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Question 5161Question

A firm operating in the short run employs labor as a variable input while keeping capital fixed. When the firm employs 44 workers, total output is 120120 units. When a 55 th worker is added, total output increases to 145145 units. What is the marginal product of the 55 th worker in units?

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Answer: 25

Answer

The marginal product of the 5th worker is 25 units.
The marginal product of the 5th worker is calculated as the difference between the total output with 5 workers (145 units) and the total output with 4 workers (120 units), which equals 25 units.

Step-by-Step Solution

1
Identify the Total Product (TPTP) corresponding to 44 and 55 workers.
TP4=120TP_4 = 120 units and TP5=145TP_5 = 145 units.
Marginal product measures the addition to total product resulting from employing one extra unit of the variable factor.
2
Calculate the change in total product (ΔTP\Delta TP) and change in labor (ΔL\Delta L).
ΔTP=145120=25\Delta TP = 145 - 120 = 25 units, ΔL=54=1\Delta L = 5 - 4 = 1 unit.
Evaluating the incremental changes provides the variables required for the marginal product formula.
3
Compute the Marginal Product (MP5MP_5).
MP5=ΔTPΔL=251=25MP_5 = \frac{\Delta TP}{\Delta L} = \frac{25}{1} = 25 units.
Dividing the increase in output by the increase in labor yields the marginal output of the 5th worker.

Key Concept

Marginal Product of Labor
Question 5162Question

A textile manufacturing firm operating in Kano State increases all of its factor inputs by 50%50\% in order to expand its scale of production. Following this scale expansion, the firm's total weekly output of fabric rises from 20,000 meters20,000\text{ meters} to 35,000 meters35,000\text{ meters}. What is the percentage increase in the firm's total output?

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Answer: 75

Answer

The percentage increase in total output is 75%75\%, indicating that output grew at a faster rate than inputs (75%>50%75\% > 50\%), which reflects increasing returns to scale.
The correct calculation evaluates the change in output relative to the initial output: 35,00020,00020,000×100%=75%\frac{35,000 - 20,000}{20,000} \times 100\% = 75\%. Since output increased by 75%75\% while inputs were scaled up by 50%50\%, the firm experienced increasing returns to scale (economies of scale).

Step-by-Step Solution

1
Calculate the absolute increase in weekly output
35,000 meters20,000 meters=15,000 meters35,000\text{ meters} - 20,000\text{ meters} = 15,000\text{ meters}
To find the percentage change, the magnitude of output expansion must first be determined.
2
Calculate the percentage increase relative to the base output
(15,00020,000)×100%=75%\left(\frac{15,000}{20,000}\right) \times 100\% = 75\%
Percentage increase measures the proportionate change from the baseline level of output.

Key Concept

Calculating Percentage Change in Output and Identifying Returns to Scale
Estimated Time:1m 15s
Question 5163Question

Despite the establishment of the Agricultural Credit Guarantee Scheme Fund (ACGSF) to absorb lending risks for commercial banks, smallholder agricultural producers in Nigeria continue to experience severe credit access constraints. Which of the following structural factors best explains why the ACGSF has not fully overcome the agricultural credit deficit for smallholder farmers?

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Answer: The persistence of customary land tenure systems and fragmented holdings that prevent smallholders from securing legal, bankable land titles required as collateral

Answer

The main structural constraint limiting credit access under the Agricultural Credit Guarantee Scheme Fund (ACGSF) is the persistence of customary land tenure systems and land fragmentation, which deprives smallholders of legal, bankable land titles required as collateral by commercial banks.
The ACGSF guarantees up to 75% of default losses to encourage commercial bank lending to agriculture. However, commercial banks still require borrowers to pledge pledged security or formal collateral. Because customary land tenure systems in Nigeria result in fragmented plots without formal legal titles (Certificates of Occupancy), smallholders cannot meet commercial bank collateral requirements.

