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-

|[2017,2018,2019],[2018,2019,2020],[ 2019,2020,2021]| (A) 2019 (B) -1 (C) 2020 (D) 0

If A=[[-4,-13]] ,then the determinant of the matrix (A^(2016)-2A^(2015)-A^(2014)) is (A) 2014(B)-175(C)2016(D)-25

determinant of this matrix :((1^2016,2^2016,3^2016,...2018^2016),(2^2016,3^2016,4^2016,...2019^2016),(3^2016,4^2016,5^2016,...2020^2016),(...2018^2016,....2019^2016,2020^2016,....4035^2016))

Find the remainder when 1^(2019)+2^(2019)+3^(2019)+....2020^(2019) is divided by 2019.

Find the value of i^(2017)+i^(2018)+i^(2019)+i^(2020) .

The function f(x)=int_(-2015)^(x)t(e^(t)-e^(2))(e^(t)-1)(t+2014)^(2015)(t-2015)^(2016)(t-2016)^(2017) dt has

The coefficient of x^(2017) in sum_(r = 0)^(2020)2020C_(r)(x-2018)^(2020-r)(2017)^(r) is