9. Evaluate
\(\sqrt{2017+2016\sqrt{2017+2016\sqrt{2017+…}}}\)
(A) 2015
(B) 2016
(C) 2017
(D) 2018
(E) 2019
10. It is given that \(a+\frac{1}{a}=5\), find \(a^4+\frac{1}{a^4}\)
(A) 523
(B) 527
(C) 631
(D) 635
(E) None of the above
11. Evaluate \(\log_{\frac{1}{2}}8+\log_2 64 – \log_5 \frac{1}{125}\)
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
12. ABCD is a rectangle with E the midpoint of AB and DF β₯ CE .
Given that AB = 6 and BC = 4 . Find the length of DF.
(A) 3.6
(B) 4.2
(C) 4.8
(D) 5.4
(E) None of the above
13. The least number which, when divided by 52 leaves a remainder 33, when divided by 78 leaves 59 as remainder and when divided by 117 leaves 98 as remainder is
(A) 553
(B) 293
(C) 468
(D) 449
(E) 458
14. In the figure shown below, the area of \(Ξπ΄π΅πΆ\) is \(8\)cmΒ², \(π΄πΈ = π·πΈ\) and \(π΅π· = 2πΆπ·\).Find the total area of the shaded regions.
(A) 3.2 cmΒ²
(B) 3.6 cmΒ²
(C) 4.0 cmΒ²
(D) 4.4 cmΒ²
(E) None of the above
15. In ΞABC, AN = BM = AB, β C = 38Β°. Find β APB.
(A) 114Β°
(B) 104Β°
(C) 118Β°
(D) 120Β°
(E) 122Β°
16. \(p\) is the difference between a real number and its reciprocal \(q\) is the difference between the square of the same real number and the square of the reciprocal. Then the value of \(p^4 + q^2 + 4p^2\) is
(A) \(2q^2\)
(B) \(3q^2\)
(C) \(\frac{1}{2}q^2\)
(D) \(\frac{3}{4}q^2\)
(E) None of the above
17. A motorboat takes 6hrs to travel from port A to port B, which is on the same side of the river. It takes the boat 8 hrs. to return to port A. It is given the speed of the current is 2.5 km/h. Find the speed of the boat in still water.
(A) 10.5 km/h
(B) 13.5 km/h
(C) 16.5 km/h
(D) 17.5 km/h
(E) 18.5 km/h
18. Given an equilateral triangle, what is the ratio of area of its inscribed circle to the area of its circumscribed circle?
(A) 1:2
(B) 1:3
(C) 1:4
(D) 1:5
(E) None of the above