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 › CUET-PG › CUET-PG 2023 Shift 2 › Q69
4 marks, −1Mathematics › Concavity, convexity and quasi-concavity › Convex sets and functionsModerateabout 1 min

CUET-PG 2023 Shift 2 Question 69: Concavity, convexity and quasi-concavity

For a strictly convex function f(x), which one of the following is true? [0<λ<1][0 < \lambda < 1][0<λ<1]

  1. λf(x1)+(1−λ)f(x2)>f[λx1+(1−λ)x2]\lambda f(x_1)+(1-\lambda)f(x_2) > f[\lambda x_1+(1-\lambda)x_2]λf(x1​)+(1−λ)f(x2​)>f[λx1​+(1−λ)x2​]
  2. λf(x1)+(1−λ)f(x2)<f[λx1+(1−λ)x2]\lambda f(x_1)+(1-\lambda)f(x_2) < f[\lambda x_1+(1-\lambda)x_2]λf(x1​)+(1−λ)f(x2​)<f[λx1​+(1−λ)x2​]
  3. λf(x1)+(1−λ)f(x2)≥f[λx1+(1−λ)x2]\lambda f(x_1)+(1-\lambda)f(x_2) \geq f[\lambda x_1+(1-\lambda)x_2]λf(x1​)+(1−λ)f(x2​)≥f[λx1​+(1−λ)x2​]
  4. λf(x1)−(1−λ)f(x2)≤f[λf(x1)+(1−λ)x2]\lambda f(x_1)-(1-\lambda)f(x_2) \leq f[\lambda f(x_1)+(1-\lambda)x_2]λf(x1​)−(1−λ)f(x2​)≤f[λf(x1​)+(1−λ)x2​]

Tap an option to check your answer.

Answer and worked solution

Checking your account…

Plain-text version

For a strictly convex function f(x), which one of the following is true? [0 < λ < 1] 1. λ f(x₁)+(1-λ)f(x₂) > f[λ x₁+(1-λ)x₂] 2. λ f(x₁)+(1-λ)f(x₂) < f[λ x₁+(1-λ)x₂] 3. λ f(x₁)+(1-λ)f(x₂) ≥ f[λ x₁+(1-λ)x₂] 4. λ f(x₁)-(1-λ)f(x₂) ≤ f[λ f(x₁)+(1-λ)x₂] (A) λ f(x₁)+(1-λ)f(x₂) > f[λ x₁+(1-λ)x₂] (B) λ f(x₁)+(1-λ)f(x₂) < f[λ x₁+(1-λ)x₂] (C) λ f(x₁)+(1-λ)f(x₂) ≥ f[λ x₁+(1-λ)x₂] (D) λ f(x₁)-(1-λ)f(x₂) ≤ f[λ f(x₁)+(1-λ)x₂]

Also written as: For a strictly convex function f(x), which one of the following is true? [0 < lambda < 1] 1. lambda f(x_1)+(1-lambda)f(x_2) > f[lambda x_1+(1-lambda)x_2] 2. lambda f(x_1)+(1-lambda)f(x_2) < f[lambda x_1+(1-lambda)x_2] 3. lambda f(x_1)+(1-lambda)f(x_2) >= f[lambda x_1+(1-lambda)x_2] 4. lambda f(x_1)-(1-lambda)f(x_2) <= f[lambda f(x_1)+(1-lambda)x_2]

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

What this question tests

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

Sets and functions with no dents, and the inequalities that define them.

TestStop has 14 past-paper questions on this subtopic.

Take this paper as a timed mockMore on Convex sets and functions

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.
  • 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
  • UGC-NET 2023 · Q74Match List I (sign of first and second derivatives) with List II (shape of the curve). List I A. f'(x) > 0 and f''(x) > 0 B. f'(x) > 0 and f''(x) 0. List II I. increas

Question from the CUET-PG 2023 Shift 2 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.