All practice questions

What is the value of the definite integral $\int_{0}^{\frac{\pi}{3}} \cos(2x) \, dx$ ?

\frac{\sqrt{3}}{4}

\frac{\sqrt{3}}{2}

-\frac{\sqrt{3}}{4}

\frac{1}{4}

Show answer & explanation

Answer: $\frac{\sqrt{3}}{4}$

Answer

\frac{\sqrt{3}}{4}

The antiderivative of

\cos(2x)

is

\frac{1}{2}\sin(2x)

. Substituting the limits gives

\frac{1}{2}\sin\left(\frac{2\pi}{3}\right) - \frac{1}{2}\sin(0) = \frac{1}{2}\left(\frac{\sqrt{3}}{2}\right) - 0 = \frac{\sqrt{3}}{4}

, which is correct.

Step-by-Step Solution

1

Find the antiderivative of

\cos(2x)

\int \cos(2x) \, dx = \frac{1}{2}\sin(2x) + C

Using standard trigonometric integration rules,

\int \cos(kx) \, dx = \frac{1}{k}\sin(kx) + C

.

2

Substitute the upper limit

x = \frac{\pi}{3}

and lower limit

x = 0

\left[\frac{1}{2}\sin(2x)\right]_{0}^{\frac{\pi}{3}} = \frac{1}{2}\sin\left(\frac{2\pi}{3}\right) - \frac{1}{2}\sin(0)

Apply the Fundamental Theorem of Calculus:

\int_{a}^{b} f(x)dx = F(b) - F(a)

.

3

Evaluate the trigonometric values and simplify

\frac{1}{2}\left(\frac{\sqrt{3}}{2}\right) - 0 = \frac{\sqrt{3}}{4}

\sin\left(\frac{2\pi}{3}\right) = \sin(120^\circ) = \frac{\sqrt{3}}{2}

and

\sin(0) = 0

.

Key Concept

Definite Integration of Trigonometric Functions

Question 6502Question →

A commercial enterprise based in Kano operates an integrated supply chain: it cultivates raw cotton on plantations, spins and weaves the cotton into textiles in processing factories, and distributes the finished fabrics to regional merchants. Which of the following activities in this production chain represents a commercial tertiary sector operation?

Harvesting raw seed cotton directly from the agricultural plantation

Spinning raw cotton fibre into yarn and weaving it into finished textile rolls

Warehousing and distributing the finished textiles to regional retail traders

Providing custom garment tailoring services directly to individual households for personal use

Show answer & explanation

Answer: Warehousing and distributing the finished textiles to regional retail traders

Answer

Warehousing and distributing the finished textiles to regional retail traders

Warehousing and distributing the finished textiles to regional retail traders belongs to the commercial tertiary sector because it involves commercial trade and auxiliary services (transportation and warehousing) that facilitate the distribution of manufactured products from producers to end markets.

Step-by-Step Solution

1

Classify the primary sector activity in the scenario

Cultivating and harvesting raw cotton represents the primary (extractive/agricultural) sector.

Primary production extracts or harvests natural resources provided by nature.

2

Classify the secondary sector activity in the scenario

Spinning cotton into yarn and weaving fabrics represents the secondary (manufacturing/processing) sector.

Secondary production transforms primary raw materials into usable manufactured goods.

3

Distinguish commercial tertiary services from primary, secondary, and direct services

Warehousing, wholesaling, and distributing fabrics facilitate trade and commercial exchange.

The commercial tertiary sector encompasses trade and auxiliaries to trade (transportation, warehousing, insurance, banking) that enable goods to move from factories to consumers.

Key Concept

Classification of Economic Sectors of Production (Primary, Secondary, Tertiary)

Estimated Time:1m 0s

Question 6503Question →

A manufacturing enterprise in Nigeria needs long-term credit facilities to purchase heavy industrial equipment and expand its factory operations. Because commercial banks primarily provide short-term loans, which specialized development bank is explicitly established to fulfill this long-term industrial capital requirement?

Federal Mortgage Bank of Nigeria

Bank of Industry

Central Bank of Nigeria

Nigerian Export-Import Bank

Show answer & explanation

Answer: Bank of Industry

Answer

The Bank of Industry is the specialized development bank established to provide long-term financing to manufacturing enterprises and industrial projects.

The Bank of Industry is mandated to accelerate industrial development by offering medium- and long-term loans for the establishment, modernization, and expansion of industrial and manufacturing enterprises.

