Problems And Solutions SEAMO PAPER F 2020

SEAMO

18. Find the least positive integer \(𝑛\) such that the equation \(⌊\frac{10^𝑛}{π‘₯}βŒ‹ = 98\) has integer solution \(π‘₯. βŒŠπ‘˜βŒ‹\) is the largest integer smaller than or equal to \(π‘˜\).
(A) 3
(B) 4
(C) 5
(D) 6
(E) None of the above


Belum tersedia


19. How many positive integers \(π‘˜ < 100\) such that \(2(5^{6𝑛})+ π‘˜(2^{3𝑛+2}) βˆ’ 1\) is divisible by \(7\) for any positive integer \(𝑛\)?
(A) 12
(B) 14
(C) 18
(D) 19
(E) None of the above


Belum tersedia


20. 𝐴, 𝐡, 𝐢 and 𝐷 are four distinct points lying on the circumference of a circle such that chords 𝐴𝐡 and 𝐢𝐷 are perpendicular at point 𝐸. Given that 𝐸𝐴 = 4, 𝐸𝐡 = 2 and 𝐸𝐢 = 6 , find the radius of the circle.


(A) \(\sqrt{221}\)
(B) \(15\)
(C) \(270\)
(D) \(18\)
(E) None of the above


Belum tersedia


21. You need to tile a \(10 Γ— 1\) hallway with a supply of \(1 Γ— 1\) red, \(2 Γ— 1\) red tiles and \(2 Γ— 1\) blue tiles. Find the number of ways you can tile the \(10 Γ— 1\) hallway.


22. π‘₯, 𝑦 and 𝑧 are real numbers such that

\(π‘₯ + 𝑦 + 𝑧 = 7\)
\(π‘₯^2 + 𝑦^2 + 𝑧^2 = 19\)
\(π‘₯^3 + 𝑦^3 + 𝑧^3 = 64\)

Evaluate \(π‘₯^4 + 𝑦^4 + 𝑧^4\).


Belum tersedia


23. In \(Δ𝐴𝐡𝐢\) shown below, \(𝐴𝐷, 𝐡𝐸\) and \(𝐢𝐹\) intersect at \(𝑃\) . SupposeΒ \(𝐴𝑃 = π‘Ž\), \(𝐡𝑃 = 𝑏, 𝐢𝑃 = 𝑐\) and \(𝐷𝑃 = 𝐸𝑃 = 𝐹𝑃 = π‘₯\). Given that \(π‘₯ = 3\) and \(π‘Ž + 𝑏 + 𝑐 = 20\) , find \(π‘Žπ‘π‘\).


Belum tersedia


24. Positive integers π‘Ž, 𝑏 and 𝑐 are randomly selected from the set \(\{1,2,3, … ,2020\}\) with replacement. Find the probability that \(π‘Žπ‘π‘ + π‘Žπ‘ + 2π‘Ž\) is divisible by \(5\).


Belum tersedia


25. \(𝐴𝐡𝐢𝐷\) is a convex quadrilateral such that \(𝐴𝐢\) intersects \(𝐡𝐷\) at \(𝐸\) . \(𝐻\) is a point lying in the segment \(𝐷𝐸\) such that \(𝐴𝐻\) is perpendicular to \(𝐷𝐸\). Suppose \(𝐡𝐸 = 𝐸𝐷, 𝐢𝐸 = 9, 𝐸𝐻 = 12, 𝐴𝐻 = 32\) and \(∠𝐡𝐢𝐴 = 90°\) . Evaluate the length of \(𝐢𝐷\).


Belum tersedia


Baca juga

SEAMO PAPER F 2019 [PROBLEM And SOLUTION]

Pages ( 3 of 3 ): Β« Previous12 3

Leave a Reply

Your email address will not be published. Required fields are marked *