All practice questions

Question 13041Question →

In a macroeconomy, National Income is measured at $\text{₦1,200 million}$ . Economic records show social security contributions of $\text{₦85 million}$ , corporate profit taxes of $\text{₦120 million}$ , undistributed corporate profits of $\text{��95 million}$ , and government transfer payments of $\text{₦150 million}$ . Calculate the total Personal Income of the economy in millions of Naira.

Show answer & explanation

Answer: 1050

Answer

The total Personal Income is 1050 million Naira.

Personal Income is calculated by adjusting National Income: subtracting corporate profit taxes, undistributed corporate profits, and social security contributions, while adding government transfer payments. Thus,

\text{Personal Income} = 1200 - (85 + 120 + 95) + 150 = 1050

million Naira.

Step-by-Step Solution

1

Calculate total deductions from National Income

300 million Naira

Social security contributions, corporate profit taxes, and undistributed profits represent earned income that households do not directly receive.

2

Adjust National Income by subtracting deductions and adding transfer payments

1050 million Naira

Transfer payments (such as pensions and welfare) are received by individuals without rendering immediate productive services, so they are added to determine total Personal Income.

Key Concept

Derivation of Personal Income from National Income

Question 13042Question →

A poultry farmer in Abakaliki spends $\text{₦}150,000$ to purchase automated feeding equipment instead of expanding his battery cage capacity. According to Lionel Robbins' definition of economics, which of the following represents the real economic cost of this decision?

The expansion of the battery cage capacity that was sacrificed

The monetary expenditure of

\text{₦}150,000

incurred on the feeding equipment

An outward shift of the poultry farm's production possibility curve

The total financial profit expected from operating the automated feeder

Show answer & explanation

Answer: The expansion of the battery cage capacity that was sacrificed

Answer

The expansion of the battery cage capacity that was sacrificed represents the real economic cost.

According to Lionel Robbins, economics focuses on allocating scarce resources among competing ends. The true economic cost of acquiring the automated feeding equipment is the next best alternative that had to be foregone—namely, the expansion of the battery cage capacity.

Step-by-Step Solution

1

Identify the core subject of Lionel Robbins' definition of economics.

Robbins defines economics as studying human behavior as a relationship between ends and scarce means which have alternative uses.

Economic decision-making requires choosing between competing ends due to scarcity.

2

Distinguish between money cost and real (opportunity) cost in the scenario.

The financial cost is

\text{₦}150,000

, but the real economic cost is the alternative project given up (battery cage expansion).

Opportunity cost evaluates the sacrificed satisfaction of the next best alternative rather than the cash paid.

Key Concept

Lionel Robbins' Definition of Economics and Opportunity Cost

Estimated Time:1m 0s

Question 13043Question →

A proton carrying a charge of $1.6 \times 10^{-19}\text{ C}$ enters a uniform magnetic field of flux density $0.50\text{ T}$ perpendicularly at a speed of $2.0 \times 10^{6}\text{ m/s}$ . What is the magnitude of the magnetic force acting on the proton?

1.6 \times 10^{-13}\text{ N}

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

6.4 \times 10^{-13}\text{ N}

1.67 \times 10^{-21}\text{ N}

Show answer & explanation

Answer: $1.6 \times 10^{-13}\text{ N}$

Answer

The magnetic force acting on the proton is

1.6 \times 10^{-13}\text{ N}

.

The magnitude of the force on a charge moving through a magnetic field is given by

F = qvB\sin\theta

. Substituting

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

,

v = 2.0 \times 10^6\text{ m/s}

,

B = 0.50\text{ T}

, and

\theta = 90^\circ

produces

1.6 \times 10^{-13}\text{ N}

.

Step-by-Step Solution

1

Identify the given physical quantities and formula

Charge

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

, velocity

v = 2.0 \times 10^{6}\text{ m/s}

, field strength

B = 0.50\text{ T}

, and angle

\theta = 90^\circ

. The formula for magnetic force on a moving charge is

F = qvB\sin\theta

.

The magnetic force on a moving charged particle depends on charge magnitude, velocity, magnetic flux density, and the angle between velocity and field vectors.

2

Substitute the values into the force equation

F = (1.6 \times 10^{-19}) \times (2.0 \times 10^{6}) \times 0.50 \times \sin(90^\circ) = 1.6 \times 10^{-13}\text{ N}

.

Since

\sin(90^\circ) = 1

, evaluating the product yields the magnetic force in newtons.

