Allied & ICAR Exam Bank • ALLIED_2649 MCQ • 1 Mark

Section 1: Engineering Mathematics

Calculus

Subtopic: Homogeneous function – Euler's theorem on homogeneous functions

Question Statement:

The function $f(x, y) = \frac{x^2 - y^2}{x^2 + y^2}$ is homogeneous of degree:

Options:

  • (A) $0$
  • (B) $1$
  • (C) $2$
  • (D) Not homogeneous

Answer Key:

A

Step-by-Step Solution & Explanation

$f(tx, ty) = \frac{t^2 x^2 - t^2 y^2}{t^2 x^2 + t^2 y^2} = t^0 f(x, y)$. Thus degree $n = 0$.
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