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If D1, D2, D3, ..... D1000 are 1000 doo...

If `D_1, D_2, D_3, ..... D_1000` are 1000 doors and `P_1, P_2, P_3, ..... P_1000` are 1000 persons. Initially all doorsare closed. Changing the status of doors means closing the door if it is open or opening it if it is closed. `P_1` changes the status of all doors. Then `P_2` changes the status of `D_2, D_4, D_6, .... D_1000` (doors having numbers which are multiples of 2). Then `P_3`; changes the status of `D_3, D_6, D_9, .....D_999` (doors having number which are multiples of 3) and this process is continued till `P_1000` changes the status of `D_1000`, then the doors which are finally open is/are

A

`D_(961)`

B

`D_(269)`

C

`D_(413)`

D

`D_(729)`

Text Solution

Verified by Experts

The correct Answer is:
A, D
`D_(m)` will be open finally if `m` is the perfect square
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