Algebra - General Aptitude - General Aptitude (GA) Previous Year Questions

Consider the following inequalities.
(i) \(3p - q < 4\)
(ii) \(3q - p < 12\)
Which one of the following expressions below satisfies the above two inequalities?

In a locality, the houses are numbered in the following way:
The house-numbers on one side of a road are consecutive odd integers starting from 301, while the house-numbers on the other side of the road are consecutive even numbers starting from 302. The total number of houses is the same on both sides of the road.
If the difference of the sum of the house-numbers between the two sides of the road is 27, then the number of houses on each side of the road is

For positive integers \(p\) and \(q\), with \(\frac{p}{q} \neq 1\), \(\left(\frac{p}{q}\right)^{\frac{p}{q}} = p^{\left(\frac{p}{q}-1\right)}\). Then,

The 12 musical notes are given as \(C, C^{\#}, D, D^{\#}, E, F, F^{\#}, G, G^{\#}, A, A^{\#}\), and \(B\). 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:

Which one of the following plots represents \(f(x) = -\frac{|x|}{x}\), where \(x\) is a non-zero real number?
Note: The figures shown are representative.