All practice questions

Question 6601Question →

Two identical insulated conducting spheres, $X$ and $Y$ , carry initial charges of $+8.0 \times 10^{-9}\text{ C}$ and $-2.0 \times 10^{-9}\text{ C}$ , respectively. They are brought into brief contact and then separated by a distance of $0.3\text{ m}$ in a vacuum. Taking Coulomb's constant $k = 9.0 \times 10^9\text{ N}\cdot\text{m}^2\text{C}^{-2}$ , what is the magnitude of the electrostatic force between the two spheres after separation?

9.0 \times 10^{-7}\text{ N}

1.6 \times 10^{-6}\text{ N}

2.5 \times 10^{-6}\text{ N}

3.6 \times 10^{-6}\text{ N}

Show answer & explanation

Answer: $9.0 \times 10^{-7}\text{ N}$

Answer

The magnitude of the electrostatic force between the spheres after separation is

9.0 \times 10^{-7}\text{ N}

.

When two identical conducting spheres touch, the total charge conserves and divides equally between them. The net charge is

(+8.0 \times 10^{-9}\text{ C}) + (-2.0 \times 10^{-9}\text{ C}) = +6.0 \times 10^{-9}\text{ C}

, yielding

+3.0 \times 10^{-9}\text{ C}

on each sphere. Substituting these equal charges and distance

0.3\text{ m}

into Coulomb's law gives

F = \frac{9.0 \times 10^9 \times (3.0 \times 10^{-9})^2}{0.09} = 9.0 \times 10^{-7}\text{ N}

.

Step-by-Step Solution

1

Calculate the total net charge after contact and the charge on each identical sphere.

Net charge

Q_{net} = (+8.0 \times 10^{-9}\text{ C}) + (-2.0 \times 10^{-9}\text{ C}) = +6.0 \times 10^{-9}\text{ C}

. Since the spheres are identical, the charge on each sphere is

q = \frac{+6.0 \times 10^{-9}\text{ C}}{2} = +3.0 \times 10^{-9}\text{ C}

.

When identical conductors touch, total charge is conserved and redistributes equally between them.

2

Apply Coulomb's Law using the redistributed charge and separation distance.

F = k \frac{q_1 q_2}{r^2} = (9.0 \times 10^9) \frac{(3.0 \times 10^{-9})(3.0 \times 10^{-9})}{(0.3)^2} = \frac{8.1 \times 10^{-7}}{0.09} = 9.0 \times 10^{-7}\text{ N}

.

Coulomb's Law calculates the magnitude of electrostatic force between two point-like charges at a given distance.

Key Concept

Charge conservation, redistribution between identical conductors, and Coulomb's Law

Estimated Time:1m 30s

Question 6602Question →

A sample of a radioactive element has a half-life of $3\text{ hours}$ . If the initial mass of the sample is $48\text{ g}$ , what mass of the element has decayed after a period of $9\text{ hours}$ ?

42\text{ g}

6\text{ g}

12\text{ g}

24\text{ g}

Show answer & explanation

Answer: $42\text{ g}$

Answer

The mass of the element that has decayed after 9 hours is

42\text{ g}

.

In a period of 9 hours, exactly 3 half-lives pass (

9/3 = 3

). The fraction of the radioactive substance remaining is

(1/2)^3 = 1/8

, which corresponds to

48\text{ g} \times (1/8) = 6\text{ g}

. Therefore, the mass that has decayed is

48\text{ g} - 6\text{ g} = 42\text{ g}

.

Step-by-Step Solution

1

Determine the number of half-lives (

n

) that have elapsed.

n = \frac{t}{T_{1/2}} = \frac{9\text{ hours}}{3\text{ hours}} = 3

Dividing the total elapsed time by the half-life period gives the number of decay cycles.

2

Calculate the mass of the sample remaining (

N

) after 3 half-lives.

N = N_0 \left(\frac{1}{2}\right)^n = 48\text{ g} \times \left(\frac{1}{2}\right)^3 = 48\text{ g} \times \frac{1}{8} = 6\text{ g}

The remaining quantity decreases by a factor of 2 for each half-life.

3

Calculate the mass of the sample that has decayed.

\text{Mass decayed} = N_0 - N = 48\text{ g} - 6\text{ g} = 42\text{ g}

The amount decayed is equal to the initial mass minus the remaining mass.

Key Concept

Radioactive Decay Law and Half-life

Estimated Time:1m 30s

Question 6603Question →

In a registered limited partnership, a limited partner contributed capital but subsequently began taking an active role in negotiating binding business contracts and managing daily operations. Under commercial law, what is the legal consequence of this partner's participation in management?

The partner loses limited liability protection and becomes personally liable for all business obligations incurred while acting in management

The partner becomes legally entitled to receive an annual salary alongside the general partners for executive services rendered

The partnership is automatically dissolved by operation of law due to structural breach of contract

The general partners' liability is converted to limited liability to maintain equitable balance among partners

Show answer & explanation

Answer: The partner loses limited liability protection and becomes personally liable for all business obligations incurred while acting in management

Answer

The partner loses limited liability protection and becomes personally liable for all business obligations incurred while acting in management.

