The population of whirligig beetles in a lake grows or declines exponentially, i.e., \( N(t) = N(0)e^{rt} \), where \( N(t) \) is the population size at time \( t \), \( N(0) \) is the initial population size, and \( r \) is the per capita rate of population change, occurring only due to birth and death.
A researcher tracks population sizes for a year and finds the following:
Assuming that the individual birth rates remain constant throughout the year and only death rates are affected, which one or more of the following statements is/are true?
From the table below, choose one or more of the options that match(es) the evolutionary biologists with the organisms they are well-known to have studied.
The table lists the top 5 nations according to the number of gold medals won in a tournament; also included are the number of silver and the bronze medals won by them. Based only on the data provided in the table, which one of the following statements is INCORRECT?
Eight students (P, Q, R, S, T, U, V, and W) are playing musical chairs. The figure indicates their order of position at the start of the game. They play the game by moving forward in a circle in the clockwise direction.
After the 1st round, the 4th student behind P leaves the game.
After the 2nd round, the 5th student behind Q leaves the game.
After the 3rd round, the 3rd student behind V leaves the game.
After the 4th round, the 4th student behind U leaves the game.
Who all are left in the game after the 4th round?
A stick of length one meter is broken at two locations at distances of \( b_1 \) and \( b_2 \) from the origin (0), as shown in the figure. Note that \( 0<b_1<b_2<1 \). Which one of the following is NOT a necessary condition for forming a triangle using the three pieces?
Note: All lengths are in meter. The figure shown is representative.