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GATE 2024 AG – Question 5

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

For positive p, q,$\log(p^2+q^2)=\log p+\log q+2\log3$. Find $(p^4+q^4)/(p^2q^2)$.

  1. 79
  2. 81
  3. 9
  4. 83

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Correct answer: (A) 79

Explanation

Log laws give $p^2+q^2=9pq$. Square: $p^4+2p^2q^2+q^4=81p^2q^2$. Subtract the middle term and divide by nonzero $p^2q^2$ to obtain **79,A**. Positivity ensures the logarithms and divisions are valid.

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