Skip to content
We use only essential cookies to keep you signed in and remember your preferences. See our Cookie Policy.
TestStop
MocksPracticeResourcesIndiaBlogPricing
Sign in
Questions › UGC-NET › UGC-NET 2023 › Q55
2 marksMathematics › Multivariable calculus › Homogeneous functions and Euler's theoremHardabout 2 min

UGC-NET 2023 Question 55: Multivariable calculus

Let H = e^Q where Q = A x^alpha y^beta. Consider the following statements.

(A) Q is a homogeneous function for all values of alpha and beta.

(B) H is a homothetic function for all values of alpha and beta.

(C) Q is a homogeneous function only if alpha + beta = 1.

(D) H is not a homogeneous function.

(E) Q is not a homogeneous function.

Choose the correct answer from the options given below:

Tap an option to check your answer.

Answer and worked solution

Checking your account…

Multivariable calculus has come up 32 times in 7 exams since 2007.

What this question tests

This question is on Homogeneous functions and Euler's theorem, part of Multivariable calculus in Mathematics.

Functions that scale in a fixed way when all inputs scale, and the identity this gives.

TestStop has 12 past-paper questions on this subtopic; the nearest in year are below.

  • IIT JAM 2022 · Q38Which of the following functions is/are homogeneous?
Take this paper as a timed mockMore on Homogeneous functions and Euler's theorem

Similar questions from other papers

  • CUET-PG 2026 · Q72Match the partial derivative of function Z = x² + xy² + y. List I A. Zₓ B. Z_y C. Z_(xy) D. Z_(yx). List II I. 2y II. 2yx + 1 III. 2x + y² IV. 2y. Choose the correct…
  • GATE 2026 · Q60Consider the function G(x,y,z)=0. This function allows us to implicitly define each of three variables as a function of the other two variables. Assume that all partial…
  • GATE 2025 · Q31Let f(x,y,z) = x² y³ z. Then, x(∂ f)/(∂ x)(x,y,z) + y(∂ f)/(∂ y)(x,y,z) + z(∂ f)/(∂ z)(x,y,z) =
  • UGC-NET 2025 · Q38If Q = f(K, L) is a homogeneous production function of degree one, which of the following satisfies Euler's theorem?
  • GATE 2024 · Q53For the function F:ℝ²→ℝ specified as F(x,y)=x³-y³+9xy, which of the following options is/are correct

Question from the UGC-NET 2023 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.