Correct Answer: D. Coal, Petroleum and water

Explanation

(a) \(S_{n} = \frac{5n^{2}}{2} + \frac{5n}{2}\)

\(S_{1} = \frac{5(1^{2})}{2} + \frac{5(1)}{2} = 5 \implies T_{1} = 5\)

\(S_{2} = \frac{5(2^{2})}{2} + \frac{5(2)}{2} = 10 + 5 = 15\)

\(S_{3} = \frac{5(3^{2})}{2} + \frac{5(3)}{2} = 30\)

\(S_{4} = \frac{5(4^{2})}{2} + \frac{5(4)}{2} = 50\)

\(T_{2} = S_{2} - S_{1} = 15 - 5 = 10\)

\(T_{3} = S_{3} - S_{2} = 30 - 15 = 15\)

\(T_{4} = 50 - 30 = 20\)

The first four terms are 5, 10, 15 and 20.

This is a linear sequence with d = 5.

\(T_{n} = a + (n - 1)d\)

= \(5 + (n - 1)5 \implies T_{n} = 5 + 5n - 5 = 5n\)

(b) \(x^{2} + y^{2} - 10x - 8y + 25 = 0\)

For circle to touch x- axis, the distance from centre of circle to the x- axis must be equal to the radius.

\(x^{2} + y^{2} - 10x - 8y + 25 = 0\)

\(2g = -10, g = -5\)

\(2f = -8 , f = -4\)

Centre = (-g, -f) = (5, 4).

\(Radius = \sqrt{g^{2} + f^{2} - c} = \sqrt{(-5)^{2} + (-4)^{2} - 25} = 4\)

\(|PQ| = \sqrt{4^{2}} = 4\)

Since PQ = radius, circle touches x- axis.

Explanation

(a)G) Dew Point: This is the temperature at which the water vapour/miosture present in the atmosphere/air is just sufficient to saturate it.

(a)(ii) Explanation of why dew forms more quickly on metal parts than rub Metal is a better conductor of heat than rubber. At night. metal loses heat faster than rubber and becomes colder.

Warm air gains latent heat of vaporization from the faster than rubber. Dews are thus formed on the metal parts.

9: (b)(i) Explanation of the statement: 400J of heat/energy is required to charge or raise the temperature of lkg of copper by 1k.

(ii) Heat = mcΔΘ

Hence; MpCpΔΘP = MqCqΔΘq

Given that: Cp : Cq = 3:1 and

Mp : Mq = 1:2

\(\frac{ΔΘp}{ΔΘq}\) = \(\frac{Cp * Mq}{Cp * Mp}\) → \(\frac{1}{3}\) * \(\frac{2}{1}\)

ΔΘp : ΔΘq = 2:3

Heat = mcΔΘ

Hence; MpCpΔΘP = MqCqΔΘq

1 * 3 * ΔΘp = 2 * 1 * ΔΘp

\(\frac{ ΔΘp }{ ΔΘq}\) = \(\frac{2}{3}\)

ΔΘp : ΔΘq = 2:3

(c) Definition of Coefficient of Thermal Conductivity: The time rate of flow of heat per unit cross sectional area per unit temperature gradient.

Θ/t = [KAΔΘ]/[ΔL]

40 X π \(\frac{10 * 10^{-3}^2}{4) * {100 - Θ}{0.15}\)

= 360 * π \(\frac{10 * 10^{-3}^2}{4} * {Θ - 0}{0.05}\) = 3.6°C

(c)(iii) Θ/t = 40π \(\frac{10^{-2}{4}^3\) \(\frac{100 - 3.6}{0.15}\) = 2.02J/S

Correct Answer: A. 100Nm^-2

Explanation

P = \(\frac{wt}{A} = \frac{200}{2 \times 1} = 100Nm^{-2}\)

Correct Answer: D. provide essential services to the people at minimal cost

Explanation

A Public Corporation can be defined as an organization, set up by an Act of Parliament and its sole purpose is to provide services to the public at an affordable price.

Correct Answer: D) Carried digested food

Explanation

The hepatic portal vein is a special vein in the body. It is important because it carries something important. The question is asking what the hepatic portal vein carries. The options to choose from are deoxygenated blood, begins and ends with capillaries, is the largest vein in mammals, or carried digested food. Option A is incorrect because the hepatic portal vein actually carries oxygenated blood. Option B is incorrect because the hepatic portal vein does not begin and end with capillaries - it starts in capillaries in the digestive system and ends in capillaries in the liver. Option C is also incorrect because the largest vein in mammals is actually the inferior vena cava. The correct answer is option D - the hepatic portal vein carries digested food. This is because it is responsible for transporting nutrients and other substances from the digestive tract to the liver, where they can be processed and stored. It's important to understand the role of the liver in digestion and metabolism. The liver performs many important functions, including detoxification of harmful substances, production of bile to aid in digestion, and storage of important nutrients like glycogen and vitamins. The hepatic portal vein plays a crucial role in allowing the liver to carry out these functions effectively. In summary, the hepatic portal vein is a special vein that carries digested food from the digestive system to the liver. It is an important part of the body's digestive and metabolic processes.

Correct Answer: C. Hosea

Correct Answer: B. meandered

Explanation

Meandered; (of a river or road) follow a winding course.

The river meandered across the plain

Correct Answer: A. Toad

Correct Answer: C. contribute to sustaining and developing its community