Step-by-Step Solution

1

Identify the primary financial requirement described in the scenario.

The enterprise requires long-term credit facilities to purchase heavy industrial equipment and expand manufacturing capabilities.

Commercial banks rely mainly on short-term demand deposits and are structured to provide short-term working capital rather than long-term industrial development funds.

2

Evaluate the primary mandates of Nigeria's specialized and development banks.

The Bank of Industry is dedicated to offering medium and long-term financing to industrial enterprises, manufacturing projects, and processing facilities.

Development institutions are sector-focused: the Bank of Industry targets manufacturing and industrial expansion, whereas mortgage banks focus on housing and export-import banks target international trade.

Key Concept

Mandates of Specialized and Development Banks in Nigeria

Question 6504Question →

The primary objective of establishing a public corporation is to provide essential services to the public rather than to maximize profit.

True

False

Show answer & explanation

Answer: True

Answer

The statement is true because public enterprises are set up by government acts to serve the public interest and provide social amenities rather than to maximize private profits.

Public enterprises are created by legislative acts primarily to ensure that critical public services and utilities are made available to all citizens at reasonable rates, placing social welfare ahead of profit maximization.

Step-by-Step Solution

1

Identify the primary motive behind the creation of public enterprises.

Government establishes public corporations to supply vital infrastructure and essential goods/services.

Establishing the core rationale clarifies why government intervention is needed in utility provision.

2

Differentiate public enterprise goals from private sector goals.

Unlike private enterprises which prioritize financial profit, public corporations focus on social utility and economic welfare.

This confirms that social service delivery is the main objective.

Key Concept

Rationale and Features of Public Enterprises

Question 6505Question →

Kensington Logistics Ltd. has an authorized capital of $1,000,000$ ordinary shares of $₦50$ each. The board of directors issued $70\%$ of these shares to subscribers. The company requested payment of $₦30$ per share, but the actual amounts remitted by shareholders total $₦25$ per share to date. What is the total value of the company's uncalled capital?

₦14,000,000

₦3,500,000

₦15,000,000

₦17,500,000

Show answer & explanation

Answer: $₦14,000,000$

Answer

₦14,000,000

The correct answer is

₦14,000,000

. Uncalled capital represents the portion of the nominal value of issued shares that the company has not yet requested shareholders to pay. Kensington Logistics Ltd. issued

700,000

shares (

70\%

of

1,000,000

). With a nominal value of

₦50

per share and a called-up amount of

₦30

per share, the uncalled amount per share is

₦20

. Multiplying

700,000

issued shares by

₦20

yields

₦14,000,000

.

Step-by-Step Solution

1

Calculate the total number of issued shares

70\% \times 1,000,000 = 700,000 \text{ shares}

Uncalled capital applies only to shares that have actually been issued to subscribers.

2

Determine the uncalled amount per issued share

₦50 - ₦30 = ₦20 \text{ per share}

Uncalled capital per share is the nominal value minus the called-up value per share.

3

Multiply the number of issued shares by the uncalled amount per share

700,000 \times ₦20 = ₦14,000,000

This yields the total value of uncalled capital for the firm.

Key Concept

Uncalled Capital in Share Capital Structure

Estimated Time:2m 0s

Question 6506Question →

Match each credit transaction scheme listed on the left with its defining legal ownership characteristic on the right.

Click a left item, then click its matching right item

Show answer & explanation

Answer

Hire Purchase Scheme matches with ownership remaining with the seller until the final installment is fully paid. Deferred Payment Scheme matches with ownership passing upon payment of the first installment. Credit Sale Scheme matches with ownership passing immediately upon contract execution.

Hire Purchase reserves legal title with the vendor until the complete contract sum is settled in full. Deferred Payment transfers ownership once the initial deposit or installment is satisfied. Credit Sale conveys legal title immediately upon contract execution prior to installment settlements.

Step-by-Step Solution

1

Determine the timing of ownership transfer for Hire Purchase.

In Hire Purchase, the buyer is technically a hirer until the final installment is paid, meaning legal ownership remains with the seller until the last payment.

The seller retains title as security until full contract payment is realized.

2

Determine the timing of ownership transfer for Deferred Payment.

Under a Deferred Payment scheme, ownership transfers to the buyer after the initial payment or deposit is made.

The contract acts as a sale where payment is deferred, transferring ownership early in the installment cycle.

