All practice questions

Question 13661Question →

A driver cell of electromotive force $E_0 = 4.0\text{ V}$ and internal resistance $r = 1.0\ \Omega$ is connected across a uniform potentiometer wire of length $100\text{ cm}$ and total resistance $R_w = 9.0\ \Omega$ . A test cell of unknown electromotive force $E_x$ and internal resistance $r_x = 0.5\ \Omega$ is connected in series with a sensitive galvanometer in the secondary circuit. When the jockey touches the wire at a distance of $60\text{ cm}$ from the high-potential end, the galvanometer indicates zero deflection. What is the electromotive force $E_x$ of the test cell?

2.16\text{ V}

2.40\text{ V}

1.96\text{ V}

3.60\text{ V}

Show answer & explanation

Answer: $2.16\text{ V}$

Answer

The electromotive force of the test cell is

2.16\text{ V}

.

The correct answer is obtained by first including the driver cell's internal resistance to find the true driver current of 0.40 A. The total voltage across the 100 cm wire is therefore 3.60 V, yielding a potential gradient of 0.036 V/cm. Multiplying by the 60 cm balance length gives an EMF of 2.16 V for the test cell.

Step-by-Step Solution

1

Calculate total resistance in the primary driver circuit.

R_{\text{total}} = R_w + r = 9.0\ \Omega + 1.0\ \Omega = 10.0\ \Omega

The driver cell's internal resistance is in series with the potentiometer wire resistance.

2

Calculate the current flowing through the driver circuit.

I = \frac{E_0}{R_{\text{total}}} = \frac{4.0\text{ V}}{10.0\ \Omega} = 0.40\text{ A}

Ohm's law applied to the complete primary circuit gives the steady driver current.

3

Determine the potential drop across the entire 100 cm potentiometer wire.

V_w = I \times R_w = 0.40\text{ A} \times 9.0\ \Omega = 3.60\text{ V}

The potential drop across the wire depends on driver current and wire resistance.

4

Calculate potential gradient and solve for the unknown EMF

E_x

at the 60 cm balance point.

k = \frac{V_w}{L_{\text{total}}} = \frac{3.60\text{ V}}{100\text{ cm}} = 0.036\text{ V/cm}

, so

E_x = k \times L = 0.036\text{ V/cm} \times 60\text{ cm} = 2.16\text{ V}

At zero galvanometer deflection, no current flows through the test cell, so its terminal voltage equals its EMF

E_x

.

Key Concept

Potentiometer balance condition and primary circuit internal resistance considerations

Question 13662Question →

Match each derived physical quantity in Column I with its equivalent SI unit expressed in terms of fundamental (base) units in Column II.

Click a left item, then click its matching right item

Show answer & explanation

Answer

Gravitational Potential matches

\text{m}^2\cdot\text{s}^{-2}

; Electrical Conductance matches

\text{kg}^{-1}\cdot\text{m}^{-2}\cdot\text{s}^3\cdot\text{A}^2

; Self-Inductance matches

\text{kg}\cdot\text{m}^2\cdot\text{s}^{-2}\cdot\text{A}^{-2}

; Impulse matches

\text{kg}\cdot\text{m}\cdot\text{s}^{-1}

.

Each derived unit is systematically expressed in terms of the fundamental SI base units (kilogram, meter, second, ampere) by substituting defining formulas. Gravitational potential is energy per unit mass (

\text{J}\cdot\text{kg}^{-1} = \text{m}^2\cdot\text{s}^{-2}

). Electrical conductance is reciprocal resistance (Siemens

= \text{A}\cdot\text{V}^{-1} = \text{kg}^{-1}\cdot\text{m}^{-2}\cdot\text{s}^3\cdot\text{A}^2

). Self-Inductance is electromotive force per rate of change of current (Henry

= \text{V}\cdot\text{s}\cdot\text{A}^{-1} = \text{kg}\cdot\text{m}^2\cdot\text{s}^{-2}\cdot\text{A}^{-2}

). Impulse is force times time (

\text{N}\cdot\text{s} = \text{kg}\cdot\text{m}\cdot\text{s}^{-1}

).

Step-by-Step Solution

1

Derive base units for Gravitational Potential

\text{m}^2\cdot\text{s}^{-2}

Gravitational potential is potential energy per unit mass (

V = \frac{E_p}{m} = \frac{\text{kg}\cdot\text{m}^2\cdot\text{s}^{-2}}{\text{kg}}

).

