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GATE 2021 CY – Question 4

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

Define $p\oplus q=(p^2+q^2)/(pq)$ and $p\odot q=p^2/q$. If $x\oplus y=2\odot2$, then x equals ______.

  1. $y/2$
  2. $y$
  3. $3y/2$
  4. $2y$

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Show answer and explanation

Correct answer: (B) $y$

Explanation

The right-hand operator gives 2⊙2=2²/2=2.

Hence (x²+y²)/(xy)=2, so x²−2xy+y²=0. This is (x−y)²=0, implying **x=y, B**, with nonzero x and y as required by the denominator.