3

Determine the timing of ownership transfer for Credit Sale Scheme.

In a Credit Sale, legal ownership passes immediately to the buyer as soon as the contract is executed.

The seller extends credit for a completed sale, relinquishing ownership upfront.

Key Concept

Timing of ownership transfer across Hire Purchase, Deferred Payment, and Credit Sale transactions

Question 6507Question →

An agricultural trading firm purchases bulk harvests of maize from scattered rural farmers, stores the grain in its private warehouses, takes legal title to the goods, and subsequently distributes smaller quantities to urban retail merchants while extending 30-day trade credit. Which of the following correctly classifies this intermediary and the primary function rendered specifically to the retail merchants?

A merchant wholesaler breaking bulk and financing retail trade

An agent broker negotiating sales contracts without holding title or providing credit

A factor issuing credit notes to manufacturers to correct undercharged sales invoices

A direct commercial service provider offering auxiliary transport services to final consumers

Show answer & explanation

Answer: A merchant wholesaler breaking bulk and financing retail trade

Answer

A merchant wholesaler breaking bulk and financing retail trade

A merchant wholesaler acquires title to merchandise, stores goods, bears financial risks, breaks bulk into smaller lots, and provides financing to retailers via trade credit terms.

Step-by-Step Solution

1

Analyze the business operations of the intermediary in the scenario.

The firm purchases in bulk, stores inventory, takes legal title, bears ownership risk, breaks bulk, and offers credit terms to retailers.

Merchant wholesalers purchase goods outright (taking title) and perform essential distribution services for both producers and retailers.

2

Distinguish between wholesaler functions rendered to producers versus functions rendered to retailers.

Breaking bulk into manageable retail quantities and granting trade credit are direct functions rendered to retailers.

Producers benefit from bulk purchasing and market feedback, whereas retailers benefit from bulk breaking, credit facilities, and variety.

3

Evaluate the option choices to identify the correct classification.

The intermediary is a merchant wholesaler performing bulk-breaking and financing for retailers.

This accurately matches the operational definition of a merchant wholesaler serving the retail link in the channel of distribution.

Key Concept

Classification and Functions of Merchant Wholesalers

Estimated Time:1m 30s

Question 6508Question →

Following the 1966 military intervention in Nigeria, Decree No. 1 (Constitution Suspension and Modification Decree) was promulgated. Which of the following best describes the primary legal effect of military decrees on the jurisdiction of regular courts regarding military enactments?

Decrees contained ouster clauses that explicitly barred regular courts from questioning their validity or constitutionality.

Decrees remained subordinate to unsuspended provisions of the constitution whenever legal conflicts arose in civilian courts.

Decrees empowered High Courts to exercise judicial review and invalidate executive actions violating fundamental human rights.

Decrees abolished regular civilian courts completely and transferred all civil and criminal jurisdiction to military tribunals.

Show answer & explanation

Answer: Decrees contained ouster clauses that explicitly barred regular courts from questioning their validity or constitutionality.

Answer

Military decrees included ouster clauses that explicitly stripped regular civilian courts of the jurisdiction to challenge or question the validity of military enactments.

Under military rule in Nigeria starting from 1966, military decrees were established as the highest source of law, superseding the constitution. To protect their laws from being challenged, military governments included ouster clauses in decrees, which legally prohibited civilian courts from questioning or invalidating any decree.

Step-by-Step Solution

1

Analyze the nature of military legislation post-1966 in Nigeria.

Identified Decree No. 1 (Constitution Suspension and Modification Decree) as establishing Decree Supremacy.

Military governance relies on decrees enacted by the supreme military body rather than acts passed by a civilian parliament.

2

Examine the legal mechanism used by military regimes to restrict judicial intervention.

Military decrees frequently incorporated 'ouster clauses'.

Ouster clauses specifically exclude the jurisdiction of regular law courts from reviewing military enactments or executive military actions.

Key Concept

Military Decree Supremacy and Judicial Ouster Clauses

Question 6509Question →

Read the unseen poetic extract below and answer the question that follows:

"Beneath the silver moonlight's heavy glare,
We walked through crowded streets of solitude;
The quiet noise of midnight filled the air,
Where ancient shadows carefully intrude."

Which literary device is predominantly featured in the expressions "crowded streets of solitude" and "quiet noise"?

