Correct Answer: C. a stable polity, buoyant economy and visionary leadership

Correct Answer: D. corrupt leadership

Correct Answer: B. air

Correct Answer: C. an increase in the cost of labour

Correct Answer: D. Paralytic

Explanation

(a)(i) Liquids consist of molecules in random motion having different velocities, hence near the surface molecules with higher velocities and kinetic energy escape from the surface. Therefore the average kinetic energy of the remaining liquid is reduced. Since the average kinetic energy is a measure of temperature, therefore temperature is lowered. Hence evaporation causes cooling.

(ii) The heat supplied to boiling water increases the kinetic energy of the molecules and also weaken the bonds between the molecules. Hence at boiling the heat supplied is used in breaking the bonds, therefore molecules escaped as steam without change in temperature.

(b) (i) Boyle's law states that the volume of a fixed mass of gas at constant temperature varies inversely as the pressure upon it.

(ii)

Introduce dry air into burette (B) and close the tap. Read and record the barometer reading H i.e. a.p., keeping B steady, raise the reservoir R, read the mercury head h from the scale, at the same time the corresponding volume V of air from the Repeat burette. Repeat the experiment with various values of H, and determine the corresponding values of h and v. Evaluate P = H ± h and V. Graph of P against V\(^{-1}\)

The graph P against V\(^{-1}\) is a straight line graph passing through the origin, showing that pressure is inversely proportional to volume.

(iii) Precautions;

– I ensured that dry air is used.

– I avoided parallax error when reading metre rule.

Correct Answer: A. fantasizing

Explanation

In the last stanza, the persona is fantasizing. This is evident from the lines 'Miniver loved the days of old' and 'The vision of a warrior bold Would set him dancing.' These lines suggest that Miniver Cheevy is imagining or fantasizing about the past.

Correct Answer: C. 1.75 km

Explanation

(a) \(y = 4x^{3}\)

\(\frac{\mathrm d y}{\mathrm d x} = 12x^{2}\)

\(12x^{2} = 108 \implies x^{2} = 9\)

\(\therefore x = \pm 3\)

When x = -3, \(y = 4(-3^{3}) = -108\)

When x = 3, \(y = 4(3^{3}) = 108\)

\(\therefore P = (-3, -108) ; Q = (3, 108)\)

(b)(i) \(\sin (A - B) = \sin A \cos B - \sin B \cos A\)

\(\sin 15 = \sin (45 - 30) = \sin 45 \cos 30 - \sin 30 \cos 45\)

= \((\frac{\sqrt{2}}{2})(\frac{\sqrt{3}}{2}) - (\frac{1}{2})(\frac{\sqrt{2}}{2})\)

= \(\frac{\sqrt{6} - \sqrt{2}}{4}\)

\(\cos (A - B) = \cos A \cos B + \sin A \sin B\)

\(\cos 15 = \cos (45 - 30) \)

= \(\cos 45 \cos 30 + \sin 45 \sin 30\)

= \((\frac{\sqrt{2}}{2})(\frac{\sqrt{3}}{2}) + (\frac{\sqrt{2}}{2})(\frac{1}{2})\)

= \(\frac{\sqrt{6} + \sqrt{2}}{4}\)

(b)(ii) \(\tan \theta = \frac{\sin \theta}{\cos \theta}\)

\(\tan 15 = \frac{\sqrt{6} - \sqrt{2}}{4} \div \frac{\sqrt{6} + \sqrt{2}}{4}\)

= \(\frac{\sqrt{6} - \sqrt{2}}{\sqrt{6} + \sqrt{2}}\)

Ratinalizing, we have

\((\frac{\sqrt{6} - \sqrt{2}}{\sqrt{6} + \sqrt{2}})(\frac{\sqrt{6} - \sqrt{2}}{\sqrt{6} - \sqrt{2}}) = \frac{6 - 2\sqrt{3} - 2\sqrt{3} + 2}{6 - 2}\)

= \(\frac{8 - 4\sqrt{3}}{4}\)

= \(2 - \sqrt{3}\)

Correct Answer: B. Second