JEE Main 2016 Mathematics question

Not in JEE syllabus

The contrapositive of the following statement, "If the side of a square doubles, then its area increases four times", is

(1)if the area of a square increases four times, then its side is not doubled.
(2)if the area of a square increases four times, then its side is doubled.
(3)if the area of a square does not increase four times, then its side is not doubled.Correct
(4)if the side of a square is not doubled, then its area does not increase four times.

Answer: (3)

Solution

The contrapositive of "if then " is "if **not** then **not** " — both the hypothesis and conclusion are negated *and* interchanged. Here is "the side of a square doubles" and is "its area increases four times". Negating and swapping gives: "if the area of a

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Question ID VK-115658