Consider a spherical globe rotating about an axis passing through its poles. There are three points P, Q, and R situated respectively on the equator, the north pole, and midway between the equator and the north pole in the northern hemisphere. Let P, Q, and R move with speeds v_p, v_Q, and V_R, respectively.

Which one of the following options is CORRECT?

Which one of the options can be inferred about the mean, median, and mode for the given probability distribution (i.e. probability mass function), 𝑃(𝑥), of a variable x?

Let a = 30! , b = 50! , and c = 100! . Consider the following numbers:

log_a c, log_c a, log_b a, log_a b

Which one of the following inequalities is CORRECT?

A square of side length 4 cm is given. The boundary of the shaded region is defined by one semi-circle on the top and two circular arcs at the bottom, each of radius 2 cm, as shown.

The area of the shaded region is __________ cm².