Problems And Solutions SEAMO PAPER D 2021

11. The integer 𝑁 is formed by writing all integers from 1001 to 1021
consecutively.

i.e. 𝑁 = 100110021003 … 1021.

Find the greatest power of 3 that is a factor of 𝑁.
(A) 9
(B) 27
(C) 81
(D) 243
(E) None of the above

12. Find the value of 𝑥 given that

\(\frac{9}{2} = 2 + \frac{1} {0 + \frac{1}{2 +\frac{1}{𝑥}}}\)

(A) 3
(B) 2
(C) 1
(D) 0
(E) None of the above

13. Find the constant term in the expansion of

\((2𝑥^2 +\frac{1}{𝑥^3})^{10}\)

(A) 12400
(B) 12440
(C) 13400
(D) 13440
(E) None of the above

14. Suppose \(𝐴𝐵𝐶𝐷\) is a square of side length of 1. \(𝑀\) is the midpoint of \(𝐴𝐵\).

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. \(𝑎, 𝑏\) and \(𝑐\) are the results of the first, second and third throws, respectively.
What is the probability that \(𝑎 > 𝑏 > 𝑐\)?
(A) \(\frac{2}{21}\)
(B) \(\frac{3}{32}\)
(C) \(\frac{4}{43}\)
(D) \(\frac{5}{24}\)
(E) None of the above