Correct Answer: D. \(\frac{n+1-r}{r}\)

Explanation

\(^{n}C_{r} = \frac{n!}{(n-r)! r!}\)

\(^{n}C_{r - 1} = \frac{n!}{(n - (r - 1))! (r - 1)!}\)

\(^{n}C_{r} ÷ ^{n}C_{r - 1} = \frac{n!}{(n - r)! r!} ÷ \frac{n!}{(n-(r-1))!(r-1)!}\)

= \(\frac{n!}{(n-r)! r!} \times \frac{(n-(r-1)! (r-1)!}{n!}\)

= \(\frac{(n + 1 - r)! (r - 1)!}{(n - r)! r!}\)

= \(\frac{(n+1-r)(n-r)! (r-1)!}{(n-r)! r (r - 1)!}\)

= \(\frac{n + 1 - r}{r}\)

Correct Answer: C. implicated

Explanation

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

Gradient = \(\frac{\mathrm d y}{\mathrm d x} = 2ax + b = 8x + 4\)

Equating, we have

\(2a = 8 \implies a = 4\)

\(b = 4\)

For minimum value, gradient = 0

\(8x + 4 = 0 \implies x = -\frac{1}{2}\)

At \(x = -\frac{1}{2}, y = 1\)

\(1 = 4(-\frac{1}{2})^{2} + 4(-\frac{1}{2}) + c\)

\(1 = 1 - 2 + c\)

\(1 = c - 1 \implies c = 2\)

\(a, b, c = 4, 4, 2\).

Correct Answer: D. France

Explanation

(a)(i)Population: This is a group of individuals; of the same species; inhabiting a particular area/habitat; at a particular point in time.

(ii)Competition: - This is the interaction between members of the same population/ species/intra - specific/two or more populations/species/inter - specific; occupying the same trophic level; to obtain mutually needed resources; that are short in supply in their environment.

(iii)Succession: - This is the step by step/orderly; and gradual replacement of communities; arising from a change in the environment/environmental factors; which leads to a climax/stable community.

(b) (i) Sources of noise pollution: -

• Electronic sound system
• Sirens
• Generators
• Airplanes
• Factory machines
• Industrial machines
• Canons shots/guns firing
• Artillery firing
• Quarry activity/construction site
• Motor vehicles.

(ii) Prevention:

• Legislation
• Education/public enlightenment
• Siting factories, industries, military site away from residential areas
• Use of sound proof/silent generators.

(c)(i) Effects of smoke on humans: -

• Causes breathing difficulties.
• Causes injury to the lining of respiratory tracts/ lungs.
• Reduces visibility; reduces photosynthesis leading to lower crop yield.
• Causes discomfort to the eyes.
• Contains carbon monoxide which is injurious to man.

(ii) Effects of sewage on human:

1. Untreated sewage discharged into water bodies makes water unfit for drinking/swimming
2. may cause spread of water borne diseases/correctly named borne disease.
3. its toxic to aquatic organisms thereby depleting food source for man.
4. makes water unsafe for domestic use.
5. leads to offensive odour.
6. poisonous substances may enter the food chain which is unsafe for man.

Correct Answer: A. brain

Correct Answer: D. hope

Correct Answer: B. Some strong wrestlers are not weightlifters

Correct Answer: D. agriculture

Correct Answer: A. #21,901

Explanation

Bank reconciliation statement helps to reconcile the cashbook and bank statement if there are disagreement. A is correct: 21,901 is correct because the cheque wrongly debited by the bank will have increase the bank balance therefore to get the value of the bank statement needed to first of all add back the cashbook