Oxymoron

Paradox

Metaphor

Assonance

Show answer & explanation

Answer: Oxymoron

Answer

Oxymoron

The expressions 'crowded streets of solitude' and 'quiet noise' join directly opposing words to produce a compressed stylistic contrast. Bringing together mutually exclusive terms side-by-side is the exact definition of an oxymoron.

Step-by-Step Solution

1

Examine the structure of the target phrases from the extract.

The phrases pair contrasting ideas directly together: 'crowded' with 'solitude', and 'quiet' with 'noise'.

Analyzing how words relate semantically reveals the figure of speech used.

2

Differentiate between oxymoron and other literary devices.

The side-by-side placement of words with contradictory meanings defines an oxymoron.

Oxymoron specifically requires adjacent contradictory terms.

Key Concept

Identification of Figures of Speech in Unseen Extracts (Oxymoron vs. Paradox)

Question 6510Question →

In prose fiction, a framed narrative (or frame story) is a structural plot device wherein an outer narrative serves to set the context for an inner primary story or a series of embedded tales.

True

False

Show answer & explanation

Answer: True

Answer

True

The statement is true because a framed narrative functions precisely by establishing a primary outer story that introduces, frames, and connects one or more inner narratives.

Step-by-Step Solution

1

Examine the definition of a framed narrative within literary plot structure.

Identify that a framed narrative consists of an outer story embedding an inner story.

Evaluating narrative devices requires accurate knowledge of plot organization patterns.

2

Compare the statement's description with standard literary principles.

The statement accurately reflects how outer framework stories operate in prose fiction.

Validating the definition confirms the statement is true.

Key Concept

Framed Narrative (Frame Story)

Estimated Time:45s

Question 6511Question →

Which structural economic policy specifically involves the sale of government-owned equity and operational control in public corporations to private investors?

Privatization

Commercialization

Deregulation

Indigenization

Show answer & explanation

Answer: Privatization

Answer

Privatization is the economic policy that involves selling government equity and transferring control of public enterprises to private investors.

Privatization directly refers to the policy of selling government equity and transferring ownership and managerial control of state-owned enterprises to private individuals or corporate investors.

Step-by-Step Solution

1

Analyze the core policy requirement described in the stem.

The requirement focuses on transferring government equity and ownership rights to private entities.

Divestment of government shares in public enterprises defines ownership transfer.

2

Distinguish between privatization, commercialization, and deregulation.

Commercialization retains state ownership, deregulation removes market restrictions, while privatization sells government equity to private buyers.

Only privatization changes the ownership structure from public to private.

Key Concept

Distinction between Privatization and Commercialization

Question 6512Question →

Public corporations established by an Act of Parliament possess separate legal entity status, and their operational staff are directly classified as civil servants subject to Civil Service Commission rules.

True

False

Show answer & explanation

Answer: False

Answer

False. Although public corporations are established as separate legal entities by an Act of Parliament, their staff are public servants controlled by their governing board, not civil servants governed by the Civil Service Commission.

Statutory public corporations possess operational autonomy and separate legal personality. Consequently, their staff are public servants accountable to the governing board rather than civil servants under the Civil Service Commission.

Step-by-Step Solution

1

Analyze the legal status of statutory public corporations.

Statutory public corporations are created by a specific Act of Parliament, giving them legal personality independent of the government.

Establishing legal personality allows corporations to sue, be sued, hold property, and enter contracts in their own name.

2

Examine the employee classification and administrative control.

Corporation employees are public servants recruited and managed by the corporation's Board of Directors, whereas civil servants work in government ministries under the Civil Service Commission.

Autonomy in staffing and administration is a defining feature designed to enable commercial efficiency distinct from ministerial bureaucracy.

3

Evaluate the validity of the statement.

The second part of the statement conflates public servants of statutory corporations with ministerial civil servants, making the overall statement false.

A true/false statement containing a factual error regarding operational control must be evaluated as false.

Key Concept

Features and Staffing Structure of Public Corporations

Question 6513Question →

A trolley of mass $0.40\text{ kg}$ moving to the right with a velocity of $5.0\text{ m s}^{-1}$ collides head-on with a second trolley of mass $0.60\text{ kg}$ moving to the left at $2.5\text{ m s}^{-1}$ . If the two trolleys stick together on impact, what is their combined velocity immediately after the collision?

