Correct Answer: D. 120cm³

Correct Answer: B. final outcome

Explanation

The resolution in a literary work refers to the final outcome of the story, where the conflicts are resolved and the story concludes. It is the part of the story's plot line in which the problem of the story is resolved or worked out. This occurs after the falling action and is typically where the story ends.

Correct Answer: A. I and IV only

Explanation

(a)G) Root-mean-square value of an alternating Current 1s the value of a.c. current that has the same heating effect as d.c. current.

(ii) Impedance is the effective resistance of an electric circuit arising from the combined effects of ohmic resistance, capacitance and inductive reactance.

(b) Current in circuit I = 60/120 = 0.5A

Voltage across device V\(_R\) = 120v

Voltage across capacitor = V\(_C\) = √[V\(^2\) - V\(_R\)\(^2\)]

V\(_C\) = √[240\(^2\) - 120°]

V\(_C\) = 207.847v

I\(_C\) = I = 0.5A

X\(_C\) = V\(_C\) / I\(_C\)

= \(\frac{207.846}{0.5) → 415.7Ω

Capicitance, C = \(\frac{X_c}{2πf}\)

= \(\frac{415.7}{2 * 3.142 * 50}\)

= 1.323F

The capacitance C of a capacitor is the ratio of the amount of charge q on its plates to the potential difference between them, i.e C = q/v

(ii) I - charge on both capacitors are the same q1 = q2

Total capacitance, C = \(\frac{C_1 C_2}{C_1 + C_2}\)

C = \(\frac{C_2}{1 + C_1/C_2}\) = \(\frac{C_2}{1 + V_1 + C_2}\)

C = \(\frac{C_2 V_2}{V_1 + C_2}\) = \(\frac{C_2 V_2}{2}\)

C = 1/2 = \(C_2 V_2\)

II - voltage across V\(_1\) = \(\frac{C_2}{C_1 + C_2}\) * V

V\(_1\) = \(\frac{1}{C_1_{C_2} + 1}\) * V

but \(\frac{C_1}{C_2}\) = \(\frac{C_1}{C_2}\) = \(\frac{5}{2}\)

V\(_1\) = \(\frac{1}{5}{2} + 1}\) * 2

= \(\frac{2}{7}\) * 2 = \(\frac{4}{7}\) V

Voltage across C\(_2\) : V\(_2\) = 2 = \(\frac{4}{7}\) = \(\frac{10}{7}\) V

Correct Answer: C. there should be no compulsion in religion

Explanation

(a)(i) The indication of features in the map area should be done on the geographical maps given

(ii) The shading of the area above 925 feet in the North-East should equally be done on the map extract

(b)(i) Actual distance on map = 28 0cm. Since the scale reads, 1:50,000, Therefore measurement on paper is multiplied by the scale and divided by 100,000 i.e =28 x 50,000k= 14km

100,000

The actual distance on land is 4km

(ii) Type of rock is limestone;

(iii) The possible industry is cement factory

(c)(i) Communication: Roads avoid areas liable to flood

(ii) There are many footpaths

(iii) There are limited roads due to many streams

(iv) The secondary road in the North-East avoids river valleys

(ii) Settlement:

(i) Fewer settlements in the West due to lack of surface water

(ii) Dispersed settlement in search of surface water

(iii) There are more settlements near the river valleys in the east

(iv) Settlements avoid areas liable to flood

(d)(i) The presence of river makes fishing possible

(ii) The presence of scrubland makes cattle rearing possible

(iii) The presence of scattered cultivation which makes farming to be possible

Correct Answer: B. economic development

Explanation

In short, production possibility curve is a curve which shows all possible combinations of two goods that can be produced by making full use of given resources and technology in an economy. A production possibility curve measures the maximum output of two goods using a fixed amount of input. The input is any combination of the four factors ofproduction. ... Each point on the curve shows how much of each good will be produced when resources shift from making more of one good and less of the other.

Correct Answer: C. sulphur

Correct Answer: A. \(f^{-1} : x \to \frac{2x + 3}{x - 1}, x \neq 1\)

Explanation

\(f(x) = \frac{x + 3}{x - 2}\)

\(f(y) = \frac{y + 3}{y - 2}\)

Let f(y) = x,

\(x = \frac{y + 3}{y - 2}\)

\(x(y - 2) = y + 3\)

\(xy - y = 2x + 3 \implies y(x - 1) = 2x + 3\)

\(y = \frac{2x + 3}{x - 1}\)

Correct Answer: B. Gambia