Self Maths Puzzle Logical Reasoning

There are N doors in a row numbered from 1 to N. Initially all are closed.
Then you make N passes by the N doors. In pass 1 you toggle the all the doors starting from the first door. In the second pass you toggle every second door. In the third pass you toggle all third doors.Similarly you make N passes.Question is what is the state of door k after N passes.

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Self Other Question

what is the next term in this series :
1,2,6,20,70,..... ?

options :
1)210
2)220
3)242
4)252
5)332
6)462
7)495
8)505
9)540
10)552
Find the appropriate answer: If 56 x 72 = 79, 32 x 4 = 81, 9 x 12 = 34, 25 x 30=56 then, 49x42=? (a) 77 (b) 52 (c)76 (d) 67