Correct Answer - Option 4 : 32

\(\frac{8}{11}\)
The universal rule is, hands of any accurate clock coincide after every 65 minutes 5/11 of a minute i.e 65 5/11.

But according to the question, the clock is taking 64 minutes to coincide.

Therefore, the error will be = (65 5/11)-(64) mints =16/11 minutes.

Now, the total minutes in a day is = 24 hrs x 60 minutes= 1440 minutes.

Since the error for 64 minutes is 16/11 minutes.

Means, in 1 min = (16/11 x 1/64)

So, in 1440 mins = (16/11 x 1/64) x 1440 = (1/44) x 1440 = 360/11 = 32\(\frac{8}{11}\).

Hence, the correct answer is "**32\(\frac{8}{11}\)**".