2

Derive base units for Electrical Conductance

\text{kg}^{-1}\cdot\text{m}^{-2}\cdot\text{s}^3\cdot\text{A}^2

Conductance is current divided by voltage (

G = \frac{I}{V} = \frac{\text{A}}{\text{kg}\cdot\text{m}^2\cdot\text{s}^{-3}\cdot\text{A}^{-1}}

).

3

Derive base units for Self-Inductance

\text{kg}\cdot\text{m}^2\cdot\text{s}^{-2}\cdot\text{A}^{-2}

Inductance is voltage multiplied by time divided by current (

L = \frac{V \cdot t}{I} = \frac{\text{kg}\cdot\text{m}^2\cdot\text{s}^{-3}\cdot\text{A}^{-1} \cdot \text{s}}{\text{A}}

).

4

Derive base units for Impulse

\text{kg}\cdot\text{m}\cdot\text{s}^{-1}

Impulse is force multiplied by time (

I = F \cdot t = (\text{kg}\cdot\text{m}\cdot\text{s}^{-2}) \cdot \text{s}

).

Key Concept

Break down derived physical quantities into fundamental SI quantities (mass in kg, length in m, time in s, electric current in A) using defining physical formulas.

Estimated Time:1m 30s

Question 13663Question →

A tennis ball of mass $0.2\text{ kg}$ moving horizontally at a speed of $15\text{ m s}^{-1}$ strikes a vertical wall and rebounds along its original path at a speed of $10\text{ m s}^{-1}$ . What is the magnitude of the impulse exerted by the wall on the ball?

5.0\text{ N s}

1.0\text{ N s}

3.0\text{ N s}

2.0\text{ N s}

Show answer & explanation

Answer: $5.0\text{ N s}$

Answer

5.0\text{ N s}

The correct answer accounts for the vector nature of velocity. Taking the initial direction as positive (

+15\text{ m s}^{-1}

), the rebound velocity is negative (

-10\text{ m s}^{-1}

). The change in velocity is

\Delta v = -10 - 15 = -25\text{ m s}^{-1}

. Multiplying by mass (

0.2\text{ kg}

) gives an impulse magnitude of

5.0\text{ N s}

.

Step-by-Step Solution

1

Assign direction signs to the initial and final velocity vectors

Initial velocity

u = +15\text{ m s}^{-1}

, final velocity after rebound

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

Velocity is a vector quantity, so reversing direction requires a change in sign.

2

Apply the impulse-momentum theorem (

I = \Delta p = m(v - u)

)

I = 0.2 \times (-10 - 15) = 0.2 \times (-25) = -5.0\text{ N s}

Impulse is equal to the net change in linear momentum.

3

Determine the magnitude of the impulse

|I| = 5.0\text{ N s}

Magnitude is the absolute value of the vector quantity.

Key Concept

Impulse-Momentum Theorem in One-Dimensional Rebound Scenarios

Question 13664Question →

A statutory public corporation is established to provide essential infrastructure and public utility services across the nation. Which of the following constitutes the primary legal feature distinguishing this enterprise from a public limited company?

It is established by a specific Act of Parliament detailing its powers and objectives rather than being registered under general company law.

It raises its initial capital by issuing ordinary shares directly to private investors on the stock exchange.

It lacks an independent legal personality and therefore cannot acquire property or enter contracts in its own name.

Its operational staff are recruited and directly controlled by the Civil Service Commission as core government ministry personnel.

Show answer & explanation

Answer: It is established by a specific Act of Parliament detailing its powers and objectives rather than being registered under general company law.

Answer

The primary legal feature distinguishing a statutory public corporation from a public limited company is that it is established by a specific Act of Parliament detailing its powers and objectives rather than being registered under general company law.

Statutory public corporations are established through special legislation enacted by Parliament or the state legislature. This Act defines their legal powers, duties, management structure, and public service objectives, whereas public limited companies are formed under standard company incorporation statutes.

Step-by-Step Solution

1

Identify the legal foundation of a statutory public corporation.

Statutory public corporations are created by a dedicated decree or Act of Parliament.

The enabling statute outlines the enterprise's mandates, structure, administrative limits, and supervisory framework.

2

Compare the legal establishment with that of a public limited company (PLC).

A PLC is incorporated under general corporate legislation (such as the Companies and Allied Matters Act) by filing a Memorandum and Articles of Association.

PLCs derive their legal existence from general registration processes rather than individual legislative acts.

