All practice questions

Question 6801Question →

Apex Flour Mills Plc and Zenith Bakery Products Ltd agree to merge their operations into a single company so that wheat flour milling and commercial bread baking are managed under one corporate structure. Which type of business combination does this merger illustrate?

Vertical combination

Horizontal combination

Commercialization

Cartel formation

Show answer & explanation

Answer: Vertical combination

Answer

Vertical combination

The correct option is vertical combination because the merger unites two businesses operating at sequential stages of the same product pipeline: flour milling provides the essential ingredient used in commercial bread baking.

Step-by-Step Solution

1

Analyze the business activities of the merging entities

Apex Flour Mills Plc produces flour (an intermediate input), while Zenith Bakery Products Ltd bakes bread (a finished consumer product).

Identifying the production stage of each firm helps determine the axis of combination.

2

Determine the relationship between the stages of production

The two firms operate at successive, complementary stages of the supply chain in the food manufacturing sector.

Combining successive stages from raw material processing to final consumption defines vertical integration.

3

Match the scenario to the appropriate business combination classification

The transaction represents a vertical combination.

Vertical combinations unite firms engaged at sequential levels of production or distribution within the same overall industry.

Key Concept

Vertical Business Combination

Question 6802Question →

A fixed mass of gas occupies a volume of $800\text{ cm}^3$ at a pressure of $1.5\text{ atm}$ under isothermal conditions. What is the final volume of the gas in $\text{cm}^3$ if the pressure is reduced to $570\text{ mmHg}$ ? ( $1\text{ atm} = 760\text{ mmHg}$ )

1600\text{ cm}^3

400\text{ cm}^3

2.11\text{ cm}^3

22400\text{ cm}^3

Show answer & explanation

Answer: $1600\text{ cm}^3$

Answer

The final volume of the gas is

1600\text{ cm}^3

.

Under isothermal conditions, Boyle's Law applies (

P_1V_1 = P_2V_2

). Converting the initial pressure of

1.5\text{ atm}

to

\text{mmHg}

gives

1140\text{ mmHg}

. Substituting the values into

1140 \times 800 = 570 \times V_2

yields

V_2 = 1600\text{ cm}^3

.

Step-by-Step Solution

1

Convert the initial pressure (

P_1

) to the same unit as the final pressure (

P_2

).

P_1 = 1.5\text{ atm} \times 760\text{ mmHg/atm} = 1140\text{ mmHg}

.

Units of pressure must be consistent before applying gas law equations.

2

Apply Boyle's Law formula for isothermal conditions.

P_1V_1 = P_2V_2 \implies 1140\text{ mmHg} \times 800\text{ cm}^3 = 570\text{ mmHg} \times V_2

.

Boyle's Law states that for a fixed mass of gas at constant temperature, pressure and volume are inversely proportional.

3

Rearrange the equation to solve for

V_2

.

V_2 = \frac{1140 \times 800}{570} = 1600\text{ cm}^3

.

Calculates the expanded volume resulting from the decrease in pressure.

Key Concept

Boyle's Law (

P_1V_1 = P_2V_2

at constant temperature)

Estimated Time:1m 30s

Question 6803Question →

An electric iron rated at $1200\,\text{W}$ is operated for $5\,\text{hours}$ each day for a period of $30\,\text{days}$ . If electrical energy costs $\text{₦}20.00$ per kilowatt-hour ( $\text{kWh}$ ), what is the total cost of electricity consumed by the iron over this period in Naira ( $\text{₦}$ )?

Show answer & explanation

Answer: 3600

Answer

The total cost of electricity consumed by the iron over the 30-day period is 3600 Naira.

To find the cost of electrical energy in commercial units, express power in kilowatts (

1.2\,\text{kW}

) and time in total hours (

150\,\text{h}

). The energy consumed is

1.2 \times 150 = 180\,\text{kWh}

. At a tariff of

\text{₦}20.00

per

\text{kWh}

, the total cost is

180 \times 20 = 3600\,\text{Naira}

.

Step-by-Step Solution

1

Convert the power rating of the appliance from watts to kilowatts

P = \frac{1200\,\text{W}}{1000} = 1.2\,\text{kW}

Commercial energy consumption is calculated in kilowatt-hours (kWh), requiring power in kilowatts.

2

Calculate the total operating time in hours

t = 5\,\text{hours/day} \times 30\,\text{days} = 150\,\text{hours}

The usage duration across the month must be expressed in total hours.

