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GATE 2022 CS – Question 2

General Aptitude · Quantitative Aptitude: Algebra, Geometry and Mensuration · 1 mark · Multiple choice

A function $y(x)$ is defined in the interval $[0,1]$ on the $x$-axis as
$y(x)=\begin{cases}2 & 0\le x<\frac{1}{3}\\ 3 & \frac{1}{3}\le x<\frac{3}{4}\\ 1 & \frac{3}{4}\le x\le 1\end{cases}$
Which one of the following is the area under the curve for the interval $[0,1]$ on the $x$-axis?

  1. $\frac{5}{6}$
  2. $\frac{6}{5}$
  3. $\frac{13}{6}$
  4. $\frac{6}{13}$

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Correct answer: (C) $\frac{13}{6}$

Explanation

Area $=2\cdot\frac13+3\cdot(\frac34-\frac13)+1\cdot\frac14=\frac23+\frac54+\frac14=\frac{13}{6}$.