Tüm alıştırma soruları

Soru 3541Soru →

At 31st December 2025, Chukwu Limited had a total trade debtors balance of ₦120,000. During the year, bad debts amounting to ₦8,000 were written off, and a debt of ₦3,000 previously written off was recovered in cash. What is the net amount of trade debtors (in ₦) to be presented in the Statement of Financial Position?

Cevabı ve açıklamayı göster

Cevap: 112000

Cevap

112,000

The net trade debtors figure in the Statement of Financial Position is calculated by subtracting bad debts written off (₦8,000) from the gross trade debtors balance (₦120,000), giving ₦112,000. Bad debts recovered (₦3,000) are recorded as income in the Profit and Loss Account and do not affect the closing trade debtors balance.

Adım Adım Çözüm

1

Identify initial trade debtors balance

Initial trade debtors = ₦120,000

This is the unadjusted trade debtors balance before accounting for bad debts written off.

2

Deduct bad debts written off

Net trade debtors = ₦120,000 - ₦8,000 = ₦112,000

Bad debts written off represent debts that are irrecoverable and must be removed from total trade receivables.

3

Analyze the impact of bad debts recovered

Net trade debtors remains ₦112,000

Bad debts recovered (₦3,000) are credited to income in the Profit and Loss Account and debited to cash/bank, so they have no effect on closing trade debtors.

Anahtar Kavram

Calculation of net trade debtors after bad debts written off and recovered

Soru 3542Soru →

Match each accounting item relating to sales and sales returns with its correct book of original entry or source document.

Soldaki öğeye tıklayın, sonra eşleşen sağdaki öğeye tıklayın

Cevabı ve açıklamayı göster

Cevap

Credit sales of trading inventory match with the Sales Journal; returns of merchandise by credit customers match with the Sales Returns Journal; the primary source document for credit sales is the Sales Invoice; and the primary source document for sales returns is the Credit Note.

Credit sales of goods are recorded in the Sales Journal supported by a Sales Invoice. Conversely, goods returned by credit customers (returns inward) are entered in the Sales Returns Journal supported by a Credit Note.

Adım Adım Çözüm

1

Identify the appropriate journal of original entry for credit transactions.

Credit sales of stock belong in the Sales Journal, and credit returns from customers belong in the Sales Returns Journal.

Specialized journals record specific types of credit transactions prior to posting to the ledger.

2

Determine the corresponding source documents for each journal.

Sales Invoices substantiate entries in the Sales Journal, whereas Credit Notes substantiate entries in the Sales Returns Journal.

Source documents provide documentary evidence required to enter transactions into day books.

Anahtar Kavram

Books of Original Entry and Source Documents for Sales and Sales Returns

Soru 3543Soru →

The following financial figures were extracted from the books of Kemi Manufacturing Enterprises for the year ended 31st December 2025:

- Prime Cost: $\text{N}150,000$
- Factory Overheads: $\text{N}45,000$
- Opening Work-in-Progress: $\text{N}12,000$
- Closing Work-in-Progress: $\text{N}17,000$

What is the Cost of Production for the year?

Cevabı ve açıklamayı göster

Cevap: 190000

Cevap

The Cost of Production is 190,000 Naira.

The Cost of Production is calculated using the formula: Prime Cost + Factory Overheads + Opening Work-in-Progress - Closing Work-in-Progress. Substituting the values:

\text{N}150,000 + \text{N}45,000 + \text{N}12,000 - \text{N}17,000 = \text{N}190,000

.

Adım Adım Çözüm

1

Add Factory Overheads to Prime Cost

\text{N}150,000 + \text{N}45,000 = \text{N}195,000

Factory overheads are added to prime cost to determine the total factory cost before work-in-progress adjustments.

2

Add Opening Work-in-Progress

\text{N}195,000 + \text{N}12,000 = \text{N}207,000

Opening work-in-progress represents unfinished goods from the previous period completed in the current period.

3

Deduct Closing Work-in-Progress

\text{N}207,000 - \text{N}17,000 = \text{N}190,000

Closing work-in-progress represents unfinished goods at the end of the period and must be deducted to find the cost of fully produced goods.

Anahtar Kavram

Calculation of Cost of Production from Prime Cost, Factory Overheads, and Work-in-Progress adjustments.