Under partnership law governing limited partnerships, a limited partner enjoys protection from personal liability only if they refrain from taking part in the management of the firm's business. If a limited partner takes an active management role, such as negotiating contracts or directing operations, they forfeit their limited liability status and become liable for all debts and obligations incurred by the firm while participating in management.

Step-by-Step Solution

1

Identify the partner's status and actions in the scenario.

The individual is a limited partner in a limited partnership who actively engages in contract negotiation and daily management operations.

Limited partnership law strictly segregates capital investment from managerial control.

2

Apply the statutory rule governing limited partner conduct.

A limited partner who takes part in the management of the partnership business loses statutory immunity and becomes liable for all debts and obligations of the firm incurred during that period.

Limited liability is contingent upon remaining a non-managing investor; control over operations exposes the partner to unlimited personal liability.

Key Concept

Liability implications of limited partners taking part in partnership management

Estimated Time:1m 0s

Question 6604Question →

Following the revocation of a licensed commercial bank's operating license due to insolvency, bank customers are concerned about recovering their savings. Which financial regulatory body is statutorily mandated to guarantee the payout of insured funds to depositors and supervise the liquidation of the bank's assets?

Nigeria Deposit Insurance Corporation (NDIC)

Securities and Exchange Commission (SEC)

Debt Management Office (DMO)

Financial Reporting Council of Nigeria (FRCN)

Show answer & explanation

Answer: Nigeria Deposit Insurance Corporation (NDIC)

Answer

The Nigeria Deposit Insurance Corporation (NDIC) is the regulatory body responsible for insuring deposit liabilities and supervising bank liquidation.

The Nigeria Deposit Insurance Corporation (NDIC) is statutorily empowered to insure all deposit liabilities of licensed banks, provide financial assistance to distressed banks, and act as the official liquidator when a bank's operating license is revoked.

Step-by-Step Solution

1

Identify the core regulatory problem in the stem

The issue involves protecting commercial bank depositors and handling bank liquidation following insolvency.

Regulatory bodies in the financial system have clearly demarcated statutory functions.

2

Distinguish between regulatory jurisdictions (SEC vs. NDIC vs. CBN)

SEC regulates capital markets (shares, bonds, stock exchange); NDIC insures bank deposits and handles distressed bank liquidations.

NDIC was specifically established to complement the Central Bank of Nigeria by providing a safety net for bank depositors.

Key Concept

Functions of Financial System Regulatory Bodies: NDIC vs. SEC

Estimated Time:1m 0s

Question 6605Question →

Read the following prose excerpt:

"The midday heat beat down relentlessly upon the overgrown compound of St. Jude's Mission, casting long, stark shadows across the cracked whitewashed walls. Outside the rusted iron gate, the distant rumble of military trucks echoed periodically through the silent village, while inside, Father Joseph sat motionless on the veranda, his sweat-stained cassock clinging to his back as he stared blankly at the uncollected mail piling up on his desk."

What dominant atmosphere is established by the spatial and temporal context described in the passage?

A tense and stagnant mood reflective of social isolation and impending conflict

A festive and bustling environment celebrating community endurance

A serene and harmonious retreat far removed from worldly disturbances

A chaotic and frantic scene of active resistance against military presence

Show answer & explanation

Answer: A tense and stagnant mood reflective of social isolation and impending conflict

Answer

A tense and stagnant mood reflective of social isolation and impending conflict

The correct answer accurately synthesizes the physical markers of decay and immobility (relentless heat, cracked walls, uncollected mail, motionless character) with the ominous auditory cue of military trucks to identify a mood characterized by stagnation, tension, and isolation.

Step-by-Step Solution

1

Analyze physical setting and sensory details

Relentless heat, cracked whitewashed walls, overgrown compound, and uncollected mail establish physical neglect and stagnation.

Physical environment directly signals the emotional and social state of the narrative setting.

2

Examine temporal and external socio-political cues

Midday heat combined with the periodic rumble of military trucks outside a silent village suggests heavy temporal oppression and impending external threat.

Temporal details (midday heat) and background sounds (military vehicles) shape the broader context of the narrative.

3

Synthesize setting elements to identify dominant atmosphere

The combination of internal paralysis (motionless priest, unread mail) and external threat (military trucks) produces an overall atmosphere of tense stagnation.

Atmosphere emerges from the synthesis of spatial location, character stance, and socio-historical context.

Key Concept

Setting, Atmosphere, and Context in Prose

Question 6606Question →

An electric motor with an efficiency of $80\%$ is used to pull a $100\text{ kg}$ object up a smooth incline inclined at $30^\circ$ to the horizontal at a constant speed of $2\text{ m s}^{-1}$ . Taking acceleration due to gravity $g = 10\text{ m s}^{-2}$ , what is the electrical power input to the motor, in watts?

