All practice questions

Question 13101Question →

A particle of mass $0.20\text{ kg}$ executes simple harmonic motion with an amplitude of $0.05\text{ m}$ and a period of oscillation of $0.20\pi\text{ s}$ . What is the maximum kinetic energy of the particle in joules?

Show answer & explanation

Answer: 0.025

Answer

The maximum kinetic energy of the particle is

0.025\text{ J}

.

The maximum kinetic energy occurs at the equilibrium position where speed reaches its maximum value

v_{\text{max}} = \omega A

. Substituting

\omega = \frac{2\pi}{0.20\pi} = 10\text{ rad/s}

into the maximum speed formula gives

v_{\text{max}} = 10 \times 0.05 = 0.50\text{ m/s}

. Computing kinetic energy yields

E_k = \frac{1}{2} (0.20) (0.50)^2 = 0.025\text{ J}

.

Step-by-Step Solution

1

Calculate angular frequency (\omega)

\omega = 10\text{ rad/s}

Using the relation

\omega = \frac{2\pi}{T}

with

T = 0.20\pi\text{ s}

.

2

Calculate maximum speed (v_{max})

v_{max} = 0.50\text{ m/s}

Maximum velocity occurs at the equilibrium position and is given by

v_{\text{max}} = \omega A

.

3

Calculate maximum kinetic energy (E_k)

E_k = 0.025\text{ J}

Using the kinetic energy formula

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

at maximum velocity.

Key Concept

Energy conservation and maximum speed in Simple Harmonic Motion

Question 13102Question →

Match each aquatic or terrestrial habitat in Column A with its corresponding defining environmental characteristic and biotic feature in Column B.

Click a left item, then click its matching right item

Show answer & explanation

Answer

Estuarine Mangrove Swamp matches fluctuating salinity and oxygen-deficient mud; Benthic Zone of a Deep Lake matches absence of sunlight and accumulation of detritus; Sahel Savanna matches sparse rainfall and short thorny shrubs; Montane Vegetation Zone matches low atmospheric temperature and dwarf cushion plants.

Each biome and aquatic habitat is matched to its primary physical constraints and characteristic plant/organism adaptations. Estuaries feature variable salinity and stilt roots; the benthic zone is deep, dark, and rich in detritus; the Sahel savanna is semi-arid with sparse thorny scrub; and montane zones present cold high-altitude conditions with dwarf vegetation.

Step-by-Step Solution

1

Analyze the abiotic and biotic factors of the Estuarine Mangrove Swamp.

Identified brackish conditions (fluctuating salinity), anaerobic mud substrates, and specialized stilt roots.

Estuaries form where rivers meet the ocean, creating salinity gradients and hypoxic soils.

2

Examine the benthic zone of deep aquatic habitats.

Matches dark, cold conditions at the bottom of water bodies where decomposers process falling organic detritus.

Sunlight cannot penetrate to the aphotic benthic substrate in deep lakes.

3

Evaluate the climatic profile of the Sahel Savanna in West Africa.

Matches extreme aridity, short rainy seasons (

200-500\text{ mm}

annually), and desert-edge vegetation like thorny acacias.

The Sahel represents the transitional zone between the Sudan Savanna and the Sahara Desert.

4

Determine the features of high-altitude Montane biomes.

Matches cold air temperatures, elevated UV radiation, and stunted cushion-forming flora.

Lapse rate reduces air temperature at higher elevations, selecting for dwarf plant growth forms.

Key Concept

Biomes and Aquatic/Terrestrial Environmental Characteristics

Question 13103Question →

Match each mammalian reproductive structure or cell type on the left with its correct physiological function on the right.

Click a left item, then click its matching right item

Show answer & explanation

Answer

Prostate gland matches with alkaline fluid secretion for neutralizing acidity; Cowper's gland matches with urethral lubrication and acid neutralization; Sertoli cells match with providing nourishment to developing sperm; Corpus luteum matches with progesterone production for endometrial maintenance.

Each structure is correctly aligned with its biological role: the prostate gland provides alkaline fluid to neutralize acidity in the tract, Cowper's gland releases pre-ejaculatory lubricating mucus, Sertoli cells nourish germ cells during spermatogenesis, and the corpus luteum produces progesterone to maintain the endometrium.

Step-by-Step Solution

1

Identify the primary secretion and function of male accessory glands.

The prostate gland secretes an alkaline fluid to neutralize acidity and promote sperm motility, whereas Cowper's gland secretes pre-ejaculatory mucus to neutralize urine traces and lubricate the urethra.

