The radian frequency value(s) for which the discrete time sinusoidal signal $x[n] = A \cos(\Omega n + \pi/3)$ has a period of 40 is/are __.

The relationship between any N-length sequence $x[n]$ and its corresponding N-point discrete Fourier transform $X[k]$ is defined as

$X[k] = \mathcal{F}\{x[n]\}$.

Another sequence $y[n]$ is formed as below

$y[n] = \mathcal{F}\{ \mathcal{F}\{ \mathcal{F}\{ \mathcal{F}\{x[n]\}\}\}\}\}$.

For the sequence $x[n] = \{1, 2, 1, 3\}$, the value of $Y[0]$ is _________.

If ‘→’ denotes increasing order of intensity, then the meaning of the words [charm → enamor → bewitch] is analogous to [bored → _______ → weary]. Which one of the given options is appropriate to fill the blank?

P, Q, R, S, and T have launched a new startup. Two of them are siblings. The office of the startup has just three rooms. All of them agree that the siblings should not share the same room.

If S and Q are single children, and the room allocations shown below are acceptable to all,

PR | TS | Q

PQ | RT | S

Then, which one of the given options is the siblings?