Step-by-Step Solution

1
Analyze the core objective of the Agricultural Credit Guarantee Scheme Fund (ACGSF).
The ACGSF was created by the Federal Government and the Central Bank of Nigeria to guarantee loans made by commercial banks to agriculture, pledging to absorb up to 75% of default losses.
Understanding the policy mechanism helps isolate why credit flow to smallholders remains constrained despite risk-sharing guarantees.
2
Examine the operational bottlenecks faced by smallholders when interacting with commercial financial institutions.
Commercial banks still require formal collateral and loan documentation before approving credit applications.
Risk guarantee schemes lower bank exposure but do not eliminate fundamental commercial lending standards.
3
Evaluate the role of land tenure systems in Nigeria's agricultural sector.
Under customary land tenure rules, farmland is communally inherited and heavily fragmented. Farmers lack registered Certificates of Occupancy (C of O), making land non-transferable and legally unacceptable as bank collateral.
Land title insecurity is the primary structural barrier preventing smallholders from accessing institutional credit.

Key Concept

Agricultural Financing Constraints and Land Tenure Problems in Nigeria
Question 5164Question

In the pre-colonial Oyo political system, which institutional body exercised the supreme constitutional check of rejecting an oppressive Alaafin by presenting him with an empty calabash or parrot's eggs?

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Answer: The Oyomesi

Answer

The Oyomesi
In the pre-colonial Yoruba political administrative system, authority was shared among distinct organs to prevent dictatorship. The Oyomesi, a council of seven noble kingmakers headed by the Bashorun, served as a primary legislative organ that held the constitutional authority to check an tyrannical Alaafin. If the king acted autocratically or violated traditional customs, the Oyomesi would present him with an empty calabash or parrot's eggs, signifying that the gods, earth, and people had rejected him, which required him to commit ritual suicide.

Step-by-Step Solution

1
Identify the core institutional organ responsible for executive oversight in the pre-colonial Oyo kingdom.
Recognize that the council of seven chief kingmakers held legislative power and acted as a major check on the ruler's power.
Pre-colonial Yoruba governance relied on systemic checks and balances to prevent absolute monarchy.
2
Determine the constitutional mechanism used by this council to dethrone a tyrannical Alaafin.
The council, known as the Oyomesi and led by the Bashorun, presented the monarch with an empty calabash or parrot's eggs to signify rejection.
This symbolic act constituted a non-negotiable demand for the king to commit ritual suicide.

Key Concept

Constitutional checks and balances in the pre-colonial Yoruba system
Question 5165Question

Match each type of sovereignty listed on the left with its corresponding definition or legal characteristic on the right.

Click a left item, then click its matching right item

Items

Legal Sovereignty
Political Sovereignty
De Facto Sovereignty
External Sovereignty

Matches

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Answer

Legal Sovereignty matches the ultimate constitutional authority to make, amend, and enforce law; Political Sovereignty matches the supreme power vested in the electorate; De Facto Sovereignty matches supreme power exercised through physical force without legal backing; External Sovereignty matches the power of a state to manage its affairs free from foreign control.
Each sovereign classification matches its precise political science definition: legal sovereignty pertains to formal law-making bodies, political sovereignty rests with the voting populace, de facto sovereignty reflects actual control, and external sovereignty designates international independence.

Step-by-Step Solution

1
Distinguish between legal authority and practical authority
Identified Legal Sovereignty as legal law-making authority and De Facto Sovereignty as power established by force or effective control.
Constitutional law establishes legal sovereignty, whereas real-world dominance establishes de facto sovereignty.
2
Examine popular and international dimensions of sovereignty
Identified Political Sovereignty as electorate power and External Sovereignty as state independence from foreign control.
Citizens hold political sovereignty through franchise, while non-interference by foreign powers defines external sovereignty.

Key Concept

Types and Characteristics of Sovereignty
Question 5166Question

Match each electoral term relating to franchise and suffrage on the left with its corresponding legal definition or characteristic on the right.

Click a left item, then click its matching right item

Items

Universal Adult Suffrage
Restricted Franchise
Property Qualification
Legal Disenfranchisement

Matches

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Answer

Universal Adult Suffrage matches with the legal granting of voting rights to all adult citizens without wealth or gender discrimination. Restricted Franchise matches with an electoral system limiting voting eligibility to citizens meeting specific statutory criteria. Property Qualification matches with requiring prospective voters to prove ownership of real estate or income above a constitutional threshold. Legal Disenfranchisement matches with statutory or constitutional deprivation of voting rights based on disqualifications such as felony convictions or mental unfitness.
Each electoral concept correctly aligns with its formal legal definition: Universal Adult Suffrage ensures non-discriminatory voting rights for all statutory adults; Restricted Franchise encompasses general eligibility barriers; Property Qualification targets asset/wealth requirements; and Legal Disenfranchisement specifies grounds for legal withdrawal of voting privileges.

