Sangita decided to get the railway reservation in October, for the journey she wants to make in December, to Mumbai.
Decide which of the assumptions is implicit in the statement:
% Assumptions
I. The railways issue reservations two months in advance.
II. There are more than one train to Mumbai.
III. There will be vacancy in the desired class.
The 12 musical notes are given as \( C, C^\#, D, D^\#, E, F, F^\#, G, G^\#, A, A^\#, B \). Frequency of each note is \( \sqrt[12]{2} \) times the frequency of the previous note. If the frequency of the note C is 130.8 Hz, then the ratio of frequencies of notes F# and C is:
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?

Shown on the left is a set of equations. Which option belongs to the same set? 
Shown below is an arrangement of closely stacked spheres. Assume each one to be in contact with its immediate neighbour. What is the total number of points where the spheres touch each other?