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Questions › DSE › DSE 2021 › Q13
4 marks, −1Mathematics › Concavity, convexity and quasi-concavity › Convex sets and functionsModerateabout 2 min

DSE 2021 Question 13: Concavity, convexity and quasi-concavity

One girl is training for a half marathon in Delhi. She runs xix_ixi​ kilometres on the iii-th day for the next 12 days (x1x_1x1​ on day 1, x2x_2x2​ on day 2, and so on). On the last day she finds that she trained 121212 kilometres per day on average. Which of the following statements is true?

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One girl is training for a half marathon in Delhi. She runs xᵢ kilometres on the i -th day for the next 12 days (x₁ on day 1, x₂ on day 2, and so on). On the last day she finds that she trained 12 kilometres per day on average. Which of the following statements is true? (A) Σᵢ₌₁¹² log₁₂ xᵢ < 12 (B) Σᵢ₌₁¹² log₁₂ xᵢ > 12 (C) Σᵢ₌₁¹² log₁₂ xᵢ = 12 (D) Σᵢ₌₁¹² log₁₂ xᵢ = 12¹²

Also written as: One girl is training for a half marathon in Delhi. She runs x_i kilometres on the i -th day for the next 12 days (x_1 on day 1, x_2 on day 2, and so on). On the last day she finds that she trained 12 kilometres per day on average. Which of the following statements is true?

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.

Practise Concavity, convexity and quasi-concavityMore on Convex sets and functions

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