Step-by-Step Solution

1
Analyze Universal Adult Suffrage
Identify that Universal Adult Suffrage represents democratic non-discrimination, conferring voting rights on all citizens reaching the legal voting age.
Universal franchise prohibits restricting voting based on property, tax status, or gender.
2
Analyze Restricted Franchise
Match Restricted Franchise to general limitations placed on voter eligibility based on specified conditions.
Historically, constitutional systems restricted suffrage using qualifications like tax payments, sex, or race.
3
Analyze Property Qualification
Match Property Qualification specifically to wealth and real estate prerequisites for electoral registration.
Property qualification is a sub-type of restricted suffrage requiring voters to hold land or minimum asset value.
4
Analyze Legal Disenfranchisement
Match Legal Disenfranchisement to the constitutional revocation of voting rights.
Disenfranchisement acts as a disqualifying mechanism for individuals who breach legal standards (e.g., criminal conviction or treason).

Key Concept

Electoral Franchise, Suffrage Qualifications, and Disenfranchisement
Question 5167Question

A democratic government enacts legislation that curtails the activities of minority political parties and opposition groups, justifying its action on the premise that the ruling party reflects the supreme will of the majority electorate. Which fundamental pillar of liberal democracy does this enactment directly violate?

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Answer: The constitutional guarantee of political pluralism and minority rights

Answer

The constitutional guarantee of political pluralism and minority rights
In a liberal democracy, majority rule is limited by constitutional safeguards that protect fundamental rights, freedom of association, and political pluralism. Using majority status to outlaw or suppress political opposition violates the core democratic principle that minority voices and alternative political choices must be protected.

Step-by-Step Solution

1
Analyze the scenario described in the question stem.
The government is using majority rule to suppress minority political parties and opposition assemblies.
Democratic systems require evaluating whether majority actions breach democratic constraints.
2
Distinguish between pure majoritarianism and liberal democracy.
Liberal democracy requires majority rule to be tempered by constitutional protections for minority rights, freedom of association, and political pluralism.
Without safeguards for opposition, majority rule degenerates into electoral autocracy or tyranny of the majority.
3
Identify the primary violated principle.
Directly suppressing opposition groups violates political pluralism and minority rights.
Pluralism guarantees equal opportunity for political competition and expression.

Key Concept

Pillars of Liberal Democracy and Protection of Minority Rights
Estimated Time:1m 30s
Question 5168Question

In tomato plants (*Solanum lycopersicum*), purple stem (PP) is dominant over green stem (pp), and cut leaf (CC) is dominant over potato leaf (cc). A plant heterozygous for both traits (PpCcPpCc) is crossed with a homozygous recessive plant (ppccppcc). What proportion of the offspring is expected to have purple stems and potato leaves?

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Answer: 1/4 (25%)

Answer

1/4 (25%)
In a dihybrid test cross between a double heterozygote (PpCcPpCc) and a double homozygous recessive individual (ppccppcc), the heterozygous parent produces four gamete types (PCPC, PcPc, pCpC, pcpc) in equal proportions (1/41/4 each). When combined with the recessive parent's pcpc gamete, four phenotypic classes result with an expected frequency of 1/41/4 (25%25\%) each. Therefore, the proportion of offspring showing purple stems and potato leaves (PpccPpcc) is 1/41/4.

Step-by-Step Solution

1
Identify parental genotypes and determine gametes produced
The heterozygous parent (PpCcPpCc) produces four types of gametes in equal proportions: PCPC, PcPc, pCpC, and pcpc (1/41/4 each). The homozygous recessive parent (ppccppcc) produces only one type of gamete: pcpc (100%100\%).
Mendel's Law of Independent Assortment states that alleles for different traits segregate independently during gamete formation.
2
Determine offspring genotypes and phenotypes
Combining gametes yields four offspring genotypes: PpCcPpCc (purple stem, cut leaf), PpccPpcc (purple stem, potato leaf), ppCcppCc (green stem, cut leaf), and ppccppcc (green stem, potato leaf), each occurring at a frequency of 1/4.
A test cross matches each distinct gamete from the heterozygous parent with a recessive allele pair from the tester parent.
3
Calculate the expected proportion for the targeted phenotype
The proportion of offspring displaying purple stems (P_) and potato leaves (cccc), represented by genotype PpccPpcc, is 1/4 or 25%.
Exactly one of the four equally probable phenotypic outcomes exhibits the dominant stem color and recessive leaf form.