Show answer & explanation

Answer: 1250

Answer

1250 W

The force needed to move the mass up the smooth incline at constant speed is the parallel component of weight,

F = mg \sin(30^\circ) = 500\text{ N}

. The useful power output is

P_{\text{out}} = Fv = 500 \times 2 = 1000\text{ W}

. Dividing by the efficiency of

0.80

yields the electrical power input

P_{\text{in}} = 1250\text{ W}

.

Step-by-Step Solution

1

Determine the force required along the inclined plane.

F = mg \sin(30^\circ) = 100\text{ kg} \times 10\text{ m s}^{-2} \times 0.5 = 500\text{ N}

At constant velocity, the applied force balances the component of weight parallel to the incline.

2

Calculate the useful power output delivered by the motor.

P_{\text{out}} = F \times v = 500\text{ N} \times 2\text{ m s}^{-1} = 1000\text{ W}

Mechanical power output is the product of pulling force and constant speed.

3

Calculate the total electrical power input required.

P_{\text{in}} = \frac{P_{\text{out}}}{\text{Efficiency}} = \frac{1000\text{ W}}{0.80} = 1250\text{ W}

Efficiency is defined as the ratio of useful power output to total power input.

Key Concept

Mechanical power on inclined planes and system efficiency

Question 6607Question →

A point charge of $+6.0 \times 10^{-6}\text{ C}$ experiences an attractive electrostatic force of $0.54\text{ N}$ when placed at a distance of $1.0\text{ m}$ from a second point charge in a vacuum. Taking Coulomb's constant $k = 9.0 \times 10^9\text{ N}\cdot\text{m}^2\text{C}^{-2}$ , what is the magnitude of the second charge in microcoulombs ( $\mu\text{C}$ )?

Show answer & explanation

Answer: 10

Answer

The magnitude of the second charge is 10 µC.

Using Coulomb's law

F = \frac{k |q_1 q_2|}{r^2}

, substituting

F = 0.54\text{ N}

,

q_1 = 6.0 \times 10^{-6}\text{ C}

,

r = 1.0\text{ m}

, and

k = 9.0 \times 10^9\text{ N}\cdot\text{m}^2\text{C}^{-2}

yields

|q_2| = 1.0 \times 10^{-5}\text{ C}

, which equals

10\text{ }\mu\text{C}

.

Step-by-Step Solution

1

State Coulomb's Law formula

F = \frac{k |q_1 q_2|}{r^2}

Coulomb's Law describes the electrostatic force between two point charges.

2

Substitute given parameters into the equation

0.54 = \frac{9.0 \times 10^9 \times 6.0 \times 10^{-6} \times |q_2|}{1.0^2}

Knowns:

F = 0.54\text{ N}

,

q_1 = 6.0 \times 10^{-6}\text{ C}

,

r = 1.0\text{ m}

,

k = 9.0 \times 10^9\text{ N}\cdot\text{m}^2\text{C}^{-2}

.

3

Solve for the unknown charge magnitude

q_2

|q_2| = 1.0 \times 10^{-5}\text{ C}

Rearranging yields

|q_2| = \frac{0.54}{5.4 \times 10^4} = 1.0 \times 10^{-5}\text{ C}

.

4

Convert the value from Coulombs to microcoulombs

10\text{ }\mu\text{C}

1\text{ }\mu\text{C} = 10^{-6}\text{ C}

, so

1.0 \times 10^{-5}\text{ C} = 10\text{ }\mu\text{C}

.

Key Concept

Coulomb's Law

Question 6608Question →

Read the following extract carefully:

"For years, the townspeople revered the solitary lighthouse keeper as a selfless guardian of the coast. Yet, in his private journals disclosed after his passing, he confessed that his isolation was not born of devotion to humanity, but of a quiet contempt for society's pettiness. He maintained the beacon solely to preserve his own sanctuary from the chaotic world outside."

Based on the extract above, which of the following best expresses the central theme revealed about the lighthouse keeper's life?

The illusion of heroic altruism concealing an underlying motive of personal detachment.

The ultimate triumph of civic duty over individual disillusionment in hostile environments.

The struggle of a first-person narrator to overcome maritime hazards while preserving moral integrity.

The inevitable destruction of coastal heritage due to institutional corruption and neglect.

Show answer & explanation

Answer: The illusion of heroic altruism concealing an underlying motive of personal detachment.

Answer

The illusion of heroic altruism concealing an underlying motive of personal detachment.

The passage highlights a sharp contradiction between the public's perception of the lighthouse keeper as a selfless hero and his true private motivation, which was misanthropic self-isolation. The option emphasizing the illusion of heroic altruism concealing personal detachment correctly interprets this central theme.

Step-by-Step Solution

1

Analyze the contrast between public perception and private reality presented in the text.

