Official PYQ · 2024Set 1 · Q5MCQ1 mark

GATE CS 2024 Set 1 Q5 — General Aptitude

For positive non-zero real variables $p$ and $q$ , if

$\log \left(p^2+q^2\right)=\log p+\log q+2 \log 3,$

then, the value of $\frac{p^4+q^4}{p^2 q^2}$ is

View worked solution

Answer: A

Given the logarithmic equation for positive non-zero real variables $p$ and $q$ :

\log \left(p^2+q^2\right) = \log p + \log q + 2 \log 3

Using the properties of logarithms, we can simplify the right-hand side:

Substituting this back into the equation:

\log \left(p^2+q^2\right) = \log(9pq)

Since the logarithm function is one-to-one, we can equate the arguments:

p^2 + q^2 = 9pq

To find the value of $\frac{p^4+q^4}{p^2 q^2}$ , we square both sides of the equation:

\left(p^2 + q^2\right)^2 = (9pq)^2

p^4 + q^4 + 2p^2q^2 = 81p^2q^2

Subtracting $2p^2q^2$ from both sides:

p^4 + q^4 = 79p^2q^2

Dividing both sides by $p^2q^2$ :

\frac{p^4+q^4}{p^2 q^2} = 79

Thus, the correct option is A.

Free practice · Your answers on this page are not saved.

Published 10 Oct 2026

Related questions