Correct Answer: D. carriage

Explanation

The correct option is D. carriage.

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• Gait refers to a person's manner of walking or stepping.

• Carriage refers to the way a person carries themselves, particularly their posture and bearing while standing or walking, making it the closest in meaning.

*(Other options: Stature refers to height or standing, Figure refers to body shape, and Elegance refers to a general quality of gracefulness rather than specifically the manner of walking.)*

Explanation

(a) The roots of the equation are -1.5 or 2.

(b) C = 6 (intercept on the positive vertical axis)

\(ax^{2} + bx + c = 0\)

When x = 2, c = 6

\(4a + 2b + 6 = 0 \implies 4a + 2b = -6 ....(1)\)

When x = -1.5, c = 6

\(a(-1.5)^{2} + b(-1.5) = -6\)

\(\frac{9a}{4} - \frac{3b}{2} = -6 \implies 9a - 6b = -24 ... (2)\)

Multiply (1) by 3 : \(12a + 6b = -18 ... (1a)\)

(1a) + (2) : \(12a + 9a = -18 - 24 \implies 21a = -42\)

\(a = -2\)

\(4a + 2b = -6 \implies 4(-2) + 2b = -6\)

\(2b = -6 + 8 = 2 \implies b = 1\)

(a, b, c) = (-2, 1, 6)

Hence the relation illustrated in the graph is \(y = -2x^{2} + x + 6\).

(c) When \(x = 0.2, y_{max} = 6.2\)

(d) When \(y = 2, x = \text{ -1.2 or 1.7}\)

Explanation

(a) (i)

\(\cos C = \frac{a^{2} + b^{2} - c^{2}}{2ab}\)

\(\cos C = \frac{12^{2} + 10^{2} - 17^{2}}{2(12)(10)}\)

\(\cos C = \frac{-45}{240} = -0.1875\)

\(C = \cos^{-1} (-0.1875)\)

= \(100.81°\)

(ii) Area of \(\Delta ABC = \frac{1}{2} ab \sin C\)

= \(\frac{1}{2} \times 12 \times 10 \times \sin 100.81\)

= \(60 \times 0.9822\)

= \(58.936 m^{2}\)

(b) \(\tan 63 = \frac{38}{x}\)

\(x = \frac{38}{\tan 63}\)

\(x = 19.362 m\)

\(\approxeq 19 m\)

Correct Answer: A. vowed

Explanation

The correct option is A. vowed.

To pledge means to make a solemn or serious promise to do something.

• Vowed is the nearest in meaning, as it also means to solemnly promise or commit to something.

*(Note: In the sentence, pledge is used in the past participle context after has, equivalent to pledged / vowed.)*

Explanation

(a) (i) Glucose

(ii) Citric acid

(b)(i) The process of obtaining paraffin from crude oil is called fractional distillation

(ii) The process of obtaining benzene from ethyne is called polymerization.

Correct Answer: B. \(24Nm^{-2}\)

Explanation

\(\frac{P_1}{T_1}=\frac{P_2}{T_2};P_2= \frac{22.5\times320K}{300K}=24Nm^{-2}\)

Correct Answer: B. national integration

Explanation

A multi-party system affords that opportunity to the citizenry to have as many choices as possible. Another advantage of a multi-party system is that it allows for a peaceful change of government. The existence of many parties means that there are other parties waiting for their turn to be voted into power.

Correct Answer: B. giveng his daughter in marriage to the person

Correct Answer: A. N380m

Explanation

(b) One method of mining petroleum is drilling:

(i) The underground rocks are sampled and tested for traces of oil

(ii) When oil is discovered, a well is sunk to reach it by the help of a drilling rig or derrick

(iii) The oil is then pumped out

(iv) A system of valves called "Christmas tree" is created to control the flow into tanks

(c) Four problems associated with mining in West Africa;

(i) Lack of fund

(ii) Lack of technical know-how

(iii) Absence of minerals

(iv) Lack of sources of efficient and reliable power