The townspeople view the keeper as a 'selfless guardian', but his journals reveal 'contempt for society's pettiness'.

Themes in prose often emerge from the tension between outward character actions and inward motivations.

2

Evaluate the primary reason why the keeper maintains the beacon.

He maintains the flame 'solely to preserve his own sanctuary'.

Identifying core motivations clarifies the central thematic message of the passage.

3

Select the statement that captures this thematic dichotomy.

The statement highlighting the illusion of altruism masking personal detachment accurately represents the passage.

It captures both the superficial appearance of duty and the true underlying desire for isolation.

Key Concept

Themes and Thematic Interpretation in Prose

Question 6609Question →

At $60^\circ\text{C}$ , the solubility of a trioxonitrate(V) salt $Y$ (molar mass $= 160\text{ g mol}^{-1}$ ) is $1.25\text{ mol dm}^{-3}$ . When the solution is cooled to $20^\circ\text{C}$ , its solubility decreases to $0.25\text{ mol dm}^{-3}$ . What mass of salt $Y$ will crystallize out when $300\text{ g}$ of a saturated solution of $Y$ at $60^\circ\text{C}$ is cooled to $20^\circ\text{C}$ ? (Assume the density of water is $1.0\text{ g cm}^{-3}$ ).

40.0\text{ g}

48.0\text{ g}

50.0\text{ g}

160.0\text{ g}

Show answer & explanation

Answer: $40.0\text{ g}$

Answer

The mass of salt

Y

that crystallizes out upon cooling is

40.0\text{ g}

.

Converting concentrations to mass per

1000\text{ g}

of water gives

200\text{ g}

at

60^\circ\text{C}

and

40\text{ g}

at

20^\circ\text{C}

. A

300\text{ g}

sample of saturated solution at

60^\circ\text{C}

contains

50\text{ g}

of solute dissolved in

250\text{ g}

of solvent (water). Upon cooling to

20^\circ\text{C}

,

250\text{ g}

of water can only hold

10\text{ g}

of solute. Thus,

50\text{ g} - 10\text{ g} = 40.0\text{ g}

crystallizes out.

Step-by-Step Solution

1

Convert solubility at

60^\circ\text{C}

from

\text{mol dm}^{-3}

to

\text{g dm}^{-3}

\text{Solubility at } 60^\circ\text{C} = 1.25\text{ mol dm}^{-3} \times 160\text{ g mol}^{-1} = 200\text{ g dm}^{-3}

Solubility calculations involving mass of solution require mass concentration (

\text{g dm}^{-3}

).

2

Determine mass of water in

300\text{ g}

of saturated solution at

60^\circ\text{C}

\text{Mass of solution per dm}^3 = 1000\text{ g (water)} + 200\text{ g (salt)} = 1200\text{ g}

. Therefore,

\text{mass of water in } 300\text{ g solution} = \frac{1000\text{ g}}{1200\text{ g}} \times 300\text{ g} = 250\text{ g}

.

Solubility expresses mass of solute per fixed mass of solvent (

1000\text{ g}

water).

3

Convert solubility at

20^\circ\text{C}

to

\text{g dm}^{-3}

and find mass of salt remaining dissolved in

250\text{ g}

water

\text{Solubility at } 20^\circ\text{C} = 0.25\text{ mol dm}^{-3} \times 160\text{ g mol}^{-1} = 40\text{ g dm}^{-3}

. In

250\text{ g}

of water, dissolved salt

= 40\text{ g} \times \frac{250\text{ g}}{1000\text{ g}} = 10\text{ g}

.

Determining how much solute stays dissolved at the lower temperature.

4

Calculate the mass of salt precipitated

\text{Original salt in solution} = 200\text{ g} \times \frac{250\text{ g}}{1000\text{ g}} = 50\text{ g}

.

\text{Mass precipitated} = 50\text{ g} - 10\text{ g} = 40.0\text{ g}

.

Mass precipitated is the difference between initial dissolved mass and remaining dissolved mass.

Key Concept

Mass of salt precipitated upon cooling saturated solutions

Estimated Time:2m 30s

Question 6610Question →

At constant temperature and pressure,

30\text{ cm}^3

of hydrogen gas reacts completely with

15\text{ cm}^3

of oxygen gas to form steam according to the balanced equation:

2\text{H}_2(g) + \text{O}_2(g) \rightarrow 2\text{H}_2\text{O}(g)

What is the volume of steam produced, and which law of chemical combination governs this gas volume relationship?

30\text{ cm}^3

; Gay-Lussac's Law of Combining Volumes

45\text{ cm}^3

; Law of Conservation of Mass

15\text{ cm}^3

; Law of Definite Proportions

22.4\text{ cm}^3

; Gay-Lussac's Law of Combining Volumes

Show answer & explanation

Answer: $30\text{ cm}^3$ ; Gay-Lussac's Law of Combining Volumes

Answer

The volume of steam produced is

30\text{ cm}^3

, governed by Gay-Lussac's Law of Combining Volumes.