Male accessory glands contribute fluid components that optimize semen pH and lubricate reproductive tracts.

2

Analyze the nutritive and supporting cells in testicular tissue.

Sertoli cells act as nurse cells within the seminiferous tubules, supplying metabolic nutrients to germ cells during spermatogenesis.

Spermatids require specialized cell support to successfully mature into spermatozoa.

3

Determine the endocrine function of post-ovulatory ovarian structures.

The corpus luteum secretes progesterone to sustain the vascular uterine lining required for potential embryo implantation.

Progesterone maintains endometrial thickness and prevents premature menstruation during early gestation.

Key Concept

Functions of mammalian male accessory glands, testicular nurse cells, and female luteal tissue

Question 13104Question →

Match each of the poetic extracts below with the dominant tone, mood, or persona it conveys.

Click a left item, then click its matching right item

Show answer & explanation

Answer

The extract describing golden goblets and begging children matches the indignant tone toward social disparity; the excerpt set on a lonely shore at twilight matches the melancholic mood of nostalgic loss; the lines about surviving the winter grip match the optimistic persona of collective resilience; and the warning regarding the dragon's lair matches the apprehensive tone.

Each poetic extract contains distinct stylistic markers: social critique creates an indignant tone, twilight memory creates a melancholic mood, group endurance creates an optimistic persona, and cautionary advice creates an apprehensive tone.

Step-by-Step Solution

1

Analyze diction and thematic focus of the first extract.

Juxtaposing wealth ("golden goblets") with poverty ("starving children") demonstrates a sharp, critical stance.

Tone is determined by the author's or speaker's attitude toward the subject matter.

2

Examine the imagery and emotional atmosphere of the second extract.

The twilight setting and memories of swept-away laughter foster a feeling of sadness and nostalgia.

Mood refers to the atmosphere or emotional feel created for the reader.

3

Identify the voice and perspective in the third extract.

The collective "We" asserting endurance through winter expresses confidence and hope.

Persona represents the speaker's constructed identity and voice within the poem.

4

Determine the speaker's intent in the fourth extract.

Direct imperatives like "Tread softly" urge caution in the face of latent danger.

Warnings of danger establish a cautious, apprehensive tone.

Key Concept

Distinguishing between Tone, Mood, and Persona in Poetry

Question 13105Question →

Read the excerpt below from Wole Soyinka's prescribed African drama, Death and the King's Horseman:

"PRAISE-SINGER: They love to meander. Praise-singers the world over have no place for short cuts... The horseman of the King does not turn back to view the city he has left behind."

In the context of the play, what is the primary dramatic function of the Praise-Singer's utterances to Elesin Oba in this scene?

To reinforce Elesin's ritual obligation while subtly probing his lingering earthly attachments

To express private inner thoughts directly to the audience without other characters hearing

To mock Elesin's hubris and celebrate his eventual refusal to perform the ritual suicide

To signal that the colonial administration has already halted the ancestral ceremony

Show answer & explanation

Answer: To reinforce Elesin's ritual obligation while subtly probing his lingering earthly attachments

Answer

The primary dramatic function of the Praise-Singer's utterances is to reinforce Elesin's ritual obligation while subtly probing his lingering earthly attachments.

The Praise-Singer serves as a vital ceremonial figure in Wole Soyinka's Death and the King's Horseman. His dialogue during the opening act serves to spur Elesin Oba toward fulfilling his ancestral mandate of ritual suicide while gently warning him that looking back—symbolizing attachment to physical pleasures—endangers the spiritual balance of the community.

Step-by-Step Solution

1

Analyze the speaker and context of the dramatic excerpt

The Praise-Singer is chanting to Elesin Oba as he prepares for his ritual transition into the ancestral realm.

Understanding the character's role as communal memory and guide clarifies the purpose of the dialogue.

2

Examine the figurative meaning of 'does not turn back to view the city'

It serves as an admonition against allowing physical temptations or worldly pleasures to delay or derail his cosmic responsibility.

The imagery emphasizes total commitment to the ritual passage without hesitation.

3

Evaluate the choices against the text and thematic development

The correct interpretation captures both the supportive praise and the underlying warning regarding Elesin's tragic vulnerability.

Elesin's weakness for earthly pleasures is foreshadowed through the Praise-Singer's cautious reminders.

