All practice questions

Question 4001Question →

A cocoa processing firm in Nigeria faces various market developments and regulatory shifts. Match each economic scenario on the left with its corresponding impact on the supply of processed cocoa on the right.

Click a left item, then click its matching right item

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Answer

Advanced automated processing technology matches with a rightward shift of the supply curve driven by technological advancement. A sharp rise in market selling price matches with an upward movement along the existing supply curve indicating an increase in quantity supplied. An increase in import duty on processing chemicals matches with a leftward shift of the supply curve caused by higher input costs. Provision of a direct per-unit financial grant matches with a rightward shift resulting from reduced unit costs via state intervention.

Each scenario correctly applies the economic principles of supply determinants: price variations of the product itself produce movements along the curve, while non-price parameters like technological innovation, input taxation, and government subsidies shift the supply curve in directions dictated by their net effect on production costs.

Step-by-Step Solution

1

Differentiate between factors that shift the supply curve and factors that cause movement along the supply curve.

Identified that own-price changes alter quantity supplied (movement along the curve), while non-price determinants (technology, input prices, government taxes/subsidies) alter supply (shift of the curve).

The law of supply establishes price-quantity relationships along a given schedule, whereas external non-price factors re-establish a completely new supply schedule.

2

Evaluate the effect of technological innovation.

Technological progress increases output per unit of input, lowering marginal cost and shifting the supply curve rightward.

Firms can produce more efficiently at existing market prices.

3

Evaluate the effect of a change in own-price.

An increase in the commodity's selling price leads to an upward movement along the current curve.

Producers expand output along their existing production frontier to capitalize on higher profit margins per unit.

4

Analyze government policies and input price changes.

Increased duties on inputs raise costs (shifting supply leftward), while subsidies reduce costs (shifting supply rightward).

Taxes act as cost additions whereas subsidies act as cost reductions.

Key Concept

Distinction between Shifts in Supply and Movements along the Supply Curve

Question 4002Question →

Chlorofluorocarbons (CFCs) released into the atmosphere diffuse into the stratosphere, where they are decomposed by intense solar ultraviolet radiation. Which active reactive species generated during this photolysis process directly catalyzes the catalytic breakdown of ozone ( $\text{O}_3$ ) molecules?

Carbon(IV) oxide molecule (

\text{CO}_2

)

Chlorine free radical (

\text{Cl}^\bullet

)

Methane molecule (

\text{CH}_4

)

Dinitrogen(I) oxide molecule (

\text{N}_2\text{O}

)

Show answer & explanation

Answer: Chlorine free radical ( $\text{Cl}^\bullet$ )

Answer

The chlorine free radical (

\text{Cl}^\bullet

) released from the photolysis of chlorofluorocarbons directly catalyzes the depletion of stratospheric ozone molecules.

Under stratospheric ultraviolet (UV) irradiation, chlorofluorocarbon (CFC) molecules undergo homolytic cleavage to produce reactive chlorine free radicals (

\text{Cl}^\bullet

). A chlorine radical attacks an ozone molecule (

\text{O}_3

) to form a chlorine monoxide radical (

\text{ClO}^\bullet

) and a diatomic oxygen molecule (

\text{O}_2

). The chlorine monoxide radical subsequently reacts with atomic oxygen to regenerate the free chlorine radical (

\text{Cl}^\bullet

). Because the radical is regenerated, it acts as a catalyst in the continuous breakdown of the protective ozone layer.

Step-by-Step Solution

1

Identify the photolysis reaction of CFCs in the stratosphere.

Ultraviolet radiation breaks a

\text{C-Cl}

bond in CFCs (e.g.,

\text{CF}_2\text{Cl}_2 + h\nu \rightarrow \text{CF}_2\text{Cl}^\bullet + \text{Cl}^\bullet

), releasing reactive chlorine free radicals.

High-energy UV photons possess sufficient energy to cleave the chemical bond in the tropospheric-stable CFC molecules upon reaching the stratosphere.

2

Analyze the catalytic cycle of ozone destruction.

\text{Cl}^\bullet + \text{O}_3 \rightarrow \text{ClO}^\bullet + \text{O}_2

followed by

\text{ClO}^\bullet + \text{O} \rightarrow \text{Cl}^\bullet + \text{O}_2

.

The chlorine free radical acts as a true catalyst because it is regenerated at the end of the reaction cycle, allowing a single radical to destroy up to

100,000

ozone molecules.

3

Distinguish between greenhouse gases and ozone-depleting catalysts.

\text{CO}_2

and

\text{CH}_4

trap infrared heat (greenhouse effect), whereas

\text{Cl}^\bullet

radicals chemically decompose ozone (ozone layer depletion).

Conflating global warming mechanisms with ozone depletion mechanisms is a common conceptual error.

