GATE CY 2025 Question Paper (15-Feb-2025) (Shift-1)

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 ₹ $1000(X\text{–}0.2)$, what is the average amount (in ₹) she has earned per shift in the past 100 shifts?
Note: The figure shown is representative.

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

A regular dodecagon (12-sided regular polygon) is inscribed in a circle of radius $r$ 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 $r$ 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.

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?

Column-I has statements made by Shanthala; and, Column-II has responses given by Kanishk.Identify the option that has the correct match between Column-I and Column-II.