Key Concept

Dihybrid Test Cross Ratio
Estimated Time:1m 30s
Question 5169Question

Match each fundamental economic concept relating to the concept and law of demand on the left with its corresponding definition on the right. Which of the following pairs correctly connects each concept with its appropriate economic definition?

Click a left item, then click its matching right item

Items

Law of Demand
Effective Demand
Demand Curve
Ceteris Paribus

Matches

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Answer

Law of Demand matches with the principle stating that quantity demanded decreases as price increases; Effective Demand matches with a consumer's desire backed by willingness and ability to pay; Demand Curve matches with a graphical representation showing the negative relationship between price and quantity demanded; Ceteris Paribus matches with the operational assumption that all external non-price determinants remain constant.
Each concept correctly links to its underlying economic principle: Law of Demand reflects the price-quantity inverse relationship; Effective Demand requires purchasing power; the Demand Curve is the visual graph of demand; and Ceteris Paribus holds other determinants constant.

Step-by-Step Solution

1
Define the Law of Demand
Identified that Law of Demand posits an inverse relationship between price and quantity demanded.
This corresponds to the principle stating that quantity demanded decreases as price increases.
2
Distinguish Effective Demand from mere desire
Recognized that economic demand requires ability to pay alongside willingness.
This matches the definition of desire backed by purchasing power.
3
Identify the Demand Curve
Understood the demand curve as the graphical expression of demand.
It visualizes price on the vertical axis and quantity demanded on the horizontal axis with a downward slope.
4
Define Ceteris Paribus
Recognized Ceteris Paribus as the isolating assumption in demand theory.
It holds income, taste, and prices of related goods constant to isolate the price effect.

Key Concept

Core Concepts and Law of Demand
Question 5170Question

Charging judicial salaries and allowances directly to the Consolidated Revenue Fund is a key constitutional mechanism designed to safeguard judicial independence from executive and legislative interference.

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Answer: True

Answer

The statement is true because statutory funding through the Consolidated Revenue Fund guarantees financial autonomy for judges, preventing arbitrary salary cuts or financial coercion by the other branches of government.
The statement accurately reflects constitutional principles governing the rule of law. Charging judicial salaries directly to the Consolidated Revenue Fund secures financial autonomy for the bench by removing judicial pay from political debate and executive discretion.

Step-by-Step Solution

1
Examine the legal mechanism of charging salaries to the Consolidated Revenue Fund.
Statutory charges are paid automatically from national revenue without needing annual legislative appropriation.
Judicial independence requires that judicial pay cannot be altered or withheld at the whim of the executive or legislative arms.
2
Connect financial autonomy to the enforcement of the Rule of Law.
Judges can deliver impartial judgments against political officeholders without fear of personal financial retaliation.
Guaranteed remuneration supports security of tenure and upholds impartial justice.

Key Concept

Judicial Financial Autonomy and the Rule of Law
Question 5171Question

What is the primary motive guiding the economic activities and investment decisions of private enterprises in a capitalist system?

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Answer: Profit maximization

Answer

The primary motive guiding private enterprise in a capitalist economic system is profit maximization.
In a capitalist economic system, individuals and private corporations own the means of production and are driven by the profit motive. Profit serves as the main incentive for innovation, risk-taking, and economic production.

Step-by-Step Solution

1
Identify the central economic feature of capitalism.
Capitalism relies on private ownership of the means of production.
Private owners invest capital with the expectation of earning financial returns on their risk.
2
Determine the primary incentive driving private entrepreneurs.
The profit motive encourages individuals and firms to produce goods and services efficiently.
Unlike socialism, which prioritizes social welfare and state planning, capitalism relies on self-interest and profit to direct resource allocation.

Key Concept

Profit Motive in Capitalism
Estimated Time:45s
Question 5172Question

Arrange the following sequential biochemical events of the light-independent stage (Calvin cycle) of photosynthesis in the correct chronological order from beginning to end.