Key Concept

Magnetic Force on a Moving Charge

Question 13044Question →

A lithium-6 nucleus $^{6}_{3}\text{Li}$ has a measured nuclear mass of $6.0151\text{ u}$ . Given that the mass of a proton is $1.0078\text{ u}$ and the mass of a neutron is $1.0087\text{ u}$ , calculate the binding energy per nucleon of the nucleus in $\text{MeV}$ . (Take $1\text{ u} = 931\text{ MeV}$ )

Show answer & explanation

Answer: 5.34

Answer

The binding energy per nucleon of the

^{6}_{3}\text{Li}

nucleus is approximately

5.34\text{ MeV}

(or

5.34\text{ MeV/nucleon}

).

The total mass of 3 free protons and 3 free neutrons is

6.0495\text{ u}

. Subtracting the actual nuclear mass (

6.0151\text{ u}

) yields a mass defect of

0.0344\text{ u}

. Multiplying by

931\text{ MeV/u}

gives a total binding energy of

32.0264\text{ MeV}

. Dividing by the

6

nucleons in lithium-6 yields

5.34\text{ MeV}

per nucleon.

Step-by-Step Solution

1

Determine the number of protons and neutrons and compute the total constituent mass.

Protons

Z = 3

, Neutrons

N = 3

. Total nucleon mass

m_{\text{nucleons}} = 3(1.0078\text{ u}) + 3(1.0087\text{ u}) = 6.0495\text{ u}

.

Free nucleons have a combined mass greater than the bound nucleus.

2

Calculate the mass defect (

\Delta m

).

\Delta m = 6.0495\text{ u} - 6.0151\text{ u} = 0.0344\text{ u}

.

The difference between total constituent mass and measured nuclear mass represents the lost mass converted into binding energy.

3

Convert mass defect to total binding energy in

\text{MeV}

.

E_b = 0.0344\text{ u} \times 931\text{ MeV/u} = 32.0264\text{ MeV}

.

Using the equivalence

1\text{ u} = 931\text{ MeV}

.

4

Calculate binding energy per nucleon by dividing by mass number

A = 6

.

\frac{32.0264\text{ MeV}}{6} = 5.3377\text{ MeV} \approx 5.34\text{ MeV}.

Binding energy per nucleon measures the stability per particle in the nucleus.

Key Concept

Mass Defect and Binding Energy per Nucleon

Question 13045Question →

A specimen of a mammalian vertebra observed in the laboratory features a massive, thick centrum, a broad neural spine, and long, forward-pointing transverse processes, but lacks both rib facets and vertebrarterial canals. Which region of the vertebral column does this vertebra belong to?

Lumbar region, adapted for bearing heavy body weight and supporting abdominal muscle attachment

Thoracic region, adapted for articulating with ribs to form the protective chest cage

Cervical region, adapted for protecting vertebral blood vessels leading to the brain

Sacral region, adapted for fusion into a rigid structure that articulates with the pelvic girdle

Show answer & explanation

Answer: Lumbar region, adapted for bearing heavy body weight and supporting abdominal muscle attachment

Answer

Lumbar region, adapted for bearing heavy body weight and supporting abdominal muscle attachment

The lumbar region contains vertebrae with the largest, most massive centra to support the weight of the upper body. They feature long, well-developed transverse processes pointing anteriorly for the attachment of powerful trunk and abdominal muscles, and they lack both rib facets (found only in thoracic vertebrae) and vertebrarterial canals (found in cervical vertebrae).

Step-by-Step Solution

1

Analyze the structural features described in the stem.

Identified key features: massive/thick centrum, long forward-directed transverse processes, absence of rib facets, and absence of vertebrarterial canals.

Each region of the mammalian vertebral column has specific morphological adaptations corresponding to its anatomical location and functional role.

2

Rule out cervical and thoracic regions based on absent diagnostic features.

Absence of vertebrarterial canals excludes cervical vertebrae; absence of rib facets excludes thoracic vertebrae.

Vertebrarterial canals passage vertebral arteries in cervical vertebrae, while rib facets are exclusive to thoracic vertebrae.

3

Match the specimen features with the correct vertebral region.

The presence of a massive centrum and prominent transverse processes without rib/canal features is characteristic of lumbar vertebrae.

Lumbar vertebrae bear the largest gravitational weight of the trunk, requiring a sturdy centrum and large processes for powerful back and abdominal muscle attachment.

Key Concept

Mammalian Vertebral Structural Adaptations

Estimated Time:1m 0s

Question 13046Question →

An ice block of mass $0.15\text{ kg}$ at $-10^\circ\text{C}$ absorbs thermal energy until it turns completely into liquid water at $0^\circ\text{C}$ . Taking the specific heat capacity of ice as $2100\text{ J kg}^{-1}\text{ K}^{-1}$ and the specific latent heat of fusion of ice as $3.36 \times 10^5\text{ J kg}^{-1}$ , what is the total thermal energy supplied in joules?

Show answer & explanation

Answer: 53550

Answer

The total thermal energy supplied is 53,550 J.

To transform sub-zero ice into liquid water at its melting point, thermal energy is absorbed in two distinct stages: warming the ice from

-10^\circ\text{C}

to

0^\circ\text{C}

(

Q_1 = 0.15 \times 2100 \times 10 = 3150\text{ J}

) and melting the ice completely at

0^\circ\text{C}

(

Q_2 = 0.15 \times 3.36 \times 10^5 = 50400\text{ J}

). Adding these yields a total energy of

53550\text{ J}

.

Step-by-Step Solution

1

Calculate the thermal energy required to warm the solid ice from

-10^\circ\text{C}

to its melting point (

0^\circ\text{C}

).

Q_1 = 3150\text{ J}

Before the phase transition can begin, sensible heat must be supplied to raise the ice temperature using

Q_1 = m c_{\text{ice}} \Delta T

.

2

Calculate the thermal energy required to melt the ice at constant temperature (

0^\circ\text{C}

).

Q_2 = 50400\text{ J}

Phase transformation at constant temperature requires latent heat of fusion using

Q_2 = m L_f

.

3

Sum the energy required for both stages to determine total energy.

Q_{\text{total}} = 53550\text{ J}

The total energy supplied is the sum of sensible warming heat (

Q_1

) and latent melting heat (

Q_2

).

Key Concept

Multi-step heat energy calculation involving sensible heat (

m c \Delta T

) and latent heat of fusion (

m L_f

).

Question 13047Question →

An alpha particle carrying a positive charge of $+3.2 \times 10^{-19}\text{ C}$ moves horizontally along the $+x$ -axis at a velocity of $5.0 \times 10^6\text{ m/s}$ . It enters a velocity selector region containing a uniform electric field of $4.0 \times 10^4\text{ V/m}$ directed along the $+y$ -axis. What magnitude and direction of uniform magnetic field $\vec{B}$ are required for the particle to traverse the region undeflected?

8.0 \times 10^{-3}\text{ T}

directed along the

+z

-axis (out of the page)

8.0 \times 10^{-3}\text{ T}

directed along the

-z

-axis (into the page)

2.0 \times 10^{11}\text{ T}

directed along the

+z

-axis (out of the page)

1.25 \times 10^{-2}\text{ T}

directed along the

-y

-axis

Show answer & explanation

Answer: $8.0 \times 10^{-3}\text{ T}$ directed along the $+z$ -axis (out of the page)

Answer

The required magnetic field has a magnitude of

8.0 \times 10^{-3}\text{ T}

directed along the

+z

-axis (out of the page).

The condition for undeflected movement through crossed electric and magnetic fields (velocity selector) requires the magnetic force to be equal and opposite to the electric force. The magnitude is

B = E / v = (4.0 \times 10^4) / (5.0 \times 10^6) = 8.0 \times 10^{-3}\text{ T}

. For a positively charged particle moving along the

+x

-axis with an electric force in the

+y

-direction, Fleming's left-hand rule (or right-hand vector cross product) specifies that the magnetic field must point out of the page along the

+z

-axis to direct the magnetic force along the

-y

-direction.

Step-by-Step Solution

1

Set up the force balance condition for undeflected motion.

Net force

F_{net} = F_E - F_B = 0 \implies qE = qvB \sin\theta

. Since

\vec{v}

and

\vec{B}

are perpendicular,

\sin\theta = 1

, giving

qE = qvB

.

For zero deflection, the electric force and magnetic force must be equal in magnitude and opposite in direction.

2

Calculate the magnitude of the magnetic field

B

.

B = \frac{E}{v} = \frac{4.0 \times 10^4\text{ V/m}}{5.0 \times 10^6\text{ m/s}} = 8.0 \times 10^{-3}\text{ T}

.

Dividing electric field strength by particle speed yields the required magnetic field strength.

3

Determine the direction of the magnetic field using vector cross-product rules.

Electric force

\vec{F}_E = q\vec{E}

points in the

+y

-direction. Thus, magnetic force

\vec{F}_B = q(\vec{v} \times \vec{B})

must point in the

-y

-direction. With

\vec{v}

in the

+x

-direction (

\hat{i}

),

\hat{i} \times \hat{k} = -\hat{j}

, so

\vec{B}

must point along the

+z

-axis (out of the page).

Opposing vector directions are necessary to achieve equilibrium between electric and magnetic forces.

Key Concept

Velocity Selector and Lorentz Force Equilibrium

Estimated Time:2m 0s

Question 13048Question →

Two satellites, $X$ and $Y$ , move in circular orbits around a planet with orbital radii of $r$ and $4r$ , respectively. If satellite $X$ travels at an orbital speed of $v$ , what is the orbital speed of satellite $Y$ ?

\frac{v}{2}

\frac{v}{4}

2v

4v

Show answer & explanation

Answer: $\frac{v}{2}$

Answer

The orbital speed of satellite

Y

is

\frac{v}{2}

.

The orbital speed

v

of a satellite in a circular orbit of radius

r

around a planet of mass

M

is given by

v = \sqrt{\frac{GM}{r}}

. When the radius increases by a factor of 4 from

r

to

4r

, the new speed becomes

v_Y = \sqrt{\frac{GM}{4r}} = \frac{1}{2} \sqrt{\frac{GM}{r}} = \frac{v}{2}

.

Step-by-Step Solution

1

Write the formula for orbital speed of a satellite

v = \sqrt{\frac{GM}{r}}

Orbital speed depends on the gravitational mass

M

of the central body and the orbital radius

r

.

2

Set up the ratio between the orbital speeds of satellites

Y

and

X

\frac{v_Y}{v_X} = \sqrt{\frac{r_X}{r_Y}}

Since

G

and

M

are constant, orbital speed is inversely proportional to

\sqrt{r}

.

3

Substitute the given values

r_X = r

,

r_Y = 4r

, and

v_X = v

v_Y = v \sqrt{\frac{r}{4r}} = v \sqrt{\frac{1}{4}} = \frac{v}{2}

Evaluating the square root yields a factor of

\frac{1}{2}

.

Key Concept

Orbital Speed of a Satellite

Estimated Time:1m 0s

Question 13049Question →

Match each monetary concept on the left with its precise economic role or manifestation in a modern financial economy on the right.

Click a left item, then click its matching right item

Show answer & explanation

Answer

Unit of Account matches with providing a common denominator for expressing relative prices and accounting; Standard of Deferred Payment matches with establishing an agreed monetary measure for settling future debt obligations; Store of Value matches with allowing economic agents to defer consumption by holding liquid purchasing power; Cognizability matches with ensuring currency notes are readily identifiable to prevent fraud.

Unit of Account establishes a common price metric for accounting; Standard of Deferred Payment facilitates credit agreements payable in the future; Store of Value enables wealth accumulation across time; and Cognizability represents the physical quality of being easily recognized and verified.

Step-by-Step Solution

1

Identify the primary accounting role of money

Unit of Account serves as the pricing baseline.

Money acts as a common numerator/measure in which all economic goods are priced and balance sheets are prepared.

2

Examine money's role in credit transactions

Standard of Deferred Payment governs future debt settlements.

It allows borrowing and lending by specifying that debt contracted today is repaid in monetary units later.

3

Analyze money as an asset for holding liquidity over time

Store of Value preserves command over goods.

Holding money links earnings in the present to consumption in future periods, subject to general price level stability.

4

Distinguish physical/legal characteristics from economic functions

Cognizability refers to ease of recognition.

Money must have distinct visual and tactile features so traders instantly verify its authenticity.

Key Concept

Functions and Characteristics of Money

Question 13050Question →

An electronic appliance assembling enterprise in Lagos divided its production process into small, repetitive technical tasks to increase output. However, management noticed that further division of labor could not be economically sustained because consumer demand for the finished appliances remained very low across surrounding markets. Which factor primarily restricts the extent of division of labor in this firm?

The size and extent of the market

The geographical concentration of competing assembly plants in the region

The immediate onset of diminishing returns to additional labor units

The shift of production overhead from variable costs to fixed costs

Show answer & explanation

Answer: The size and extent of the market

Answer

The size and extent of the market primarily restricts the division of labor in this enterprise.

Specialization requires mass production to be profitable. When the market demand for a product is limited, a firm cannot sell high quantities, thereby restricting how far task division can be implemented effectively.

Step-by-Step Solution

1

Analyze the scenario details

The firm introduced specialization, but further division of labor was hindered by low consumer demand for its appliances.

Identifying the bottleneck in the production process reveals which economic principle limits specialization.

2

Apply economic principles of production

Adam Smith's principle states that 'division of labor is limited by the extent of the market.'

When market size is small or demand is low, firms cannot sell the massive volume of goods produced under intense specialization.

Key Concept

Extent of the Market as a Limitation on Division of Labor

Estimated Time:1m 0s

Question 13051Question →

Arrange the following structural body plans of animals in order of increasing evolutionary complexity, from the most primitive organization to the most advanced.

Drag items to arrange them in the correct order

Show answer & explanation

Answer

The correct evolutionary sequence of animal body plans from primitive to advanced is: Diploblastic body plan with two germ layers and radial symmetry → Triploblastic acoelomate body plan with bilateral symmetry but no internal body cavity → Triploblastic pseudocoelomate body plan with a body cavity partially lined by mesoderm → Triploblastic coelomate body plan with a true body cavity completely lined by mesodermal epithelium.

The correct order reflects the fundamental evolutionary sequence of animal organization: primitive radial diploblastic forms evolved first, followed by bilateral triploblastic acoelomates, then pseudocoelomates with a persistent blastocoel, and finally coelomates possessing a peritoneum-lined true coelom.

Step-by-Step Solution

1

Identify the germ layer organization and symmetry of primitive multicellular animals.

Diploblastic animals possessing two germ layers (ectoderm and endoderm) with radial symmetry evolved first among tissue-grade organisms.

Radial diploblastic body plans preceded the development of mesoderm and bilateral symmetry.

2

Determine the emergence of the third germ layer (mesoderm) and bilateral symmetry without a body cavity.

Triploblastic acoelomate organization evolved next, introducing a middle germ layer (mesoderm) and cephalization, but remaining solid between digestive tract and body wall.

Acoelomates represent the first triploblastic lineage prior to body cavity formation.

3

Distinguish between false body cavity (pseudocoelom) and true body cavity (coelom) evolution.

Pseudocoelomates evolved a cavity derived from the blastocoel, followed by coelomates where mesoderm fully lines the cavity to form a peritoneum.

A true coelom allows complex organ suspensions and muscularized digestive tracts.

Key Concept

Evolutionary progression of germ layers, body symmetry, and body cavity organization in animals

Estimated Time:1m 0s

Question 13052Question →

In a developing country operating a mixed economic system, the government deregulates the downstream petroleum sector while simultaneously introducing a price subsidy scheme for private agricultural producers of staple foods. Which of the following best explains how resource allocation decisions are determined in these two sectors following these policy implementations?

Resource allocation in the petroleum sector is governed primarily by the market price mechanism, while allocation in the staple food sector is determined by price signals modified by state intervention.

The price mechanism will completely dictate resource allocation in both sectors without any governmental distortion.

Central planning authorities will directly assign production inputs and quotas across both sectors to ensure national equity.

Government administrative directives will fix all petroleum prices while private producers independently set food prices above market equilibrium.

Show answer & explanation

Answer: Resource allocation in the petroleum sector is governed primarily by the market price mechanism, while allocation in the staple food sector is determined by price signals modified by state intervention.

Answer

Resource allocation in the petroleum sector is governed primarily by the market price mechanism, while allocation in the staple food sector is determined by price signals modified by state intervention.

In a mixed economy, resource allocation relies on a combination of the price mechanism and state intervention. In deregulated sectors, consumer demand and producer supply freely determine prices and resource flows. In subsidized sectors, market price signals continue to operate but are adjusted by government financial support to meet public policy objectives.

Step-by-Step Solution

1

Analyze the resource allocation mechanism in the deregulated petroleum sector.

Deregulation removes state administrative price controls, allowing market demand and supply (the price mechanism) to determine prices and allocate resources.

Private sector operations without price controls rely directly on market forces in a mixed economy.

2

Analyze the impact of state subsidies on the staple food sector.

Subsidies lower production costs or support producer revenue, altering market price signals to encourage resource flow into food production.

State intervention in a mixed economy modifies price signals to achieve socio-economic goals such as food security.

3

Synthesize the dual nature of resource allocation in a mixed economy.

The economy combines pure market allocation in one sector with market-assisted state intervention in another.

A mixed economic system integrates the price mechanism with government regulation to address market outcomes.

Key Concept

Dual Resource Allocation in a Mixed Economy

Question 13053Question →

Arrange the following organic compounds in order of INCREASING solubility in water, starting with the least soluble compound:

Drag items to arrange them in the correct order

Show answer & explanation

Answer

The correct sequence from least soluble to most soluble in water is: Pentane, Pentan-1-ol, Butane-1,4-diol, Ethane-1,2-diol.

Water solubility in organic compounds is determined by the balance between hydrophilic (water-attracting) functional groups and hydrophobic (water-repelling) carbon chains. Pentane is non-polar and cannot form hydrogen bonds, making it the least soluble. Pentan-1-ol has one

-\text{OH}

group but a large 5-carbon hydrophobic chain, giving it low solubility. Butane-1,4-diol contains two

-\text{OH}

groups, significantly enhancing hydrogen bonding with water molecules. Ethane-1,2-diol has two

-\text{OH}

groups and the shortest hydrophobic carbon chain (2 carbons), making it the most soluble in water.

Step-by-Step Solution

1

Analyze the functional groups present in each compound.

Pentane has no polar functional groups. Pentan-1-ol has one

-\text{OH}

group. Butane-1,4-diol has two

-\text{OH}

groups. Ethane-1,2-diol has two

-\text{OH}

groups.

Water is a polar solvent that dissolves compounds capable of forming hydrogen bonds through polar functional groups like

-\text{OH}

.

2

Compare the hydrophobic alkyl chain lengths for compounds with the same functional group capability.

Ethane-1,2-diol has a smaller non-polar carbon chain (2 carbons) compared to Butane-1,4-diol (4 carbons).

A larger non-polar alkyl region increases hydrophobic interaction, reducing solubility in water.

3

Establish the complete order of increasing solubility.

Pentane < Pentan-1-ol < Butane-1,4-diol < Ethane-1,2-diol.

Solubility increases with an increasing ratio of hydrophilic functional groups (

-\text{OH}

) to non-polar alkyl chain length.

Key Concept

Solubility of organic compounds based on functional group polarity and hydrophobic alkyl chain length

Question 13054Question →

A particle of constant mass has a de Broglie wavelength of $\lambda$ . If the kinetic energy of the particle is increased to nine times its initial value, what is its new de Broglie wavelength?

\frac{\lambda}{9}

\frac{\lambda}{3}

3\lambda

9\lambda

Show answer & explanation

Answer: $\frac{\lambda}{3}$

Answer

The new de Broglie wavelength is

\frac{\lambda}{3}

.

The de Broglie wavelength of a particle is given by

\lambda = \frac{h}{\sqrt{2mE_k}}

, showing that wavelength is inversely proportional to the square root of its kinetic energy. When kinetic energy is increased by a factor of 9, the square root factor becomes

\sqrt{9} = 3

, reducing the new wavelength to one-third of its original value (

\frac{\lambda}{3}

).

Step-by-Step Solution

1

Relate de Broglie wavelength to momentum and kinetic energy.

\lambda = \frac{h}{p} = \frac{h}{\sqrt{2mE_k}}

Since kinetic energy is

E_k = \frac{p^2}{2m}

, linear momentum is

p = \sqrt{2mE_k}

.

2

Set up the ratio for the new kinetic energy

E_k' = 9E_k

.

\lambda' = \frac{h}{\sqrt{2m(9E_k)}} = \frac{h}{3\sqrt{2mE_k}}

Substitute the new kinetic energy into the de Broglie wavelength equation.

3

Express the new wavelength in terms of the initial wavelength

\lambda

.

\lambda' = \frac{\lambda}{3}

Comparing

\lambda'

to

\lambda = \frac{h}{\sqrt{2mE_k}}

gives

\lambda' = \frac{\lambda}{3}

.

Key Concept

De Broglie Wavelength and Kinetic Energy Relationship

Question 13055Question →

In a financial system where the Central Bank mandates a minimum cash reserve ratio of $10\%$ , commercial banks decide to voluntarily raise their total cash reserves to $15\%$ of deposits by holding excess reserves. Assuming public preference for holding currency remains constant, how will this decision impact the bank credit multiplier and the total volume of narrow money supply ( $M_1$ )?

The credit multiplier expands from

10

to

15

, causing an increase in the total volume of narrow money supply (

M_1

).

The credit multiplier contracts from

10

to approximately

6.67

, causing a decrease in the total volume of narrow money supply (

M_1

).

The narrow money supply (

M_1

) increases because commercial bank vault cash is added directly to currency in circulation outside banks.

The narrow money supply (

M_1

) remains unchanged because voluntary excess reserve decisions alter broad money (

M_2

) only.

Show answer & explanation

Answer: The credit multiplier contracts from $10$ to approximately $6.67$ , causing a decrease in the total volume of narrow money supply ( $M_1$ ).

Answer

The credit multiplier contracts from 10 to approximately 6.67, causing a decrease in the total volume of narrow money supply (M1).

The credit multiplier is inversely related to the total cash reserve ratio maintained by commercial banks (

K = \frac{1}{r}

). When banks voluntarily increase total cash reserves from

10\%

to

15\%

, the multiplier falls from

10

to approximately

6.67

. As banks retain more funds as reserves, their secondary lending capacity shrinks, reducing demand deposit creation and contracting the overall narrow money supply (

M_1

).

Step-by-Step Solution

1

Calculate the initial credit multiplier under the mandatory reserve ratio

Initial Multiplier =

\frac{1}{\text{Required Reserve Ratio}} = \frac{1}{0.10} = 10

The credit multiplier measures the total demand deposit expansion resulting from an initial deposit based on the cash reserve ratio.

2

Calculate the effective credit multiplier with voluntary excess reserves

Effective Multiplier =

\frac{1}{\text{Effective Reserve Ratio}} = \frac{1}{0.15} \approx 6.67

When banks hold additional excess reserves (5%), the total cash reserves ratio increases to 15% (0.15), reducing the fraction of deposits available for lending.

3

Analyze the impact on narrow money supply (

M_1

)

Narrow money supply (

M_1

) decreases.

M_1

consists of currency outside banks plus demand deposits. With a lower credit multiplier, commercial banks create fewer demand deposits, leading to a overall reduction in

M_1

.

Key Concept

Credit Multiplier and Money Supply Determinants

Estimated Time:2m 0s

Question 13056Question →

In public finance, the stabilization objective of government fiscal policy is primarily directed toward reducing income inequalities between high- and low-income households through progressive taxation.

True

False

Show answer & explanation

Answer: False

Answer

False. Reducing income inequality is the primary goal of the distribution function of public finance, whereas the stabilization function aims to manage macroeconomic fluctuations such as inflation and unemployment.

The statement is false because narrowing the gap between the rich and the poor is the central goal of the distribution function of public finance. The stabilization function is instead targeted at macro-level balance, such as controlling inflation, sustaining economic growth, and achieving full employment.

Step-by-Step Solution

1

Analyze the specific goal presented in the statement.

The statement describes using progressive taxation to lessen income gaps among households.

Identifying the target outcome helps determine which core objective of public finance is being described.

2

Classify the outcome under the standard objective functions of public finance.

Promoting equity and redistributing income falls under the distribution function. The stabilization function deals with economic cycles, unemployment, and inflation control.

Public finance distinguishes clearly between resource allocation, income distribution, and macroeconomic stabilization.

Key Concept

Distinction between the distribution function and stabilization function of public finance

Question 13057Question →

Match each economic action on the left with the corresponding basic economic concept it demonstrates on the right.

Click a left item, then click its matching right item

Show answer & explanation

Answer

Arranging wants in priority order matches with Scale of preference; selecting the top item matches with Economic choice; giving up the next best alternative matches with Opportunity cost.

A scale of preference ranks unsatisfied wants according to their urgency, allowing a consumer to make a choice. The alternative item that is given up as a result of that choice represents the opportunity cost.

Step-by-Step Solution

1

Identify the concept associated with ranking wants by importance.

Listing items according to urgency forms a scale of preference.

Consumers use a scale of preference to organize their desires before making spending decisions.

2

Identify the concept for picking a preferred item from the list.

Selecting the most pressing need is the act of economic choice.

Scarcity forces consumers to choose specific items over others.

3

Identify the concept for the sacrificed alternative.

The next best item forgone is the opportunity cost.

Opportunity cost is defined by the satisfaction sacrificed from the unchosen alternative.