Key Concept

Photolysis of CFCs and Catalytic Cycle of Ozone Layer Depletion

Question 4003Question →

Match each of the following Balance of Payments transaction items with its correct account classification.

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Answer

Export of crude oil matches Visible Trade Account; Payment for international freight services matches Invisible Trade Account; Foreign direct investment into domestic real estate matches Capital and Financial Account.

Tangible merchandise like crude oil is recorded in the visible trade section of the current account. Services such as shipping and freight are intangibles recorded in the invisible trade section of the current account. Financial movements such as foreign direct investments involve capital asset creation and belong to the capital and financial account.

Step-by-Step Solution

1

Identify the nature of the transaction for Export of crude oil.

Crude oil is a physical, tangible commodity (merchandise).

Tangible exports and imports are classified as visible trade in the Current Account.

2

Identify the nature of the transaction for Freight services payment.

Shipping/freight is a service (intangible item).

Intangible service transactions are classified as invisible trade in the Current Account.

3

Identify the nature of Foreign direct investment.

FDI involves international capital movement and ownership of physical assets/capital.

Long-term investment flows and ownership of foreign assets belong to the Capital and Financial Account.

Key Concept

Structure of the Balance of Payments

Question 4004Question →

A dominant firm operating in a non-collusive oligopoly currently sells its product at a prevailing market price of $P_0 = \text{N}4,000$ . The price elasticity of demand for its product is $|E_d| = 2.8$ for prices above $P_0$ , and $|E_d| = 0.35$ for prices below $P_0$ . If an automated production process reduces the firm's marginal cost from $MC_1 = \text{N}2,500$ to $MC_2 = \text{N}2,100$ , and this new marginal cost line continues to intersect the vertical gap in the marginal revenue curve, how will the firm adjust its price and output to maximize profits?

Maintain both the current price at

\text{N}4,000

and the existing output level, because the marginal cost shift remains within the discontinuous segment of the marginal revenue curve.

Lower the market price below

\text{N}4,000

and expand output to exploit the decrease in marginal cost.

Raise the market price above

\text{N}4,000

to maximize profit along the elastic segment of the demand curve.

Reduce output while keeping the price constant at

\text{N}4,000

to equate marginal revenue to the lower marginal cost.

Show answer & explanation

Answer: Maintain both the current price at $\text{N}4,000$ and the existing output level, because the marginal cost shift remains within the discontinuous segment of the marginal revenue curve.

Answer

The firm will maintain both its current price at

\text{N}4,000

and its existing output level because the marginal cost reduction occurs entirely within the vertical discontinuity of its marginal revenue curve.

Under Paul Sweezy's kinked demand curve model, non-collusive oligopolists assume rivals will match price cuts but ignore price increases. This asymmetry creates a kink in the demand curve at the prevailing price and a corresponding vertical gap in the marginal revenue curve. Any change in marginal cost that stays within this gap leaves the profit-maximizing output and price unchanged, accounting for rigid prices in oligopolistic markets.

Step-by-Step Solution

1

Analyze the demand curve structure based on rival behavior assumptions.

Above

P_0 = \text{N}4,000

, demand is elastic (

|E_d| = 2.8

) because rivals do not follow price increases. Below

P_0

, demand is inelastic (

|E_d| = 0.35

) because rivals match price cuts.

Asymmetric rival responses create a kinked demand curve at the prevailing price

P_0

.

2

Determine the impact of the kinked demand curve on the Marginal Revenue (

MR

) curve.

The abrupt drop in price elasticity at

P_0

creates a vertical gap (discontinuity) in the

MR

curve directly below the kink point.

MR

is derived from demand elasticity; a sudden drop in elasticity causes a step down in

MR

values at that specific quantity.

3

Evaluate the effect of the reduction in Marginal Cost (

MC

).

The shift from

MC_1 = \text{N}2,500

to

MC_2 = \text{N}2,100

occurs within the vertical boundaries of the

MR

gap.

Since the

MC

curve still passes through the vertical

MR

gap, the condition

MR = MC

remains fulfilled at the same output and price level, demonstrating organizational price rigidity.

Key Concept

Price Rigidity and Discontinuous Marginal Revenue in Oligopoly

Estimated Time:2m 0s

Question 4005Question →

Match each organ of the Economic Community of West African States (ECOWAS) with its correct principal function.

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Answer

Authority of Heads of State and Government matches the supreme decision-making organ determining general policy direction; Council of Ministers matches the body preparing meetings and making recommendations to the summit; ECOWAS Commission matches the permanent executive arm handling day-to-day administrative implementation.

The institutional framework of ECOWAS assigns distinct responsibilities: the Authority of Heads of State and Government is the supreme policy-making body, the Council of Ministers prepares proposals and oversees operational matters, and the ECOWAS Commission handles administrative execution.

