Q. 125.0( 1 Vote )

Which of the foll

Answer :

Given 4 sets,


i. {(x, y) : 2x + 5y < 7}


ii. {(x, y) : x2 + y2 ≤ 4}


iii. {x : |x| = 5}


iv. {(x, y) : 3x2 + 2y2 ≤ 6}


By graphing them, we can clearly figure out the convex set.


A convex set, is nothing but whose solution set is in the shape of a convex polygon.


i. {(x, y) : 2x + 5y < 7}


This inequation can be converted into an equation and by applying the intercept line format, we get,



[dividing the whole by 7]


We get,



So the graph is



ii. {(x, y) : x2 + y2 ≤ 4}


So the graph for this inequality is given by



iii. {x : |x| = 5}


The graph for the set is as below:



iv. {(x, y) : 3x2 + 2y2 ≤ 6}


The graph for the inequality is given by



From t he above graphs, we can clearly say that, only the 3rd graph is a convex set.


Hence option C is the answer.

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