Given a math problem with context and a question and 5 answer choices, the task is to provide the correct answer choice based on the problem. You must choose one of the given answer choices by letter: a, b, c, d, or e; anything else is invalid.

[Q]: Problem: what is the greatest positive integer e such that 3 ^ e is a factor of 9 ^ 10 ?
Options: a. e = 5, b. e = 9, c. e = 10, d. e = 20, e. 30
[A]: d


[Q]: Problem: if a and b are the roots of the equation x 2 - 9 x + 9 = 0, then the value of a 2 + b 2 is :
Options: a. 63, b. 24, c. 17, d. 6, e. 5
[A]: a


[Q]: Problem: a train speeds past a pole in 22 seconds and a platform 140 m long in 33 seconds. its length is ?
Options: a. 280, b. 260, c. 300, d. 290, e. 270
[A]:
a