Drag items to arrange them in the correct order

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Answer

The correct chronological sequence of the Calvin cycle is: Carbon dioxide fixation with RuBP by RuBisCO \rightarrow Formation of 3-phosphoglyceric acid (PGA) \rightarrow Reduction of PGA to glyceraldehyde-3-phosphate (G3P) using ATP and NADPH \rightarrow Synthesis of hexose sugars and regeneration of RuBP.
The Calvin cycle progresses through three main stages: Carbon Fixation, Reduction, and Regeneration. First, carbon dioxide combines with RuBP to produce an unstable 6-carbon intermediate. Second, this intermediate breaks down into two molecules of 3-phosphoglycerate (PGA). Third, PGA is phosphorylated and reduced by ATP and NADPH to form glyceraldehyde-3-phosphate (G3P). Finally, G3P is used to produce carbohydrates such as glucose and to regenerate RuBP so the cycle can continue.

Step-by-Step Solution

1
Identify the initial carboxylation step
Carbon dioxide binds with ribulose 1,5-bisphosphate (RuBP) via RuBisCO enzyme.
Photosynthetic carbon fixation begins when atmospheric CO2CO_2 enters the chloroplast stroma and reacts with the 5-carbon sugar RuBP.
2
Track the immediate cleavage of the 6-carbon intermediate
Two molecules of 3-phosphoglycerate (PGA) are formed.
The 6-carbon compound produced by carboxylation is chemically unstable and instantly hydrolyzes into two stable 3-carbon PGA molecules.
3
Identify the reduction phase requiring light reaction products
PGA is phosphorylated by ATP and reduced by NADPH to form G3P (triose phosphate).
Chemical energy (ATPATP) and reducing power (NADPHNADPH) from the light-dependent stage are consumed to reduce the carboxyl group of PGA into an aldehyde group in G3P.
4
Determine the output and regeneration phase
G3P is converted into hexose sugars (glucose) and RuBP is regenerated.
For every six molecules of G3P produced, one net G3P is allocated to carbohydrate synthesis, while the remaining five undergo enzymatic conversion using ATP to regenerate RuBP.

Key Concept

Calvin cycle sequence: Carbon fixation, cleavage to PGA, reduction to G3P (triose phosphate), and sugar synthesis/RuBP regeneration.
Question 5173Question

Complete the following statement comparing socio-economic relationships in feudal systems of government:

Fill in the blanks below

In a feudal political system, land granted by a lord to a vassal in return for military service and fealty was known as a , while the unfree peasant legally bound to the land and obligated to perform forced labor for the landlord was referred to as a .
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Answer

The terms that correctly complete the statement are 'fief' (or feud) for the granted land property and 'serf' (or villein) for the bound agricultural laborer.
In feudal political systems, political power and military obligations were linked directly to land tenure. A 'fief' was the land parcel conditional upon loyalty and military duty to the overlord, while a 'serf' represented the unfree peasantry tied to the land whose surplus product supported the ruling class.

Step-by-Step Solution

1
Identify the key institutional land-grant mechanism in a feudal political hierarchy.
In feudal socio-political structure, the foundational unit of land held in exchange for political allegiance and military service is called a fief (or feud).
Feudal authority is derived from land ownership granted by superior lords to vassals.
2
Identify the socio-economic status of the unfree agrarian laborer in feudalism.
The unfree peasant attached to the lord's manor who cannot leave the land without permission is a serf (or villein).
Serfdom defines the labor exploitation model characteristic of feudal manorialism.

Key Concept

Structural relations in Feudalism (Fief, Lord, Vassal, and Serf labor obligations)
Estimated Time:2m 0s
Question 5174Question

Following a general election, an aggrieved candidate seeks legal redress to nullify the declared return of a rival candidate based on widespread ballot box snatching and falsification of result sheets. Simultaneously, the police department files charges against several electoral officers for colluding in electoral fraud. Which judicial body possesses exclusive original jurisdiction to hear and determine the candidate's petition seeking to invalidate the election outcome?

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Answer: An Election Petitions Tribunal set up specifically to adjudicate post-election validity disputes

Answer

An Election Petitions Tribunal set up specifically to adjudicate post-election validity disputes possesses exclusive original jurisdiction to hear and determine election validity petitions.
Under constitutional electoral law, resolving disputes regarding the validity of an election return rests exclusively with specialized Election Petitions Tribunals. Regular courts handle criminal offenses arising from electoral fraud, but cannot invalidate election returns.

