Which of the following is not a homogeneous function of x ...

CBSE Class 12 Math 2025 All Sets Solved Paper

Question : 8 of 20

Marks: +1, -0

Which of the following is not a homogeneous function of x and y ?

Solution:

We know for homogeneous function

F(λ y, λ y)=λ f(x, y)

Option (A)

f(x, y)=y^{2}-x y

f(λ x, λ y)=(λ y)^{2}-(λ x)(λ y)

f(λ x, λ y)=λ^{2} (y^{2}-x y)

Option (B) f(x, y) = x - 3y

f(λ x, λ y)=λ x-3 λ y

f(λ x, λ y)=λ(x-3 y)=λ f(x, y)

Option (C)

f(x, y)=\sin ^{2} (\;{y}/{x}) +\;{y}/{x}

f(λ x, λ y)=\sin ^{2} (\;{λ y}/{λ x}) +\;{λ y}/{λ x}

f(λ x, λ y)=\sin ^{2} (\;{y}/{x}) +\;{y}/{x} ⇒ f(x, y)

Option (D)

f(x, y)=\tan x-\sec y

f(λ x, λ y)=\tan (λ x)-\sec (λ y) ≠ λ f(x, y)

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