GATE EC 2023 Set 1 Q3 — General Aptitude

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 $130.8 \: \mathrm{Hz}$, then the ratio of frequencies of notes $F^{\#}$ and $C$ is:

The following figures show three curves generated using an iterative algorithm. The total length of the curve generated after 'Iteration $n$ ' is: Note: The figures shown are representative.

A stick of length one meter is broken at two locations at distances of $b_{1}$ and $b_{2}$ from the origin $(0)$, as shown in the figure. Note that $0 < b_{1} < b_{2}<1$. Which one of the following is NOT a necessary condition for forming a triangle using the three pieces? Note: All lengths are in meter. The figure shown is representative.

An organization allows its employees to work independently on consultancy projects but charges an overhead on the consulting fee. The overhead is $20 \%$ of the consulting fee, if the fee is up to ₹$5,00,000$. For higher fees, the overhead is ₹$1,00,000$ plus $10 \%$ of the amount by which the fee exceeds ₹ $5,00,000$. The government charges a …

​​​​Five years ago, the ratio of Aman's age to his father's age was $1: 4$, and five years from now, the ratio will be $2:5$. What was his father's age when Aman was born?

​​​​For a real number $x>1$, $$\frac{1}{\log _{2} x}+\frac{1}{\log _{3} x}+\frac{1}{\log _{4} x}=1$$ The value of $x$ is