The GATE Grind

GATE 2022 CE (CE1) – Question 2

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

Two straight lines pass through the origin $(0,0)$. One passes through $(1,3)$ and the other through $(1,2)$. What is the area enclosed between the straight lines in the interval $[0,1]$ on the x-axis?

  1. 0.5
  2. 1.0
  3. 1.5
  4. 2.0

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: (A) 0.5

Explanation

The lines have equations $y=3x$ and $y=2x$, since both pass through the origin. On $0\le x\le1$, the first is above the second.

Their enclosed area is $\int_0^1(3x-2x)dx=[x^2/2]_0^1=\mathbf{0.5}$, **A**.