Key Concept

Features and Legal Status of Statutory Public Corporations

Question 13665Question →

Calculate the magnitude of the linear momentum, in $\text{kg m s}^{-1}$ , of a body of mass $6\text{ kg}$ moving at a constant velocity of $15\text{ m s}^{-1}$ .

Show answer & explanation

Answer: 90

Answer

The magnitude of the linear momentum is

90\text{ kg m s}^{-1}

.

Linear momentum (

p

) is the product of an object's mass (

m

) and its velocity (

v

). Substituting

m = 6\text{ kg}

and

v = 15\text{ m s}^{-1}

yields

p = 6 \times 15 = 90\text{ kg m s}^{-1}

.

Step-by-Step Solution

1

Identify the given physical quantities

Mass

m = 6\text{ kg}

and velocity

v = 15\text{ m s}^{-1}

These are the parameters provided in the problem statement.

2

Apply the linear momentum formula

p = mv = 6\text{ kg} \times 15\text{ m s}^{-1} = 90\text{ kg m s}^{-1}

Linear momentum is defined as the product of an object's mass and its velocity.

Key Concept

Linear Momentum Definition

Estimated Time:30s

Question 13666Question →

An international trading firm replaces its physical paper-based authorization process for purchase requisitions with a digital software solution that automatically routes approval requests to departmental managers based on predefined business rules. Which office automation system is directly performing this routing process?

Electronic Data Interchange

Workflow Management System

Management Information System

Point of Sale System

Show answer & explanation

Answer: Workflow Management System

Answer

Workflow Management System

A Workflow Management System is explicitly engineered to automate internal organizational procedures by directing documents, information, or tasks from one employee to another according to structured operational rules.

Step-by-Step Solution

1

Analyze the operational function described in the scenario.

The company requires a technology that moves internal purchase requisitions electronically to managers according to predefined business rules.

Identifying the specific administrative task (internal task sequencing and document routing) defines the category of software required.

2

Match the requirement against office automation software definitions.

Workflow Management Systems are specifically built to automate structured business procedures by routing work sequentially to authorized individuals.

This directly fulfills the business need of eliminating paper-based approval delays.

Key Concept

Workflow Automation in Office Automation Systems

Question 13667Question →

Trans-State Logistics Plc acquires 60% of the voting shares in QuickPack Courier Ltd. Following the acquisition, QuickPack Courier Ltd continues to trade under its registered corporate name as a distinct legal entity, while Trans-State Logistics Plc exercises corporate control over its strategic decisions. Which of the following best describes the resulting structural relationship between the two companies?

A holding company and subsidiary company relationship

A complete absorption resulting in the immediate legal dissolution of QuickPack Courier Ltd

A general business partnership characterized by joint unlimited liability

An internal administrative reorganization regulated solely by Articles of Association

Show answer & explanation

Answer: A holding company and subsidiary company relationship

Answer

A holding company and subsidiary company relationship

When one company purchases more than 50% of the voting shares of another firm, it gains controlling interest as a holding company. Because the acquired company continues to exist and operate under its own registered corporate name as a separate legal entity, it is classified as a subsidiary company.

Step-by-Step Solution

1

Analyze the equity ownership percentage and operational structure described in the scenario.

Trans-State Logistics Plc acquired 60% (more than 50%) of the voting shares in QuickPack Courier Ltd.

Holding majority voting equity grants controlling interest over another firm.

2

Determine the legal status of the acquired firm following the transaction.

QuickPack Courier Ltd retains its registered corporate name and distinct legal personality.

In a holding-subsidiary arrangement, unlike complete mergers or absorptions, the acquired entity does not lose its separate legal entity status.

3

Identify the standard commercial business combination concept.

The acquiring firm is the holding company and the acquired firm is the subsidiary company.

By definition, a corporate entity controlling another distinct company via majority equity ownership forms a holding-subsidiary combination.

Key Concept

Holding and Subsidiary Companies

Estimated Time:1m 0s

Question 13668Question →

Chidi and Zainab independently attempt to solve a mathematics problem. The probability that Chidi solves it is $\frac{3}{5}$ and the probability that Zainab solves it is $\frac{2}{3}$ . What is the probability that exactly one of them solves the problem?

\frac{2}{5}

\frac{4}{15}

\frac{7}{15}

\frac{13}{15}

Show answer & explanation

Answer: $\frac{7}{15}$

Answer

The probability that exactly one of them solves the problem is

\frac{7}{15}

.

