If today is Sunday, then which day is it exactly on ${10}^{10}\text{th}$ day?

Correct Option (b)

The sequence of days of the week repeats every 7 days. To determine the day after a specific number of days, one must find the remainder when that number is divided by 7. This remainder signifies the number of "odd days" to count forward from the starting day.

In this problem, the number of days is ${10}^{10}$, which is 10,000,000,000. When ${10}^{10}$ is divided by 7, the remainder obtained is 4.

Starting from Sunday as the reference day (day 0):

• 1st day after Sunday: Monday
• 2nd day after Sunday: Tuesday
• 3rd day after Sunday: Wednesday
• 4th day after Sunday: Thursday

Therefore, the day exactly on the ${10}^{10}\text{th}$ day will be Thursday.

Incorrect Options:

Options (a) Wednesday, (c) Friday, and (d) Saturday are incorrect. These options would correspond to different remainders when ${10}^{10}$ is divided by 7. A remainder of 3 would result in Wednesday, a remainder of 5 would result in Friday, and a remainder of 6 would result in Saturday. Since the accurate calculation yields a remainder of 4 odd days, only Thursday is the correct answer.