profile-img
Vijay posted an Question
December 15, 2021 • 06:15 am 30 points
  • IIT JAM
  • Mathematics (MA)

Sp2019;55. please send the solution to the problem given in the attachment.

SP2019;55. please send the solution to the problem given in the attachment.

1 Answer(s) Answer Now
  • 0 Likes
  • 1 Comments
  • 0 Shares
  • comment-profile-img
    Navdeep goyal 1 Best Answer

    check attachment

    cropped5895079594543419416.jpg
    eduncle-logo-app

    no. of elements in the set pata karna hai where x^4=e kaise pata karenge sir?

    eduncle-logo-app

    given x⁴=e means order of X is 4 we find 4 order elements of S3 in set

    eduncle-logo-app

    {e, (12) ,(23),(13)} sir i think these 4 elements in S3 gives identity in there 4th power .. question is not asking about order 4 element ... it says how many elements give identity in there 4 power... i am just thinking (kya yese v ho sakta hai)

    eduncle-logo-app

    {e, (12) ,(23),(13)} 4 power of thses elements is e

    eduncle-logo-app

    4th power tak check karne me bahut time nahi chalajaega is there a short trick ?

    eduncle-logo-app

    short trick order hai (1,2) ka order 2 hai so x²=e ab iski power kuch bhi lo e hi aayga

    eduncle-logo-app

    each element ka order calculate karo

    eduncle-logo-app

    exactly there are 4 elements is S3 whose 4th power is Identity... so i think ans is 4

    eduncle-logo-app

    Navdeep sir isme short trick kaha hai?

    eduncle-logo-app

    (1,2) 2 length ka permutations hai so iska order 2 hai I.e (1,2)²=e (1,2)⁴=e

    eduncle-logo-app

    order 3 wala element identity qu nahi hoga sir?

    eduncle-logo-app

    3 order ke liye x³=e hoga

    eduncle-logo-app

    haan par hamare set me toh 4 order wala element hai he nahi na toh x^4 =e kaise milega?

    eduncle-logo-app

    2 order ke elements hai so x²=e => x⁴=e

whatsapp-btn

Do You Want Better RANK in Your Exam?

Start Your Preparations with Eduncle’s FREE Study Material

  • Updated Syllabus, Paper Pattern & Full Exam Details
  • Sample Theory of Most Important Topic
  • Model Test Paper with Detailed Solutions
  • Last 5 Years Question Papers & Answers