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

to the right

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

to the right

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

to the right

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

to the right

Show answer & explanation

Answer: $0.50\text{ m s}^{-1}$ to the right

Answer

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

to the right

By adopting a standard vector sign convention where movement to the right is positive and movement to the left is negative, the initial momentum is

p_i = (0.40 \text{ kg} \times 5.0 \text{ m s}^{-1}) + (0.60 \text{ kg} \times -2.5 \text{ m s}^{-1}) = 2.0 - 1.5 = 0.50 \text{ kg m s}^{-1}

. Because the trolleys stick together, their total mass becomes

0.40 \text{ kg} + 0.60 \text{ kg} = 1.0 \text{ kg}

. Dividing the total momentum by the combined mass gives a final velocity of

+0.50 \text{ m s}^{-1}

, indicating movement to the right.

Step-by-Step Solution

1

Assign a directional sign convention for velocity vectors

Rightward velocity

u_1 = +5.0\text{ m s}^{-1}

, Leftward velocity

u_2 = -2.5\text{ m s}^{-1}

Linear momentum is a vector quantity, so direction must be accounted for using opposite algebraic signs.

2

Calculate total initial linear momentum of the system

p_i = m_1 u_1 + m_2 u_2 = (0.40 \times 5.0) + (0.60 \times (-2.5)) = 2.0 - 1.5 = +0.50\text{ kg m s}^{-1}

Sum the individual initial momenta of both trolleys.

3

Apply the principle of conservation of linear momentum to solve for final combined velocity

v = \frac{p_i}{m_1 + m_2} = \frac{+0.50}{0.40 + 0.60} = +0.50\text{ m s}^{-1}

Since no external net force acts on the system, total initial momentum equals total final momentum.

Key Concept

Conservation of Linear Momentum in Inelastic Collisions

Estimated Time:1m 30s

Question 6514Question →

Match each feature, capital source, merit, or demerit of a sole proprietorship listed on the left with its correct description or classification on the right.

Click a left item, then click its matching right item

Show answer & explanation

Answer

Unlimited Liability matches with the feature where personal assets can be seized for debts. Retained Earnings matches with the internal capital source obtained from ploughed-back profits. Quick Decision-Making matches with the operational merit of acting without consultation. Lack of Continuity matches with the structural weakness where the business usually ends upon the death of the owner.

Each item accurately corresponds to its core definition within sole proprietorship concepts: Unlimited Liability attaches personal property to debts; Retained Earnings serves as ploughed-back internal capital; Quick Decision-Making is a prompt administrative advantage; and Lack of Continuity reflects the absence of perpetual succession.

Step-by-Step Solution

1

Identify legal features of sole proprietorship

Unlimited liability links directly to the owner's personal liability for business obligations.

The sole proprietorship lacks a separate legal entity from its owner.

2

Analyze capital sources available to a sole trader

Retained earnings represent ploughed-back profits stored for re-investment.

It is an internal financial resource, unlike loans or debentures.

3

Evaluate operational merits and demerits

Quick decision-making is an operational benefit, whereas lack of continuity is a key structural demerit.

Sole control enables fast choices, but lack of perpetual succession threatens long-term existence.

Key Concept

Sole Proprietorship Features, Merits, Demerits, and Capital Sources

Question 6515Question →

A constant force of $12\text{ N}$ acts for $4.0\text{ s}$ on a body of mass $3.0\text{ kg}$ that is initially moving at $5.0\text{ m s}^{-1}$ in the direction opposite to the force. What is the final velocity of the body in the direction of the applied force?

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

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

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

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

Show answer & explanation

Answer: $11\text{ m s}^{-1}$

Answer

The final velocity of the body in the direction of the force is

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

.

By the impulse-momentum theorem, the impulse

F \Delta t = 12 \times 4.0 = 48\text{ N s}

causes a velocity change

\Delta v = \frac{48}{3.0} = 16\text{ m s}^{-1}

in the direction of the force. Since the body initially moved in the opposite direction at

-5.0\text{ m s}^{-1}

, the final velocity is

-5.0 + 16 = 11\text{ m s}^{-1}

in the direction of the force.

Step-by-Step Solution

1

Assign direction signs to physical quantities based on a chosen coordinate system.

Let the direction of the applied force be positive (+). Then

F = +12\text{ N}

,

m = 3.0\text{ kg}

,

t = 4.0\text{ s}

, and initial velocity

u = -5.0\text{ m s}^{-1}

.

