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Questions › IIT JAM › IIT JAM 2024 › Q9
1 mark, −0.333Mathematics › Concavity, convexity and quasi-concavity › Convex sets and functionsModerateabout 2 min

IIT JAM 2024 Question 9: Concavity, convexity and quasi-concavity

Let S1={(x,y)∈R2:x+y≥1, x+y≤2, y≥x2, x,y≥0}S_1 = \{(x,y) \in R^2 : x + y \ge 1,\ x + y \le 2,\ y \ge x^2,\ x,y \ge 0\}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}S_2 = \{(x,y) \in R^2 : x + y \ge 1,\ x + y \le 2,\ y \le x^2,\ x,y \ge 0\}S2​={(x,y)∈R2:x+y≥1, x+y≤2, y≤x2, x,y≥0}. Then, which of the following is CORRECT?

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Let 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? (A) Both S₁ and S₂ are convex sets (B) S₁ is a convex set but S₂ is not a convex set (C) S₂ is a convex set but S₁ is not a convex set (D) Neither S₁ nor S₂ are convex sets

Also written as: Let S_1 = {(x,y) in R^2: x + y >= 1, x + y <= 2, y >= x^2, x,y >= 0} and S_2 = {(x,y) in R^2: x + y >= 1, x + y <= 2, y <= x^2, x,y >= 0}. Then, which of the following is CORRECT?

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.

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