3

Determine electrical energy consumed in kWh

E = P \times t = 1.2\,\text{kW} \times 150\,\text{h} = 180\,\text{kWh}

Energy is the product of power in kilowatts and time in hours.

4

Calculate total cost of energy consumed

\text{Total Cost} = 180\,\text{kWh} \times \text{₦}20.00/\text{kWh} = \text{₦}3600

Total cost is found by multiplying energy in kWh by the unit tariff rate.

Key Concept

Commercial electrical energy unit (kWh) and billing calculation

Question 6804Question →

Concentrated tetraoxosulfate(VI) acid ( $H_2SO_4$ ) is added to hydrated copper(II) tetraoxosulfate(VI) crystals ( $CuSO_4 \cdot 5H_2O$ ), turning their blue color to white. In a separate vessel, dilute tetraoxosulfate(VI) acid reacts with zinc granules to evolve hydrogen gas ( $H_2$ ). Which chemical properties of tetraoxosulfate(VI) acid are demonstrated in the first and second reactions, respectively?

Dehydrating property and acidic property

Oxidizing property and acidic property

Dehydrating property and oxidizing property

Acidic property and dehydrating property

Show answer & explanation

Answer: Dehydrating property and acidic property

Answer

Dehydrating property and acidic property

The removal of water of crystallization from blue

CuSO_4 \cdot 5H_2O

to leave white anhydrous

CuSO_4

demonstrates the dehydrating property of concentrated

H_2SO_4

. The reaction of dilute

H_2SO_4

with zinc to yield hydrogen gas demonstrates a fundamental chemical property of acids.

Step-by-Step Solution

1

Analyze the first reaction involving concentrated

H_2SO_4

and hydrated copper(II) tetraoxosulfate(VI)

Concentrated

H_2SO_4

acts as a dehydrating agent by removing the five molecules of water of crystallization from blue

CuSO_4 \cdot 5H_2O

to form white anhydrous

CuSO_4

.

Dehydration is the chemical removal of chemically combined water molecules from a compound.

2

Analyze the second reaction involving dilute

H_2SO_4

and zinc granules

Dilute

H_2SO_4

reacts with zinc (

Zn

) according to

Zn_{(s)} + H_2SO_{4(aq)} \rightarrow ZnSO_{4(aq)} + H_{2(g)}

, liberating hydrogen gas.

A characteristic property of acids is reacting with metals above hydrogen in the reactivity series to form a salt and hydrogen gas.

3

Combine the identified properties in sequential order

The first reaction exhibits a dehydrating property, and the second reaction exhibits an acidic property.

The question asks for the properties demonstrated in the first and second experiments respectively.

Key Concept

Distinct behavior of concentrated vs dilute tetraoxosulfate(VI) acid

Question 6805Question →

Match each commercial organization listed on the left with its principal aim or scope of operation on the right.

Click a left item, then click its matching right item

Show answer & explanation

Answer

Trade Association matches with establishing standardized trade practices within the same industry; Chamber of Commerce matches with promoting economic interests across sectors in a specific region; Employers' Association matches with representing business owners in collective bargaining with labor unions.

Trade Associations unify companies in the exact same business line to establish ethics and industry standards. Chambers of Commerce unite merchants across diverse fields within a defined geographic territory to advance overall regional commerce. Employers' Associations specifically handle employer-employee relations and collective bargaining with labor unions.

Step-by-Step Solution

1

Analyze the operational scope of a Trade Association.

Trade Associations bind firms in the exact same trade or industry together.

Their goal is to promote standardized practices, technical research, and uniform codes of conduct for their specific sector.

2

Analyze the operational scope of a Chamber of Commerce.

Chambers of Commerce bring together diverse commercial entities from a particular city or territory.

Their focus is geographically bounded rather than sector-bound, aiming to boost overall regional business growth and trade relations.

3

Differentiate Employers' Associations from general trade bodies.

Employers' Associations focus on industrial relations and labor management.

They provide a unified voice for employers during wage negotiations and dispute resolutions with labor unions.

Key Concept

Distinct structural boundaries, aims, and functions of Trade Associations, Chambers of Commerce, and Employers' Associations.

Question 6806Question →

A major manufacturing firm in Lagos seeks to expand its operations by obtaining a substantial loan from a commercial bank. To approve the loan facility, the bank demands assurance that the firm's assets are protected against unexpected catastrophic events such as fire or industrial accidents. How does insurance primarily assist the firm in fulfilling this credit requirement?

