Correct Answer: A. longitudinal spread along the coast

Correct Answer: (d) Corporate Affairs Commission

Explanation

(a) \(f : x \to x^{2} + 1\)

\(g : x \to 5 - 3x\)

(i) \(f(x) = x^{2} + 1\)

Let y = f(x).

\(y = x^{2} + 1 \implies x^{2} = y - 1\)

\(x = \sqrt{y - 1}\)

\(\implies f^{-1} (x) = \sqrt{x - 1}\)

\(Dom(f^{-1} (x)) = x \geq 1\)

(ii) \(g(x) = 5 - 3x\)

Let y = g(x)

\(y = 5 - 3x \implies 3x = 5 - y\)

\(x = \frac{5 - y}{3}\)

\(g^{-1} (x) = \frac{5 - x}{3}\)

\(g^{-1} (2) = \frac{5 - 2}{3} = 1\)

(b) \(\int \frac{x + 3}{x^{2} + 6x + 9} \mathrm {d} x\)

\(\frac{x + 3}{x^{2} + 6x + 9} = \frac{x + 3}{(x + 3)^{2}}\)

= \(\frac{1}{x + 3}\)

\(\therefore \int \frac{x + 3}{x^{2} + 6x + 9} \mathrm {d} x = \int \frac{1}{x + 3} \mathrm {d} x\)

= \(\ln |x + 3| + c\)

Correct Answer: A. Time

Correct Answer: B. A gorge

Correct Answer: B. III only

Explanation

(a)Balance of Payment:This shows the relationship between a country's total payments to other countries and its total receipts from them within a given period.

(b) Methods adopted to correct an adverse balance of payment:

(i) Export Promotion

(ii) Discourage importation

(iii) Borrowing

(iv) Gifts and debts cancellation

(v) Debt rescheduling/ postponement

(vi) Devaluation

(vii) Sale of Assets abroad

(viii) Counter trade

(ix) Encouraging local industries.

(b)(i)Export Promotion: This refers to government activities aimed at production of goods for export, e.g. creation of Export Free Zone.

(ii)Discourage importation:Reduction in importation of goods through the imposition of restrictions like tariff, embargoes, exchange control measures, quotas, etc.

(iii)Borrowing: The government can borrow from the international financial institutions like I.M.F. to settle deficit on her balance of payment.

(iv)Gifts and debt cancellation:Gifts and debt cancellation by friendly countries can be used in financing the balance of payment.

(v)Debt Postponement: Payment for debts in the current year can be postponed to another so as not to be used in the preparation of the balance of payment for the year under consideration.

(vi)Devaluation: Devaluation of the country's currency-bringing the value of the currency lower in relation to other currencies so as to attract foreign investment. This is the last resort that can be adopted.

(vii)Sale of Assets abroad: Selling of gold reserves and assets overseas can be used to correct adverse balance of payment.

(viii)Counter Trade: Exchange of country's goods for other country's goods can also be used.

(ix)Encouraging Local Industries:This can be done through provision of subsidies and tax concessions to local producers.

Correct Answer: D. Jesus of Nazareth

Correct Answer: A. General Assembly

Correct Answer: C. boundary disputes