Key Concept

Scale of Preference

Question 13058Question →

An increase in the market price of palm oil causes a corresponding rise in the demand for groundnut oil as households seek alternative cooking media. Which type of demand is demonstrated by groundnut oil in relation to palm oil?

Competitive demand

Joint demand

Composite demand

Derived demand

Show answer & explanation

Answer: Competitive demand

Answer

Competitive demand, as palm oil and groundnut oil serve as substitutes satisfying the same household need.

Competitive demand occurs when two or more commodities serve as substitutes to satisfy a single want. Because palm oil and groundnut oil are substitutes, a price increase in palm oil shifts consumer demand toward groundnut oil.

Step-by-Step Solution

1

Identify the relationship between the two commodities

Palm oil and groundnut oil are alternative goods used for cooking, fulfilling the same basic purpose for consumers.

Determining whether two goods are substitutes or complements is necessary to classify the type of interrelated demand.

2

Analyze the impact of a price change in palm oil on the demand for groundnut oil

As palm oil becomes more expensive, consumers switch to groundnut oil, causing the demand for groundnut oil to increase.

A positive relationship between the price of one commodity and the demand for another defines competitive (substitute) demand.

Key Concept

Competitive Demand (Substitute Goods)

Estimated Time:1m 0s

Question 13059Question →

Organize the following structures of the earthworm's (Annelida) digestive tract in the correct sequential order through which ingested organic matter passes.

Drag items to arrange them in the correct order

Show answer & explanation

Answer

The correct sequence of structures through which food moves in an earthworm's alimentary canal is: Muscular pharynx, Thin-walled crop, Thick-walled gizzard, and Long intestine.

In earthworms (phylum Annelida), the digestive pathway follows a specific anteroposterior sequence: swallowed food passes through the pharynx and esophagus into the crop for storage, then into the gizzard for mechanical trituration, and finally into the intestine where chemical digestion and nutrient absorption take place.

Step-by-Step Solution

1

Identify the initial organ of ingestion following the mouth.

Organic material and soil are pulled in by the muscular pharynx.

The pharynx creates suction to ingest soil and organic particles.

2

Identify the organ used for temporary food storage.

Ingested material travels down the esophagus into the crop.

The thin-walled crop holds food temporarily before mechanical digestion.

3

Determine the organ responsible for mechanical grinding.

Food moves from the crop into the gizzard.

The muscular gizzard uses ingested mineral grains to grind food into small particles.

4

Identify the final site of enzymatic digestion and absorption.

Pulverized food enters the long intestine.

Enzymatic digestion and nutrient absorption occur across the intestinal epithelium before undigested waste exits the anus.

Key Concept

Annelid Alimentary Canal Structural Sequence

Estimated Time:1m 0s

Question 13060Question →

To ensure the sustainable management of a forest reserve while meeting local timber demands, environmental agencies advocate for selective logging rather than clear-cutting. Which of the following best explains why selective logging effectively conserves forest resources?

It preserves structural canopy cover and root systems, thereby minimizing soil erosion and maintaining habitat biodiversity.

It completely halts ecological succession, retaining the forest permanently in a pioneer lichen stage.

It converts the ecosystem into an inverted pyramid of energy, increasing biomass at higher trophic levels.

It eliminates the activity of nitrifying bacteria in the soil, preventing nitrogen loss to the atmosphere.

Show answer & explanation

Answer: It preserves structural canopy cover and root systems, thereby minimizing soil erosion and maintaining habitat biodiversity.

Answer

Selective logging conserves forest resources by preserving canopy structure and root systems, which prevents soil erosion and maintains biodiversity.

Selective logging preserves the ecological integrity of the forest by removing only designated mature trees. This practice leaves the surrounding vegetation, root networks, and canopy intact, protecting topsoil from erosion by wind and water while preserving microhabitats for fauna.

Step-by-Step Solution

1

Analyze the ecological impact of selective logging versus clear-cutting.

Selective logging targets only specific mature or commercial trees while leaving the rest of the vegetation standing.

Maintaining plant cover keeps the root matrix anchored in the soil and protects microclimates within the forest.

2

Identify the key environmental benefit related to conservation of natural resources.

Intact root systems prevent rain runoff from washing away topsoil, while standing timber preserves habitats for diverse species.

Soil retention and habitat preservation are central pillars of sustainable natural resource management.

Key Concept

Sustainable Forest Resource Management

Estimated Time:1m 0s

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept