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 › DSE › DSE 2019 › Q18
0 marksMathematics › Concavity, convexity and quasi-concavity › Testing concavity and convexityHardabout 3 min

DSE 2019 Question 18: Concavity, convexity and quasi-concavity

Given nonempty subsets Y1,…,YnY_1,\dots,Y_nY1​,…,Yn​ of ℜ2\Re^2ℜ2, let Y∗={∑j=1nyj:y1∈Y1,…,yn∈Yn}Y^*=\{\sum_{j=1}^n y_j : y_1\in Y_1,\dots,y_n\in Y_n\}Y∗={∑j=1n​yj​:y1​∈Y1​,…,yn​∈Yn​}. Given p∈ℜ2p\in\Re^2p∈ℜ2 and a nonempty set Y⊂ℜ2Y\subset\Re^2Y⊂ℜ2, let v(p,Y)=sup⁡{p⋅y:y∈Y}v(p,Y)=\sup\{p\cdot y : y\in Y\}v(p,Y)=sup{p⋅y:y∈Y}. Then, for every ppp:

Tap an option to check your answer.

Answer and worked solution

Checking your account…

Plain-text version

Given nonempty subsets Y₁,…,Yₙ of ℜ², let Y*={Σⱼ₌₁ⁿ yⱼ: y₁∈ Y₁,…,yₙ∈ Yₙ}. Given p∈ℜ² and a nonempty set Y⊂ℜ², let v(p,Y)=sup {p· y: y∈ Y}. Then, for every p: (A) v(p,Y*)≥ Σⱼ₌₁ⁿ v(p,Yⱼ) (B) v(p,Y*)=Σⱼ₌₁ⁿ v(p,Yⱼ) (C) v(p,Y*)≤ Σⱼ₌₁ⁿ v(p,Yⱼ) (D) v(p,Y*)<Σⱼ v(p,Yⱼ) or v(p,Y*)≥Σⱼ v(p,Yⱼ)

Also written as: Given nonempty subsets Y_1,...,Y_n of Re^2, let Y*={ sum_(j=1)^n y_j: y_1 in Y_1,...,y_n in Y_n}. Given p in Re^2 and a nonempty set Y subset Re^2, let v(p,Y)=sup {p* y: y in Y}. Then, for every p:

Concavity, convexity and quasi-concavity has come up 39 times in 6 exams since 2006.

What this question tests

This question is on Testing concavity and convexity, part of Concavity, convexity and quasi-concavity in Mathematics.

Checking concavity or convexity from a definition, derivatives or operations that preserve it.

TestStop has 17 past-paper questions on this subtopic.

Practise Concavity, convexity and quasi-concavityMore on Testing concavity and convexity

Similar questions from other papers

  • CUET-PG 2025 · Q4Which of the following statements is not correct?
  • IIT JAM 2024 · Q9Let S₁ = {(x,y) ∈ R²: x + y ≥ 1, x + y ≤ 2, y ≥ x², x,y ≥ 0} and S₂ = {(x,y) ∈ R²: x + y ≥ 1, x + y ≤ 2, y ≤ x², x,y ≥ 0}. Then, which of the following is CORRECT?
  • CUET-PG 2023 Shift 1 · Q28A function is strictly concave in the interval I, if for all a, b ∈ I and λ ∈ (0, 1) 1. f[(1-λ)a + λ b] > (1-λ)f(a) + λ f(b) 2. f[(1-λ)a + λ b] < (1-λ)f(a) + λ f(b) 3.
  • CUET-PG 2023 Shift 2 · Q47The function e^(-1/2x²) is:
  • IIT JAM 2023 · Q2Let f, g: ℝ → ℝ be f(x)=x+2 for x≤1, 2x+1 for x>1; and g(x)=2x for x≤2, x+2 for x>2. Then

Question from the DSE 2019 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.