Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 12

# Which of the Following Sets Are Convex? (A) {(X, Y) : X2 + Y2 ≥ 1} (B) {(X, Y) : Y2 ≥ X} (C) {(X, Y) : 3x2 + 4y2 ≥ 5} (D) {(X, Y) : Y ≥ 2, Y ≤ 4} - Mathematics

MCQ

Which of the following sets are convex?

#### Options

• {(xy) : x2 + y2 ≥ 1}

•  {(xy) : y2 ≥ x}

•  {(xy) : 3x2 + 4y2 ≥ 5}

•  {(xy) : y ≥ 2, y ≤ 4}

#### Solution

{(xy) : y ≥ 2, y ≤ 4}

{(xy) : y ≥ 2, y ≤ 4} is the region between two parallel lines, so any line segment joining any two points in it lies in it. Hence, it is a convex set.

Concept: Introduction of Linear Programming
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#### APPEARS IN

RD Sharma Class 12 Maths
Chapter 30 Linear programming
MCQ | Q 3 | Page 67