JEE Main 2024MathematicsStraight LinesEasyMCQ

JEE Main 2024 — Straight Lines Question with Solution

JEE Main 2024 (27 Jan Shift 2)

Question

Let A and B be two finite sets with m and n elements respectively. The total number of subsets of the set A is 56 more than the total number of subsets of B. Then the distance of the point P(m,n) from the point Q(-2,-3) is

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Show full solutionCorrect option: A
Correct answer
A10

Step-by-step explanation

We know that, the total number of subsets of a set having n elements is 2n.

⇒2m-2n=56

⇒2n2m-n-1=23×7

⇒2n=23 and 2m-n-1=7

⇒n=3  and 2m-n=8

⇒n=3 and m-n=3

⇒n=3 and m=6

Distance between P6, 3 and Q-2,-3 is given by,

PQ=6+22+3+32

⇒PQ=82+62

⇒PQ=100

⇒PQ=10 units

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About this question

This is a previous-year question from JEE Main 2024, covering the Straight Lines 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.