The correct answer is

\frac{7}{15}

. 'Exactly one' means either Chidi solves the problem while Zainab fails (

P(C \cap Z') = \frac{3}{5} \times \frac{1}{3} = \frac{3}{15}

) OR Zainab solves it while Chidi fails (

P(C' \cap Z) = \frac{2}{5} \times \frac{2}{3} = \frac{4}{15}

). Summing these mutually exclusive probabilities gives

\frac{3}{15} + \frac{4}{15} = \frac{7}{15}

.

Step-by-Step Solution

1

Find the complement probabilities of failure for each student.

Probability Chidi fails,

P(C') = 1 - \frac{3}{5} = \frac{2}{5}

. Probability Zainab fails,

P(Z') = 1 - \frac{2}{3} = \frac{1}{3}

.

Required to determine individual non-occurrence probabilities.

2

Calculate the joint probability for each mutually exclusive scenario.

Scenario 1 (Chidi solves, Zainab fails):

\frac{3}{5} \times \frac{1}{3} = \frac{3}{15}

. Scenario 2 (Chidi fails, Zainab solves):

\frac{2}{5} \times \frac{2}{3} = \frac{4}{15}

.

Since the events are independent, individual probabilities multiply.

3

Sum the probabilities of the two mutually exclusive outcomes.

Total probability =

\frac{3}{15} + \frac{4}{15} = \frac{7}{15}

.

By the Addition Law of probability for mutually exclusive compound outcomes.

Key Concept

Probability of Compound Independent Events

Question 13669Question →

What is the smallest positive angle $\theta$ , in degrees, that satisfies the trigonometric equation $\sqrt{3}\tan(3\theta) = 3$ ?

Show answer & explanation

Answer: 20

Answer

The smallest positive value of

\theta

is

20^\circ

.

Isolating

\tan(3\theta)

gives

\tan(3\theta) = \frac{3}{\sqrt{3}} = \sqrt{3}

. The principal acute angle whose tangent is

\sqrt{3}

is

60^\circ

. Equating

3\theta = 60^\circ

and solving for

\theta

yields

\theta = 20^\circ

.

Step-by-Step Solution

1

Isolate the trigonometric function

\tan(3\theta)

\tan(3\theta) = \sqrt{3}

Dividing both sides by \sqrt{3} isolates the tangent term and rationalizes the fraction to \sqrt{3}.

2

Determine the principal angle for

3\theta

3\theta = 60^\circ

The smallest positive angle whose tangent equals \sqrt{3} is 60^\circ.

3

Solve for

\theta

\theta = 20^\circ

Dividing the principal angle 60^\circ by the coefficient 3 gives the smallest positive angle \theta.

Key Concept

Solving trigonometric equations with multiple angle arguments

Question 13670Question →

A potentiometer wire of length $100\text{ cm}$ has a resistance of $5.0\ \Omega$ . It is connected in series with a driver cell of e.m.f. $3.0\text{ V}$ (having negligible internal resistance) and a protective series resistor $R_s$ . A balance point is obtained at $60.0\text{ cm}$ along the wire for a cell of e.m.f. $1.2\text{ V}$ . What is the value of the series resistor $R_s$ in ohms?

Show answer & explanation

Answer: 2.5

Answer

The resistance of the series resistor

R_s

is

2.5\ \Omega

.

At balance, the potential drop across the

60.0\text{ cm}

portion of the potentiometer wire equals the test cell e.m.f. (

1.2\text{ V}

). Since the

100\text{ cm}

wire has a total resistance of

5.0\ \Omega

, the

60.0\text{ cm}

section has a resistance of

3.0\ \Omega

. This requires a main circuit current of

I = \frac{1.2\text{ V}}{3.0\ \Omega} = 0.4\text{ A}

. The total driver circuit resistance is

R_{total} = \frac{3.0\text{ V}}{0.4\text{ A}} = 7.5\ \Omega

. Subtracting the wire's

5.0\ \Omega

resistance gives

R_s = 2.5\ \Omega

.

Step-by-Step Solution

1

Calculate the resistance of the balanced portion of the potentiometer wire.

R_{balance} = 5.0\ \Omega \times \frac{60.0\text{ cm}}{100\text{ cm}} = 3.0\ \Omega

The resistance of a uniform wire is directly proportional to its length.

2

Determine the current in the main potentiometer circuit.

I = \frac{1.2\text{ V}}{3.0\ \Omega} = 0.4\text{ A}

At the balance point, no current flows through the galvanometer branch, so the potential difference across the balance length equals the e.m.f. of the test cell.

