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Physics QUESTION #7033

Determine the dimensional formula for the permittivity of a vacuum ($\epsilon_0$). Given the fundamental quantities: $M$ = mass, $L$ = length, $T$ = time, and $A$ = electric current.

$[\epsilon_0] = [M^{-1} L^{-3} T^2 A]$
$[\epsilon_0] = [M^{-1} L^{-3} T^4 A^2]$✔️
$[\epsilon_0] = [M^{-1} L^2 T^4 A^{-2}]$
$[\epsilon_0] = [M^{-1} L^2 T^{-1} A]$

Correct Answer Logic:

According to Coulomb's Law, the force $F$ between two charges $q_1$ and $q_2$ separated by distance $r$ is:

$F = \frac{1}{4\pi\epsilon_0} \frac{q_1 q_2}{r^2}$

Rearranging for permittivity:

$\epsilon_0 = \frac{q^2}{4\pi F r^2}$

Dimensional analysis:

Charge $[q] = [AT]$
Force $[F] = [MLT^{-2}]$
Distance $[r] = [L]$

$[\epsilon_0] = \frac{[A^2 T^2]}{[M L T^{-2}] [L^2]} = [M^{-1} L^{-3} T^4 A^2]$

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Accounting & Finance QUESTION #6106

Question 2

A suspense account was opened after a trial balance failed to agree. Errors found:

Sales invoice for $1,240 completely omitted.
Purchases entered as $85,600 instead of $87,580.
Rent paid $2,600 posted as $6,200 in rent account.

What was the original balance on the suspense account?

$1,620 credit✔️
$1,620 debit
$5,580 credit
$5,580 debit

Correct Answer Logic:

Option A ($1,620 credit) is correct.

Only one-sided errors affect the suspense account:

Error 1 (complete omission): Does NOT affect suspense.
Error 2: Purchases understated by $1,980 → Debit Purchases, Credit Suspense $1,980.
Error 3: Rent overposted by $3,600 → Debit Suspense, Credit Rent $3,600.

Net: Dr $3,600 − Cr $1,980 = Dr $1,620 needed → original balance was $1,620 credit.

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English QUESTION #8554

Question 3

We should not hanker _______ worldly pleasures.

far
about
after✔️
None of these

Correct Answer Logic:

'Hanker after' means to desire strongly.

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Constitutional Law QUESTION #5814

Question 4

A state passes a law prohibiting the importation of out-of-state 'solid waste' to protect the health and safety of its citizens and to preserve its remaining landfill space. Is this law constitutional?

Yes, because health and safety are legitimate exercises of the state's police power.
Yes, because the state is acting as a 'market participant' in managing its landfills.
No, because it violates the Negative Implications of the Commerce Clause by discriminating against out-of-state commerce.✔️
No, because it violates the Privileges and Immunities Clause of Article IV.

Correct Answer Logic:

A state law that is facially discriminatory against out-of-state commerce is virtually per se invalid under the Dormant Commerce Clause unless the state can show it serves a legitimate local purpose that cannot be served by non-discriminatory means. Landfill space preservation is not sufficient to justify a ban on out-of-state waste.

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Chemistry QUESTION #7418

Question 5

In which of the following options does the arrangement NOT agree with the property variation indicated against it?

$\text{Al}^{3+} < \text{Mg}^{2+} < \text{Na}^+ < \text{F}^-$ (increasing ionic size)
B < C < N < O (increasing first ionisation enthalpy)✔️
$\text{I} < \text{Br} < \text{Cl} < \text{F}$ (increasing electron gain enthalpy)
Li < Na < K < Rb (increasing metallic radius)

Correct Answer Logic:

IE₁ trend in Period 2:
Generally increases left to right, but N (half-filled 2p³) has unexpectedly higher IE₁ than O (2p⁴, one electron paired → easier to remove). So:

Correct order: B < C < O < N (N before O is reversed)

The statement B < C < N < O suggests O has higher IE₁ than N — this is wrong. Option (2) is incorrect.

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Civil Procedure QUESTION #3757

Question 6

What is the 'Rule Against Perpetuities' (RAP) designed to prevent?

Landlords charging too much rent.
Property interests from vesting too far into the future (dead hand control).✔️
Neighbors from building fences too high.
The government from taking land without compensation.

Correct Answer Logic:

RAP invalidates any interest in property that might not vest within 21 years of a 'life in being' at the time of the creation of the interest.