Soru 3544Soru →

Which of the following transactions should be recorded in the Purchases Journal of a business entity?

Purchase of goods on credit for resale

Purchase of office machinery on credit

Purchase of a delivery van on credit

Purchase of office furniture on credit

Cevabı ve açıklamayı göster

Cevap: Purchase of goods on credit for resale

Cevap

Purchase of goods on credit for resale

The correct answer is the purchase of goods on credit for resale because the Purchases Journal (Purchases Day Book) is specifically designed to record only credit purchases of merchandise intended for resale.

Adım Adım Çözüm

1

Identify the accounting rule governing the Purchases Journal

The Purchases Journal (Purchases Day Book) only records credit purchases of trading stock meant for resale.

It acts as a book of original entry specifically designed to summarize trade credit purchases before posting to individual creditor accounts and the ledger.

2

Evaluate the nature of non-current asset purchases on credit

Capital expenditures, such as office machinery, delivery vans, and office furniture, are excluded from the Purchases Journal.

Assets bought for long-term use rather than resale must be recorded in the General Journal (Journal Proper).

3

Select the option representing trading inventory acquired on credit terms

The purchase of goods on credit for resale is the correct transaction.

It satisfies both criteria: being bought on credit and intended for resale.

Anahtar Kavram

Scope of Purchases Journal

Soru 3545Soru →

Match each commercial contract scenario in Column I with its corresponding legal classification, mode of discharge, or remedy in Column II.

Soldaki öğeye tıklayın, sonra eşleşen sağdaki öğeye tıklayın

Cevabı ve açıklamayı göster

Cevap

The haulage scenario matches discharge by frustration due to supervening illegality; the vendor's false statement matches fraudulent misrepresentation rendering the contract voidable; the contractor's partial performance matches a claim on quantum meruit; and the destroyed grain scenario matches common mistake as to subject matter existence rendering the contract void ab initio.

Each scenario illustrates a distinct legal principle in commercial contract law: supervening statutory illegality automatically terminates performance via frustration; intentional deceit regarding goods vitiates consent through fraudulent misrepresentation; wrongful prevention of performance permits equitable recovery on quantum meruit for rendered value; and mutual ignorance of destroyed goods forms a common mistake voiding the agreement ab initio.

Adım Adım Çözüm

1

Analyze the interstate haulage scenario involving an unexpected federal prohibition.

Classify as discharge by frustration due to supervening illegality.

An unforeseen statutory change rendering performance illegal post-formation terminates contractual obligations without fault.

2

Analyze the vendor scenario involving a deliberate false representation of origin.

Classify as a vitiating element of fraudulent misrepresentation.

Intentional false statements of fact inducing contract entry make the agreement voidable at the option of the defrauded party.

3

Analyze the contractor scenario where partial renovation work was wrongfully halted by the client.

Match with the remedy of quantum meruit.

Quantum meruit ('as much as he has earned') provides equitable restitution for work done when full performance is wrongfully prevented.

4

Analyze the grain cargo scenario where subject matter destruction occurred prior to agreement without either party's knowledge.

Classify as common mistake (res extincta).

Shared operative mistake regarding the fundamental existence of the contract subject matter nullifies the contract ab initio.

Anahtar Kavram

Law of Contract: Modes of Discharge, Vitiating Elements, and Equitable Remedies

Soru 3546Soru →

If $(125)_x + (32)_x = (201)_x$ , where $x$ represents the base of the numerals, what is the value of $x$ ?

6

7

5

8

Cevabı ve açıklamayı göster

Cevap: 6

Cevap

The base

x

is equal to

6

.

Expanding the base-

x

numbers into base 10 polynomials yields

(x^2 + 2x + 5) + (3x + 2) = 2x^2 + 1

. Simplifying this equation gives

x^2 - 5x - 6 = 0

, which factors as

(x - 6)(x + 1) = 0

. Since a number base must be positive and greater than the highest digit in the expression (which is 5), the only valid solution is 6.

Adım Adım Çözüm

1

Expand all numbers in base

x

into positional power notation (base 10 equivalent)

(125)_x = 1 \cdot x^2 + 2 \cdot x^1 + 5 \cdot x^0 = x^2 + 2x + 5

,

(32)_x = 3 \cdot x^1 + 2 \cdot x^0 = 3x + 2

, and

(201)_x = 2 \cdot x^2 + 0 \cdot x^1 + 1 \cdot x^0 = 2x^2 + 1

Converting all terms to base 10 allows setup of a algebraic equation in

x

.