By providing financial security against risk, thereby enhancing business creditworthiness and enabling assets to serve as collateral

By converting the private manufacturing business into a state-owned commercialized enterprise

By guaranteeing the total elimination of operational risks and physical disasters

By offering non-commercial direct personal services exclusively to individual company executives

Show answer & explanation

Answer: By providing financial security against risk, thereby enhancing business creditworthiness and enabling assets to serve as collateral

Answer

Insurance primarily assists businesses by providing financial security against loss, which protects asset value, instills confidence in lenders, and allows insurance coverage to enhance creditworthiness for business loans.

Insurance plays a vital role in commerce by spreading financial risk across a pool of policyholders. By protecting business assets against loss, insurance instills confidence in lenders, elevates the firm's credit rating, and enables insured assets or insurance policies to be pledged as security for loans.

Step-by-Step Solution

1

Analyze the firm's requirement in the scenario.

The manufacturing firm needs a commercial bank loan, but the bank demands risk mitigation to ensure the firm remains solvent if assets are destroyed.

Lending institutions require assurance that funded or pledged assets will retain value even if unexpected perils occur.

2

Examine the role of insurance as an auxiliary to trade.

Insurance transfers and pools risks, providing financial indemnification and security to businesses.

By reducing financial uncertainty, insurance encourages capital investment and facilitates credit acquisition.

3

Identify the correct function matching the scenario.

Providing security against risks directly satisfies the lender's requirement by guaranteeing financial compensation in the event of loss.

Risk protection enhances business creditworthiness and satisfies collateral requirements.

Key Concept

Role of Insurance in Credit Enhancement and Business Security

Question 6807Question →

A wholesaler dispatched goods valued at ₦150,000 to a retailer but accidentally billed the retailer ₦135,000 on the commercial invoice. Which commercial document will the wholesaler issue to rectify this undercharge?

A Credit Note

A Debit Note

An Advice Note

A Delivery Note

Show answer & explanation

Answer: A Debit Note

Answer

A Debit Note

A Debit Note is sent by a seller to notify the buyer that their account balance has been increased to rectify an undercharge on a previously issued invoice.

Step-by-Step Solution

1

Identify the financial transaction discrepancy.

The retailer was billed ₦135,000 instead of ₦150,000, creating an undercharge of ₦15,000.

The seller needs to collect the remaining unpaid balance from the customer.

2

Determine the commercial document used to increase a customer's account debt in home trade.

A Debit Note is selected.

A Debit Note informs the buyer that their account has been debited for an additional amount to correct an undercharge.

Key Concept

Debit Note function in Home Trade

Question 6808Question →

Two electric lamps rated at $60\,\text{W}, 220\,\text{V}$ and $100\,\text{W}, 220\,\text{V}$ respectively are connected in series across a $220\,\text{V}$ supply line. What is the total electric power dissipated by the combination?

37.5\,\text{W}

80.0\,\text{W}

160.0\,\text{W}

40.0\,\text{W}

Show answer & explanation

Answer: $37.5\,\text{W}$

Answer

The total electric power dissipated by the two lamps in series is

37.5\,\text{W}

.

For two appliances designed for the same rated voltage

V

connected in series across that voltage

V

, the equivalent power is given by the formula

P_{\text{total}} = \frac{P_1 P_2}{P_1 + P_2}

. Substituting

P_1 = 60\,\text{W}

and

P_2 = 100\,\text{W}

gives

P_{\text{total}} = \frac{60 \times 100}{60 + 100} = 37.5\,\text{W}

.

Step-by-Step Solution

1

Calculate the resistance of each lamp from its rating.

R_1 = \frac{V^2}{P_1} = \frac{220^2}{60} = 806.67\,\Omega

and

R_2 = \frac{V^2}{P_2} = \frac{220^2}{100} = 484.00\,\Omega

Electrical devices are rated at a specific voltage, allowing their resistance to be determined via

R = \frac{V^2}{P}

.

2

Find the total resistance of the series circuit.

R_{\text{total}} = R_1 + R_2 = 806.67 + 484.00 = 1290.67\,\Omega

Resistors in series add directly.

3

Calculate total power drawn from the

220\,\text{V}

supply.

