Question Of The Day

At time t = 0 light switches 1, 2, 3 …. 10,000 are all OFF. At each time 1, 2, 3, ……10,000 the positions of the switches t, 2t, 3t, ……. are reversed (ON/OFF of OFF/ON). At the end of the operation

a) Switch 1936 in ON & 1935 is OFF

b) Switches 1936 is OFF & 1935 if ON

c) Both switches 1935 and 1936 are ON.

d) Both switches 1935 and 1936 are OFF.

Ans: a) Switch 1936 in ON & 1935 is OFF

A perfect square number has an odd no. of factor. Thus, if N is a perfect square, the light switch N will change its status (ONN/OFF) or OFF/ONN) and is B is not a perfect square, it will not change its status. Answer is (a).