The remainder when the determinant `|[2014^(2014),2015^(2015),2016^(2016)],[(2017^(2017),2018^(2018),2019^(2019)],[2020^(2020),2021^(2021),2022^(2022)
The remainder when the determinant
`|[2014^(2014),2015^(2015),2016^(2016)],[(2017^(2017),2018^(2018),2019^(2019)],[2020^(2020),2021^(2021),2022^(2022)]|`
is divided by 5 is-
A. 1
B. 2
C. 3
D. 4
5 views
1 Answers
Correct Answer - D
`"Determinant"=|:((2015-1)^(2014),(2015)^(2015),(2015+1)^(2016),),((2015+2)^(2017),(2020-2)^(2018),(2020-1)^(2019),),((2020)^(2020),(2020+1)^(2021),(2020+2)^(2022),):|`
`"Determinant of remainder"=|:((1)^(2014),0,1,),(2^(2017),2^(2018),(-1)^(2019),),(0,1^(2021),2^(2022),):|`
`=1{2^(4040)+1}+1{2^(2017}}`
`={(4)^(2020)+1}+2.2^(2016)`
`rArr(5-1)^(2020)+1+2.4^(1008)`
`=(5-1)^(2020)+1+2.(5-1)^(1008)`
`"remainder",(-1)^(2020)+1+2.(-1)^(1008)`
=1+1+2=4
5 views
Answered