Step-by-Step Solution

1
Distinguish between civil election petitions and criminal prosecution of electoral malpractices
Recognized that challenging election outcomes (validity of returns) is a special constitutional proceeding distinct from criminal prosecution of electoral offenders.
Election petitions require specialized fast-track judicial bodies, whereas criminal acts are tried in regular courts.
2
Identify the constitutional body empowered to invalidate election returns
Determined that Election Petitions Tribunals hold exclusive original jurisdiction over election petitions under constitutional electoral law.
Regular High Courts (State or Federal) are excluded from hearing election petition disputes unless designated by explicit constitutional provisions (such as specific appeals).

Key Concept

Distinction between judicial mechanisms for electoral dispute resolution (Election Tribunals) and criminal prosecution of electoral offenses (Regular High Courts)
Estimated Time:1m 30s
Question 5175Question

The table below outlines a country's progressive personal income tax brackets:

Income BracketMarginal Tax Rate
First N100,000\text{N}100,0005%5\%
Next N200,000\text{N}200,000 (N100,001N300,000\text{N}100,001 - \text{N}300,000)10%10\%
Next N300,000\text{N}300,000 (N300,001N600,000\text{N}300,001 - \text{N}600,000)15%15\%
Above N600,000\text{N}600,00020%20\%

If a taxpayer earns a total gross taxable income of N500,000\text{N}500,000 in a year, what is their effective (average) tax rate?

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Answer: 11.0%11.0\%

Answer

The effective (average) tax rate is 11.0%11.0\%.
Under a graduated progressive tax schedule, tax liability is computed segment by segment. For an income of N500,000\text{N}500,000, tax on the first N100,000\text{N}100,000 is N5,000\text{N}5,000 (5%5\%), on the next N200,000\text{N}200,000 is N20,000\text{N}20,000 (10%10\%), and on the remaining N200,000\text{N}200,000 is N30,000\text{N}30,000 (15%15\%). Adding these amounts gives a total tax liability of N55,000\text{N}55,000. Dividing this total tax liability by total income yields an effective average tax rate of N55,000N500,000×100%=11.0%\frac{\text{N}55,000}{\text{N}500,000} \times 100\% = 11.0\%.

Step-by-Step Solution

1
Calculate the tax payable in the first bracket
N100,000×0.05=N5,000\text{N}100,000 \times 0.05 = \text{N}5,000
The first N100,000\text{N}100,000 of income is taxed at the 5%5\% rate.
2
Calculate the tax payable in the second bracket
N200,000×0.10=N20,000\text{N}200,000 \times 0.10 = \text{N}20,000
The next N200,000\text{N}200,000 of income (from N100,001\text{N}100,001 to N300,000\text{N}300,000) is taxed at 10%10\%.
3
Calculate the tax payable in the third bracket for the remaining income
(N500,000N300,000)×0.15=N200,000×0.15=N30,000(\text{N}500,000 - \text{N}300,000) \times 0.15 = \text{N}200,000 \times 0.15 = \text{N}30,000
Only N200,000\text{N}200,000 of income falls into the third bracket, taxed at 15%15\%.
4
Sum total tax liability and compute the average tax rate
Total Tax = N5,000+N20,000+N30,000=N55,000\text{N}5,000 + \text{N}20,000 + \text{N}30,000 = \text{N}55,000; Average Rate = (N55,000/N500,000)×100%=11.0%(\text{N}55,000 / \text{N}500,000) \times 100\% = 11.0\%
Average tax rate is defined as total tax paid divided by total gross taxable income.

Key Concept

Distinction between Marginal Tax Rate and Average (Effective) Tax Rate in a Progressive Tax System
Question 5176Question

A field biologist examines a grass species growing in an open savanna and notices that its flowers lack petals and nectaries, but possess long filaments with exposed anthers and large, feathery stigmas. Which of the following best explains the structural adaptation of these feathery stigmas?

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Answer: They provide a large surface area to efficiently catch light, airborne pollen grains carried by wind currents.

Answer

Feathery stigmas provide a large surface area to efficiently catch light, airborne pollen grains carried by wind currents.
In wind-pollinated (anemophilous) plants such as grasses, feathery stigmas extend outside the flower to form a large, branched surface designed to intercept light, dry pollen grains drifting on air currents.

