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GATE 2021 EC – Question 2

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

$p$ and $q$ are positive integers and $\frac pq+\frac qp=3$, then $\frac{p^2}{q^2}+\frac{q^2}{p^2}=$

  1. 3
  2. 7
  3. 9
  4. 11

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Correct answer: (B) 7

Explanation

Squaring, $\left(\frac pq+\frac qp\right)^2=\frac{p^2}{q^2}+2+\frac{q^2}{p^2}=9$, so $\frac{p^2}{q^2}+\frac{q^2}{p^2}=9-2=7$.