Question Bank • QB_SUB_EM_0043 NAT • 2 Marks

Section 1: Engineering Mathematics

Calculus

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

Question Statement:

If $u(x, y) = x^4 + y^4 + x y^3$ is a homogeneous function of degree $n = 4$, the value of $x \frac{\partial u}{\partial x} + y \frac{\partial u}{\partial y}$ when $u = 5.0$ is:

Answer Key:

20.0

Step-by-Step Solution & Explanation

By Euler's theorem on homogeneous functions of degree $n$: $x \frac{\partial u}{\partial x} + y \frac{\partial u}{\partial y} = n u$ Here $n = 4$ and $u = 5.0$: $x u_x + y u_y = 4 \times 5.0 = 20.00$
← Previous (QB_SUB_EM_0042) Next (QB_EXP_EM_003) →

Practice In Authentic CBT Exam Interface

Test your skills under authentic timed conditions with live scoring and AIR percentile ranking.

Launch CBT Mock Test