Step-by-Step Solution

1
Analyze floral characteristics given in the scenario
The absence of colorful petals and nectaries, combined with exposed anthers, indicates wind pollination (anemophily).
Wind-pollinated flowers do not invest energy in petals, scent, or nectar since they rely on air movement rather than animal vectors.
2
Identify the functional role of feathery stigmas in anemophilous plants
Feathery, branching structures extend outside the floral envelope to maximize the likelihood of trapping passing airborne pollen grains.
Because wind carries pollen randomly, a net-like or feathery receptive surface increases capture efficiency.

Key Concept

Floral Adaptations for Wind Pollination (Anemophily)
Question 5177Question

During periods of rapid inflation, individuals tend to spend money immediately rather than holding onto cash savings because purchasing power declines over time. Which function of money is directly impaired in this situation while its role in facilitating daily trade continues?

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Answer: Store of value

Answer

Store of value
The store of value function allows money to retain purchasing power over time so wealth can be saved for future consumption. During inflation, rising prices decrease what a fixed sum of money can buy, directly damaging this specific function.

Step-by-Step Solution

1
Identify the core effect described in the scenario
Money loses purchasing power over time due to rapid inflation, making holding cash unprofitable.
Inflation erodes the real value of money held over any time interval.
2
Map the effect to the primary and secondary functions of money
The ability to preserve purchasing power across time corresponds directly to the store of value function.
Money serves as a store of value when it enables individuals to transfer purchasing power from the present into the future.

Key Concept

Functions of Money under Inflationary Pressure
Question 5178Question

In tomato plants, the allele for red fruit (RR) is completely dominant over the allele for yellow fruit (rr). If a heterozygous red-fruited plant is self-pollinated and produces 400400 offspring in the F2F_2 generation, how many of these plants are expected to be heterozygous red-fruited?

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Answer: 200200

Answer

The expected number of heterozygous red-fruited plants is 200.
Crossing two heterozygous individuals (Rr×RrRr \times Rr) produces genotypes in a 1 RR:2 Rr:1 rr1\ RR : 2\ Rr : 1\ rr ratio according to Mendel's First Law. Therefore, half (50%50\%) of the 400400 total offspring are expected to have the heterozygous genotype (RrRr), which equals 200200 plants.

Step-by-Step Solution

1
Determine the parental genotypes and set up the monohybrid cross.
The self-pollinated plant is heterozygous (RrRr), so the cross is Rr×RrRr \times Rr.
Mendel's First Law (Law of Segregation) states that paired alleles segregate during gamete formation so each gamete carries only one allele.
2
Calculate the genotypic ratio of the F2 generation.
The offspring genotypic ratio is 1 RR:2 Rr:1 rr1\ RR : 2\ Rr : 1\ rr, meaning 1/41/4 homozygous dominant, 2/42/4 (or 1/21/2) heterozygous, and 1/41/4 homozygous recessive.
Random combination of parental gametes (RR and rr) yields probabilities of 25% RR25\%\ RR, 50% Rr50\%\ Rr, and 25% rr25\%\ rr.
3
Compute the expected count of heterozygous offspring out of 400 total plants.
Heterozygous count = 24×400=200\frac{2}{4} \times 400 = 200 plants.
Multiplying the probability of the heterozygous genotype (1/21/2) by the total number of offspring gives the expected number.

Key Concept

Mendel's Law of Segregation and Monohybrid Genotypic Ratios
Question 5179Question

What is the volume of chlorine gas produced at s.t.p., in dm3\text{dm}^3, when 8.7 g8.7\text{ g} of manganese(IV) oxide (MnO2MnO_2) reacts completely with excess concentrated hydrochloric acid (HClHCl)? [Molar volume of gas at s.t.p. = 22.4 dm3mol122.4\text{ dm}^3\text{mol}^{-1}, Mn=55Mn = 55, O=16O = 16]

Show answer & explanation

Answer: 2.24

Answer

The volume of chlorine gas produced at s.t.p. is 2.24 dm32.24\text{ dm}^3.
In the laboratory preparation of chlorine, manganese(IV) oxide acts as an oxidizing agent according to MnO2+4HClMnCl2+Cl2+2H2OMnO_2 + 4HCl \rightarrow MnCl_2 + Cl_2 + 2H_2O. Since 8.7 g8.7\text{ g} of MnO2MnO_2 represents 0.1 mol0.1\text{ mol}, exactly 0.1 mol0.1\text{ mol} of Cl2Cl_2 gas is produced. At s.t.p., 0.1 mol×22.4 dm3mol1=2.24 dm30.1\text{ mol} \times 22.4\text{ dm}^3\text{mol}^{-1} = 2.24\text{ dm}^3.

