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CBSE Class 12 Math 2025 All Sets Solved Paper

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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(λy,λy)=λf(x,y)F(\lambda y, \lambda y)=\lambda f(x, y)
Option (A) f(x,y)=y2−xyf(x, y)=y^{2}-x y
f(λx,λy)=(λy)2−(λx)(λy)f(\lambda x, \lambda y)=(\lambda y)^{2}-(\lambda x)(\lambda y)
f(λx,λy)=λ2(y2−xy)f(\lambda x, \lambda y)=\lambda^{2} (y^{2}-x y)
Option (B) f(x, y) = x - 3y
f(λx,λy)=λx−3λyf(\lambda x, \lambda y)=\lambda x-3 \lambda y
f(λx,λy)=λ(x−3y)=λf(x,y)f(\lambda x, \lambda y)=\lambda(x-3 y)=\lambda f(x, y)
Option (C) f(x,y)=sin⁡2(  yx)+  yxf(x,y)=\sin^{2}\left(\;\frac{y}{x}\right)+\;\frac{y}{x}
f(λx,λy)=sin⁡2(  λyλx)+  λyλxf(\lambda x, \lambda y)=\sin^{2}\left(\;\frac{\lambda y}{\lambda x}\right)+\;\frac{\lambda y}{\lambda x}
f(λx,λy)=sin⁡2(  yx)+  yx⇒f(x,y)f(\lambda x, \lambda y)=\sin^{2}\left(\;\frac{y}{x}\right)+\;\frac{y}{x} \Rightarrow f(x, y)
Option (D) f(x,y)=tan⁡x−sec⁡yf(x, y)=\tan x-\sec y
f(λx,λy)=tan⁡(λx)−sec⁡(λy)≠λf(x,y)f(\lambda x, \lambda y)=\tan(\lambda x)-\sec(\lambda y) \neq \lambda f(x, y)
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