sol> 2 series is 2,4,6,8.................then 2^1096 give last digit 6......2^2248 gives last digit 6 then............................................................................... now through option if 2^4022 then last digit8.................if 2^4024 then last digit 6........if 2^4020 then last digit 6 and for 2^4016 then last digit 6................................................................................ then trying to sum with all 3 numbers =sum of their last digit 6+6+8 is only number give last digit 0..................................which may be perfect square..............................................................................and for other case 6+6+6=last digit 8 will never perfect square..............thats why 2011 is the ans