Which of the specified pairs of years features identical calendars?

The correct option is 1915 & 1926.

To determine if two specified years feature identical calendars, two primary conditions must be satisfied:
1. Both years must be of the same type (either both are ordinary years or both are leap years).
2. The total number of odd days accumulated between the start of the first year and the start of the second year must be a multiple of 7 (yielding a remainder of 0 when divided by 7).

Step 1: Determine the type of years
• 1915 is not divisible by 4, making it an ordinary year (365 days).
• 1926 is not divisible by 4, making it an ordinary year (365 days).
Since both 1915 and 1926 are ordinary years, the first condition is satisfied.

Step 2: Count the ordinary years and leap years between 1915 and 1926
The interval from January 1, 1915, to January 1, 1926, comprises 11 years (1915 through 1925):
• Leap years in this interval (divisible by 4): 1916, 1920, and 1924 (total = 3 leap years).
• Ordinary years in this interval: 11 - 3 = 8 ordinary years.

Step 3: Calculate total odd days
An ordinary year consists of 365 days, which gives 1 odd day (365 divided by 7 leaves a remainder of 1).
A leap year consists of 366 days, which gives 2 odd days (366 divided by 7 leaves a remainder of 2).

$\text{Total Odd Days}=(8\times 1)+(3\times 2)=8+6=14$

$\text{Remainder when 14 is divided by 7}=14\text{mod}7=0$

Conclusion:
Because the total number of odd days is 14 (divisible by 7 with 0 remainder) and both 1915 and 1926 are ordinary years, the calendar for 1915 & 1926 is identical.