Case 1 : 4-digit numbers Given digits - 0,1,2,3,4,5 As the numbers should be greater than 2000 , first digit can be 2, 3, 4 and 5 For remaining digits, we need to arrange 3 digits from the remaining 5 digits, i.e. 5×4×3=60ways Total number of possible 4-digit numbers =4×60=240 Case 2: 5-digit numbers First digit cannot be zero. Therefore, total number of cases =5×5×4×3×2=600
Case 3: 6-digit numbers First digit cannot be zero. Therefore, total number of cases =5×5×4×3×2×1=600 Total number of integers possible =600+600+240=1440 The answer is option A.