CDS 2023 PYQ with Answer — Let p = (y⁴ − z²x²)/(x⁴ − y²z²), q = (z⁴ − x²y²)/(y⁴ − z²x²), r = (x⁴…

2023 · Q38

Let p = (y⁴ − z²x²)/(x⁴ − y²z²), q = (z⁴ − x²y²)/(y⁴ − z²x²), r = (x⁴ − y²z²)/(z⁴ − x²y²). What is x²(px² + qy² + rz²) + qr − p² equal to?

Elementary MathematicsAlgebra

A0
B1
Cp + q + r
Dx² + y² + z²

Explanation

The question stem as transcribed is damaged — the definitions of p, q, r follow a cyclic pattern in x, y, z, but the expression to be evaluated cannot be reconstructed unambiguously from the source text. The stored key (A) is therefore retained exactly as transcribed, without independent verification. This item should be re-checked against the official UPSC key or a clean scan of the paper before use.