Correct Answer: C. 8s

Explanation

F = ma

\(200 = 20a \implies a = 10m/s^{2}\)

\(s = ut + \frac{1}{2}at^{2}\)

\(320 = (0 \times t) + \frac{1}{2} 10t^{2}\)

\(320 = 5t^{2} \implies t^{2} = 64\)

\(t = 8secs\)

Explanation

∠OAB = ∠OBA=34°

∠OBA=90

∠OBD = ∠ABD - ∠0BA = 90 - 34 = 56

From triangle OBC

∠BOC + ∠OBC + ∠OCB= 180°

∠BOD =∠2OAB=68°

= 68° + 90° + ∠0CB=180

∠OCB= 180-158 =22

Correct Answer: C. p = 6, k = 6

Explanation

\(\frac{P}{2} + \frac{k}{3}\) = 5

\(\frac{3p + 2k}{6}\) = 5

2p + 3k = 30

- 2p - k = 6

\(\overline{\frac{4k}{4} = \frac{24}{4}}\)

k = 6

From 2p - k = 6

2p - 6 = 6

\(\frac{2p}{2} = \frac{12}{2}\)

p = 6

Correct Answer: D. 2\(\sqrt{5}\)

Explanation

\(\frac{3\sqrt{5} \times 4\sqrt{6}}{2 \sqrt{3} \times 3\sqrt{2}}\)

= \(\frac{\sqrt{5} \times 2\sqrt{6}}{\sqrt{2} \times \sqrt{3}}\)

= \(\frac{\sqrt{5} \times 2 \sqrt{6}}{\sqrt{6}}\)

= 2\(\sqrt{5}\)

Correct Answer: A. 61

Explanation

x - 1 = 2

x = 3

f(2) = (3)\(^3\) + 3(3)\(^2\) + 4(3) - 5

f(2) = 27 + 27 + 12 - 5

= 61

Correct Answer: A. 2

Correct Answer: C. 8.6 x 10^-1

Explanation

ai. To find all the elements in the set M, we have to solve the inequality.

2n - 3 ≤ 37

2n = 37 + 3 = 40.

2n ≤ 40

n ≤ \(\frac{40}{2}\)

n ≤ 20

so, the set M contains all positive numbers n such that n is less than or equal to 20

Therefore, set M elements are {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20}

(α)

Pr(multiple of 3) = \(\frac{multiples of 3}{ Total number of element in M}\)

But the multiples of 3 in set M are = {3, 6, 9, 12, 15, 18} = 6

? Pr(multiples of 3) = \(\frac{6}{20} = \frac{3}{10}\)

(β)

Pr( factors of 10) = \(\frac{? of factors of 10}{ Total ? of set M elements}\)

factors of 10 in set M = { 1, 2, 5, and 10} = 4

? Pr( factors of 10) = \(\frac{4}{20} = \frac{1}{5}\)

bi. Let the total amount shared = y

Gapson's age = \(\frac{3}{2}\times Kontor's age\). Since kontor is 20yrs old then Gapson's age = \(\frac{3}{2}\times20\) = 30years.

sharing ratio = 20 : 30 = 2 : 3

total ratio = 2 + 3 = 5

Since Kontor received Le200,000

\(\frac{2}{5} \times y\) = 200,000

\(\frac{2y}{5} = 200,000\)

cross multiplying, we have

2y = 5 x 200,000 = 1000,000

y = \(\frac{1000,000}{2}\) = 500,000.

? Total amount shared = Le500,000.

ii. Gapson's share = Total - kontor's share

= 500,000 - 200,000 = Le300,000.

Correct Answer: D. 2 x 2 x 2 x 2 x 3

Explanation

48 = 2 x 2 x 2 x 2 x 3

Correct Answer: B. 4x² - 11x - 3 = 0