Velocity and force are vector quantities; motion opposite to the force must carry a negative sign.

2

Calculate the impulse delivered by the force.

\text{Impulse} = F \times \Delta t = 12\text{ N} \times 4.0\text{ s} = 48\text{ N s}

.

Impulse equals force multiplied by the time interval over which it acts.

3

Apply the impulse-momentum theorem

F \Delta t = m(v - u)

to solve for final velocity

v

.

48 = 3.0 \times (v - (-5.0)) \implies 16 = v + 5.0 \implies v = 11\text{ m s}^{-1}

.

The change in linear momentum of an object is equal to the net impulse applied to it.

Key Concept

Impulse-Momentum Theorem and Vector Sign Conventions

Question 6516Question →

Unlike commercial banks, primary mortgage institutions in Nigeria are legally restricted from operating demand deposits and providing cheque-clearing facilities for their retail customers.

True

False

Show answer & explanation

Answer: True

Answer

True

Primary Mortgage Institutions are specialized non-bank financial intermediaries meant for real estate and housing finance; regulations strictly bar them from offering demand deposit current accounts or operating cheque-clearing services.

Step-by-Step Solution

1

Examine the scope of operations defined for non-bank financial institutions such as Primary Mortgage Institutions.

Primary Mortgage Institutions focus strictly on mortgage loans and housing savings schemes.

Non-bank financial institutions operate under specialized mandates distinct from general commercial banking.

2

Assess whether demand deposit creation and cheque clearing fall within their statutory powers.

Demand deposits and cheque clearing are exclusive privileges of licensed commercial banks.

Financial regulations forbid non-bank financial intermediaries from accepting current/chequing accounts to preserve monetary policy control.

Key Concept

Operational boundaries and regulatory restrictions of Non-Bank Financial Institutions

Question 6517Question →

To eliminate chronic fiscal deficits, the federal government restructured a national railway corporation by granting it complete managerial autonomy, withdrawing all operational grants and subsidies, and requiring it to cover both operational and capital expenditures strictly through market-driven tariffs, while maintaining 100% state equity ownership. Which public enterprise reform strategy does this enterprise transformation demonstrate?

Outright privatization

Partial commercialization

Full commercialization

Market deregulation

Show answer & explanation

Answer: Full commercialization

Answer

Full commercialization is the reform strategy where a state-owned enterprise operates as a fully profit-driven corporate entity with total financial self-sufficiency and zero government subsidies, while remaining entirely under state ownership.

Full commercialization occurs when a public enterprise is restructured to operate strictly as a commercial profit-making entity without any financial subvention or subsidy from the government, while maintaining total public ownership of its equity.

Step-by-Step Solution

1

Analyze equity ownership state in the scenario

The state retains 100% equity ownership, ruling out privatization options.

Privatization fundamental criteria involves divestment of government shareholding to private individuals or entities.

2

Evaluate subsidy status and financial autonomy requirement

The enterprise must cover all capital and operational expenses without any government grants or subsidies.

Complete withdrawal of state subvention for both capital and recurrent expenditure distinguishes full commercialization from partial commercialization.

3

Distinguish enterprise restructuring from sector regulation

The action reshapes an existing state corporation's internal operating mandate rather than opening the industry market statutory rules.

Deregulation changes market entry rules, whereas commercialization changes enterprise financial and operational structures.

Key Concept

Full Commercialization vs. Partial Commercialization and Privatization

Estimated Time:1m 30s

Question 6518Question →

A container of heat capacity $80\text{ J K}^{-1}$ holds $0.4\text{ kg}$ of a liquid. When $9.6\text{ kJ}$ of heat energy is supplied to the system, the temperature of the container and liquid rises by $20\text{ K}$ . What is the specific heat capacity of the liquid?

1000\text{ J kg}^{-1}\text{ K}^{-1}

1200\text{ J kg}^{-1}\text{ K}^{-1}

400\text{ J kg}^{-1}\text{ K}^{-1}

480\text{ J kg}^{-1}\text{ K}^{-1}

Show answer & explanation

Answer: $1000\text{ J kg}^{-1}\text{ K}^{-1}$

Answer

1000\text{ J kg}^{-1}\text{ K}^{-1}

The option specifying

1000\text{ J kg}^{-1}\text{ K}^{-1}

is correct because out of the

9600\text{ J}

supplied,

1600\text{ J}

(

80 \times 20

) is absorbed by the container. The remaining

8000\text{ J}

raises the temperature of

0.4\text{ kg}

of liquid by

20\text{ K}

, yielding

c = \frac{8000}{0.4 \times 20} = 1000\text{ J kg}^{-1}\text{ K}^{-1}

.

