2016 Phase 2|PYQs Special

If a = sqrt((2016)^(2) + (2016) + 2017) , then the value of a is

Suppose a,b,c in R. Let quad (a+2016)^(2)quad (b+2016)^(2)quad (c+2016)^(2)(a-2016)^(2)quad (b-2016)^(2)quad (c-2016)^(2) If Delta=k(2016)^(3)(a-b)(b-c)(c-a). then k is equal to

The value of (5)/(log_(2)(2016))+(2)/(log_(3)(2016))+(1)/(log_(7)(2016)) is

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))