Step-by-Step Solution

1

Identify the highest political authority in ECOWAS.

The Authority of Heads of State and Government holds supreme decision-making authority.

It brings together national leaders to set high-level community policies.

2

Identify the ministerial advisory organ.

The Council of Ministers reviews policies and prepares agenda recommendations.

It acts as a preparatory body composed of member state ministers.

3

Identify the administrative organ.

The ECOWAS Commission carries out day-to-day administrative functions.

It operates as the civil service and executive secretariat of the organisation.

Key Concept

Institutional structure and organ functions of ECOWAS

Question 4006Question →

Chidubem Ventures PLC has an authorized capital of ₦500,000 divided into 1,000,000 ordinary shares of 50k each. Out of these, 600,000 shares have been issued and fully paid-up. If the directors declare a dividend of 8% on ordinary share capital, what is the total dividend amount to be debited to the Profit and Loss Appropriation Account?

₦24,000

₦40,000

₦48,000

₦16,000

Show answer & explanation

Answer: ₦24,000

Answer

₦24,000

Dividends must be calculated strictly on the paid-up capital. The paid-up capital is 600,000 shares multiplied by ₦0.50 (50k), yielding ₦300,000. Computing 8% of ₦300,000 gives ₦24,000, which is the total dividend amount transferred from the Profit and Loss Appropriation Account.

Step-by-Step Solution

1

Calculate total paid-up share capital

600,000 shares × ₦0.50 = ₦300,000

Dividends are paid only on shares actually issued and paid for, converted from kobo to Naira (50k = ₦0.50).

2

Calculate the total dividend declared

8% × ₦300,000 = ₦24,000

The declared dividend percentage is applied directly to the total paid-up ordinary share capital.

Key Concept

Dividend Calculation on Paid-Up Capital

Estimated Time:45s

Question 4007Question →

An electronics wholesaler delivers 50 television sets to a retailer under an agreement stating that ownership remains with the wholesaler until the full price is paid in three monthly installments. Before making the first payment, the retailer sells 10 sets in the ordinary course of business to retail customers who buy them in good faith without knowledge of the retention-of-title clause. The retailer subsequently defaults on payment and becomes insolvent. Which of the following best explains the legal position regarding title to the 10 sets and the remedies available under the Sale of Goods Act?

The retail customers obtain valid title under the 'buyer in possession' exception to nemo dat, leaving the wholesaler with a personal remedy to sue the retailer for the contract price.

The retail customers obtain valid title because under all installment credit schemes and hire purchase contracts, ownership passes automatically to the purchaser upon physical delivery.

The wholesaler can repossess the 10 sets from the retail customers because the retailer committed a breach of warranty, which automatically repudiates all secondary transactions.

The retail customers acquire no title because displaying goods in a retail store constitutes a binding legal offer that prevents third parties from acquiring rights when the retailer lacks actual title.

Show answer & explanation

Answer: The retail customers obtain valid title under the 'buyer in possession' exception to nemo dat, leaving the wholesaler with a personal remedy to sue the retailer for the contract price.

Answer

The retail customers acquire valid title under the buyer in possession exception to the nemo dat rule, leaving the wholesaler with a personal remedy against the retailer for the contract price.

Under Section 25 of the Sale of Goods Act, when a buyer who has bought or agreed to buy goods obtains possession of them with the seller's consent, delivering those goods under a sale to an innocent third party acting in good faith confers valid legal title on that third party. Consequently, the original seller loses the right to repossess those goods and must rely on a personal remedy (suing the defaulting buyer for the contract price).

Step-by-Step Solution

1

Analyze the general rule of title transfer (Nemo Dat Quod Non Habet).

Normally, a seller cannot transfer a better title than they possess, so a buyer under a retention-of-title agreement lacks full legal title until payment.

Establishing the baseline statutory rule under the Sale of Goods Act.

2

Identify statutory exceptions to the Nemo Dat rule.

Where a buyer has obtained possession of goods with the consent of the seller ('buyer in possession'), any sale by that buyer to an innocent third party acting in good faith without notice delivers valid title.

Determining whether third-party buyers are protected under commercial law.

3

Evaluate the seller's available remedies under the circumstances.

Because title has validly passed to the third-party retail customers, the original unpaid seller loses real rights over those 10 sets (right of lien or repossession) and is limited to personal remedies against the defaulting buyer for the price of the goods.

Matching statutory buyer/seller remedies to the specific factual outcome.

Key Concept

Nemo Dat Quod Non Habet Exceptions and Remedies of the Unpaid Seller

Question 4008Question →

A metal plate is initially in the form of a rectangle $ABCD$ measuring $14\text{ cm}$ by $10\text{ cm}$ , where $AB = 14\text{ cm}$ . A semicircular piece with diameter $AB$ is cut out from side $AB$ . On the opposite side $CD$ , an isosceles triangular plate with base $CD$ and height $24\text{ cm}$ is attached externally. Taking $\pi = \frac{22}{7}$ , what is the total area of the resulting plate in $\text{cm}^2$ ?