Key Concept

Dramatic dialogue and character function in prescribed African drama

Question 13106Question →

An electron carrying a charge of magnitude $1.6 \times 10^{-19}\text{ C}$ moves with a velocity of $4.0 \times 10^6\text{ m s}^{-1}$ at an angle of $30^\circ$ relative to a uniform magnetic field. If the magnetic force acting on the electron is $3.2 \times 10^{-13}\text{ N}$ , what is the magnetic flux density of the field?

0.5\text{ T}

1.0\text{ T}

2.0\text{ T}

0.25\text{ T}

Show answer & explanation

Answer: $1.0\text{ T}$

Answer

The magnetic flux density of the field is

1.0\text{ T}

.

Applying the Lorentz force equation for a charged particle

F = qvB\sin\theta

, substituting the given values yields

3.2 \times 10^{-13} = (1.6 \times 10^{-19})(4.0 \times 10^6) B \sin(30^\circ)

. Solving for

B

gives

B = 1.0\text{ T}

.

Step-by-Step Solution

1

Identify the formula for magnetic force on a moving charge

F = qvB\sin\theta

A charged particle moving at an angle through a magnetic field experiences a force proportional to the velocity component perpendicular to the field.

2

Substitute the given physical values into the equation

3.2 \times 10^{-13} = (1.6 \times 10^{-19}) \times (4.0 \times 10^6) \times B \times \sin(30^\circ)

Values provided: charge

q = 1.6 \times 10^{-19}\text{ C}

, velocity

v = 4.0 \times 10^6\text{ m s}^{-1}

, force

F = 3.2 \times 10^{-13}\text{ N}

, and angle

\theta = 30^\circ

.

3

Evaluate

\sin(30^\circ)

and simplify the numerical product

3.2 \times 10^{-13} = (1.6 \times 10^{-19}) \times (4.0 \times 10^6) \times 0.5 \times B = 3.2 \times 10^{-13} \times B

Since

\sin(30^\circ) = 0.5

, multiplying

1.6 \times 10^{-19} \times 4.0 \times 10^6 \times 0.5

yields

3.2 \times 10^{-13}

.

4

Solve for the magnetic flux density

B

B = \frac{3.2 \times 10^{-13}}{3.2 \times 10^{-13}} = 1.0\text{ T}

Dividing both sides of the equation by

3.2 \times 10^{-13}\text{ N C}^{-1}\text{ m}^{-1}\text{ s}

yields the magnetic flux density.

Key Concept

Magnetic Force on a Moving Charge

Question 13107Question →

A poultry farm operates in a perfectly competitive market where the market price per crate of eggs is $\text{N}70$ . The farm's short-run total cost function is $TC = 2Q^2 + 10Q + 200$ , where $Q$ is the quantity of crates produced and $TC$ is the total cost in Naira. What is the maximum economic profit, in Naira, realized by the farm?

Show answer & explanation

Answer: 250

Answer

The maximum economic profit realized by the farm is 250 Naira.

In a perfectly competitive market, the firm is a price taker so marginal revenue equals market price (

MR = P = 70

). Equating marginal revenue to marginal cost (

MC = 4Q + 10

) gives an equilibrium output of

Q = 15

units. Substituting

Q = 15

into Total Revenue (

TR = 70 \times 15 = 1050

) and Total Cost (

TC = 2(15)^2 + 10(15) + 200 = 800

) yields an economic profit of

1050 - 800 = \text{N}250

.

Step-by-Step Solution

1

Derive the Marginal Cost equation from Total Cost

MC = 4Q + 10

Marginal Cost represents the rate of change of Total Cost with respect to output.

2

Equate Marginal Revenue (which equals price in perfect competition) to Marginal Cost

70 = 4Q + 10 \implies Q = 15

units

A price-taking firm maximizes profit where price equals marginal cost (

P = MC

).

3

Calculate Total Revenue at optimal output level

TR = 70 \times 15 = \text{N}1050

Total revenue is the product of price per unit and total output sold.

4

Calculate Total Cost at optimal output level

TC = 2(15)^2 + 10(15) + 200 = \text{N}800

Substitute optimal output into the total cost function.

5

Subtract Total Cost from Total Revenue to find economic profit

\text{Profit} = 1050 - 800 = \text{N}250

Economic profit is the surplus remaining after deducting total explicit and fixed cost from total revenue.

Key Concept

Profit Maximization in Perfect Competition

Estimated Time:1m 30s

Question 13108Question →

An unidentified arthropod specimen has a body divided into two main tagmata (cephalothorax and abdomen), possesses four pairs of jointed walking legs, and completely lacks antennae. Which class of organisms does this specimen belong to?

