11. The integer π is formed by writing all integers from 1001 to 1021
consecutively.
i.e. π = 100110021003 β¦ 1021.
Find the greatest power of 3 that is a factor of π.
(A) 9
(B) 27
(C) 81
(D) 243
(E) None of the above
12. Find the value of π₯ given that
\(\frac{9}{2} = 2 + \frac{1} {0 + \frac{1}{2 +\frac{1}{π₯}}}\)
(A) 3
(B) 2
(C) 1
(D) 0
(E) None of the above
13. Find the constant term in the expansion of
\((2π₯^2 +\frac{1}{π₯^3})^{10}\)
(A) 12400
(B) 12440
(C) 13400
(D) 13440
(E) None of the above
14. Suppose \(π΄π΅πΆπ·\) is a square of side length of 1. \(π\) is the midpoint of \(π΄π΅\).
Find the area of the shaded region.
(A) \(\frac{1}{8}\)
(B) \(\frac{1}{10}\)
(C) \(\frac{1}{12}\)
(D) \(\frac{2}{25}\)
(E) None of the above
15. A fair die is numbered 1 to 6 on each face. \(π, π\) and \(π\) are the results of the first, second and third throws, respectively.
What is the probability that \(π > π > π\)?
(A) \(\frac{2}{21}\)
(B) \(\frac{3}{32}\)
(C) \(\frac{4}{43}\)
(D) \(\frac{5}{24}\)
(E) None of the above