Show answer & explanation

Answer: 231

Answer

The total area of the resulting plate is

231\text{ cm}^2

.

The net area of the plate is found by starting with the area of the rectangle (

140\text{ cm}^2

), subtracting the area of the semicircular cutout (

77\text{ cm}^2

), and adding the area of the attached isosceles triangle (

168\text{ cm}^2

), resulting in

140 - 77 + 168 = 231\text{ cm}^2

.

Step-by-Step Solution

1

Calculate the area of the original rectangle ABCD

140 cm²

The area of a rectangle is calculated as

\text{length} \times \text{width} = 14\text{ cm} \times 10\text{ cm} = 140\text{ cm}^2

.

2

Calculate the area of the removed semicircular section

77 cm²

The radius of the semicircle is

r = \frac{14}{2} = 7\text{ cm}

. The area of a semicircle is

\frac{1}{2}\pi r^2 = \frac{1}{2} \times \frac{22}{7} \times 7^2 = 77\text{ cm}^2

.

3

Calculate the area of the attached triangular section

168 cm²

The area of a triangle is

\frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 14\text{ cm} \times 24\text{ cm} = 168\text{ cm}^2

.

4

Combine the area components to determine the final net area

231 cm²

Subtract the removed semicircular area from the rectangle's area and add the attached triangle's area:

140 - 77 + 168 = 231\text{ cm}^2

.

Key Concept

Perimeter and Area of Composite Plane Figures

Question 4009Question →

What is the equation of the normal to the curve $y = 2x^2 - 3x + 1$ at the point where $x = 2$ ?

x + 5y - 17 = 0

5x - y - 7 = 0

x - 5y + 13 = 0

x + 5y - 13 = 0

Show answer & explanation

Answer: $x + 5y - 17 = 0$

Answer

x + 5y - 17 = 0

Evaluating

y = 2x^2 - 3x + 1

at

x = 2

gives the point

(2, 3)

. Differentiating gives

\frac{dy}{dx} = 4x - 3

, which evaluates to

5

at

x = 2

. The normal line gradient is therefore

-\frac{1}{5}

. Using the point-slope formula

y - 3 = -\frac{1}{5}(x - 2)

and rearranging to standard linear form results in

x + 5y - 17 = 0

.

Step-by-Step Solution

1

Find the

y

-coordinate of the point of contact on the curve when

x = 2

.

Substitute

x = 2

into

y = 2x^2 - 3x + 1

:

y = 2(2)^2 - 3(2) + 1 = 8 - 6 + 1 = 3

. The point is

(2, 3)

.

The line of normal passes through the point of tangency on the curve.

2

Differentiate

y = 2x^2 - 3x + 1

with respect to

x

to find the gradient of the tangent.

\frac{dy}{dx} = 4x - 3

. At

x = 2

,

m_t = 4(2) - 3 = 5

.

The derivative of a curve evaluated at a point yields the gradient of the tangent line at that point.

3

Determine the gradient of the normal line.

Since the normal is perpendicular to the tangent,

m_n = -\frac{1}{m_t} = -\frac{1}{5}

.

Perpendicular lines have gradients whose product is

-1

(

m_t \cdot m_n = -1

).

4

Form the equation of the normal line passing through

(2, 3)

with gradient

m_n = -\frac{1}{5}

.

y - 3 = -\frac{1}{5}(x - 2) \implies 5(y - 3) = -(x - 2) \implies 5y - 15 = -x + 2 \implies x + 5y - 17 = 0

.

Applying the point-slope form

y - y_1 = m(x - x_1)

establishes the linear equation.

Key Concept

Tangents and Normals to Curves

Question 4010Question →

A commercial bank receives a new cash deposit of $\text{N}250,000$ . Following multiple rounds of lending across the banking system, the total credit created in the economy expands to $\text{N}1,250,000$ . What is the Cash Reserve Ratio enforced by the monetary authority?

20\%

25\%

80\%

5\%

Show answer & explanation

Answer: $20\%$

Answer

The Cash Reserve Ratio enforced by the monetary authority is

20\%

.

The relationship between initial cash deposits, total credit expanded, and the reserve ratio is given by

\text{Total Credit Created} = \frac{\text{Initial Deposit}}{\text{Cash Reserve Ratio}}

. Substituting

\text{N}1,250,000 = \frac{\text{N}250,000}{\text{Cash Reserve Ratio}}

and solving for the ratio gives

\frac{\text{N}250,000}{\text{N}1,250,000} = 0.20

, or

20\%

.

Step-by-Step Solution

1

Recall the credit creation formula linking initial deposit, total credit created, and the cash reserve ratio.

\text{Total Credit Created} = \frac{\text{Initial Deposit}}{\text{Cash Reserve Ratio}}

The total volume of credit created by commercial banks depends inversely on the stipulated reserve percentage.

2

Rearrange the formula to isolate the Cash Reserve Ratio.

\text{Cash Reserve Ratio} = \frac{\text{Initial Deposit}}{\text{Total Credit Created}}

Dividing initial deposit by total credit expanded gives the reserve ratio directly.

3

Substitute the given numerical values into the equation and calculate.

\text{Cash Reserve Ratio} = \frac{\text{N}250,000}{\text{N}1,250,000} = 0.20 = 20\%

Executing the division yields

0.20

, which converts to

20\%

.

Key Concept

Credit Multiplier and Reserve Requirements in Commercial Banking

Question 4011Question →

The length of the mercury column in an uncalibrated liquid-in-glass thermometer is $2.0\,\text{cm}$ at the ice point ( $0^\circ\text{C}$ ) and $18.0\,\text{cm}$ at the steam point ( $100^\circ\text{C}$ ). What is the temperature when the length of the mercury column is $9.2\,\text{cm}$ ?

40^\circ\text{C}

45^\circ\text{C}

55^\circ\text{C}

57.5^\circ\text{C}

Show answer & explanation

Answer: $45^\circ\text{C}$

Answer

The temperature corresponding to a mercury column length of

9.2\,\text{cm}

is

45^\circ\text{C}

.

The temperature on the Celsius scale is given by the formula

\theta = \frac{L_\theta - L_0}{L_{100} - L_0} \times 100^\circ\text{C}

. Substituting

L_0 = 2.0\,\text{cm}

,

L_{100} = 18.0\,\text{cm}

, and

L_\theta = 9.2\,\text{cm}

yields

\theta = \frac{7.2}{16.0} \times 100^\circ\text{C} = 45^\circ\text{C}

.

Step-by-Step Solution

1

Identify the fixed points and the thermometric property values.

Ice point length

L_0 = 2.0\,\text{cm}

, steam point length

L_{100} = 18.0\,\text{cm}

, and observed length

L_\theta = 9.2\,\text{cm}

.

The linear scale equation requires establishing the reference points on the Celsius scale.

2

Calculate the fundamental interval length (

L_{100} - L_0

).

L_{100} - L_0 = 18.0\,\text{cm} - 2.0\,\text{cm} = 16.0\,\text{cm}

.

The fundamental interval represents the total change in length corresponding to

100^\circ\text{C}

.

3

Apply the linear interpolation formula

\theta = \frac{L_\theta - L_0}{L_{100} - L_0} \times 100^\circ\text{C}

.

\theta = \frac{9.2 - 2.0}{16.0} \times 100^\circ\text{C} = \frac{7.2}{16.0} \times 100^\circ\text{C} = 45^\circ\text{C}

.

This scales the fractional change in thermometric property above the ice point to degrees Celsius.

Key Concept

Linear interpolation on empirical temperature scales

Estimated Time:1m 30s

Question 4012Question →

Nigeria's thermal electricity generation relies predominantly on domestic fossil fuel deposits. Which of the following thermal power stations was historically built to utilize coal extracted from the Anambra Basin rather than natural gas from the Niger Delta?

Egbin Power Station

Oji River Power Station

Afam Power Station

Sapele Power Station

Show answer & explanation

Answer: Oji River Power Station

Answer

Oji River Power Station

Oji River Power Station in Enugu State is historically renowned as Nigeria's key coal-fired thermal power installation, established to leverage the sub-bituminous coal deposits of the Enugu coalfields within the Anambra Basin. By contrast, facilities like Egbin, Afam, and Sapele are gas-fired thermal stations linked directly to petroleum and natural gas fields in the Niger Delta region.

Step-by-Step Solution

1

Identify the geographical distribution of fossil fuel resources in Nigeria

Coal deposits are concentrated in the sub-bituminous coal belt of the Anambra Basin (Enugu/Kogi/Benue region), whereas natural gas is abundant in the southern Niger Delta sedimentary basin.

Understanding resource geography helps correlate raw fuel locations with power infrastructure.

2

Match the specified thermal power station to its original primary fuel supply

Oji River Power Station was established in Enugu State specifically to harness coal from the local coalfield for thermal power generation.

Oji River is Nigeria's prime historical example of a coal-fired power plant built near coal mines.

Key Concept

Spatial distribution and utilization of coal versus natural gas for thermal power generation in Nigeria

Estimated Time:1m 15s

Question 4013Question →

Mr. Adebayo employs a personal chauffeur for his family, a private cook for his household, an insurance agent to manage his company's risk policies, and a housemaid for domestic chores. Which of these individuals is engaged in a commercial occupation?

