JEE Main 2014MathematicsSets and RelationsMediumMCQ

JEE Main 2014 — Sets and Relations Question with Solution

JEE Main 2014 (09 Apr Online)

Question

Let P be the relation defined on the set of all real numbers such that P=a,b:sec2a-tan2b=1. Then, P is

Choose an option

Show full solutionCorrect option: D
Correct answer
Dan equivalence relation

Step-by-step explanation

P=a,b:sec2a-tan2b=1

P=a,a:sec2a-tan2a=1

its reflexive relation.

Now P=a,b:sec2a-tan2b=1

sec2a-tan2b=1

⇒sec2a=1+tan2b

⇒sec2a=sec2b

⇒sec a=sec b

sec2a-tan2b=1

1+tan2a-sec2b+1=1

sec2b-tan2a=1

Hence, it is symmetric.

If sec a=sec b and sec b=sec c then sec a=sec c⇒ transitive 

So, it is an equivalence relation.

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 2014, 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.