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Nilanjan Bhowmick AIR 3, CSIR NET (Earth Science)
- 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.
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Anonymous User Best Answer
check attachment
no. of elements in the set pata karna hai where x^4=e kaise pata karenge sir?
given x⁴=e means order of X is 4 we find 4 order elements of S3 in set
{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)
{e, (12) ,(23),(13)} 4 power of thses elements is e
4th power tak check karne me bahut time nahi chalajaega is there a short trick ?
short trick order hai (1,2) ka order 2 hai so x²=e ab iski power kuch bhi lo e hi aayga
each element ka order calculate karo
exactly there are 4 elements is S3 whose 4th power is Identity... so i think ans is 4
Navdeep sir isme short trick kaha hai?
(1,2) 2 length ka permutations hai so iska order 2 hai I.e (1,2)²=e (1,2)⁴=e
order 3 wala element identity qu nahi hoga sir?
3 order ke liye x³=e hoga
haan par hamare set me toh 4 order wala element hai he nahi na toh x^4 =e kaise milega?
2 order ke elements hai so x²=e => x⁴=e