Match List I with List II

Homogeneous function

Degree

A.
\(\rm f(x, y)=\frac{x^{\frac{1}{3}}+y^{\frac{1}{3}}}{x^{\frac{1}{2}}+y^{\frac{1}{2}}}\)
I.

3

B.
\(\rm f(x, y)=\frac{x+y}{\sqrt x+\sqrt y}\)
II.
\(\frac{1}{2}\)

C.
\(\rm f(x, y)=\frac{x^4+y^4}{x+y}\)
III.

1

D.
\(\rm f(x, y)=\frac{\sqrt{x^3+y^3}}{\sqrt x+\sqrt y}\)
IV.
\(\rm -\frac{1}{6}\)

Choose the most appropriate answer from the options given below:

Question

Homogeneous function		Degree
A.	\(\rm f(x, y)=\frac{x^{\frac{1}{3}}+y^{\frac{1}{3}}}{x^{\frac{1}{2}}+y^{\frac{1}{2}}}\)	I.	3
B.	\(\rm f(x, y)=\frac{x+y}{\sqrt x+\sqrt y}\)	II.	\(\frac{1}{2}\)
C.	\(\rm f(x, y)=\frac{x^4+y^4}{x+y}\)	III.	1
D.	\(\rm f(x, y)=\frac{\sqrt{x^3+y^3}}{\sqrt x+\sqrt y}\)	IV.	\(\rm -\frac{1}{6}\)