3

Compute the total resistance of the driver circuit.

R_{total} = \frac{3.0\text{ V}}{0.4\text{ A}} = 7.5\ \Omega

According to Ohm's law, total resistance equals the total e.m.f. divided by the circuit current.

4

Calculate the value of the series resistor

R_s

.

R_s = 7.5\ \Omega - 5.0\ \Omega = 2.5\ \Omega

The total resistance is the sum of the potentiometer wire resistance and the series resistance.

Key Concept

Potentiometer balance condition and circuit analysis

Estimated Time:1m 30s

Question 13671Question →

Match each foreign trade payment method or instrument with its defining operational characteristic.

Click a left item, then click its matching right item

Show answer & explanation

Answer

Irrevocable Letter of Credit matches with the bank guarantee of payment upon presentation of compliant documents. Usance Bill of Exchange matches with the written order allowing a credit period to settle on a future maturity date. Telegraphic Transfer matches with electronic payment via banking telecommunication channels. Open Account Trading matches with goods being delivered before payment, placing maximum risk on the exporter.

Each instrument accurately corresponds to its foreign trade payment mechanism: Irrevocable Letter of Credit acts as a binding bank commitment; Usance Bill of Exchange provides time credit before settlement; Telegraphic Transfer is direct fast electronic remittance; Open Account involves shipping prior to receiving payment.

Step-by-Step Solution

1

Analyze Irrevocable Letter of Credit

Identified as a binding undertaking by an issuing bank that cannot be altered unilaterally.

It offers high security to exporters by substituting bank creditworthiness for buyer risk.

2

Analyze Usance Bill of Exchange

Identified as a credit instrument payable at a specified future period.

Unlike sight bills, usance bills provide short-term credit facility to the buyer.

3

Analyze Telegraphic Transfer

Identified as a direct cable/electronic bank remittance.

It utilizes cable or SWIFT systems for direct and fast funds transfer.

4

Analyze Open Account Trading

Identified as shipping goods on credit terms without bank collateral guarantees.

Payment takes place after invoice receipt and goods delivery, favoring the importer.

Key Concept

Means of Payment in Foreign Trade

Question 13672Question →

A forest reserve is represented as a rectangular feature measuring $8\text{ cm}$ by $10\text{ cm}$ on Map X, which is drawn to a scale of $1 : 50,000$ . On a newly drawn map, Map Y, the same forest reserve occupies an area of $320\text{ cm}^2$ . What is the representative fraction scale of Map Y?

1 : 25,000

1 : 12,500

1 : 100,000

1 : 200,000

Show answer & explanation

Answer: $1 : 25,000$

Answer

The representative fraction scale of Map Y is

1 : 25,000

.

The original map area is

80\text{ cm}^2

and the enlarged area on Map Y is

320\text{ cm}^2

, giving an area scale factor of

4

. Taking the square root gives a linear scale factor of

2

. Dividing the original scale denominator of

50,000

by

2

gives

25,000

, resulting in a scale of

1 : 25,000

.

Step-by-Step Solution

1

Calculate the area of the forest reserve on Map X

\text{Area on Map X} = 8\text{ cm} \times 10\text{ cm} = 80\text{ cm}^2

Finding the initial area on the original map is required to determine the area enlargement ratio.

2

Calculate the area scale factor between Map X and Map Y

\text{Area Scale Factor} = \frac{\text{Area on Map Y}}{\text{Area on Map X}} = \frac{320\text{ cm}^2}{80\text{ cm}^2} = 4

The area scale factor indicates how many times larger the surface area appears on Map Y compared to Map X.

3

Determine the linear scale factor

\text{Linear Scale Factor} = \sqrt{\text{Area Scale Factor}} = \sqrt{4} = 2

Because surface area changes as the square of linear dimensions (

n^2

), the linear scale factor

n

is the square root of the area factor.

4

Calculate the new representative fraction scale for Map Y

\text{New Scale Denominator} = \frac{50,000}{2} = 25,000 \Rightarrow 1 : 25,000

Map enlargement increases the scale of the map, which means decreasing the scale denominator by dividing it by the linear scale factor.

Key Concept

Linear vs. Area Scale Relationship in Map Enlargement

Estimated Time:1m 30s

Question 13673Question →

An electric cart moving along a straight horizontal track at an initial speed of $10\text{ m/s}$ accelerates uniformly at $3\text{ m/s}^2$ for a duration of $4\text{ s}$ . Immediately after this phase, it applies its brakes and decelerates uniformly at $2\text{ m/s}^2$ until it comes to a complete stop. What is the total distance, in meters, traveled by the cart during the entire motion?