The personal chauffeur

The insurance agent

The private cook

The housemaid

Show answer & explanation

Answer: The insurance agent

Answer

The insurance agent is engaged in a commercial occupation.

Insurance is an auxiliary to trade. Individuals working in insurance provide essential services that facilitate trade and business risk management, making the role a commercial occupation.

Step-by-Step Solution

1

Define commercial and direct service occupations.

Commercial occupations involve trading activities and auxiliaries to trade (such as banking, insurance, warehousing, and commercial transport), whereas direct service occupations involve personal services rendered directly to individuals for non-commercial personal satisfaction.

Classification depends on whether the occupation facilitates commercial trade or directly satisfies personal individual needs.

2

Classify each profession mentioned in the stem.

The personal chauffeur, private cook, and housemaid render personal domestic services directly to the employer's family. The insurance agent provides risk management, which is an auxiliary to trade.

Insurance directly assists commercial enterprises and trade activities, establishing it as a commercial occupation.

Key Concept

Distinction Between Commercial and Direct Service Occupations

Question 4014Question →

Which credit instrument is issued by an importer's bank to guarantee payment to an exporter upon the presentation of specified shipping documents?

Letter of Credit

Bill of Lading

Promissory Note

Credit Note

Show answer & explanation

Answer: Letter of Credit

Answer

Letter of Credit

A Letter of Credit is an undertaking by a buyer's bank assuring the seller that payment will be made provided the required shipping documents are presented in compliance with the agreement.

Step-by-Step Solution

1

Identify the primary function described in the scenario.

The instrument serves as a bank-backed payment guarantee in foreign trade.

Exporters require assurance that they will receive payment before shipping goods overseas.

2

Match the function to the correct credit instrument.

A Letter of Credit is the standard financial instrument used by commercial banks to guarantee foreign trade payments.

It substitutes the creditworthiness of the bank for that of the importer.

Key Concept

Forms and Instruments of Credit - Letter of Credit

Estimated Time:45s

Question 4015Question →

Post-independence Nigerian political history witnessed a series of military interventions and regime changes. Arrange the following military coups and regime transitions in the correct chronological order from earliest to latest.

Drag items to arrange them in the correct order

Show answer & explanation

Answer

The correct chronological sequence of military interventions from earliest to latest is: Major Chukwuma Nzeogwu leading the first military coup (January 1966), followed by Lieutenant Colonel Yakubu Gowon assuming power after the counter-coup (July 1966), followed by General Murtala Muhammed overthrowing General Yakubu Gowon (July 1975), and finally Major-General Ibrahim Babangida ousting Major-General Muhammadu Buhari (August 1985).

The correct sequence begins with the inaugural coup of January 1966 led by Major Nzeogwu, followed by the July 1966 counter-coup establishing Yakubu Gowon's military leadership, followed by the July 1975 coup that brought Murtala Muhammed to power, and concludes with the August 1985 palace coup led by Ibrahim Babangida.

Step-by-Step Solution

1

Identify the date of the first military coup d'état led by Major Chukwuma Nzeogwu.

Establishes January 15, 1966 as the starting event of military rule in Nigeria.

This marked the initial collapse of civilian democratic rule in the First Republic.

2

Identify the date of the counter-coup that brought Lieutenant Colonel Yakubu Gowon to head the Federal Military Government.

Establishes July 29, 1966 as the second chronological event.

The July counter-coup directly followed the political fallout of the January coup and the promulgation of Decree No. 34.

3

Identify the date of General Murtala Muhammed's takeover from General Yakubu Gowon.

Establishes July 29, 1975 as the third chronological event.

Murtala Muhammed removed Gowon after nine years in power due to delays in executing a democratic transition program.

4

Identify the date of Major-General Ibrahim Babangida's palace coup against Major-General Muhammadu Buhari.

Establishes August 27, 1985 as the fourth chronological event.

Babangida ousted Buhari following disagreements over economic policies and military governance strategies.

Key Concept

Chronological timeline of military interventions and regime changes in post-independence Nigeria

Question 4016Question →

What is the pH of an aqueous solution containing $0.365\text{ g dm}^{-3}$ of hydrochloric acid ( $\text{HCl}$ )? [Molar mass of $\text{HCl} = 36.5\text{ g mol}^{-1}$ ]

2.0

12.0

0.44

1.0

Show answer & explanation

Answer: $2.0$

Answer

The pH of the solution is 2.0.

The solution has a molar concentration of

0.01\text{ mol dm}^{-3}

(

0.365\text{ g dm}^{-3} / 36.5\text{ g mol}^{-1}

). Taking the negative base-10 logarithm of

1.0 \times 10^{-2}\text{ mol dm}^{-3}

yields a pH of 2.0.

Step-by-Step Solution

1

Convert mass concentration to molar concentration (molarity)

[\text{HCl}] = \frac{0.365\text{ g dm}^{-3}}{36.5\text{ g mol}^{-1}} = 0.01\text{ mol dm}^{-3} = 1.0 \times 10^{-2}\text{ mol dm}^{-3}

pH calculations require concentration in units of

\text{mol dm}^{-3}

.

2

Determine the hydrogen ion concentration

[\text{H}^+]

[\text{H}^+] = 1.0 \times 10^{-2}\text{ mol dm}^{-3}

Hydrochloric acid is a strong monoprotic acid that fully dissociates in water.

3

Calculate the pH using the pH formula

\text{pH} = -\log_{10}[\text{H}^+] = -\log_{10}(1.0 \times 10^{-2}) = 2.0

pH is defined as the negative logarithm to base 10 of the hydrogen ion concentration.

Key Concept

Calculating pH from mass concentration of a strong acid

Estimated Time:1m 0s

Question 4017Question →

A bullet of mass $20\text{ g}$ is moving horizontally at a speed of $400\text{ m s}^{-1}$ . It strikes a stationary block of wood and emerges from the opposite side with a speed of $100\text{ m s}^{-1}$ . What is the magnitude of the work done by the bullet against the resistance of the block, in Joules?

Show answer & explanation

Answer: 1500

Answer

The magnitude of the work done by the bullet in penetrating the block is

1500\text{ J}

.

According to the Work-Energy Theorem, the net work done on an object equals the change in its kinetic energy. The reduction in kinetic energy as the bullet slows from

400\text{ m s}^{-1}

to

100\text{ m s}^{-1}

equals the work done against the resistive force of the wooden block.

Step-by-Step Solution

1

Convert the mass of the bullet into standard SI units (kilograms)

m = \frac{20}{1000} = 0.02\text{ kg}

The standard SI unit for mass in energy equations is the kilogram.

2

Determine the initial kinetic energy of the bullet before entering the block

E_{ki} = \frac{1}{2} \times 0.02\text{ kg} \times (400\text{ m s}^{-1})^2 = 1600\text{ J}

Kinetic energy is defined as

E_k = \frac{1}{2} m v^2

.

3

Determine the final kinetic energy of the bullet as it emerges from the block

E_{kf} = \frac{1}{2} \times 0.02\text{ kg} \times (100\text{ m s}^{-1})^2 = 100\text{ J}

The bullet loses speed upon passing through the block, reducing its kinetic energy.

4

Apply the Work-Energy Theorem to find the work done against resistive forces

W = \Delta E_k = 1600\text{ J} - 100\text{ J} = 1500\text{ J}

The net work done on the bullet equals its change in kinetic energy.

Key Concept

Work-Energy Theorem

Question 4018Question →

A boat sails $10\text{ km}$ from a port $P$ on a bearing of $040^\circ$ to a point $Q$ . From $Q$ , it changes direction and sails $10\sqrt{3}\text{ km}$ on a bearing of $130^\circ$ to reach a point $R$ . What is the bearing of port $P$ from point $R$ ?

280^\circ

100^\circ

250^\circ

160^\circ

Show answer & explanation

Answer: $280^\circ$

Answer

The bearing of port P from point R is

280^\circ

.

By drawing North reference lines at P, Q, and R, the back bearing of P from Q is

040^\circ + 180^\circ = 220^\circ

. The bearing of R from Q is

130^\circ

, creating an interior right angle of

220^\circ - 130^\circ = 90^\circ

at Q. Using right-triangle trigonometry,

\tan(\angle QPR) = \frac{10\sqrt{3}}{10} = \sqrt{3}

, giving

\angle QPR = 60^\circ

. Adding this to the initial bearing of

040^\circ

gives the bearing of R from P as

100^\circ

. Finally, adding

180^\circ

gives the reverse bearing of P from R as

280^\circ

.

Step-by-Step Solution

1

Determine the interior angle

\angle PQR

at vertex

Q

\angle PQR = 90^\circ

The back bearing of P from Q is

040^\circ + 180^\circ = 220^\circ

. The bearing of R from Q is

130^\circ

. The interior angle between QP and QR is

220^\circ - 130^\circ = 90^\circ

.

2

Calculate the angle

\angle QPR

inside right-angled triangle

PQR

\angle QPR = 60^\circ

Since triangle

PQR

is right-angled at

Q

,

\tan(\angle QPR) = \frac{\text{opposite}}{\text{adjacent}} = \frac{QR}{PQ} = \frac{10\sqrt{3}}{10} = \sqrt{3}

. Therefore,

\angle QPR = \arctan(\sqrt{3}) = 60^\circ

.