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Home Economics QUESTION #6291

Question 7

In the 'SMCRE' model of communication, what does the 'E' stand for?

Education
Effect (or Feedback)✔️
Environment
Equipment

Correct Answer Logic:

The model stands for Source, Message, Channel, Receiver, and Effect.

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Physics QUESTION #408

Question 8

Work done on a body equals change in its __________ energy.

Total
Potential
Kinetic
All of these✔️

Correct Answer Logic:

Work-energy theorem applies to all forms

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Boilers Mechanical Engineering QUESTION #2392

Question 9

The final value theorem, used to find the steady-state output $x_o(\infty)$ from the Laplace transform $X_o(s)$, states:

$x_o(\infty) = \lim_{s\to\infty} s X_o(s)$
$x_o(\infty) = \lim_{s\to 0} s X_o(s)$✔️
$x_o(\infty) = \lim_{s\to 0} X_o(s)$
$x_o(\infty) = \lim_{s\to\infty} X_o(s)$

Correct Answer Logic:

Final value theorem: $x_o(\infty)=\lim_{t\to\infty}x_o(t)=\lim_{s\to0}sX_o(s)$. Valid when all poles of $sX_o(s)$ are in the left-half s-plane. Used to find steady-state error without inverting the Laplace transform.

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Electrical Engineering QUESTION #2153

Question 10

In Power Electronics, a Freewheeling Diode is used in an inductive load circuit to:

Increase the output voltage
Prevent high-voltage spikes $L\frac{di}{dt}$ during turn-off✔️
Rectify the AC input
Smooth the ripple in the capacitor

Correct Answer Logic:

The diode provides a path for the inductive current to continue flowing when the switch opens, preventing damaging $L\frac{di}{dt}$ voltage spikes.

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Economics QUESTION #1701

Question 11

Among the most persistent structural criticisms levelled at Pakistan's privatisation drives since the 1990s, which of the following has been the most prominent?

Significant decline in government tax revenues post-privatisation
Absence of transparency, competitive bidding, and accountability in the divestiture process✔️
Excessive regulatory burden imposed on newly privatised entities
None of these

Correct Answer Logic:

The most consistent and widely documented criticism of Pakistan's privatisation policy is the lack of transparency and accountability — assets were often sold below fair market value, through non-competitive processes, to politically connected buyers. The privatisation of entities like PTCL, Pakistan Steel Mills deliberations, and banking sector sales have all attracted scrutiny on these grounds. Regulatory capture of privatised sectors, not over-regulation, has also been a concern.

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Physics QUESTION #7066

Question 12

A cube of maximum possible volume is cut from a solid sphere of mass $M$ and radius $R$. Find the moment of inertia of this cube about an axis that passes through its center and is perpendicular to one of its faces.

$\frac{MR^2}{32\sqrt{2}\pi}$
$\frac{MR^2}{16\sqrt{2}\pi}$
$\frac{4 MR^2}{9\sqrt{3}\pi}$✔️
$\frac{4 MR^2}{3\sqrt{3}\pi}$

Correct Answer Logic:

1. Find Cube Side ($a$): The body diagonal of the cube equals the diameter of the sphere. $\sqrt{3}a = 2R \implies a = \frac{2R}{\sqrt{3}}$.

2. Find Cube Mass ($m$): Density $\rho = \frac{M}{\frac{4}{3}\pi R^3}$. Mass of cube $m = \rho \times a^3 = \left(\frac{3M}{4\pi R^3}\right) \times \left(\frac{8R^3}{3\sqrt{3}}\right) = \frac{2M}{\pi \sqrt{3}}$.

3. Moment of Inertia ($I$): For a cube about the center-face axis, $I = \frac{ma^2}{6}$.
$I = \frac{1}{6} \left( \frac{2M}{\pi \sqrt{3}} \right) \left( \frac{4R^2}{3} \right) = \frac{8MR^2}{18\pi \sqrt{3}} = \frac{4MR^2}{9\sqrt{3}\pi}$.

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Accounting & Finance QUESTION #6155

Question 13

Sales revenue $500,000; Total costs $400,000; Fixed costs $120,000. What was the total contribution?

$100,000
$220,000✔️
$280,000
$380,000

Correct Answer Logic:

Option B ($220,000) is correct.

