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Mathematics QUESTION #1328

In the D'Alembert solution, the function $\dfrac{1}{2c}\int_{x-ct}^{x+ct}g(s)\,ds$ represents the contribution from:

The initial displacement $f(x)$
The initial velocity $g(x)$✔️
The boundary conditions
The wave speed $c$

Correct Answer Logic:

In the D'Alembert solution $u(x,t)=\dfrac{f(x+ct)+f(x-ct)}{2}+\dfrac{1}{2c}\int_{x-ct}^{x+ct}g(s)\,ds$, the first term comes from initial displacement $u(x,0)=f(x)$ and the second term arises from the initial velocity condition $u_t(x,0)=g(x)$.

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Security Measures to Maintain Law and Order QUESTION #852

Question 2

Under Section 7(1), a search must be conducted with "strict regard to decency." For a female passenger, this legally implies:

Search by any officer
Search only by a female officer✔️
No search allowed
Search in public view

Correct Answer Logic:

Professional conduct and human rights protocols require that body searches of females be conducted only by female staff in a private setting.

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Islamic Studies QUESTION #230

Question 3

At what time is the Kusoof prayer performed?

Wind
Solar eclipse✔️
Lunar eclipse
None of these

Correct Answer Logic:

Salat al-Kusoof is offered during a solar eclipse; Salat al-Khusoof is for a lunar eclipse.

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Electrical Engineering QUESTION #2183

Question 4

In AM with modulation index $\mu = 0.5$, the efficiency (ratio of useful sideband power to total transmitted power) is:

$11.1\%$✔️
$25.0\%$
$33.3\%$
$20.0\%$

Correct Answer Logic:

$\eta = \frac{\mu^2/2}{1+\mu^2/2}\times100 = \frac{0.125}{1.125}\times100 \approx 11.1\%$. At $\mu=1$ (100% modulation), efficiency peaks at only $33.3\%$, illustrating DSB-FC inefficiency.

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Mathematics QUESTION #1309

Question 5

For $f(x)=x-\cos x$, the derivative $f'(x)$ used in Newton-Raphson is:

$1+\sin x$✔️
$1-\sin x$
$-\sin x$
$\cos x$

Correct Answer Logic:

$f(x)=x-\cos x\Rightarrow f'(x)=1+\sin x$. The Newton-Raphson iteration becomes: $x_{n+1}=x_n-\dfrac{x_n-\cos x_n}{1+\sin x_n}$. Starting near $x=\pi/4\approx0.7854$ converges to the root $\approx0.7391$.

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Urdu QUESTION #5072

Question 6

یوسفِ بے کارواں کا مفہوم کیا ہے؟

مظلوم و ستم زدہ✔️
اکیلا
لاثانی
رہبر و راہنما

Correct Answer Logic:

یوسفِ بے کارواں سے مراد وہ شخص ہے جو ستم زدہ اور مظلوم ہو۔

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Chemistry QUESTION #5583

Question 7

Phenol reacts with KBr/KBrO₃ solution (which generates $Br_2$ in situ). The major product obtained is:

3-Bromophenol
4-Bromophenol
2,4,6-Tribromophenol✔️
2-Bromophenol

Correct Answer Logic:

The –OH group in phenol is a powerful ortho/para director and activates all three positions (2, 4, and 6). With excess $Br_2$ in water (generated from $KBr + KBrO_3$), all three activated positions undergo electrophilic aromatic substitution to give 2,4,6-tribromophenol as the major product (white precipitate).

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Islamic Studies QUESTION #232

Question 8

Which of the following is among the Ummahat ul Momineen?

Khaula
Umme Hani
Atiya
None of these✔️

Correct Answer Logic:

None of the listed names are among the primary wives of the Prophet (ﷺ).

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Pakistan Affairs QUESTION #143

Question 9

When did Pakistan join SEATO?

1953
1954✔️
1956
1955

Correct Answer Logic:

Pakistan joined the South East Asia Treaty Organization (SEATO) in September 1954.

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Civil Engineering QUESTION #6607

Question 10

When designing a fillet weld, the effective throat thickness $t_e$ used for strength calculations of a $45^\circ$ weld with leg size $w$ is:

$w$
$0.500 w$
$0.707 w$✔️
$1.414 w$

Correct Answer Logic:

The effective throat of a fillet weld is the shortest distance from the root to the face. For a standard equal-leg fillet weld, this is $w \sin(45^\circ) \approx 0.707w$.

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MCQs Section QUESTION #4895

Question 11

A fire in an enclosed space burns with the aid of reflected radiation that preheats the fuel, making ignition much easier and _____.

flames spreading
flame spreads
flames are caused to spread
causing flames to spread✔️

Correct Answer Logic:

Causing flames to spread' is parallel with 'making ignition much easier' — both are participial phrases modifying the main clause. Options A, B, and C all break this participial parallel structure. Option E (causing spreading of the flames) would be unnecessarily wordy.

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Paper-I (Anatomy/Physiology and Biochemistry/Microbiology) QUESTION #3342

Question 12

'Septicemia' is also known as:

Fever
Blood poisoning✔️
Skin rash
Stomach ache

Correct Answer Logic:

It involves the systemic spread of pathogens and their toxins in the blood.

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Disaster Management QUESTION #6529

Question 13

In designing a microinsurance scheme for vulnerable households, what represents the primary barrier to uptake?

Lack of insurance companies
Affordability and awareness of benefits among low-income populations✔️
Complex claim procedures
Regulatory constraints

Correct Answer Logic:

Section 9.3 identifies affordability as a key barrier, proposing government-backed subsidies, partnerships with microfinance institutions, and awareness campaigns. For vulnerable populations, premium costs and understanding of insurance value are primary constraints rather than product availability.

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Islamic Studies QUESTION #350

Question 14

"Mubahala" (Religious challenge) was offered by the Holy Prophet (ﷺ) to:

Banu Quraiza
Banu Nazir
Banu Bakr
Delegate of Najran✔️

Correct Answer Logic:

The event of Mubahala took place between the Prophet (ﷺ) and the Christian delegation from Najran.+1

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Paper-II (Pharmacology and Social Behaviour, Law & Ethics and Computer Sciences) QUESTION #5782

Question 15

The process of retranslating a sender's symbols into a meaningful message is known as:

Encoding
Decoding✔️
Feedback
Medium

Correct Answer Logic:

Decoding is the process of translating symbols back into meaning[cite: 7].

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Sociology QUESTION #1676

Question 16

Anthony Giddens introduced the concept of 'double hermeneutics' to describe a distinctive epistemological condition unique to the social sciences. This concept refers to which methodological challenge?

The impossibility of achieving objective knowledge in any scientific discipline
The two-way interpretive relationship in which social scientists must interpret a social world that is itself already pre-interpreted by the actors within it, whose concepts in turn re-enter and reshape social life✔️
The hermeneutic circle in which texts can only be understood in terms of the whole, and the whole in terms of its parts
The double-blind methodology required for unbiased social scientific experimentation

Correct Answer Logic:

Giddens introduced 'double hermeneutics' in 'New Rules of Sociological Method' (1976) to describe how social science involves a double layer of interpretation: social scientists interpret a world that lay actors have already interpreted using their own concepts. Moreover, social scientific concepts can be appropriated by lay actors, feeding back into social reality and transforming it — a reflexive dynamic absent in natural science.

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Home Economics QUESTION #6239

Question 17

Which of the following is a mass contact method in extension?

Farm and home visit
Telephone call
Television✔️
Personal letter

Correct Answer Logic:

Mass methods like TV reach a large number of people simultaneously.

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Paper-II (Pharmacology and Social Behaviour, Law & Ethics and Computer Sciences) QUESTION #5778

Question 18

Which drug class is used for the 'eradication of worms'?

Antiviral
Antiprotozoal
Anthelmintic✔️
Antitubercular

Correct Answer Logic:

Anthelmintics are specifically used to treat helminth (worm) infections.

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Therapeutics and Patient Care QUESTION #3885

Question 19

Which topical clotrimazole treatment regimen is considered the most clinically appropriate for vaginal candidiasis?

$500$ mg as a single dose at bedtime✔️
$100$ mg daily at bedtime for $10$ days
$500$ mg daily at bedtime for $3$ days
$100$ mg daily at bedtime for $14$ days

Correct Answer Logic:

A single intravaginal application of clotrimazole $500$ mg pessary is an evidence-based first-line regimen for uncomplicated vaginal candidiasis.

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Library Sciences QUESTION #1550

Question 20

Which of the following best describes 'span of control' as an organizational principle in library management?

The geographic area covered by a branch library system
The number of subordinates a manager can effectively supervise directly✔️
The range of subjects covered by a library's collection
The total budget under a library director's authority

Correct Answer Logic:

Span of control refers to the number of subordinates a manager can effectively supervise directly. A narrow span means few subordinates (enabling close supervision), while a wide span means many subordinates (enabling greater autonomy). Optimal span depends on task complexity and staff skill levels.

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