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GATE 2024 MT – Question 5

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

For positive real $p,q$, $\log(p^2+q^2)=\log p+\log q+2\log3$. The value of $(p^4+q^4)/(p^2q^2)$ is

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

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Correct answer: (A) 79

Explanation

Combining logarithms gives p²+q²=9pq.

Squaring: p⁴+2p²q²+q⁴=81p²q².

Subtract 2p²q² and divide by the positive product to obtain **79, A**.