Show answer & explanation

Answer: 185

Answer

The total distance traveled by the cart during the entire motion is

185\text{ m}

.

The total distance is calculated by analyzing the two distinct stages of motion. In the first phase, traveling at an initial velocity of

10\text{ m/s}

with an acceleration of

3\text{ m/s}^2

for

4\text{ s}

yields a distance of

64\text{ m}

and a peak velocity of

22\text{ m/s}

. In the second phase, decelerating from

22\text{ m/s}

to rest at

2\text{ m/s}^2

requires a distance of

121\text{ m}

. Adding both distances (

64\text{ m} + 121\text{ m}

) yields the total distance of

185\text{ m}

.

Step-by-Step Solution

1

Determine the distance (

s_1

) and final velocity (

v_1

) during the uniform acceleration phase

s_1 = 64\text{ m}

and

v_1 = 22\text{ m/s}

Using kinematic formulas

s_1 = u_1 t_1 + \frac{1}{2} a_1 t_1^2

and

v_1 = u_1 + a_1 t_1

for constant acceleration.

2

Determine the stopping distance (

s_2

) during the uniform deceleration phase

s_2 = 121\text{ m}

Using

v_2^2 = v_1^2 - 2 a_2 s_2

with final speed

v_2 = 0\text{ m/s}

.

3

Sum the distances from both stages

S_{\text{total}} = 185\text{ m}

Total displacement for multi-stage motion along a straight line is the sum of displacements in each stage.

Key Concept

Multi-stage linear motion with constant acceleration and deceleration

Question 13674Question →

Match each commercial document used in home trade with its appropriate functional description.

Click a left item, then click its matching right item

Show answer & explanation

Answer

The Letter of Inquiry matches the document sent by a prospective buyer asking for price and availability details; the Order matches the buyer's formal document requesting goods supply; the Proforma Invoice matches the preliminary bill demanding payment prior to dispatch; and the Statement of Account matches the periodic document summarizing transactions and net balances.

Each commercial document aligns directly with its primary function in home trade operations: inquiring about goods, placing an order, requesting advance payment via proforma invoice, and summarizing financial balances through a statement of account.

Step-by-Step Solution

1

Identify the document used at the preliminary stage of home trade inquiry.

The Letter of Inquiry is paired with requesting details on prices, stock availability, and trade terms.

It initiates the buying process before any transaction occurs.

2

Identify the document that places the order.

The Order is paired with issuing a formal request to supply specified goods.

It indicates the buyer's firm commitment to purchase.

3

Identify the document used for advance payment request.

The Proforma Invoice is paired with a preliminary bill demanding payment before dispatch.

Sellers issue it when credit is not extended or pre-payment is required.

4

Identify the periodic accounting document.

The Statement of Account is paired with summarizing sales, receipts, and balances over a period.

It informs credit customers of their ongoing financial balance.

Key Concept

Functions of Commercial Documents in Home Trade

Question 13675Question →

Match each public enterprise reform policy on the left with its corresponding operational feature or economic mechanism on the right.

Click a left item, then click its matching right item

Show answer & explanation

Answer

Full Commercialization corresponds to retaining 100% state ownership with zero operating subventions; Partial Commercialization corresponds to retaining state ownership alongside partial subventions; Outright Privatization corresponds to transferring majority equity control to private investors; Market Deregulation corresponds to abolishing legal entry barriers and price controls.

Each economic reform tool addresses a distinct operational or structural objective: full commercialization removes state operating subventions while retaining 100% public ownership; partial commercialization combines user fees with partial subventions; outright privatization transfers equity ownership to private investors; and deregulation removes statutory monopoly barriers to permit free enterprise competition.

Step-by-Step Solution

1

Analyze full commercialization.

Under full commercialization, the state retains complete ownership but withdraws all operating financial subsidies, compelling the enterprise to run strictly for profit.

This policy restructures operational goals without altering legal ownership.

2

Analyze partial commercialization.

Partial commercialization allows government subventions to continue in part so that essential public social services remain affordable while commercial fees cover remaining operational expenses.

Certain public enterprises deliver social services that justify ongoing state financial support.

3

Analyze outright privatization.

Outright privatization shifts ownership by selling controlling equity shares of public corporations to private individuals or financial institutions.

Privatization directly alters the ownership and capital structure of public enterprises.