According to Gay-Lussac's Law of Combining Volumes, gases combine in simple numerical ratios by volume at constant temperature and pressure. In the balanced reaction

2\text{H}_2(g) + \text{O}_2(g) \rightarrow 2\text{H}_2\text{O}(g)

, 2 volumes of hydrogen combine with 1 volume of oxygen to yield 2 volumes of steam. Thus,

30\text{ cm}^3

of hydrogen produces

30\text{ cm}^3

of steam.

Step-by-Step Solution

1

Identify the mole/volume ratio from the balanced chemical equation.

The coefficient ratio for

\text{H}_2(g) : \text{O}_2(g) : \text{H}_2\text{O}(g)

is

2 : 1 : 2

.

By Gay-Lussac's Law of Combining Volumes, when gases react at constant temperature and pressure, their reacting volumes and the volume of gaseous products are in simple numerical ratios equal to their stoichiometric coefficients.

2

Calculate the volume of steam produced from the volume of reacting hydrogen gas.

\text{Volume of } \text{H}_2\text{O}(g) = 30\text{ cm}^3 \times \frac{2}{2} = 30\text{ cm}^3

Since the ratio of hydrogen to steam is

2 : 2

(or

1 : 1

),

30\text{ cm}^3

of hydrogen produces an equal volume (

30\text{ cm}^3

) of steam.

3

Identify the law of chemical combination illustrated.

Gay-Lussac's Law of Combining Volumes.

This specific law deals with the simple integer ratios between reacting gas volumes under identical conditions of temperature and pressure.

Key Concept

Gay-Lussac's Law of Combining Volumes states that when gases react, they do so in volumes which bear a simple whole-number ratio to one another and to the volume of any gaseous product, provided temperature and pressure remain constant.

Estimated Time:1m 15s

Question 6611Question →

At a weather recording station, the air temperature is $25^\circ\text{C}$ and the relative humidity is recorded as $60\%$ . If the saturated vapour pressure of water at $25^\circ\text{C}$ is $24.0\text{ mmHg}$ , what is the actual partial vapour pressure of water present in the atmosphere?

14.4\text{ mmHg}

40.0\text{ mmHg}

9.6\text{ mmHg}

24.0\text{ mmHg}

Show answer & explanation

Answer: $14.4\text{ mmHg}$

Answer

The actual partial vapour pressure of water present in the atmosphere is

14.4\text{ mmHg}

.

Relative humidity is defined as the ratio of actual partial vapour pressure to saturated vapour pressure at the same temperature, expressed as a percentage. Therefore, the actual partial vapour pressure is

60\%

of

24.0\text{ mmHg}

, which equals

14.4\text{ mmHg}

.

Step-by-Step Solution

1

State the standard relationship defining relative humidity in terms of vapour pressures.

\text{Relative Humidity (R.H.)} = \frac{\text{Partial Vapour Pressure}}{\text{Saturated Vapour Pressure at Air Temp}} \times 100\%

Relative humidity quantifies how close the air is to maximum moisture saturation at a given temperature.

2

Substitute the given numerical values into the relative humidity formula.

60\% = \frac{P}{24.0\text{ mmHg}} \times 100\%

Here

P

represents the unknown actual partial vapour pressure of water in the atmosphere.

3

Rearrange the equation to isolate and solve for

P

.

P = 0.60 \times 24.0\text{ mmHg} = 14.4\text{ mmHg}

Multiplying the saturated vapour pressure by

0.60

yields the actual partial vapour pressure.

Key Concept

Relative Humidity and Vapour Pressure Calculation

Question 6612Question →

A radioactive detector records an initial disintegration rate of $6400\text{ counts per minute}$ from a freshly prepared isotope. If the half-life of the isotope is $5\text{ hours}$ , determine the total time, in hours, required for the count rate to decrease to $400\text{ counts per minute}$ .

Show answer & explanation

Answer: 20

Answer

The total time required for the disintegration rate to decrease to

400\text{ counts per minute}

is

20\text{ hours}

.

The fraction of activity remaining is

\frac{400}{6400} = \frac{1}{16}

. Expressing this as a power of one-half,

\left(\frac{1}{2}\right)^4 = \frac{1}{16}

, shows that

4

half-lives have elapsed. Multiplying

4

half-lives by

5\text{ hours}

per half-life yields a total duration of

20\text{ hours}

.

Step-by-Step Solution

1

Calculate the ratio of remaining activity to initial activity

\frac{N}{N_0} = \frac{400}{6400} = \frac{1}{16}

To find the fraction of the original radioactive substance that remains undecayed.

2

Determine the number of elapsed half-lives

n = 4

Since \left(\frac{1}{2}\right)^n = \frac{1}{16} = \left(\frac{1}{2}\right)^4, four complete half-lives have passed.

3

Compute the total elapsed time

t = 4 \times 5 = 20\text{ hours}

Total time equals the number of half-lives multiplied by the duration of one half-life.

Key Concept

Radioactive Decay Law and Half-life

Estimated Time:1m 30s

Question 6613Question →

A sample of dinitrogen tetraoxide ( $\text{N}_2\text{O}_4$ ) gas occupies a volume of $5.6\text{ dm}^3$ at standard temperature and pressure (STP). What is the total number of oxygen atoms contained in this sample? $[\text{Molar volume of gas at STP} = 22.4\text{ dm}^3\text{mol}^{-1}, N_A = 6.02 \times 10^{23}\text{ mol}^{-1}]$

6.02 \times 10^{23}

5.62 \times 10^{23}

1.51 \times 10^{23}

9.03 \times 10^{23}

Show answer & explanation

Answer: $6.02 \times 10^{23}$

Answer

6.02 \times 10^{23}

oxygen atoms

The sample contains

0.25\text{ mol}

of

\text{N}_2\text{O}_4

gas because

5.6\text{ dm}^3 / 22.4\text{ dm}^3\text{mol}^{-1} = 0.25\text{ mol}

. Since each molecule of

\text{N}_2\text{O}_4

contains 4 oxygen atoms, the total amount of oxygen atoms is

0.25 \times 4 = 1.0\text{ mol}

. Multiplying

1.0\text{ mol}

by Avogadro's constant (

6.02 \times 10^{23}\text{ mol}^{-1}

) yields

6.02 \times 10^{23}

oxygen atoms.

Step-by-Step Solution

1

Calculate the number of moles of dinitrogen tetraoxide (

\text{N}_2\text{O}_4

) gas at STP

n(\text{N}_2\text{O}_4) = \frac{\text{Volume}}{\text{Molar Volume}} = \frac{5.6\text{ dm}^3}{22.4\text{ dm}^3\text{mol}^{-1}} = 0.25\text{ mol}

At STP, one mole of any ideal gas occupies

22.4\text{ dm}^3

.

2

Determine the moles of oxygen atoms present in

0.25\text{ mol}

of

\text{N}_2\text{O}_4

n(\text{O}) = 0.25\text{ mol} \times 4 = 1.0\text{ mol}

of oxygen atoms

Each molecule of

\text{N}_2\text{O}_4

contains 4 oxygen atoms.

3

Compute the absolute number of oxygen atoms using Avogadro's constant

N(\text{O}) = n(\text{O}) \times N_A = 1.0\text{ mol} \times 6.02 \times 10^{23}\text{ mol}^{-1} = 6.02 \times 10^{23}

atoms

One mole of any substance contains

N_A

particles.

Key Concept

Molar gas volume at STP and Avogadro's constant stoichiometric conversions

Estimated Time:2m 0s

Question 6614Question →

Read the lines below:

"Fleet feet sweep through the deep street,
Where silent dreams and shadows meet."

Which sound device is predominantly featured in the first line of the extract?

Assonance

Alliteration

Consonance

Onomatopoeia

Show answer & explanation

Answer: Assonance

Answer

Assonance

Assonance is the correct choice because the line creates musicality through the repetition of the vowel sound /iː/ across multiple adjacent words ("Fleet", "feet", "sweep", "deep", "street").

Step-by-Step Solution

1

Analyze the sound pattern within the first line of the extract.

The words "Fleet", "feet", "sweep", "deep", and "street" share the identical long vowel sound /iː/.

Determining whether the repeated sound consists of vowels or consonants clarifies the specific device.

2

Map the identified sound pattern to literary sound device definitions.

The repetition of internal vowel sounds within neighbouring words is defined as assonance.

Distinguishing vowel repetition from consonant repetition sets assonance apart from alliteration and consonance.

Key Concept

Assonance in Poetry

Question 6615Question →

A $100\text{ cm}^3$ sample of dry air is passed slowly over excess heated copper turnings in a combustion tube until no further contraction in volume occurs. Assuming oxygen accounts for $21\%$ of air by volume, what is the volume of the remaining unreacted gas in $\text{cm}^3$ at room temperature and pressure?

Show answer & explanation

Answer: 79

Answer

The volume of the remaining unreacted gas is

79\text{ cm}^3

.

Dry atmospheric air is made up of approximately

21\%

oxygen gas and

79\%

non-reactive gases (primarily nitrogen along with argon and carbon dioxide). When passed over heated copper, only oxygen reacts to form solid copper(II) oxide. The volume of oxygen removed is

21\text{ cm}^3

, leaving

100\text{ cm}^3 - 21\text{ cm}^3 = 79\text{ cm}^3

of unreacted gaseous mixture.

Step-by-Step Solution

1

Calculate the volume of oxygen absorbed by the heated copper

Volume of

\text{O}_2 = \frac{21}{100} \times 100\text{ cm}^3 = 21\text{ cm}^3

Air contains approximately

21\%

oxygen by volume, which reacts quantitatively with heated copper turnings.

