Problems And Answers PHIMO MOCK 2020 SENIOR SECONDARY

21. How many ways are there to put 7 identical oranges into 4 identical packages so that each package has at least one apple?

22. Determine the exact value of

\(\frac{2}{\frac{1}{\sqrt 2 + \sqrt[4]8 +2}+\frac{1}{\sqrt 2 + \sqrt[4]8 – 2}}\)

23. Find the integer which is closests to \(\frac{(1+\sqrt 3)^4}{4}\)

24. Find the 2021th-smallest \(x\) with \(x > 1\), that satisfes the following relation:

\(\sin(\ln x) + 2 \cos(3 \ln x) \sin(2 \ln x) = 0\).

25. A circle is inscribed in a right triangle with sides \(a, b,\) and \(c\), where \(c\) is the hypotenuse, as shown in the diagram. Find the radius of the circle using the sides of the triangle.

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