Consider the discrete time system $(S)$ with input $x[n]$ and output $y[n]$ as shown in the Figure. The two sub-systems represented by their impulse responses $h_1[n]$ and $h_2[n]$ are linear and time invariant.

Which of the following statements is necessarily TRUE?

Let $x_1(t)=\cos (2 \pi n t)$ and $x_2(t)=2 \sin (4 \pi n t)$ represent two sinusoids for a positive integer $n$ and $-\infty

Which of the following statements about $x_1(t)$ and $x_2(t)$ is/are valid?

Among the following options, the antonym of the word 'nocturnal' is $\_\_\_\_$ .

The statements (S1), (S2), and (S3) pertain to the scores obtained by students in an exam. The maximum possible marks in the exam is 150.

(S1) The highest score is 100.

(S2) The fourth highest score is 76.

(S3) There are at least four students whose scores are within 25 of each other.

Which one of the following options is necessarily correct?