JEE Main 2021MathematicsSets and RelationsEasyMCQ

JEE Main 2021 — Sets and Relations Question with Solution

JEE Main 2021 (26 Aug Shift 1)

Question

Out of all the patients in a hospital 89% are found to be suffering from heart ailment and 98% are suffering from lungs infection. If K% of them are suffering from both ailments, then K can not belong to the set:

Choose an option

Show full solutionCorrect option: A
Correct answer
A{79,81,83,85}

Step-by-step explanation

Let H and L is set of people suffered from heart ailment and lungs infections respectively.

nH=89%

nL=98%

nH∩L=K%

maxn(H), nL≤nH∪L≤nU

Where, U is the universal set.

⇒98≤nH∪L≤100

⇒98≤nH+nL-nH∩L≤100

⇒98≤89+98-k≤100

⇒0≤89-k≤2

⇒-89≤-k≤-87

⇒87≤K≤89

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About this question

This is a previous-year question from JEE Main 2021, covering the Sets and Relations chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.