4

Analyze market deregulation.

Deregulation dismantles legal market protections and price regulation, enabling non-state entities to enter and compete in the market.

Deregulation alters industry structure and market access rather than internal enterprise ownership.

Key Concept

Public Enterprise Reform Frameworks

Question 13676Question →

A sonometer wire of length $0.80\text{ m}$ and mass $2.0\text{ g}$ is maintained under a tension of $100\text{ N}$ . What is the fundamental frequency of vibration of the wire?

125\text{ Hz}

250\text{ Hz}

62.5\text{ Hz}

12.5\text{ Hz}

Show answer & explanation

Answer: $125\text{ Hz}$

Answer

The fundamental frequency of vibration of the wire is

125\text{ Hz}

.

The linear mass density is

\mu = \frac{0.002\text{ kg}}{0.80\text{ m}} = 0.0025\text{ kg/m}

. The velocity of waves on the string is

v = \sqrt{\frac{100}{0.0025}} = 200\text{ m/s}

. The fundamental frequency is

f = \frac{v}{2L} = \frac{200}{2 \times 0.80} = 125\text{ Hz}

.

Step-by-Step Solution

1

Convert mass to kilograms and calculate linear mass density

(\mu)

.

m = 2.0\text{ g} = 0.002\text{ kg}

. Thus,

\mu = \frac{m}{L} = \frac{0.002\text{ kg}}{0.80\text{ m}} = 0.0025\text{ kg/m} = 2.5 \times 10^{-3}\text{ kg/m}

.

Standard SI units must be used for tension in Newtons and length in meters.

2

Calculate the speed of the transverse wave on the string

(v)

.

v = \sqrt{\frac{T}{\mu}} = \sqrt{\frac{100}{0.0025}} = \sqrt{40000} = 200\text{ m/s}

.

Wave speed on a stretched string depends directly on tension and inversely on linear density.

3

Calculate the fundamental frequency

(f_1)

.

f_1 = \frac{v}{2L} = \frac{200}{2 \times 0.80} = \frac{200}{1.6} = 125\text{ Hz}

.

For a fixed string vibrating in its fundamental mode, the length equals half the wavelength (

\,L = \frac{\lambda}{2}\,

).

Key Concept

Fundamental frequency of a stretched string

Question 13677Question →

Match each description of contour line configuration on the left with the corresponding relief feature it depicts on the right.

Click a left item, then click its matching right item

Show answer & explanation

Answer

Depression matches inwardly decreasing closed contours; Conical hill matches inwardly increasing closed contours; Concave slope matches closely spaced upper contours transitioning to widely spaced lower contours; Escarpment matches extremely tight parallel contours along a linear slope face.

Each landform is uniquely characterized by its contour signature: closed loops decreasing inward represent depressions, closed loops increasing inward mark conical hills, contours spreading out downhill indicate concave slopes, and tightly clustered parallel contours represent escarpments.

Step-by-Step Solution

1

Examine contour patterns for closed loop elevations.

Decreasing inward values indicate a depression, while increasing inward values represent a hill.

Contour values represent height above sea level; dropping values inside a loop signify a basin or pit.

2

Analyze contour spacing relative to elevation changes.

Close spacing near the top and wide spacing near the bottom forms a concave slope.

Closer contour lines represent steeper gradients, whereas wider spacing indicates flatter terrain.

3

Identify linear tight contour clustering.

Merged or nearly touching contours along a slope face depict an escarpment or cliff.

A steep vertical cliff compresses horizontal distance between successive vertical intervals.

Key Concept

Interpretation of relief landforms from contour line spacing and elevation trends

Estimated Time:1m 15s

Question 13678Question →

A field surveyor analyzing a topographical map with a scale of $1 : 50,000$ measures a straight line distance of $4\text{ cm}$ along a road connecting Hilltop Village at an elevation of $350\text{ m}$ and Valley Junction at an elevation of $150\text{ m}$ . What is the gradient of the road between these two settlements?

1 \text{ in } 10

1 \text{ in } 1,000

1 \text{ in } 8

1 \text{ in } 1

Show answer & explanation

Answer: $1 \text{ in } 10$

Answer

The gradient of the road is

1 \text{ in } 10

.

The gradient is determined by dividing Vertical Interval (VI) by Horizontal Equivalent (HE). With a VI of

200\text{ m}

(

350\text{ m} - 150\text{ m}

) and a ground distance HE of

2,000\text{ m}

(

4\text{ cm} \times 50,000 = 200,000\text{ cm} = 2,000\text{ m}

), the ratio

\frac{200}{2,000}

simplifies to

\frac{1}{10}

or

1 \text{ in } 10

.

Step-by-Step Solution

1

Calculate the Vertical Interval (VI)

\text{VI} = 350\text{ m} - 150\text{ m} = 200\text{ m}

Vertical Interval is the difference in elevation between the two points.

2

Calculate the Horizontal Equivalent (HE) in meters

\text{HE} = 4\text{ cm} \times 50,000 = 200,000\text{ cm} = 2,000\text{ m}

Horizontal Equivalent is the actual ground distance converted to the same unit as VI.

3

Compute the slope gradient ratio

\text{Gradient} = \frac{\text{VI}}{\text{HE}} = \frac{200\text{ m}}{2,000\text{ m}} = \frac{1}{10}

or

1 \text{ in } 10

Gradient is defined as the ratio of Vertical Interval to Horizontal Equivalent.

Key Concept

Topographic Slope and Gradient Calculation

Question 13679Question →

A Bill of Sight is a customs declaration document completed by an importer when full details or documentation of imported goods are missing, allowing customs officers to physically inspect the cargo to assess the appropriate duties.

True

False

Show answer & explanation

Answer: True

Answer

True

The statement is correct because a Bill of Sight serves as a temporary entry document lodged by an importer who lacks complete details or invoices for arriving goods. It gives customs authorities the legal right to open and inspect the goods in order to compute accurate import duties.

Step-by-Step Solution

1

Identify the purpose and user of a Bill of Sight in foreign trade.

A Bill of Sight is used by an importer when standard shipping invoices or trade documents are unavailable upon arrival of goods at customs.

Importers need a mechanism to legally unload and examine cargo even if full shipping documents are missing.

2

Evaluate the statement against standard international customs procedure.

The statement correctly identifies that a Bill of Sight authorizes customs officials to inspect cargo physically so that tariffs can be determined.

Without accurate invoices, physical examination via a Bill of Sight is required for duty assessment.

Key Concept

Bill of Sight in Foreign Trade

Question 13680Question →

A micrometer screw gauge has a pitch of $0.5\text{ mm}$ and $50$ divisions on its circular thimble scale. When its anvil and spindle are fully brought together without any object, the zero mark of the thimble scale lies $4$ divisions past the main scale index line in the tightening direction (a positive zero error). When the wall thickness of a hollow metal pipe is measured with this micrometer, the main scale reading is $3.5\text{ mm}$ and the $32\text{nd}$ thimble division aligns with the index line. If the outer diameter of the pipe is separately measured to be $25.40\text{ mm}$ , what is the corrected inner diameter of the metal pipe in millimeters?

Show answer & explanation

Answer: 17.84

Answer

17.84 mm

The least count of the micrometer screw gauge is

\frac{0.5\text{ mm}}{50} = 0.01\text{ mm}

. The observed wall thickness is

3.5\text{ mm} + (32 \times 0.01\text{ mm}) = 3.82\text{ mm}

. Accounting for the positive zero error of

+0.04\text{ mm}

gives a true wall thickness of

3.82\text{ mm} - 0.04\text{ mm} = 3.78\text{ mm}

. Subtracting twice the wall thickness from the outer diameter yields the inner diameter:

25.40\text{ mm} - 2(3.78\text{ mm}) = 17.84\text{ mm}

.

Step-by-Step Solution

1

Calculate the least count (precision) of the micrometer screw gauge

Least count = 0.01 mm

Least count is defined as pitch divided by total circular scale divisions: 0.5 mm / 50 = 0.01 mm.

2

Determine the observed wall thickness from the instrument readings

Observed thickness = 3.82 mm

Observed reading = Main scale reading + (Thimble division * Least count) = 3.5 mm + (32 * 0.01 mm) = 3.82 mm.

3

Correct the observed thickness for positive zero error

Corrected wall thickness = 3.78 mm

Positive zero error (+0.04 mm) must be subtracted from the observed reading: 3.82 mm - 0.04 mm = 3.78 mm.

4

Calculate the corrected inner diameter of the hollow pipe

Inner diameter = 17.84 mm

The inner diameter equals the outer diameter minus twice the wall thickness: 25.40 mm - 2(3.78 mm) = 25.40 mm - 7.56 mm = 17.84 mm.

Key Concept

Measurement of length, micrometer zero error correction, and geometry of hollow cylinders

Estimated Time:2m 30s

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