JEE Main 2020 — Sets And Relations Question with Solution
From: JEE Main 2020 (Online) 7th January Evening Slot
Question
Let X = {n N : 1 n 50}. If
A = {n X: n is a multiple of 2} and
B = {n X: n is a multiple of 7}, then the number of elements in the smallest subset of X containing both A and B is ________.
A = {n X: n is a multiple of 2} and
B = {n X: n is a multiple of 7}, then the number of elements in the smallest subset of X containing both A and B is ________.
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Show full solutionCorrect answer: 29
Correct answer
29
Step-by-step explanation
X = {1, 2, 3, 4, …, 50}
A = {2, 4, 6, 8, …, 50} = 25 elements
B = {7, 14, 21, 28, 35, 42, 49} = 7 elements
Here n(AB) = n(A) + n(B) – n(AB)
= 25 + 7 – 3 = 29
A = {2, 4, 6, 8, …, 50} = 25 elements
B = {7, 14, 21, 28, 35, 42, 49} = 7 elements
Here n(AB) = n(A) + n(B) – n(AB)
= 25 + 7 – 3 = 29
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This is a previous-year question from JEE Main 2020, 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.