Arachnida

Insecta

Crustacea

Chilopoda

Show answer & explanation

Answer: Arachnida

Answer

Arachnida

Members of the class Arachnida are uniquely characterized within the phylum Arthropoda by having bodies divided into a fused cephalothorax (prosoma) and an abdomen (opisthosoma), four pairs of thoracic walking legs, and no antennae.

Step-by-Step Solution

1

Analyze the anatomical features described in the specimen stem

Body plan consists of two tagmata (cephalothorax and abdomen), 4 pairs of walking legs (8 legs total), and 0 antennae.

Diagnostic anatomical structures such as leg count, body segmentation, and antennae presence distinguish the main classes of Arthropoda.

2

Compare given features against diagnostic arthropod class criteria

Arachnids are defined by 4 leg pairs and 0 antennae. Insects have 3 leg pairs and 1 antenna pair. Crustaceans have 5+ leg pairs and 2 antenna pairs. Chilopods have 1 pair of legs per segment.

Matching structural characteristics identifies Arachnida as the correct class.

Key Concept

Diagnostic anatomical features of Arthropoda classes

Estimated Time:1m 0s

Question 13109Question →

Match each economic market scenario on the left with its corresponding type of demand on the right.

Click a left item, then click its matching right item

Show answer & explanation

Answer

Yam tubers and cassava flour match with Competitive demand; Fountain pens and writing ink match with Joint demand; Timber used for construction, furniture, and paper matches with Composite demand; Processed leather purchased by a footwear manufacturing plant matches with Derived demand.

Each economic scenario aligns strictly with the standard classification of interrelated demand: competitive demand applies to substitutes (yam and cassava flour); joint demand applies to complements (pens and ink); composite demand applies to versatile raw materials with multiple uses (timber); and derived demand applies to production inputs (leather for footwear).

Step-by-Step Solution

1

Analyze substitute goods fulfilling alternative needs

Yam tubers and cassava flour compete for household staple consumption, making their relationship competitive demand.

When two goods can easily replace each other to satisfy the same want, demand for one is competitive with the other.

2

Analyze complementary goods used together

Fountain pens require ink to function, indicating that their demand is joint (complementary).

Goods that must be combined to render utility demonstrate joint demand.

3

Analyze raw materials required for multiple distinct uses

Timber serves several separate functions (roofing, furniture, paper), demonstrating composite demand.

Demand for a commodity that caters to several alternative uses is classified as composite demand.

4

Analyze intermediate goods or factors of production

Demand for processed leather depends directly on consumer demand for finished leather boots, defining it as derived demand.

Demand for inputs or raw materials is derived from the demand for the final goods they help manufacture.

Key Concept

Types of Demand

Estimated Time:1m 30s

Question 13110Question →

The table below presents the Total Utility ( $TU$ ) obtained by a consumer from consuming successive bottles of sparkling water:

Quantity ( $Q$ )	Total Utility ( $TU$ ) in utils
1	16
2	30
3	40
4	46
5	46
6	40

Based on the table above, at which unit of consumption does the consumer reach the point of satiety?

The 5th unit

The 4th unit

The 6th unit

The 3rd unit

Show answer & explanation

Answer: The 5th unit

Answer

The consumer reaches the point of satiety at the 5th unit of consumption.

The correct answer identifies the 5th unit because the point of satiety occurs when Marginal Utility (

MU = \Delta TU / \Delta Q

) drops to zero and Total Utility (

TU

) reaches its absolute peak. Calculating

MU

for the 5th unit gives

MU_5 = 46 - 46 = 0

utils.

Step-by-Step Solution

1

Calculate the Marginal Utility (

MU

) for each unit using the formula

MU_n = TU_n - TU_{n-1}

.

MU_1 = 16

,

MU_2 = 14

,

MU_3 = 10

,

MU_4 = 6

,

MU_5 = 0

,

MU_6 = -6

.

Marginal Utility measures the change in Total Utility from consuming one additional unit.

2

Identify the point of satiety by finding where Marginal Utility (

MU

) equals zero and Total Utility (

TU

) is maximized.

At

Q = 5

,

MU = 0

and

TU = 46

(maximum).

The point of satiety is defined as the consumption level where consumer satisfaction is maximized and additional consumption yields no extra utility.

Key Concept

Point of Satiety in Law of Diminishing Marginal Utility

Question 13111Question →

A spherical black body radiator with an initial radius of $0.10\text{ m}$ emits thermal radiation at a rate of $E_1$ when its surface temperature is $400\text{ K}$ . If the radius of the sphere is doubled to $0.20\text{ m}$ and its absolute temperature is reduced to $200\text{ K}$ , what is the value of the ratio of the new rate of heat radiation to the initial rate, $\frac{E_2}{E_1}$ ?

Show answer & explanation

Answer: 0.25

Answer

The ratio of the new rate of heat radiation to the initial rate is

0.25

.

According to the Stefan-Boltzmann law, the rate of thermal radiation emitted by a black body is directly proportional to its surface area (

A \propto r^2

) and the fourth power of its absolute temperature (

T^4

). Doubling the radius increases the surface area by a factor of

2^2 = 4

, while halving the absolute temperature decreases the radiation rate per unit area by a factor of

(1/2)^4 = 1/16

. The net ratio of the new emission rate to the initial emission rate is

4 \times (1/16) = 0.25

.

Step-by-Step Solution

1

Apply Stefan-Boltzmann's law of radiation to formulate the rate of heat emission.

The total power radiated by a sphere of radius

r

at thermodynamic temperature

T

is given by

P = \sigma A T^4 = 4\pi \sigma r^2 T^4

, where

\sigma

is the Stefan-Boltzmann constant.

Thermal radiation emission rate depends directly on surface area (

A = 4\pi r^2

) and the fourth power of absolute temperature (

T^4

).

2

Formulate the ratio

\frac{E_2}{E_1}

using the scaled physical parameters.

\frac{E_2}{E_1} = \frac{4\pi \sigma r_2^2 T_2^4}{4\pi \sigma r_1^2 T_1^4} = \left(\frac{r_2}{r_1}\right)^2 \left(\frac{T_2}{T_1}\right)^4

Constants

4\pi\sigma

cancel out when evaluating relative changes.

3

Substitute the given numerical ratios into the equation and compute the result.

Given

\frac{r_2}{r_1} = \frac{0.20}{0.10} = 2

and

\frac{T_2}{T_1} = \frac{200}{400} = 0.5

, we get

\frac{E_2}{E_1} = (2)^2 \times (0.5)^4 = 4 \times \frac{1}{16} = 0.25

.

Evaluating

2^2 = 4

and

(0.5)^4 = 1/16

yields a final ratio of

4/16 = 0.25

.

Key Concept

Stefan-Boltzmann Law of Radiation

Question 13112Question →

A light ray strikes a plane mirror. Keeping the direction of the incident ray fixed, the mirror is rotated through an angle of $15^\circ$ about an axis lying in its plane. What is the angle of rotation, in degrees, of the reflected ray?

Show answer & explanation

Answer: 30

Answer

The reflected ray turns through an angle of

30^\circ

.

When a plane mirror is rotated through an angle

\theta

while keeping the incident ray direction constant, the normal turns by

\theta

. This changes the angle of incidence by

\theta

and the angle of reflection by

\theta

, causing the reflected ray to rotate by a total angle of

2\theta

. For a mirror rotation of

15^\circ

, the reflected ray rotates through

2 \times 15^\circ = 30^\circ

.

Step-by-Step Solution

1

Analyze the effect of mirror rotation on the normal line

When the plane mirror rotates by

15^\circ

, the normal to the mirror surface also rotates by

15^\circ

.

The normal line is always perpendicular to the surface of the mirror.

2

Determine the change in the angle of incidence and reflection

The angle of incidence changes by

15^\circ

, so the angle of reflection relative to the new normal also changes by

15^\circ

.

According to the law of reflection, the angle of incidence equals the angle of reflection (

i = r

).

3

Calculate the total angular deviation of the reflected ray

The total shift of the reflected ray relative to its original path is

15^\circ + 15^\circ = 30^\circ

.

The rotation of the reflected ray is twice the angle of rotation of the mirror.

Key Concept

Rotation of Reflected Ray by a Plane Mirror

Question 13113Question →

Match each fundamental factor affecting economic growth listed below with its primary transmission mechanism in expanding aggregate national output.

Click a left item, then click its matching right item

Show answer & explanation

Answer

Human Capital Accumulation pairs with worker skill enhancement and labor efficiency gains; Infrastructure Investment pairs with reducing supply chain bottlenecks and operational costs; Technological Innovation pairs with improving total factor productivity to shift output frontiers; and Institutional Quality pairs with securing property rights to incentivize investment.

Human Capital Accumulation maps directly to labor force skill and productivity gains; Infrastructure Investment maps to reducing systemic logistics and energy costs; Technological Innovation maps to boosting multi-factor productivity and expanding potential output; and Institutional Quality maps to protecting property rights and incentivizing private capital formation.

Step-by-Step Solution

1

Identify the economic definition and core contribution of each factor on the left.

Recognized human capital as labor quality, infrastructure as physical capital facilities, technology as know-how/productivity, and institutions as legal/governance structures.

A precise understanding of factor definitions is required to trace their macroeconomic impact.

2

Analyze each transmission channel described on the right to identify the specific economic pathway.

Associated labor productivity with human capital, cost-reducing connectivity with infrastructure, total factor productivity with technological change, and property rights protection with institutional framework.

Different factors expand economic capacity through distinct macroeconomic channels.

3

Pair each factor with its unique economic mechanism.

Successfully aligned all four growth determinants with their corresponding transmission mechanism.

Verifies accurate structural understanding of economic growth determinants.

Key Concept

Transmission Channels of Long-run Economic Growth Determinants

Question 13114Question →

Read the prose extract below:

"To save the village from total destruction, the chief understood that they must surrender their most sacred inheritance to the enemy; only through losing their heritage could they truly preserve their identity."

Which literary device is prominently demonstrated in the statement 'only through losing their heritage could they truly preserve their identity'?

Oxymoron

Paradox

Metaphor

Mood

Show answer & explanation

Answer: Paradox

Answer

Paradox

The correct answer is Paradox because the statement presents an apparent contradiction—that losing one's heritage is necessary to preserve identity—which, upon closer reflection, reveals a deeper truth about cultural resilience. This structural self-contradiction containing a hidden truth is the defining feature of a paradox.

Step-by-Step Solution

1

Examine the targeted statement within the prose extract.

The statement asserts that 'losing their heritage' is the only way to 'preserve their identity'.

Analyzing the relationship between key concepts in the extract is necessary to identify the stylistic device.

2

Evaluate the nature of the contradiction.

The assertion appears contradictory on the surface, yet expresses a meaningful truth regarding survival.

A full sentence or proposition that seems self-contradictory while conveying an underlying truth is a paradox.

Key Concept

Paradox in Prose

Estimated Time:1m 0s

Question 13115Question →

A weather balloon inflated with helium has a volume of $5.0\text{ dm}^3$ at ground level where the atmospheric pressure is $100\text{ kPa}$ and the temperature is $27^\circ\text{C}$ . The balloon ascends to an altitude where the ambient pressure drops to $40\text{ kPa}$ . Assuming isothermal conditions are maintained throughout the ascent, what is the new volume of the helium gas in the balloon?

12.5\text{ dm}^3

2.0\text{ dm}^3

1.125\text{ dm}^3

8.0\text{ dm}^3

Show answer & explanation

Answer: $12.5\text{ dm}^3$

Answer

12.5\text{ dm}^3

Boyle's Law states that for a fixed mass of gas at constant temperature, the volume is inversely proportional to the pressure (

P_1 V_1 = P_2 V_2

). Substituting the initial pressure of

100\text{ kPa}

, initial volume of

5.0\text{ dm}^3

, and final pressure of

40\text{ kPa}

gives

V_2 = (100 \times 5.0) / 40 = 12.5\text{ dm}^3

.

Step-by-Step Solution

1

Identify the given parameters and constant conditions

P_1 = 100\text{ kPa}

,

V_1 = 5.0\text{ dm}^3

,

P_2 = 40\text{ kPa}

. Temperature is constant (isothermal condition).

Boyle's Law applies when a fixed mass of gas is kept at a constant temperature.

2

State Boyle's Law formula

P_1 V_1 = P_2 V_2

Pressure and volume of a fixed mass of ideal gas are inversely proportional at constant temperature.

3

Rearrange the formula to solve for the unknown final volume (

V_2

)

V_2 = \frac{P_1 V_1}{P_2}

Isolating

V_2

allows direct substitution of known variables.

4

Substitute the given numerical values into the equation and calculate

V_2 = \frac{100\text{ kPa} \times 5.0\text{ dm}^3}{40\text{ kPa}} = \frac{500}{40} = 12.5\text{ dm}^3

Units of pressure (

\text{kPa}

) cancel out, leaving the volume in

\text{dm}^3

.

Key Concept

Boyle's Law (

P_1 V_1 = P_2 V_2

at constant temperature)

Question 13116Question →

Consider a nation implementing diverse trade policies to achieve macro-economic objectives. Match each commercial policy instrument on the left with its corresponding economic mechanism and fiscal impact on the right.

Click a left item, then click its matching right item

Show answer & explanation

Answer

The correct matches pair: (1) Ad valorem tariff with revenue generation based on monetary valuation; (2) Export subsidy with expanded producer surplus and potential international countervailing duties; (3) Voluntary export restraint with quantitative restriction where foreign firms capture quota rents; and (4) Total trade embargo with a complete halt in trade creating severe domestic supply deficits.

Each instrument accurately aligns with its definitive economic mechanism: ad valorem tariffs tax percentage value; export subsidies boost domestic export surplus while risking trade disputes; voluntary export restraints transfer quota rents to foreign firms; and embargoes legally cut off trade completely.

Step-by-Step Solution

1

Analyze the operational mechanism of an ad valorem tariff.

Identified that 'ad valorem' means 'according to value'. It yields revenue proportional to monetary value.

Tariffs based on valuation directly add a percentage tax to imports, raising revenue for the state treasury.

2

Analyze the impact of export subsidies on domestic producers and foreign trade partners.

Identified that financial assistance to exporters increases domestic producer surplus and lowers export prices abroad.

Subsidies lower costs for domestic exporters, expanding output but potentially distorting international market prices.

3

Examine how Voluntary Export Restraints (VERs) differ from standard import quotas in terms of rent capture.

Identified that VERs allow foreign exporting firms to capture the quota rents due to price increases in the destination market.

Because the exporting country self-administers the limit, foreign firms set higher prices and retain the economic rent.

4

Evaluate the absolute economic constraint imposed by a trade embargo.

Identified that an embargo is a zero-trade mandate causing total cessation of legal imports and acute market shortages.

Embargoes completely eliminate legal supply channels rather than merely taxing or limiting them.

Key Concept

Mechanisms and welfare impacts of commercial policy instruments (tariffs, quotas, subsidies, embargoes, and voluntary export restraints).

Question 13117Question →

A sudden increase in the market price of beef causes many household consumers to switch to purchasing fish as an alternative source of protein. Which of the following best describes the resulting effect on the demand curve for fish?

A rightward shift of the demand curve

An upward movement along the demand curve

A leftward shift of the demand curve

A downward movement along the demand curve

Show answer & explanation

Answer: A rightward shift of the demand curve

Answer

A rightward shift of the demand curve

Beef and fish are competitive goods (substitutes). An increase in the price of beef causes consumers to seek alternative protein sources, thereby increasing the demand for fish at every price level. Because this change is driven by a non-price factor (the price of a related commodity), it causes an outward (rightward) shift of the entire demand curve for fish.

Step-by-Step Solution

1

Identify the economic relationship between beef and fish

Beef and fish serve as alternative protein sources, making them competitive demand items (substitutes).

Understanding whether goods are substitutes or complements determines the direction of the demand change.

2

Analyze the impact of a price increase in beef on the demand for fish

When the price of beef rises, consumers reduce their beef consumption and increase their demand for fish at any given price.

An increase in the price of a substitute commodity increases the demand for the alternative commodity.

3

Determine the geometric effect on the demand curve for fish

Since the change is driven by a non-price factor of fish (the price of a related good), it causes an outward (rightward) shift of the entire demand curve.

Changes in non-price determinants shift the demand curve, whereas changes in own price cause movement along the curve.

Key Concept

Impact of substitute goods' prices on demand curve shifts

Estimated Time:1m 0s

Question 13118Question →

Read the following poetic lines:

"The soldiers marched into the gathering dusk,
Bearing the burden of silent thunder."

Which figure of speech is used in the phrase "silent thunder"?

Oxymoron

Paradox

Metaphor

Dramatic irony

Show answer & explanation

Answer: Oxymoron

Answer

Oxymoron

The phrase 'silent thunder' places two contradictory terms—'silent' (soundless) and 'thunder' (a roaring noise)—immediately next to each other to convey suppressed emotional tension. This direct pairing of opposite words is an oxymoron.

Step-by-Step Solution

1

Analyze the components of the target phrase

The phrase combines 'silent' (absence of sound) and 'thunder' (a loud sound).

Identifying the literal meanings of the two words reveals that they are mutually contradictory.

2

Examine the structural arrangement of the words

The two contradictory words are directly juxtaposed next to each other.

Direct side-by-side placement of opposing terms defines an oxymoron.

Key Concept

Oxymoron

Estimated Time:1m 0s

Question 13119Question →

The financial records of Folake Traders at the close of the trading year show the following balance sheet balances:

Financial Item	Amount ( $\text{₦}$ )
Premises	$1,200,000$
Motor Vehicles	$800,000$
Stock of Goods	$450,000$
Trade Debtors	$250,000$
Cash at Bank	$150,000$
Trade Creditors	$300,000$
Bank Overdraft	$150,000$
$10$ -Year Bank Loan	$500,000$

What is the working capital of Folake Traders?

\text{₦}400,000

\text{₦}1,300,000

\text{₦}550,000

\text{₦}250,000

Show answer & explanation

Answer: $\text{₦}400,000$

Answer

\text{₦}400,000

Working capital is calculated as

\text{Current Assets} - \text{Current Liabilities}

. Summing the current assets gives

\text{Stock} (\text{₦}450,000) + \text{Debtors} (\text{₦}250,000) + \text{Cash at Bank} (\text{₦}150,000) = \text{₦}850,000

. Summing the current liabilities gives

\text{Trade Creditors} (\text{₦}300,000) + \text{Bank Overdraft} (\text{₦}150,000) = \text{₦}450,000

. Subtracting current liabilities from current assets gives

\text{₦}850,000 - \text{₦}450,000 = \text{₦}400,000

. Note that long-term liabilities such as the

10

-Year Bank Loan and fixed assets such as Premises and Motor Vehicles are excluded.

Step-by-Step Solution

1

Identify and sum all Current Assets

Current Assets = Stock of Goods (

\text{₦}450,000

) + Trade Debtors (

\text{₦}250,000

) + Cash at Bank (

\text{₦}150,000

) =

\text{₦}850,000

Current assets consist of short-term liquid assets convertible to cash within one financial period. Fixed assets (Premises and Motor Vehicles) are excluded.

2

Identify and sum all Current Liabilities

Current Liabilities = Trade Creditors (

\text{₦}300,000

) + Bank Overdraft (

\text{₦}150,000

) =

\text{₦}450,000

Current liabilities are short-term debts due within one year. Long-term liabilities (

10

-Year Bank Loan) are excluded.

3

Apply the Working Capital formula

Working Capital = Current Assets - Current Liabilities =

\text{₦}850,000 - \text{₦}450,000 = \text{₦}400,000

Working capital measures a business's operational liquidity available for day-to-day business activities.

Key Concept

Working Capital Calculation

Question 13120Question →

A glass prism with a refracting angle of $60^\circ$ has a refractive index of $\sqrt{2}$ . What is the angle of minimum deviation, in degrees, experienced by a light ray passing through this prism?

Show answer & explanation

Answer: 30

Answer

The angle of minimum deviation is

30^\circ

.

Using the prism minimum deviation relation

n = \frac{\sin\left((A + D_m)/2\right)}{\sin(A/2)}

, substituting

n = \sqrt{2}

and

A = 60^\circ

yields

\sin\left((60^\circ + D_m)/2\right) = \frac{1}{\sqrt{2}}

. This gives

(60^\circ + D_m)/2 = 45^\circ

, so

D_m = 30^\circ

.

Step-by-Step Solution

1

Apply the prism minimum deviation equation.

n = \frac{\sin\left(\frac{A + D_m}{2}\right)}{\sin\left(\frac{A}{2}\right)}

This relates refractive index, prism refracting angle, and minimum deviation angle.

2

Substitute the given values

A = 60^\circ

and

n = \sqrt{2}

.

\sqrt{2} = \frac{\sin\left(\frac{60^\circ + D_m}{2}\right)}{\sin(30^\circ)}

Dividing the refracting angle

60^\circ

by 2 gives

30^\circ

for the denominator angle.

3

Calculate the numerator sine term.

\sin\left(\frac{60^\circ + D_m}{2}\right) = \frac{1}{\sqrt{2}}

Multiplying

\sqrt{2}

by

\sin(30^\circ) = 0.5

gives

\frac{\sqrt{2}}{2} = \frac{1}{\sqrt{2}}

.

4

Solve for the angle

D_m

.

D_m = 30^\circ

Since

\arcsin\left(\frac{1}{\sqrt{2}}\right) = 45^\circ

, we have

\frac{60^\circ + D_m}{2} = 45^\circ

, leading to

60^\circ + D_m = 90^\circ

.

Key Concept

Minimum Deviation in Triangular Prisms

Answer

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