Step-by-Step Solution

1

Calculate the thermal energy absorbed by the container

Q_{\text{container}} = 1600\text{ J}

The heat absorbed by a body of heat capacity

C

during a temperature change

\Delta T

is given by

Q_{\text{container}} = C \Delta T = 80\text{ J K}^{-1} \times 20\text{ K} = 1600\text{ J}

.

2

Determine the net thermal energy absorbed by the liquid

Q_{\text{liquid}} = 8000\text{ J}

By energy conservation,

Q_{\text{total}} = Q_{\text{container}} + Q_{\text{liquid}}

, so

Q_{\text{liquid}} = 9600\text{ J} - 1600\text{ J} = 8000\text{ J}

.

3

Calculate the specific heat capacity of the liquid

c_{\text{liquid}} = 1000\text{ J kg}^{-1}\text{ K}^{-1}

Using the specific heat capacity relationship

Q = m c \Delta T

,

c_{\text{liquid}} = \frac{Q_{\text{liquid}}}{m \Delta T} = \frac{8000\text{ J}}{0.4\text{ kg} \times 20\text{ K}} = 1000\text{ J kg}^{-1}\text{ K}^{-1}

.

Key Concept

Distinction and calculation involving heat capacity of a container and specific heat capacity of a substance

Question 6519Question →

Examine the line of poetry provided below and identify the figurative language device that completes the analysis statement.

Fill in the blanks below

In the line 'All hands on deck were summoned as the storm approached the shore', the figure of speech in which a physical part ('hands') is used to represent the whole entity (the sailors) is known as .

Show answer & explanation

Answer

The correct figure of speech is synecdoche.

Synecdoche is a trope wherein a part of something is used to signify the whole (or the whole for a part). Using 'hands' to mean the entire crew of sailors is a classic example of synecdoche.

Step-by-Step Solution

1

Analyze the poetic line to identify the highlighted word and what it represents.

The word 'hands' refers specifically to the workers or sailors on the ship.

The word 'hands' is a physical part of a person's body.

2

Determine the relationship between the term used and the actual object/person described.

A part ('hands') represents the whole ('sailors').

When a part of an object or person represents the entire whole, the device is synecdoche.

Key Concept

Identification of Synecdoche in Poetry

Estimated Time:1m 0s

Question 6520Question →

Match each line (Line 1 to Line 4) from the unseen poetic passage below with the predominant literary device it demonstrates:

Line 1: 'The sun was a golden coin tossed into the ocean of night.'
Line 2: 'The engine groaned in agony before sputtering to a complete stop.'
Line 3: 'He possessed a terrifying innocence that unnerved his companions.'
Line 4: 'His words cut through the tension as sharp as a newly honed blade.'

Click a left item, then click its matching right item

Show answer & explanation

Answer

Line 1 matches Metaphor; Line 2 matches Personification; Line 3 matches Oxymoron; Line 4 matches Simile.

Each line exhibits a distinct literary device: Line 1 uses a direct identification between two unlike objects (Metaphor), Line 2 endows an inanimate mechanical part with human feeling (Personification), Line 3 pairs mutually contradictory terms together (Oxymoron), and Line 4 employs explicit comparative language with 'as... as' (Simile).

Step-by-Step Solution

1

Analyze Line 1 for direct versus indirect comparison markers.

The line equates the sun directly to a golden coin without 'like' or 'as', identifying it as a Metaphor.

Direct comparisons between two unlike things without explicit comparative words form metaphors.

2

Examine Line 2 for human qualities attributed to inanimate entities.

The engine is described as groaning in agony, identifying it as Personification.

Giving human emotions or physical reactions to non-human objects is personification.

3

Inspect Line 3 for paired contradictory terms.

The adjacent pairing of 'terrifying' and 'innocence' identifies it as an Oxymoron.

An oxymoron juxtaposes two contradictory words in immediate sequence.

4

Identify the comparative marker in Line 4.

The phrase uses 'as sharp as' to compare words to a blade, identifying it as a Simile.

Explicit comparisons using 'like' or 'as' are similes.

Key Concept

Unseen Text Appreciation and Analysis

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept