JEE Main 2012 — Sets And Relations Question with Solution
From: AIEEE 2012
Question
Let X = {1, 2, 3, 4, 5}. The number of different ordered pairs (Y, Z) that can be formed such that Y X, Z X and Y Z is empty, is :
Choose an option
Show full solutionCorrect option: A
Correct answer
A35
Step-by-step explanation
For any element xi present in X, 4 cases arises while making subsets Y and Z.
Case- 1 : xi Y, xi Z Y Z
Case- 2 : xi Y, xi Z Y Z =
Case- 3 : xi Y, xi Z Y Z =
Case- 4 : xi Y, xi Z Y Z =
For every element, number of ways = 3 for which Y Z =
Total ways = 3 × 3 × 3 × 3 × 3 [ no. of elements in set X = 5]
= 35
Case- 1 : xi Y, xi Z Y Z
Case- 2 : xi Y, xi Z Y Z =
Case- 3 : xi Y, xi Z Y Z =
Case- 4 : xi Y, xi Z Y Z =
For every element, number of ways = 3 for which Y Z =
Total ways = 3 × 3 × 3 × 3 × 3 [ no. of elements in set X = 5]
= 35
Practice this on the real CBT interface
Solve this JEE Main question (and the rest of the Sets And Relations chapter) on PrepSharp's TCS iON-style CBT player — with timer, bookmarks and session analytics.
Solve interactively →About this question
This is a previous-year question from JEE Main 2012, 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.