Correct Answer: B. \(\frac{-2}{7}\)

Correct Answer: C. \(\frac{3}{8}\)

Explanation

[(\(\frac{16}{9}\))\(^{\frac{-3}{2}}\) x 16\(^{\frac{-3}{2}}\)]\(^{\frac{1}{3}}\)

= [(\(\frac{9}{16}\))]\(^{\frac{3}{2}}\) x [(\(\frac{1}{16}\))\(^{\frac{3}{4}}\)]\(^{\frac{1}{3}}\)

= [(\(\sqrt{\frac{9}{10}}\))\(^3\) x (4\(\sqrt{\frac{1}{16}})^3\)]\(^{\frac{1}{3}}\)

= [(\(\frac{3}{4})^3 \times (\frac{1}{2})^3\)]\(^\frac{1}{3}\)

(\(\frac{27}{64} \times \frac{1}{8}\))\(^\frac{1}{3}\) = \({3}\sqrt{\frac{27}{64} \times \frac{1}{8}}\)

= \(\frac{3}{4} \times \frac{1}{2}\) = \(\frac{3}{8}\)

Correct Answer: C. 4x - 2y = 1

Explanation

(c) Straight line graph of y = 2x + 3

(d) The roots of 2x\(^2\) -3x - 5 = 0 are x=-1±0.1 or 2.5±0.1

(ii) The range of values of x for which -x -2 < 0is (-0.7±0.1) < x < (1.3±0.1)

Correct Answer: C. (-1/3) cos 3x + c

Correct Answer: C. \(\frac{1}{8}\)

Explanation

Girl = \(\frac{1}{2}\)

Blue eyes = \(\frac{1}{4}\)

probability that she will give birth to a girl with blue eyes: \(\frac{1}{2}\) x \(\frac{1}{4}\)

= \(\frac{1}{8}\)

Explanation

Given \(\sin x = 0.6 = \frac{3}{5}\)

\(\therefore Opp = 3; Hyp = 5\)

Using Pythagoras theorem,

\(5^{2} = 3^{2} + Adj^{2}\)

\(Adj = \sqrt{5^{2} - 3^{2}}\)

\(Adj = \sqrt{25 - 9} = \sqrt{16} = 4\)

\(\therefore \cos x = \frac{4}{5} = 0.8\)

\(2\cos x + 3\sin x = 2(\frac{4}{5}) + 3(\frac{3}{5})\)

= \(\frac{8}{5} + \frac{9}{5}\)

= \(\frac{17}{5}\).

(b)

Join O to X and O to Y.

Considering either \(\Delta OXC\) or \(\Delta OYC\),

\(\sin 65 = \frac{r}{30}\)

\(r = 30 \sin 65\)

\(r = 30 \times 0.9063\)

\(r = 27.189 cm \approxeq 27.2 cm\) (to one decimal place)

(b) Area of shaded portion = Area of triangle ABC - Area of semi-circle WXYZ.

= \(\frac{1}{2} bh - \frac{1}{2} \pi r^{2}\)

= \((\frac{1}{2} \times 2c \times 30) - (\frac{1}{2} \times \frac{22}{7} \times (27.189)^{2})\)

From \(\Delta COA, \tan 65 = \frac{c}{30}\)

\(\implies c = 30 \tan 65 \approxeq 64.34 cm\)

\(\therefore\) Area of shaded portion = \(30(64.34) - \frac{8131.659}{7}\)

= \(1930.056 - 1161.666\)

= \(768.39 cm^{2}\)

Correct Answer: C. x = 2, y = 0

Correct Answer: D. -34

Correct Answer: B. \(\frac{3}{4}\)

Explanation

Gradient = \(\frac{-4 - 4}{-3 - 3}\)

= \(\frac{-8}{6}\)

= \(\frac{4}{3}\)

Normal = -(\(\frac{1}{\frac{1}{4}}\))

= \(\frac{-3}{4}\)