a_2$.

Which one of the following statements is correct about their age on the day when they attain the same weight?

A regular dodecagon (12-sided regular polygon) is inscribed in a circle of radius $r \mathrm{~cm}$ as shown in the figure. The side of the dodecagon is d cm . All the triangles (numbered 1 to 12) in the figure are used to form squares of side $r \mathrm{~cm}$ and each numbered triangle is used only once to form a square.

The number of squares that can be formed and the number of triangles required to form each square, respectively, are:

Note: The figure shown is representative.

If a real variable $x$ satisfies $3^{x^2}=27 \times 9^x$, then the value of $\frac{2^{x^2}}{\left(2^x\right)^2}$ is :

The number of patients per shift ( $X$ ) consulting Dr. Gita in her past 100 shifts is shown in the figure. If the amount she earns is Rs $1000(X-0.2)$, what is the average amount (in she has earned per shift in the past 100 shifts?

Note : The figure shown is representative.