Step-by-Step Solution

1
Write the balanced equation for the preparation of chlorine gas from manganese(IV) oxide and concentrated hydrochloric acid.
MnO2+4HClMnCl2+Cl2+2H2OMnO_2 + 4HCl \rightarrow MnCl_2 + Cl_2 + 2H_2O
Establishes the stoichiometric relationship between MnO2MnO_2 and Cl2Cl_2.
2
Calculate the molar mass of manganese(IV) oxide (MnO2MnO_2).
87 g mol187\text{ g mol}^{-1}
Required to convert the given mass of MnO2MnO_2 into moles.
3
Calculate the moles of MnO2MnO_2 supplied.
8.7 g87 g mol1=0.1 mol\frac{8.7\text{ g}}{87\text{ g mol}^{-1}} = 0.1\text{ mol}
Determines the exact amount of reactant taking part in the reaction.
4
Multiply moles of Cl2Cl_2 by the molar volume of a gas at s.t.p.
0.1 mol×22.4 dm3 mol1=2.24 dm30.1\text{ mol} \times 22.4\text{ dm}^3\text{ mol}^{-1} = 2.24\text{ dm}^3
One mole of any ideal gas occupies 22.4 dm322.4\text{ dm}^3 at s.t.p.

Key Concept

Laboratory preparation and stoichiometry of chlorine gas evolution.
Estimated Time:1m 30s
Question 5180Question

Under the same conditions of temperature and pressure, 50 cm350\text{ cm}^3 of sulfur(IV) oxide diffuses through a porous plug in 20 seconds20\text{ seconds}. How long will it take for an equal volume of methane gas (CH4CH_4) to diffuse through the same plug under identical conditions? [H=1,C=12,O=16,S=32][H = 1, C = 12, O = 16, S = 32]

Show answer & explanation

Answer: 10 seconds10\text{ seconds}

Answer

The time required for an equal volume of methane gas to diffuse is 10 seconds10\text{ seconds}.
According to Graham's Law of diffusion, the time required for a fixed volume of gas to diffuse is directly proportional to the square root of its molar mass (tMt \propto \sqrt{M}). Since the molar mass of sulfur(IV) oxide (SO2SO_2) is 64 g mol164\text{ g mol}^{-1} and that of methane (CH4CH_4) is 16 g mol116\text{ g mol}^{-1}, the ratio of their diffusion times is 1664=12\sqrt{\frac{16}{64}} = \frac{1}{2}. Therefore, methane takes half as long as sulfur(IV) oxide (20×0.5=10 seconds20 \times 0.5 = 10\text{ seconds}).

Step-by-Step Solution

1
Calculate the molar masses of sulfur(IV) oxide (SO2SO_2) and methane (CH4CH_4).
M(SO2)=32+(2×16)=64 g mol1M(SO_2) = 32 + (2 \times 16) = 64\text{ g mol}^{-1} and M(CH4)=12+(4×1)=16 g mol1M(CH_4) = 12 + (4 \times 1) = 16\text{ g mol}^{-1}.
Molar masses are required to apply Graham's Law of diffusion.
2
Set up Graham's Law equation relating diffusion time (tt) to molar mass (MM) for equal volumes.
t(CH4)t(SO2)=M(CH4)M(SO2)\frac{t(CH_4)}{t(SO_2)} = \sqrt{\frac{M(CH_4)}{M(SO_2)}}.
The rate of diffusion is inversely proportional to the square root of density or molar mass (R=Vt1MR = \frac{V}{t} \propto \frac{1}{\sqrt{M}}).
3
Substitute the known values into the equation and solve for t(CH4)t(CH_4).
t(CH4)20=1664=14=12\frac{t(CH_4)}{20} = \sqrt{\frac{16}{64}} = \sqrt{\frac{1}{4}} = \frac{1}{2}, so t(CH4)=20×12=10 secondst(CH_4) = 20 \times \frac{1}{2} = 10\text{ seconds}.
Because methane has a smaller molar mass, it diffuses faster and takes less time to diffuse.

Key Concept

Graham's Law of Diffusion
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