P_{\text{total}} = \frac{V^2}{R_{\text{total}}} = \frac{220^2}{1290.67} = 37.5\,\text{W}

Total power is total voltage squared divided by equivalent resistance.

Key Concept

Power combination in series circuits

Estimated Time:1m 30s

Question 6809Question →

Match each specialized banking service or payment instrument with the commercial trading need it satisfies for a business enterprise.

Click a left item, then click its matching right item

Show answer & explanation

Answer

Credit Transfer matches with settlement of multiple creditor payments via a single instruction. Discounting Bill of Exchange matches with immediate cash payment for a term trade debt before maturity. Bank Draft matches with a guaranteed cheque drawn on the bank's own funds. Night Safe Facility matches with depositing daily cash receipts outside operating hours.

Each commercial banking instrument specifically addresses a distinct financial operational challenge in trade: credit transfers aggregate multiple payments, discounting bills unlocks tied-up receivables before maturity, bank drafts offer guaranteed settlement for high-risk sales, and night safes safeguard after-hours cash proceeds.

Step-by-Step Solution

1

Identify the payment consolidation service

Credit transfer transfers funds from one customer account to multiple payee accounts in a single batch transaction.

Traders use credit transfers to streamline supplier payments and payroll.

2

Identify the short-term working capital facility for trade bills

Discounting a bill of exchange converts a future receivable into immediate cash less interest.

This improves merchant cash flow without waiting for the credit term to elapse.

3

Identify the guaranteed bank payment instrument

A bank draft is drawn directly on the bank, guaranteeing payment security.

Creditors accept bank drafts when personal or business cheques carry a risk of dishonor.

4

Identify the after-hours cash protection service

Night safe facilities provide secure access to drop cash after regular branch closing times.

This protects traders from overnight theft risks.

Key Concept

Banking Functions and Services to Trade

Question 6810Question →

Match each chemical reaction involving acids or bases listed on the left with its correct characteristic observation or product on the right.

Click a left item, then click its matching right item

Show answer & explanation

Answer

Reaction of dilute

HCl

with

Na_2CO_3

pairs with effervescence of carbon(IV) oxide gas; heating

NH_4Cl

with aqueous

NaOH

pairs with evolution of pungent ammonia gas; reaction of dilute

H_2SO_4

with zinc metal pairs with liberation of hydrogen gas; and reaction of aqueous

NaOH

with dilute

HNO_3

pairs with neutralization forming a salt and water without gas evolution.

Each acid and base chemical property produces a distinct, diagnostic observation: acid + carbonate yields carbon(IV) oxide (

CO_2

), base + ammonium salt yields ammonia (

NH_3

), acid + reactive metal yields hydrogen (

H_2

), and acid + base (hydroxide) results in neutralisation forming salt and water.

Step-by-Step Solution

1

Analyze acid-trioxocarbonate(IV) reaction property.

2HCl_{(aq)} + Na_2CO_{3(aq)} \rightarrow 2NaCl_{(aq)} + H_2O_{(l)} + CO_{2(g)}

. The evolved

CO_2

gas causes effervescence and turns lime water milky.

Acids liberate carbon(IV) oxide gas from trioxocarbonates(IV).

2

Analyze base-ammonium salt reaction property.

NH_4Cl_{(s)} + NaOH_{(aq)} \rightarrow NaCl_{(aq)} + H_2O_{(l)} + NH_{3(g)}

. Ammonia gas is pungent and alkaline, turning moist red litmus paper blue.

Soluble bases displace ammonia from ammonium salts when heated.

3

Analyze acid-metal displacement reaction property.

Zn_{(s)} + H_2SO_{4(aq)} \rightarrow ZnSO_{4(aq)} + H_{2(g)}

. Hydrogen gas burns with a pop sound.

Dilute acids react with metals above hydrogen in the electrochemical series to yield hydrogen gas.

4

Analyze acid-base neutralization property.

NaOH_{(aq)} + HNO_{3(aq)} \rightarrow NaNO_{3(aq)} + H_2O_{(l)}

. This is a neutralisation reaction yielding salt and water.

Soluble metal hydroxides react with acids to form salt and water only.

Key Concept

Chemical properties of acids and bases including gas evolution tests and neutralization

Question 6811Question →

For a fixed mass of gas maintained at a constant temperature, a plot of pressure ( $P$ ) against volume ( $V$ ) produces a straight line passing through the origin.

True

False

Show answer & explanation

Answer: False

Answer

The statement is False. At constant temperature, gas pressure is inversely proportional to volume (

P \propto \frac{1}{V}

), resulting in a hyperbolic curve when plotting

P

versus

V

, rather than a straight line.

Boyle's law dictates that the pressure of a fixed mass of gas is inversely proportional to its volume at constant temperature (

P \propto \frac{1}{V}

). As a result, graphing pressure (

P

) directly against volume (

V

) produces a non-linear, downward-sloping curve known as a rectangular hyperbola. To produce a straight line passing through the origin, pressure (

P

) must be plotted against the reciprocal of volume (

\frac{1}{V}

).

Step-by-Step Solution

1

State the mathematical formulation of Boyle's law for a fixed mass of gas at constant temperature.

P \propto \frac{1}{V}

or

P \cdot V = k

, where

k

is a constant.

Boyle's law describes an inverse relationship between pressure and volume.

2

Analyze the nature of a graph where one variable is plotted directly against another inversely proportional variable (

P

vs

V

).

The resulting curve is a rectangular hyperbola that approaches the axes asymptotically.

Inversely proportional quantities do not produce a linear plot when graphed directly against each other.

3

Determine the graphical condition required to obtain a straight line passing through the origin.

Plotting pressure (

P

) against reciprocal volume (

\frac{1}{V}

) yields a straight line with slope equal to constant

k

.

Linearity is achieved by plotting one variable against the reciprocal of the other when

P \propto \frac{1}{V}

.

Key Concept

Graphical representation of Boyle's Law (

P

-

V

relationship)

Question 6812Question →

In commercial practice, while both Trade Associations and Chambers of Commerce aim to promote business activities, which of the following features uniquely characterizes a Chamber of Commerce?

Membership comprises firms across different lines of business within a specific geographical area.

Membership is strictly restricted to businesses operating within the same industry or trade.

It is an association formed primarily by employees to negotiate better working conditions and wages.

It is a statutory government body established to promote foreign trade and collect customs duties.

Show answer & explanation

Answer: Membership comprises firms across different lines of business within a specific geographical area.

Answer

Membership comprises firms across different lines of business within a specific geographical area.

The correct answer accurately states that a Chamber of Commerce is a multi-industry business association structured around a defined geographical boundary (such as a city, state, or country) to foster local economic development, organize trade fairs, and advocate for business interests.

Step-by-Step Solution

1

Identify the organizational scope of a Chamber of Commerce.

A Chamber of Commerce unites business enterprises across varied sectors based on geographical location.

Unlike sector-specific bodies, Chambers of Commerce represent general commercial interests within a locality or region.

2

Differentiate a Chamber of Commerce from related commercial organizations.

Trade Associations are sector-specific, Trade Unions represent workers, and statutory export councils are government agencies.

Analyzing organizational goals and membership boundaries isolates the distinctive feature of a Chamber of Commerce.

Key Concept

Structural and functional distinctions between Chambers of Commerce and Trade Associations

Estimated Time:1m 0s

Question 6813Question →

A sample of oxygen gas occupies a volume of $450\text{ cm}^3$ at a temperature of $27^\circ\text{C}$ . If the pressure remains constant, what will be the volume of the gas when its temperature is increased to $207^\circ\text{C}$ ?

720\text{ cm}^3

3450\text{ cm}^3

281\text{ cm}^3

630\text{ cm}^3

Show answer & explanation

Answer: $720\text{ cm}^3$

Answer

The volume of the gas at

207^\circ\text{C}

is

720\text{ cm}^3

.

According to Charles's Law, the volume of a gas is directly proportional to its absolute temperature when pressure remains constant (

V_1/T_1 = V_2/T_2

). Converting the temperatures to Kelvin (

T_1 = 27 + 273 = 300\text{ K}

and

T_2 = 207 + 273 = 480\text{ K}

) and calculating gives

V_2 = 450 \times (480 / 300) = 720\text{ cm}^3

.

Step-by-Step Solution

1

Convert temperatures from Celsius to the absolute (Kelvin) scale.

T_1 = 27 + 273 = 300\text{ K}

and

T_2 = 207 + 273 = 480\text{ K}

.

Gas laws require temperatures to be expressed on the absolute temperature scale (Kelvin).

2

Apply Charles's Law equation.

\frac{V_1}{T_1} = \frac{V_2}{T_2} \implies V_2 = V_1 \times \frac{T_2}{T_1}

.

At constant pressure, the volume of a fixed mass of gas is directly proportional to its absolute temperature.

3

Substitute the known values and calculate

V_2

.

V_2 = 450 \times \frac{480}{300} = 450 \times 1.6 = 720\text{ cm}^3

.

Completing the arithmetic yields the final volume.

Key Concept

Charles's Law states that at constant pressure, the volume of a given mass of gas is directly proportional to its absolute temperature (

V \propto T

).

Question 6814Question →

A rigid metallic cylinder contains a fixed mass of gas at an initial pressure of $1.2\text{ atm}$ and a temperature of $27^\circ\text{C}$ . If the gas is heated until its temperature reaches $177^\circ\text{C}$ while the volume remains constant, what is the final pressure of the gas in atmospheres?

Show answer & explanation

Answer: 1.8

Answer

The final pressure of the gas is

1.8\text{ atm}

.

Converting the temperatures to Kelvin (

T_1 = 300\text{ K}

and

T_2 = 450\text{ K}

) and applying Gay-Lussac's Pressure Law

\frac{P_1}{T_1} = \frac{P_2}{T_2}

gives

P_2 = 1.2 \times \frac{450}{300} = 1.8\text{ atm}

.

Step-by-Step Solution

1

Convert given temperatures to the Kelvin scale

T_1 = 300\text{ K}

and

T_2 = 450\text{ K}

Gas laws require absolute temperature values measured in Kelvin (

T_K = t_C + 273

).

2

Set up Gay-Lussac's Pressure Law proportion

\frac{P_1}{T_1} = \frac{P_2}{T_2}

P_2 = P_1 \times \frac{T_2}{T_1} = 1.2 \times \frac{450}{300}

At constant volume, the pressure of a fixed mass of gas is directly proportional to its absolute temperature.

3

Perform the multiplication to determine the final pressure

P_2 = 1.8\text{ atm}

Multiplying

1.2

by the ratio

1.5

yields

1.8\text{ atm}

.

Key Concept

Pressure Law (Gay-Lussac's Law) states that for a given mass of gas at constant volume, the pressure is directly proportional to its absolute temperature in Kelvin (

P \propto T

).

Question 6815Question →

Match each electrical operational scenario on the left with its corresponding effect on electrical energy or power on the right.

Click a left item, then click its matching right item

Show answer & explanation

Answer

Doubling current quadruples heat energy (

H \propto I^2

); halving voltage reduces power to one-quarter (

P \propto V^2

); connecting two identical resistors in parallel doubles total power (

P \propto 1/R_{\text{eq}}

); and operating a 500 W appliance for 2 hours consumes 1.0 kWh.

Each left-side scenario correctly aligns with fundamental laws of electrical energy and power: doubling current quadruples heat energy via

H \propto I^2

; halving voltage reduces power to one-quarter via

P \propto V^2

; parallel resistor connection halves total resistance and doubles power; and operating a 0.5 kW appliance for 2 hours consumes 1.0 kWh.

Step-by-Step Solution

1

Apply Joule's Law of Heating (

H = I^2 R t

) to determine the effect of changing current.

Doubling current from

I

to

2I

results in

H' = (2I)^2 R t = 4 I^2 R t = 4H

, so heat quadruples.

Heat generation depends on the square of current when resistance and time are constant.

2

Apply the voltage-power relationship (

P = \frac{V^2}{R}

) for changing voltage.

Halving potential difference to

V/2

yields

P' = \frac{(V/2)^2}{R} = \frac{V^2}{4R} = \frac{P}{4}

, so power drops to one-quarter.

Power is directly proportional to the square of potential difference across a constant resistance.

3

Calculate parallel resistance and total circuit power.

Equivalent resistance of two parallel resistors is

R/2

. Total power is

P_{\text{total}} = \frac{V^2}{R/2} = 2 \frac{V^2}{R}

, which is double the single resistor power.

Parallel combination reduces net resistance by half, thereby doubling total current and power drawn from a constant voltage source.

4

Calculate energy consumption in commercial units (kWh).

E = 0.5\,\text{kW} \times 2\,\text{h} = 1.0\,\text{kWh}

.

Commercial energy is computed by expressing power in kW and time in hours.

Key Concept

Mathematical relationships governing electrical power (

P = I^2 R = \frac{V^2}{R}

), Joule heating (

H = I^2 R t

), and commercial energy units (kWh).

Question 6816Question →

A dip needle placed in the magnetic meridian at a location on the Earth's surface makes an angle of $30^\circ$ with the horizontal. If the total intensity of the Earth's magnetic field at this location is $6.0 \times 10^{-5}\text{ T}$ , what is the vertical component of the Earth's magnetic field?

3.0 \times 10^{-5}\text{ T}

5.2 \times 10^{-5}\text{ T}

6.0 \times 10^{-5}\text{ T}

1.2 \times 10^{-4}\text{ T}

Show answer & explanation

Answer: $3.0 \times 10^{-5}\text{ T}$

Answer

The vertical component of the Earth's magnetic field is

3.0 \times 10^{-5}\text{ T}

.

The vertical component of the Earth's magnetic field is given by

B_v = B \sin \theta

. Substituting

B = 6.0 \times 10^{-5}\text{ T}

and

\theta = 30^\circ

yields

B_v = 6.0 \times 10^{-5} \times 0.5 = 3.0 \times 10^{-5}\text{ T}

.

Step-by-Step Solution

1

Identify the given physical quantities from the problem statement.

Total intensity

B = 6.0 \times 10^{-5}\text{ T}

and inclination angle

\theta = 30^\circ

.

These parameters are required to compute the resolved component.

2

Recall the formula for resolving the vertical component of Earth's magnetic field.

B_v = B \sin \theta

The vertical component corresponds to the vertical side of the right triangle formed by total field

B

and angle of dip

\theta

.

3

Substitute the given values into the formula and calculate.

B_v = (6.0 \times 10^{-5}\text{ T}) \times \sin(30^\circ) = (6.0 \times 10^{-5}) \times 0.5 = 3.0 \times 10^{-5}\text{ T}

.

Since

\sin(30^\circ) = 0.5

, multiplying

6.0 \times 10^{-5}

by

0.5

yields

3.0 \times 10^{-5}\text{ T}

.

Key Concept

Resolution of Earth's total magnetic field into horizontal and vertical components

Question 6817Question →

A textile merchant in Aba receives a 90-day bill of exchange from a buyer in Onitsha for goods delivered on credit. Wanting immediate funds to replenish inventory before the bill matures, the merchant presents the document to a commercial bank for immediate cash settlement at a slight deduction. Which banking service has the merchant utilized?

Discounting a bill of exchange

Opening a letter of credit

Executing a standing order

Obtaining a bank overdraft

Show answer & explanation

Answer: Discounting a bill of exchange

Answer

Discounting a bill of exchange is the banking service that enables a seller to obtain immediate liquidity by selling an un-matured bill of exchange to a commercial bank at a discount.

Discounting a bill of exchange allows a trader to convert a debt owed to them into cash before the bill's maturity date. The bank pays the trader the face value minus a discount fee for early settlement.

Step-by-Step Solution

1

Analyze the merchant's financial scenario and requirement

The merchant holds a 90-day trade credit instrument (bill of exchange) but requires cash before the 90-day maturity period ends.

Identifying the specific financial need helps distinguish between credit facilities and negotiable instrument services.

2

Evaluate the commercial bank functions that provide early cash settlement for trade credit instruments

Commercial banks purchase un-matured bills of exchange from traders at a value lower than the face value, deducting a discount fee to cover interest.

Discounting bills of exchange acts as a short-term working capital solution for trade debts.

Key Concept

Discounting Bills of Exchange in Commercial Banking Services to Trade

Estimated Time:1m 0s

Question 6818Question →

An aqueous solution of barium hydroxide, $\text{Ba(OH)}_2$ , has a molar concentration of $0.0005\text{ mol dm}^{-3}$ . Assuming complete dissociation of the base at $25^\circ\text{C}$ , what is the pH of this solution?

11.0

3.0

10.7

3.3

Show answer & explanation

Answer: $11.0$

Answer

The pH of the solution is

11.0

.

Barium hydroxide (

\text{Ba(OH)}_2

) produces two hydroxide ions (

\text{OH}^-

) per formula unit upon complete dissociation. Thus, a

0.0005\text{ mol dm}^{-3}

solution produces

[\text{OH}^-] = 2 \times 0.0005 = 0.001\text{ mol dm}^{-3} = 1.0 \times 10^{-3}\text{ mol dm}^{-3}

. The pOH is

-\log_{10}(1.0 \times 10^{-3}) = 3.0

. Subtracting pOH from 14.0 yields a pH of

11.0

.

Step-by-Step Solution

1

Determine the concentration of hydroxide ions

[\text{OH}^-]

from the mole ratio of

\text{Ba(OH)}_2

.

Since each mole of

\text{Ba(OH)}_2

dissociates into two moles of

\text{OH}^-

,

[\text{OH}^-] = 2 \times 0.0005\text{ mol dm}^{-3} = 0.001\text{ mol dm}^{-3} = 1.0 \times 10^{-3}\text{ mol dm}^{-3}

.

Barium hydroxide is a strong dibasic base that fully dissociates in aqueous solution.

2

Calculate the pOH of the solution.

\text{pOH} = -\log_{10}[\text{OH}^-] = -\log_{10}(1.0 \times 10^{-3}) = 3.0

.

The pOH scale is defined as the negative logarithm of the hydroxide ion concentration.

3

Calculate the pH using the relationship

\text{pH} + \text{pOH} = 14.0

.

\text{pH} = 14.0 - 3.0 = 11.0

.

At

25^\circ\text{C}

, the sum of pH and pOH for any dilute aqueous solution equals 14.0.

Key Concept

pH and pOH calculations for strong basic solutions considering stoichiometry

Estimated Time:1m 0s

Question 6819Question →

Money serves as a standard of deferred payment when it acts as the common unit used to express and compare the current market prices of different goods and services.

True

False

Show answer & explanation

Answer: False

Answer

False. Expressing and comparing current prices of goods and services describes the 'unit of account' function of money, whereas the 'standard of deferred payment' refers to settling future debts and credit transactions.

The statement is false because measuring and comparing the relative monetary values of goods and services is the 'unit of account' function. The 'standard of deferred payment' function specifically concerns facilitating credit sales and deferred financial contracts.

Step-by-Step Solution

1

Identify the specific function of money described in the statement (expressing and comparing current market prices).

The function that acts as a measure of value for pricing goods is the 'unit of account'.

Unit of account provides a common metric for pricing and financial record-keeping in current transactions.

2

Define the 'standard of deferred payment' function of money.

The standard of deferred payment allows financial obligations to be created today and settled at a specified future date.

This is a secondary function enabling deferred trade, loans, and credit sales.

3

Compare the function in the statement with the actual definition of standard of deferred payment.

The statement misattributes the primary function of unit of account to the secondary function of standard of deferred payment.

Because the statement confuses current price valuation with future debt settlement, it is logically false.

Key Concept

Distinction between Primary (Unit of Account) and Secondary (Standard of Deferred Payment) Functions of Money

Question 6820Question →

An electric heating element rated at $1000\,\text{W}$ and $220\,\text{V}$ is connected to a $110\,\text{V}$ power line. Assuming the electrical resistance of the heating element remains constant, what is the power dissipated by the heater when operating at this reduced voltage?

250\,\text{W}

500\,\text{W}

1000\,\text{W}

2000\,\text{W}

Show answer & explanation

Answer: $250\,\text{W}$

Answer

250\,\text{W}

The electrical power rating of an appliance defines its fixed resistance via

R = \frac{V^2}{P}

. With

R = 48.4\,\Omega

, connecting the appliance to a

110\,\text{V}

supply yields

P = \frac{110^2}{48.4} = 250\,\text{W}

. Alternatively, because

P \propto V^2

for a constant resistance, halving the voltage reduces the power by a factor of

(1/2)^2 = 1/4

, giving

1000\,\text{W} \times \frac{1}{4} = 250\,\text{W}

.

Step-by-Step Solution

1

Calculate the resistance

R

of the heater from its rated values.

R = \frac{V_{\text{rated}}^2}{P_{\text{rated}}} = \frac{220^2}{1000} = \frac{48400}{1000} = 48.4\,\Omega

The resistance of a heating element is determined by its physical design and rated specifications.

2

Calculate the power

P_{\text{new}}

dissipated when connected to the

110\,\text{V}

supply.

P_{\text{new}} = \frac{V_{\text{new}}^2}{R} = \frac{110^2}{48.4} = \frac{12100}{48.4} = 250\,\text{W}

Electric power dissipated across a constant resistance varies with the square of the applied voltage.

Key Concept

Relationship between voltage, resistance, and electrical power dissipation

Estimated Time:1m 30s

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