Elementary Statistics - General Aptitude - General Aptitude (GA) Previous Year Questions

Three identical closed systems of a pure gas are taken from an initial temperature and pressure (\(T_1, P_1\)) to a final state (\(T_2, P_2\)), each by a different path. Which of the following is ALWAYS TRUE for the three systems? (\(\Delta\) represents the change between the initial and final states; U, S, G, Q and W are internal energy, entropy, Gibbs free energy, heat added and work done, respectively.)

Students taking an exam are divided into two groups, P and Q such that each group has the same number of students. The performance of each of the students in a test was evaluated out of 200 marks. It was observed that the mean of group P was 105, while that of group Q was 85. The standard deviation of group P was 25, while that of group Q was 5. Assuming that the marks were distributed on a normal distribution, which of the following statements will have the highest probability of being TRUE?

The following sequence of numbers is arranged in increasing order: 1, x, x, x, y, y, 9, 16, 18. Given that the mean and median are equal, and are also equal to twice the mode, the value of y is