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GATE 2021 MT – Question 12

Engineering Mathematics · Calculus and vector calculus · 1 mark · Multiple choice

Which is a homogeneous function of degree three?

  1. $x^3+2x^2y^2$
  2. $y^2x+2yx^2$
  3. $y^3+2x^2$
  4. $xy^2+3xy$

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Show answer and explanation

Correct answer: (B) $y^2x+2yx^2$

Explanation

A polynomial is homogeneous of degree three when every monomial has total degree three. In y²x+2yx² both degrees are three; the alternatives mix degrees.

Thus **B**, also satisfying f(tx,ty)=t³f(x,y).