3

Find the forward bearing of point

R

from port

P

Bearing of

R

from

P = 100^\circ

The bearing of Q from P is

040^\circ

. Since R lies to the right (clockwise) of segment PQ, add

\angle QPR = 60^\circ

to

040^\circ

:

040^\circ + 60^\circ = 100^\circ

.

4

Compute the back bearing of port

P

from point

R

Bearing of

P

from

R = 280^\circ

The back bearing is obtained by adding

180^\circ

to the forward bearing from P to R:

100^\circ + 180^\circ = 280^\circ

.

Key Concept

Three-point bearing calculations using right-triangle trigonometry and back bearings

Estimated Time:2m 30s

Question 4019Question →

A line $L_1$ is given by the equation $3x + 4y - 24 = 0$ , intersecting the x-axis at point $A$ and the y-axis at point $B$ . A second line $L_2$ has the equation $4x - 3y + k = 0$ , where $k > 0$ . If the perpendicular distance from the midpoint of the line segment $AB$ to $L_2$ is $5$ units, what is the value of $k$ ?

Show answer & explanation

Answer: 18

Answer

The value of

k

is

18

.

To find

k

, first determine the intercepts of

L_1

: setting

y=0

gives

A(8, 0)

and setting

x=0

gives

B(0, 6)

. The midpoint

M

of segment

AB

is

\left(\frac{8+0}{2}, \frac{0+6}{2}\right) = (4, 3)

. Using the perpendicular distance formula

d = \frac{|Ax_0 + By_0 + C|}{\sqrt{A^2 + B^2}}

for point

M(4,3)

and line

4x - 3y + k = 0

, we get

d = \frac{|4(4) - 3(3) + k|}{\sqrt{4^2 + (-3)^2}} = \frac{|7 + k|}{5}

. Setting

d = 5

gives

|7 + k| = 25

. Since

k > 0

, solving

7 + k = 25

gives the correct value

k = 18

.

Step-by-Step Solution

1

Determine the coordinates of points A and B

A = (8, 0)

and

B = (0, 6)

Setting

y = 0

in

3x + 4y - 24 = 0

yields

3x = 24 \implies x = 8

. Setting

x = 0

yields

4y = 24 \implies y = 6

.

2

Calculate the midpoint M of segment AB

M = (4, 3)

Using the midpoint formula

M = \left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right) = \left(\frac{8 + 0}{2}, \frac{0 + 6}{2}\right) = (4, 3)

.

3

Set up the perpendicular distance equation from M(4,3) to line L₂

d = \frac{|7 + k|}{5}

Applying the distance formula

d = \frac{|Ax_0 + By_0 + C|}{\sqrt{A^2 + B^2}}

gives

d = \frac{|4(4) - 3(3) + k|}{\sqrt{4^2 + (-3)^2}} = \frac{|16 - 9 + k|}{\sqrt{25}} = \frac{|7 + k|}{5}

.

4

Solve for k given d = 5 and k > 0

k = 18

Equating distance to

5

gives

\frac{|7 + k|}{5} = 5 \implies |7 + k| = 25

. Since

k > 0

,

7 + k = 25

, which yields

k = 18

.

Key Concept

Perpendicular Distance from a Point to a Straight Line

Estimated Time:2m 30s

Question 4020Question →

If $214_x = 312_5$ , where $x$ represents a positive integer base, find the value of $x$ .

Show answer & explanation

Answer: 6

Answer

The value of the base

x

is 6.

Expanding

312_5

to base 10 gives

3(25) + 1(5) + 2(1) = 82

. Expanding

214_x

gives

2x^2 + x + 4

. Equating both expressions yields

2x^2 + x - 78 = 0

. Factoring as

(2x + 13)(x - 6) = 0

gives the positive integer root

x = 6

.

Step-by-Step Solution

1

Convert the right side of the equation from base 5 to base 10

312_5 = 3 \times 5^2 + 1 \times 5^1 + 2 \times 5^0 = 75 + 5 + 2 = 82_{10}

Converting known non-decimal bases to base 10 provides a standard baseline for algebraic manipulation.

2

Expand the left side expression in terms of powers of

x

214_x = 2x^2 + x + 4

Positional values in base

x

correspond to powers of

x

(

x^2, x^1, x^0

).

3

Formulate and rearrange the resulting quadratic equation in standard form

2x^2 + x + 4 = 82 \implies 2x^2 + x - 78 = 0

Setting the base 10 expansions equal forms a quadratic equation.

4

Solve the quadratic equation for positive integer values of

x

x = 6

Factoring

(2x + 13)(x - 6) = 0

gives

x = 6

or

x = -6.5

. A base must be a positive integer larger than all individual digits appearing in the number (digits are 2, 1, 4, so

x > 4

).

Key Concept

Converting non-decimal numbers to base 10 using positional expansion to solve polynomial equations involving unknown bases.

Answer

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