Variable costs = $400,000 − $120,000 = $280,000

Contribution = $500,000 − $280,000 = $220,000

(Note: Profit = $220,000 − $120,000 = $100,000 — that is Option A, not the same as contribution.)

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CISA QUESTION #1722

Question 14

Which of the following statements most accurately characterises the concept of auditor independence?

Independence is not a relevant concern for auditors employed by a consulting firm.
Independence is an essential requirement specifically for external audits.✔️
An internal auditor achieves independence solely by completing a formal certification programme.
The audit committee formally confers independence upon the auditor.

Correct Answer Logic:

Auditor independence is the cornerstone of a credible and objective audit. An auditor who has a personal, financial, or organisational relationship with the entity being audited risks rendering a biased opinion. Independence is most critical — and most strictly required — in external audits, where the results will be relied upon by third parties. Internal auditors may face structural independence limitations due to their employment relationship with the auditee.

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Math Physics Chemistry Biology QUESTION #4215

Question 15

All of the following properties of water are associated with its capillary action. EXCEPT:

Adhesion
Density✔️
Cohesion
Surface tension

Correct Answer Logic:

Capillary action depends on adhesion, cohesion, and surface tension.

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Urdu QUESTION #5300

Question 16

اس زلف پہ پھبتی شبِ دیجور کی سوجھی، یہ مشہور شعر کس شاعر کا ہے؟

فیض احمد
جوش
احمد فراز
انشاء✔️

Correct Answer Logic:

یہ شعر انشاء اللہ خان انشاء کا ہے جو لکھنؤ کے مشہور شاعر تھے۔

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Nursing QUESTION #9166

Question 17

In community health nursing, primary prevention includes which of the following activities?

Early detection of hypertension through screening
Rehabilitation of stroke patients
Immunization of children against measles✔️
Management of diabetic complications

Correct Answer Logic:

The three levels of prevention are:

Level	Target	Examples
Primary	Healthy population — prevent disease onset	Immunization, health education, clean water, nutrition
Secondary	Early detection and treatment	Screening, early diagnosis, prompt treatment
Tertiary	Reduce disability, restore function	Rehabilitation, chronic disease management

Immunization is a classic example of primary prevention as it prevents disease before it occurs.

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Mathematics QUESTION #4123

Question 18

For $\int_0^2 \int_{\sqrt{x}}^2 f(x, y) \, dy \, dx$, what is the equivalent integral after changing order?

$\int_0^2 \int_0^{y^2} f(x, y) \, dx \, dy$✔️
$\int_0^{\sqrt{2}} \int_0^{y^2} f(x, y) \, dx \, dy$
$\int_0^4 \int_0^{\sqrt{x}} f(x, y) \, dx \, dy$
$\int_{\sqrt{2}}^2 \int_0^{y^2} f(x, y) \, dx \, dy$

Correct Answer Logic:

Region: $0 \leq x \leq 2$ and $\sqrt{x} \leq y \leq 2$. This equals $0 \leq y \leq 2$ and $0 \leq x \leq y^2$. New integral: $\int_0^2 \int_0^{y^2} f(x, y) \, dx \, dy$.

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Statistics QUESTION #1974

Question 19

In an experimental study, the experimental error mainly arises from which source?

Mistakes made by the experimenter
Uncontrolled extraneous (external) factors✔️
Differences in treatment effects
All of the above

Correct Answer Logic:

Experimental error primarily results from extraneous (nuisance) factors not controlled in the experiment. It represents unexplained variability beyond the treatment effects.

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Agronomy QUESTION #2064

Question 20

Zinc deficiency, the most widespread micronutrient deficiency in Pakistan and South Asia, is characterized by:

Dark green, crinkled older leaves with necrotic margins
Interveinal chlorosis and stunting of older leaves due to Zn mobility
Stunted young leaves, shortened internodes (little leaf/khaira disease in rice), interveinal chlorosis on young leaves, and delayed maturity — due to Zn's role in auxin synthesis and enzyme activation✔️
Pale yellow coloration of the entire plant with early senescence

Correct Answer Logic:

Zn deficiency causes little leaf/rosette in fruit trees, khaira disease in rice, and white bud in maize. Young leaves are affected first (Zn is relatively immobile in phloem). Zn activates >300 enzymes, is required for IAA synthesis, RNA polymerase, and ribosome structure. ZnSO₄ (21% Zn) applied at 25 kg/ha corrects deficiency.

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