2

Determine the remaining unreacted gas volume

Volume remaining =

100\text{ cm}^3 - 21\text{ cm}^3 = 79\text{ cm}^3

The unreacted component consists mainly of nitrogen (approx.

78\%

) and noble gases (approx.

1\%

) which do not react with heated copper.

Key Concept

Composition of dry air and quantitative removal of oxygen gas

Estimated Time:45s

Question 6616Question →

A $6.60\text{ g}$ sample of impure ammonium tetraoxosulfate(VI), $(\text{NH}_4)_2\text{SO}_4$ , is heated with excess sodium hydroxide solution. The evolved ammonia gas, $\text{NH}_3$ , is absorbed completely in $100.0\text{ cm}^3$ of $0.50\text{ mol dm}^{-3}$ tetraoxosulfate(VI) acid solution, $\text{H}_2\text{SO}_4$ . The unreacted acid requires $40.0\text{ cm}^3$ of $0.50\text{ mol dm}^{-3}$ sodium hydroxide solution for complete neutralization. What is the percentage purity of the ammonium tetraoxosulfate(VI) sample? $[\text{N} = 14, \text{H} = 1, \text{S} = 32, \text{O} = 16]$

Show answer & explanation

Answer: 80

Answer

80%

The correct answer is 80.0%. Through back-titration analysis, 0.020 mol of NaOH neutralizes 0.010 mol of unreacted excess H₂SO₄ out of the initial 0.050 mol, leaving 0.040 mol of H₂SO₄ to react with 0.080 mol of evolved NH₃ gas. Since 1 mole of pure ammonium tetraoxosulfate(VI) produces 2 moles of NH₃ gas, the sample contained 0.040 mol of pure (NH₄)₂SO₄. Multiplying by its molar mass (132 g/mol) yields 5.28 g of pure compound. Dividing 5.28 g by the total sample mass of 6.60 g and multiplying by 100 gives exactly 80.0%.

Step-by-Step Solution

1

Calculate the initial moles of H₂SO₄ acid solution used for absorbing ammonia.

0.050 mol H₂SO₄

Total acid available = Volume (in dm³) × Concentration (in mol dm⁻³).

2

Calculate the unreacted moles of H₂SO₄ from the titration with NaOH.

0.010 mol excess H₂SO₄

1 mole of H₂SO₄ reacts with 2 moles of NaOH, so excess H₂SO₄ = 0.5 × moles of NaOH used.

3

Calculate moles of H₂SO₄ neutralized by evolved NH₃ gas.

0.040 mol H₂SO₄ reacted

Reacted acid = Initial total acid - Excess unreacted acid.

4

Calculate the moles of NH₃ evolved from the sample.

0.080 mol NH₃

2 moles of NH₃ react with 1 mole of H₂SO₄.

5

Determine the mass of pure (NH₄)₂SO₄ present in the original sample.

5.28 g of pure (NH₄)₂SO₄

1 mole of (NH₄)₂SO₄ yields 2 moles of NH₃. Mass = moles (0.040 mol) × molar mass (132 g/mol).

6

Compute the percentage purity of the sample.

80%

Percentage Purity = (Mass of pure substance / Total mass of impure sample) × 100%.

Key Concept

Back-titration quantitative analysis for determining percentage purity

Estimated Time:3m 0s

Question 6617Question →

Match each type or source of business capital listed on the left with its correct defining characteristic or feature on the right.

Click a left item, then click its matching right item

Show answer & explanation

Answer

Debentures match with long-term loan capital issued under company seal; Bank Overdraft matches with short-term bank credit facility for overdrawing current accounts; Trade Credit matches with short-term supplier financing; Equity Shares match with permanent risk capital with voting rights.

Each business capital source is accurately paired with its duration, source, and legal character. Debentures are long-term debt instruments, equity shares are permanent risk capital, bank overdrafts are short-term bank credit facilities, and trade credit represents short-term mercantile supplier credit.

Step-by-Step Solution

1

Classify the duration horizon for each item (short-term vs long-term).

Debentures and Equity Shares are long-term sources, whereas Bank Overdraft and Trade Credit are short-term sources.

Distinguishing short-term working capital sources from long-term capital structure sources helps narrow matching options.

2

Differentiate long-term debt capital from equity ownership capital.

Debentures represent long-term creditor debt with fixed interest, while Equity Shares represent permanent proprietary ownership with variable dividends and voting rights.

Debenture holders are creditors of the firm, whereas equity shareholders are the owners.

3

Differentiate short-term bank credit from short-term mercantile credit.

Bank Overdraft is provided by commercial financial institutions on current accounts, whereas Trade Credit is extended directly by trade vendors on merchandise purchases.

Overdrafts involve bank borrowing facilities while trade credit is derived from trade supplier terms.

Key Concept

Types and Duration of Business Capital Sources

Question 6618Question →

An artisanal furniture craftsman in an urban center specializes in producing custom-carved mahogany executive desks tailored to individual client specifications. Despite the market dominance of a nearby mass-production factory offering lower unit prices, the craftsman continues to operate profitably. Which of the following factors primarily accounts for the continued survival of this small-scale enterprise?

The high consumer demand for personal attention and customized product design that mass producers cannot efficiently provide

The continuous enjoyment of external economies of scale that reduce individual raw material costs

The total elimination of worker monotony achieved through extensive division of labour in the workshop

The generation of interest as a direct factor reward for owning the physical workshop premises

Show answer & explanation

Answer: The high consumer demand for personal attention and customized product design that mass producers cannot efficiently provide

Answer

The high consumer demand for personal attention and customized product design that mass producers cannot efficiently provide.

Small-scale businesses maintain a strong competitive advantage in markets where products require personal craftsmanship, direct interaction with buyers, and custom specifications. Large mass-production factories specialize in standard uniform goods and cannot offer individual customization efficiently.

Step-by-Step Solution

1

Analyze the business operational context described in the stem.

The business is a small-scale artisanal producer creating customized items competing with a large mass-production factory.

Identifying the operational differences helps pinpoint why small firms persist despite lacking large-scale technical economies.

2

Evaluate the economic factors that allow small-scale enterprises to survive.

Small-scale firms excel in niche markets requiring personal service, flexible output, and unique custom specifications.

Mass-production firms rely on standardization and cannot easily tailor items individually without raising unit costs.

Key Concept

Factors responsible for the survival of small-scale production alongside large-scale production

Question 6619Question →

Match each prose excerpt in Column A with the dominant setting, atmosphere, or socio-cultural context it establishes in Column B.

Click a left item, then click its matching right item

Show answer & explanation

Answer

Excerpt 1 matches the claustrophobic atmosphere of tension and fear; Excerpt 2 matches the festive socio-cultural celebration; Excerpt 3 matches the bleak industrial environment; Excerpt 4 matches the tranquil coastal setting.

Each passage employs specific diction and imagery that uniquely aligns with its corresponding setting and mood: hidden underground conspirators convey secrecy and fear; communal drumming and royal arrivals signal festivity; industrial pollution and tired laborers reflect oppressive work conditions; quiet seaside scenery conveys tranquility.

Step-by-Step Solution

1

Analyze the descriptive sensory details and word choices in each prose excerpt.

Identified key indicators such as 'trembling whispers' (tension), 'royal drums' (celebration), 'soot/sulfur sky' (industrial decay), and 'gentle waves' (tranquility).

Atmosphere and setting in prose are established primarily through imagery, diction, and mood.

2

Correlate each excerpt with its corresponding spatial, emotional, or socio-cultural classification.

Paired secret cellar movement with claustrophobic tension, village festival with traditional celebration, smoggy township with industrial hardship, and peaceful pier with idyllic coastal routine.

Matching requires evaluating how environmental context influences narrative tone and backdrop.

Key Concept

Analysis of Setting, Atmosphere, and Context in Prose

Question 6620Question →

A water pump raises $600\text{ kg}$ of water through a vertical height of $20\text{ m}$ in $50\text{ s}$ . If the efficiency of the pump is $80\%$ , what is the electrical power input required to operate the pump? (Take $g = 10\text{ m s}^{-2}$ )

3.0\text{ kW}

2.4\text{ kW}

1.92\text{ kW}

120.0\text{ kW}

Show answer & explanation

Answer: $3.0\text{ kW}$

Answer

3.0\text{ kW}

The correct answer is

3.0\text{ kW}

. Raising

600\text{ kg}

of water by

20\text{ m}

requires

120,000\text{ J}

of gravitational potential energy. Doing this in

50\text{ s}

requires an output power of

2,400\text{ W}

(

2.4\text{ kW}

). Since the pump operates at

80\%

efficiency, the input power must be

\frac{2.4\text{ kW}}{0.80} = 3.0\text{ kW}

.

Step-by-Step Solution

1

Calculate the useful work output needed to elevate the water

W_{out} = mgh = 600\text{ kg} \times 10\text{ m s}^{-2} \times 20\text{ m} = 120,000\text{ J}

Work done against gravity equals the gravitational potential energy gained

2

Calculate the useful output power of the pump

P_{out} = \frac{W_{out}}{t} = \frac{120,000\text{ J}}{50\text{ s}} = 2,400\text{ W} = 2.4\text{ kW}

Power is defined as the rate at which work is performed

3

Calculate the required electrical power input using efficiency

P_{in} = \frac{P_{out}}{\text{Efficiency}} = \frac{2.4\text{ kW}}{0.80} = 3.0\text{ kW}

Efficiency is the ratio of useful output power to total input power

Key Concept

Work done against gravity, power, and mechanical/electrical efficiency

Estimated Time:1m 30s

Answer

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