2

Substitute the expanded terms back into the original equation and simplify

(x^2 + 2x + 5) + (3x + 2) = 2x^2 + 1 \implies x^2 + 5x + 7 = 2x^2 + 1

Combining like terms on the left-hand side prepares the expression for quadratic rearrangement.

3

Rearrange into standard quadratic form

ax^2 + bx + c = 0

2x^2 - x^2 - 5x + 1 - 7 = 0 \implies x^2 - 5x - 6 = 0

Subtracting

(x^2 + 5x + 7)

from both sides sets the quadratic equation to zero.

4

Solve the quadratic equation by factoring and evaluate valid base conditions

(x - 6)(x + 1) = 0 \implies x = 6

or

x = -1

. Valid base:

x = 6

A number base must be a positive integer greater than any single digit present in the given numbers (digits up to 5 appear, so

x > 5

).

Anahtar Kavram

Conversion of numbers in arbitrary base

x

to base 10 via place-value expansion to solve polynomial equations.

Soru 3547Soru →

A U-tube open at both ends contains mercury of density $13\text{}600\text{ kg/m}^3$ . Water of density $1000\text{ kg/m}^3$ is poured into one arm until the water column reaches a height of $27.2\text{ cm}$ . What is the difference in height, in $\text{cm}$ , between the mercury surfaces in the two arms?

Cevabı ve açıklamayı göster

Cevap: 2

Cevap

The difference in height between the mercury surfaces in the two arms is

2.0\text{ cm}

.

At the boundary level where water meets mercury, the pressure produced by the

27.2\text{ cm}

water column must equal the pressure of the mercury column above that same horizontal level. Using

h_w \rho_w = h_m \rho_m

, we solve for the mercury height difference:

h_m = \frac{27.2 \times 1000}{13600} = 2.0\text{ cm}

.

Adım Adım Çözüm

1

Equate the hydrostatic pressure exerted by the water column to the hydrostatic pressure exerted by the balancing mercury column at the interface level.

h_w \rho_w g = h_m \rho_m g

At the same horizontal level within a continuous fluid at rest, the pressures must be equal.

2

Cancel the acceleration due to gravity (

g

) from both sides of the equation.

h_w \rho_w = h_m \rho_m

Gravity acts equally on both liquid columns.

3

Substitute the known values (

h_w = 27.2\text{ cm}

,

\rho_w = 1000\text{ kg/m}^3

,

\rho_m = 13600\text{ kg/m}^3

) into the pressure relation.

27.2 \times 1000 = h_m \times 13600

Inserting the physical quantities isolates the unknown mercury column height

h_m

.

4

Solve for the height difference

h_m

of the mercury levels.

h_m = \frac{27200}{13600} = 2.0\text{ cm}

Dividing the water pressure head product by the density of mercury yields the height of the mercury column.

Anahtar Kavram

Hydrostatic pressure equilibrium in immiscible fluids (U-tube manometer)

Soru 3548Soru →

An electron in a hydrogen atom undergoes a transition from an energy state of $-1.51\text{ eV}$ to a lower energy state of $-3.40\text{ eV}$ . What is the energy of the emitted photon in electron-volts ( $\text{eV}$ )?

Cevabı ve açıklamayı göster

Cevap: 1.89

Cevap

The energy of the emitted photon is

1.89\text{ eV}

.

The energy of an emitted photon during an atomic transition is given by

\Delta E = E_{\text{initial}} - E_{\text{final}}

. Substituting the given levels yields

\Delta E = -1.51\text{ eV} - (-3.40\text{ eV}) = 1.89\text{ eV}

.

Adım Adım Çözüm

1

Identify the initial and final energy states.

E_i = -1.51\text{ eV}

and

E_f = -3.40\text{ eV}

The energy of the photon corresponds to the difference between these two levels.

2

Apply the energy conservation formula for atomic emission.

E_{\text{photon}} = E_i - E_f

When an electron drops to a lower energy level, a photon carrying the lost energy is released.

3

Substitute the values and evaluate the difference.

E_{\text{photon}} = -1.51 - (-3.40) = 1.89\text{ eV}

Subtracting the negative lower energy value yields a positive photon energy.

Anahtar Kavram

Photon energy from atomic level transitions

Soru 3549Soru →

A progressive transverse mechanical wave travels along a stretched string with a wavelength of $\lambda = 0.80\text{ m}$ . If the maximum speed of an oscillating particle on the string is equal to one-quarter ( $\frac{1}{4}$ ) of the propagation speed of the wave, what is the amplitude of the wave, and how are the particle vibration and energy propagation directions oriented relative to each other?

The amplitude is

\frac{1}{10\pi}\text{ m}

, and particles vibrate perpendicular to the direction of energy propagation.

The amplitude is

\frac{1}{5\pi}\text{ m}

, and particles vibrate perpendicular to the direction of energy propagation.

The amplitude is

0.20\text{ m}

, and particles vibrate parallel to the direction of energy propagation.

The amplitude is

\frac{1}{10\pi}\text{ m}

, and particles vibrate parallel to the direction of energy propagation.

Cevabı ve açıklamayı göster

Cevap: The amplitude is $\frac{1}{10\pi}\text{ m}$ , and particles vibrate perpendicular to the direction of energy propagation.

Cevap

The amplitude of the wave is

\frac{1}{10\pi}\text{ m}

, and particles vibrate perpendicular to the direction of energy propagation.

The maximum speed of a particle in simple harmonic wave motion is

v_{p,\text{max}} = \omega A = 2\pi f A

. The wave propagation speed is

v = f \lambda

. Given

v_{p,\text{max}} = \frac{1}{4}v

, we set

2\pi f A = \frac{1}{4} f \lambda

, which yields

A = \frac{\lambda}{8\pi} = \frac{0.80}{8\pi} = \frac{1}{10\pi}\text{ m}

. Because the wave is transverse, particle vibrations occur perpendicular to the direction of wave energy propagation.

Adım Adım Çözüm

1

Relate maximum particle speed to wave parameters.

Maximum transverse particle speed

v_{p,\text{max}} = \omega A = 2\pi f A

.

Particles in simple harmonic wave motion have maximum speed given by the product of angular frequency

\omega

and amplitude

A

.

2

Express wave propagation speed in terms of frequency and wavelength.

Wave speed

v = f \lambda

.

The fundamental wave equation relates wave speed

v

directly to frequency

f

and wavelength

\lambda

.

3

Set up the given proportion and solve for amplitude

A

.

2\pi f A = \frac{1}{4} (f \lambda) \implies 2\pi A = \frac{\lambda}{4} \implies A = \frac{\lambda}{8\pi} = \frac{0.80}{8\pi} = \frac{1}{10\pi}\text{ m}

.

Canceling frequency

f

from both sides allows direct evaluation of

A

.

4

Classify the direction of particle motion relative to energy propagation for a transverse wave.

Particles vibrate perpendicular to the direction of wave travel.

By definition, transverse mechanical waves involve oscillations perpendicular to the direction of wave energy propagation.

Anahtar Kavram

Relationship between particle velocity and wave velocity in transverse mechanical waves

Soru 3550Soru →

A solid block of mass $0.5\text{ kg}$ is completely immersed in water and displaces $0.2\text{ kg}$ of water. What is the magnitude of the upthrust exerted by the water on the block? (Take $g = 10\text{ m/s}^2$ )

2\text{ N}

3\text{ N}

5\text{ N}

7\text{ N}

Cevabı ve açıklamayı göster

Cevap: $2\text{ N}$

Cevap

The magnitude of the upthrust exerted on the block is

2\text{ N}

.

By Archimedes' principle, the buoyant force (upthrust) acting on a submerged object equals the weight of the liquid displaced by the object. Since the mass of displaced water is

0.2\text{ kg}

and

g = 10\text{ m/s}^2

, the weight of the displaced water is

0.2\text{ kg} \times 10\text{ m/s}^2 = 2\text{ N}

.

Adım Adım Çözüm

1

Identify Archimedes' Principle

Upthrust (

U

) is equal to the weight of the fluid displaced by the immersed body.

Archimedes' principle states that the buoyant force on a submerged body equals the weight of the fluid it displaces.

2

Calculate the weight of the displaced water

W_{\text{displaced}} = m_{\text{water}} \times g = 0.2\text{ kg} \times 10\text{ m/s}^2 = 2\text{ N}

Weight is calculated as mass multiplied by acceleration due to gravity.

3

State the upthrust

U = 2\text{ N}

The upthrust is directly equal to the weight of the displaced water.

Anahtar Kavram

Archimedes' Principle and Upthrust

Tahmini Süre:45s

Soru 3551Soru →

What value of $x$ satisfies the surd equation $\sqrt{x + 7} - \sqrt{x} = 1$ ?

9

3

16

7

Cevabı ve açıklamayı göster

Cevap: $9$

Cevap

The value of

x

that satisfies the equation is

9

.

By rearranging the equation to

\sqrt{x+7} = \sqrt{x} + 1

and squaring both sides, we get

x + 7 = x + 2\sqrt{x} + 1

. Subtracting

x + 1

from both sides gives

6 = 2\sqrt{x}

, which yields

\sqrt{x} = 3

. Squaring both sides produces

x = 9

, which correctly satisfies the original equation.

Adım Adım Çözüm

1

Isolate one of the radical terms on one side of the equation.

\sqrt{x + 7} = \sqrt{x} + 1

Isolating a square root allows squaring both sides to eliminate the outer radical.

2

Square both sides of the equation.

x + 7 = (\sqrt{x} + 1)^2 = x + 2\sqrt{x} + 1

Expanding the right-hand side using

(a+b)^2 = a^2 + 2ab + b^2

removes the radical from the left side.

3

Subtract

x

and

1

from both sides to isolate the remaining radical term.

6 = 2\sqrt{x} \implies \sqrt{x} = 3

Simplifying the linear terms leaves a simple square root equation.

4

Square both sides to find

x

.

x = 3^2 = 9

Squaring

\sqrt{x}

isolates

x

completely.

Anahtar Kavram

Solving Surd Equations by Isolating Radicals and Squaring

Soru 3552Soru →

In English phonology, letter combinations and individual consonants can produce unexpected sound values depending on their etymological origins and phonetic environments. Complete the passage below by identifying the correct International Phonetic Alphabet (IPA) symbol for the underlined consonant sound in each target word.

Aşağıdaki boşlukları doldurun

In the word 'flacid', the double consonant 'cc' before the front vowel 'i' is pronounced as the sound cluster , whereas the letter 'x' in the word 'anxiety' represents the voiced consonant sound .

Cevabı ve açıklamayı göster

Cevap

The double 'cc' in 'flaccid' is transcribed phonetically as /ks/, and the 'x' in 'anxiety' is transcribed phonetically as /z/.

In standard English pronunciation, the word 'flaccid' contains the consonant combination /ks/ represented by 'cc', and 'anxiety' contains the voiced alveolar fricative /z/ represented by the letter 'x'.

Adım Adım Çözüm

1

Analyze the phonetic environment of 'cc' in the word 'flaccid'.

The first 'c' occurs before a hard consonant position producing /k/, and the second 'c' precedes the front vowel 'i', producing the voiceless alveolar fricative /s/. Together, they form the cluster /ks/ (pronounced /ˈflæs.ɪd/ or /ˈflæk.sɪd/ in standard Received Pronunciation).

When 'cc' is followed by 'i' or 'e', it generally produces the /ks/ sound combination as in 'accent' or 'flaccid'.

2

Analyze the phonetic realization of 'x' in the word 'anxiety'.

The letter 'x' in 'anxiety' precedes a stressed vowel syllable, causing voicing assimilation which turns the typical voiceless cluster /ks/ into the voiced fricative /z/ (pronounced /æŋˈzaɪ.ə.ti/).

In English phonetics, when 'x' appears before an accented vowel, it is realized as voiced /z/ or /ɡz/ rather than voiceless /ks/.

Anahtar Kavram

Orthographic-to-Phonetic Mapping of Consonants

Tahmini Süre:1m 30s

Soru 3553Soru →

Match each thermometer type listed on the left with its corresponding thermometric property on the right.

Soldaki öğeye tıklayın, sonra eşleşen sağdaki öğeye tıklayın

Cevabı ve açıklamayı göster

Cevap

Liquid-in-glass thermometer matches change in volume of a liquid column; Constant-volume gas thermometer matches change in gas pressure; Platinum resistance thermometer matches change in electrical resistance; Thermocouple matches change in electromotive force (e.m.f.).

Each thermometer relies on a physical property that changes linearly or predictably with temperature: liquid-in-glass uses volume expansion of liquid, constant-volume gas thermometer uses gas pressure variation, platinum resistance thermometer uses electrical resistance change, and thermocouple uses electromotive force generated across thermal junctions.

Adım Adım Çözüm

1

Identify the thermometric property for a liquid-in-glass thermometer.

Expansion of liquid volume.

The liquid (mercury or alcohol) expands up a narrow capillary tube as temperature increases.

2

Identify the thermometric property for a constant-volume gas thermometer.

Pressure of a gas.

At constant volume, the pressure of an ideal gas changes linearly with absolute temperature.

3

Identify the thermometric property for a platinum resistance thermometer.

Electrical resistance.

The electrical resistance of metals increases predictably with temperature.

4

Identify the thermometric property for a thermocouple.

Electromotive force (e.m.f.).

A temperature difference between two thermoelectric junctions induces a proportional voltage.

Anahtar Kavram

Thermometric properties of common thermometers

Tahmini Süre:45s

Soru 3554Soru →

A binary operation $\otimes$ on the set of real numbers $\mathbb{R}$ is defined by $a \otimes b = a^2 + b^2 - ab$ . If $x \otimes 3 = 19$ and $x > 0$ , find the value of $x$ .

Cevabı ve açıklamayı göster

Cevap: 5

Cevap

The value of

x

is

5

.

Applying the operation rule gives

x^2 + 3^2 - 3x = 19

, which simplifies to

x^2 - 3x - 10 = 0

. Factoring this equation yields

(x - 5)(x + 2) = 0

. Since

x

is constrained to be positive (

x > 0

), the unique valid answer is

5

.

Adım Adım Çözüm

1

Apply the definition of the binary operation to

x \otimes 3

x^2 + 3^2 - 3(x) = x^2 - 3x + 9

Substitute

a = x

and

b = 3

into

a \otimes b = a^2 + b^2 - ab

.

2

Equate the result to 19 and rearrange into standard quadratic form

x^2 - 3x - 10 = 0

Subtract 19 from both sides to set the quadratic equation to zero.

3

Factor the quadratic equation and solve for

x

(x - 5)(x + 2) = 0 \implies x = 5 \text{ or } x = -2

Find two numbers that multiply to

-10

and add up to

-3

.

4

Apply the restriction

x > 0

x = 5

Reject the negative solution

x = -2

because

x

must be strictly positive.

Anahtar Kavram

Evaluation of Binary Operations and Solving Quadratic Equations

Soru 3555Soru →

A tube closed at one end has a length of $0.85\text{ m}$ . If the speed of sound in air is $340\text{ m/s}$ , what is the fundamental frequency of the sound wave produced in the tube?

100\text{ Hz}

200\text{ Hz}

400\text{ Hz}

289\text{ Hz}

Cevabı ve açıklamayı göster

Cevap: $100\text{ Hz}$

Cevap

100\text{ Hz}

For a pipe closed at one end, the fundamental frequency is given by

f = \frac{v}{4L}

. Substituting

v = 340\text{ m/s}

and

L = 0.85\text{ m}

yields

f = \frac{340}{4 \times 0.85} = \frac{340}{3.4} = 100\text{ Hz}

.

Adım Adım Çözüm

1

Determine the relationship between pipe length and wavelength for the fundamental mode of a closed pipe.

For a pipe closed at one end,

\lambda = 4L = 4 \times 0.85\text{ m} = 3.4\text{ m}

.

A closed tube forms a node at the closed end and an antinode at the open end, corresponding to one quarter of a full wavelength.

2

Calculate fundamental frequency using the wave equation

v = f\lambda

.

f = \frac{v}{\lambda} = \frac{340\text{ m/s}}{3.4\text{ m}} = 100\text{ Hz}

.

Frequency equals wave velocity divided by fundamental wavelength.

Anahtar Kavram

Fundamental frequency of a pipe closed at one end

Soru 3556Soru →

Match each electromagnetic rule or law on the left with its corresponding physical application or phenomenon on the right.

Soldaki öğeye tıklayın, sonra eşleşen sağdaki öğeye tıklayın

Cevabı ve açıklamayı göster

Cevap

Fleming's left-hand rule pairs with determining the direction of force on a current-carrying conductor; Right-hand grip rule pairs with determining the direction of magnetic field around a straight wire; Lenz's law pairs with determining the direction of an induced current.

Each rule specifically identifies a vector direction in electromagnetism: Fleming's left-hand rule identifies the force direction on a current-carrying conductor, the Right-hand grip rule gives the magnetic field pattern surrounding a current-carrying wire, and Lenz's law gives the direction of an induced current.

Adım Adım Çözüm

1

Identify the primary purpose of Fleming's left-hand rule

It relates magnetic field, current, and motion/force on a current-carrying conductor.

The thumb points to force, index finger to magnetic field, and middle finger to current.

2

Identify the primary purpose of the Right-hand grip rule

It determines the magnetic field direction around a straight wire carrying current.

Grasping the conductor with the thumb pointing in current direction causes the curled fingers to point in the field direction.

3

Identify the primary purpose of Lenz's law

It gives the polarity and direction of induced electromagnetic effects.

Lenz's law ensures conservation of energy by opposing the initial flux change.

Anahtar Kavram

Electromagnetic rules and their physical applications

Tahmini Süre:45s

Soru 3557Soru →

On a warm afternoon, the air temperature in a physics laboratory is $30^\circ\text{C}$ , where the saturated vapour pressure of water is $32.0\text{ mmHg}$ . When the air is cooled, condensation just begins to form on a metal vessel at $20^\circ\text{C}$ . Given that the saturated vapour pressure of water at $20^\circ\text{C}$ is $17.6\text{ mmHg}$ , what is the relative humidity of the air in percentage?

Cevabı ve açıklamayı göster

Cevap: 55

Cevap

The relative humidity of the air is

55\%

.

The dew point is the temperature at which condensation begins, indicating that the actual water vapour pressure present in the air equals the saturated vapour pressure at

20^\circ\text{C}

, which is

17.6\text{ mmHg}

. Dividing this actual vapour pressure by the saturated vapour pressure at the ambient air temperature of

30^\circ\text{C}

(

32.0\text{ mmHg}

) and multiplying by

100\%

yields

\frac{17.6}{32.0} \times 100\% = 55\%

.

Adım Adım Çözüm

1

Determine the actual vapour pressure in the air

Actual vapour pressure =

17.6\text{ mmHg}

Condensation starts at the dew point (

20^\circ\text{C}

), meaning the actual vapour pressure in the air equals the saturated vapour pressure at the dew point.

2

Determine the saturated vapour pressure at the air temperature

Saturated vapour pressure at

30^\circ\text{C}

=

32.0\text{ mmHg}

This is the maximum vapour pressure the air can exert at its current ambient temperature.

3

Compute the relative humidity percentage

\text{Relative Humidity} = \frac{17.6}{32.0} \times 100\% = 55\%

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

Anahtar Kavram

Calculation of relative humidity from saturated vapour pressure at dew point and air temperature

Tahmini Süre:1m 30s

Soru 3558Soru →

A metal $X$ forms two distinct chlorides. Quantitative analysis shows that in Chloride 1, $5.40\text{ g}$ of $X$ combines with $10.65\text{ g}$ of chlorine. In Chloride 2, $3.60\text{ g}$ of $X$ combines with $10.65\text{ g}$ of chlorine. If the empirical formula of Chloride 1 is $XCl_2$ , calculate the subscript value $y$ in the empirical formula $XCl_y$ of Chloride 2.

Cevabı ve açıklamayı göster

Cevap: 3

Cevap

The value of the subscript y is 3.

Applying the Law of Multiple Proportions, when a fixed mass of chlorine (

10.65\text{ g}

) reacts with different masses of metal

X

(

5.40\text{ g}

and

3.60\text{ g}

), the mass ratio of

X

is

5.40 : 3.60 = 3 : 2

. This implies that for a fixed amount of metal

X

, the ratio of chlorine atoms in Chloride 1 to Chloride 2 is

2 : 3

. Since Chloride 1 is

XCl_2

, Chloride 2 must be

XCl_3

, yielding

y = 3

.

Adım Adım Çözüm

1

Determine the mass of chlorine per gram of metal X in Chloride 1.

\frac{10.65\text{ g}}{5.40\text{ g}} = 1.9722\text{ g } Cl / \text{g } X

This establishes the baseline quantitative relationship for the formula

XCl_2

.

2

Determine the mass of chlorine per gram of metal X in Chloride 2.

\frac{10.65\text{ g}}{3.60\text{ g}} = 2.9583\text{ g } Cl / \text{g } X

This determines the mass of chlorine per unit mass of metal in the second compound.

3

Calculate the simple multiple proportion ratio between the two compounds.

\frac{2.9583}{1.9722} = 1.5

According to the Law of Multiple Proportions, the masses of chlorine combining with a fixed mass of X stand in a simple whole-number ratio.

4

Multiply the subscript of chlorine in the first compound by the calculated ratio.

y = 2 \times 1.5 = 3

Since Chloride 1 has 2 chlorine atoms (

XCl_2

), Chloride 2 must have

2 \times 1.5 = 3

chlorine atoms (

XCl_3

).

Anahtar Kavram

Law of Multiple Proportions

Soru 3559Soru →

Read the following prose extract carefully:

"For twenty years, Mr. Okafor calculated every penny, turning away his own siblings when they sought financial relief. He filled his bank accounts and secured vast tracts of land, convinced that wealth was the ultimate fortress against vulnerability. Yet, as he lay dying in his sprawling, empty mansion, surrounded only by paid hired attendants and legal executors waiting to divide his estate, he realized that no amount of money could buy a single genuine human bond."

In the extract above, what is the central theme conveyed through Mr. Okafor's predicament?

The futility of material accumulation at the expense of human relationships

The inevitability of institutional corruption in legal and financial affairs

The narrator's personal bias against wealthy property owners

The triumph of personal self-reliance over traditional family burdens

Cevabı ve açıklamayı göster

Cevap: The futility of material accumulation at the expense of human relationships

Cevap

The central theme is the futility of material accumulation at the expense of human relationships.

The passage contrasts Mr. Okafor's lifelong accumulation of land and money with his final realization that wealth cannot buy genuine human bonds, illustrating that material riches are meaningless without meaningful human relationships.

Adım Adım Çözüm

1

Analyze character motivation and actions in the text

Mr. Okafor prioritized financial hoarding over supporting his family.

Understanding character choices reveals what values are being put to the test in prose analysis.

2

Examine the narrative conflict and climax/resolution

At the end of his life, he is wealthy but emotionally isolated, feeling regret.

Theme is frequently revealed through character realizations and final outcomes.

3

Synthesize the central thematic message

Wealth cannot substitute for genuine human connection.

Connecting character outcome with moral implication establishes the overarching theme.

Anahtar Kavram

Themes and Thematic Interpretation in Prose

Soru 3560Soru →

Given that $123_x = 313_5$ , what is the value of the base $x$ ?

6

7

8

9

Cevabı ve açıklamayı göster

Cevap: 8

Cevap

8

Converting

313_5

to base 10 yields

3(25) + 1(5) + 3(1) = 83

. Expanding

123_x

yields

x^2 + 2x + 3

. Setting them equal produces

x^2 + 2x + 3 = 83

, which simplifies to

x^2 + 2x - 80 = 0

. Solving

(x-8)(x+10) = 0

gives

x = 8

since a base must be positive.

Adım Adım Çözüm

1

Convert the right-hand side

313_5

to base 10.

3(5^2) + 1(5^1) + 3(5^0) = 75 + 5 + 3 = 83_{10}

Converting all terms to base 10 allows forming a standard algebraic equation.

2

Expand the left-hand side

123_x

in powers of

x

.

1 \cdot x^2 + 2 \cdot x^1 + 3 \cdot x^0 = x^2 + 2x + 3

Expressing the number in terms of its base

x

positional values.

3

Set the two base 10 expressions equal and solve the quadratic equation.

x^2 + 2x + 3 = 83 \implies x^2 + 2x - 80 = 0 \implies (x + 10)(x - 8) = 0 \implies x = 8

The base

x

must be a positive integer greater than any digit in

123_x

(so

x > 3

), which leaves

x = 8

.

Anahtar Kavram

Solving equations with unknown number bases by expanding into base 10 polynomials.

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Cevap

Adım Adım Çözüm

Anahtar Kavram