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The meniscus shape is governed by the balance between surface tension (curvature force) and hydrostatic pressure. The capillary equation gives: \(\frac{d^2y}{dx^2} = \frac{\rho g}{S}y\). This is the standard capillary length equation where the curvature \(\approx d^2y/dx^2\) for small angles equals \(\rho g y/S\).

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Pakistan Affairs QUESTION #131

Question 7027

What was the population of Pakistan at the time of independence in 1947?

70 million
32.5 million✔️
60 million
90 million

Correct Answer Logic:

The total population was roughly 70 million across both wings; however, West Pakistan's population was approximately 32.5 million.

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Islamic Studies QUESTION #8227

Question 7028

What is Shab-e-Abi Talab (a valley near Makkah)?

The refuge of Muslims against social boycott✔️
An important trade passage
A farm House of Abi Talab
A lake for storage of water

Correct Answer Logic:

Shib Abi Talib was a valley near Makkah where Muslims and the Banu Hashim clan took refuge during a social and economic boycott imposed by the Quraish. This boycott lasted for three years (7-10 years after prophethood). During this period, Muslims faced severe hardship, hunger, and isolation. The boycott ended when some Quraish leaders tore up the agreement. This period tested the faith and endurance of early Muslims.

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Nursing QUESTION #9209

Question 7029

In quantitative nursing research, what is the PRIMARY purpose of randomization in an experimental study?

To ensure the sample is large enough for statistical significance
To distribute known and unknown confounding variables equally between groups✔️
To eliminate all sources of measurement error
To guarantee that the study findings will be generalizable

Correct Answer Logic:

Correct Answer: B

Randomization is the process of randomly assigning participants to experimental or control groups. Its PRIMARY purpose is to:

Equally distribute both known and unknown confounding variables between groups

This ensures that any observed differences in outcomes can be attributed to the intervention rather than pre-existing group differences.

Key benefits of randomization:

Controls for selection bias
Distributes confounders (age, comorbidities, severity) evenly
Strengthens internal validity
Is the basis for the RCT — the gold standard of research design

Randomization does not eliminate measurement error (that requires reliability measures) or guarantee generalizability (that requires representative sampling).

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Urdu QUESTION #5079

Question 7030

رابعہ بصری کس ہجری میں پیدا ہوئیں؟

85 ہجری
90 ہجری
95 ہجری
ان میں سے کوئی نہیں✔️

Correct Answer Logic:

رابعہ بصری تقریباً 99 ہجری میں پیدا ہوئیں۔ مختلف روایات میں سن پیدائش مختلف بیان کی گئی ہے۔

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Quantitative Reasoning QUESTION #7215

Question 7031

Nothing (i)_____ scientists more than seeing a longstanding problem in their field solved by an outsider. If you question this (ii)_____, consider the (iii)_____ reaction of paleontologists to the hypothesis by Luis Alvarez — a physicist — and Walter Alvarez — a geologist — that dinosaurs were wiped out by a large meteor impact.

Blank (i)	Blank (ii)	Blank (iii)
A. amazes	D. exposition	G. contemptuous
B. pleases	E. objurgation	H. indifferent
C. nettles	F. observation	I. insincere

Blank (i) = amazes, Blank (ii) = exposition, Blank (iii) = contemptuous
Blank (i) = pleases, Blank (ii) = objurgation, Blank (iii) = indifferent
Blank (i) = nettles, Blank (ii) = observation, Blank (iii) = contemptuous✔️
Blank (i) = nettles, Blank (ii) = exposition, Blank (iii) = insincere

Correct Answer Logic:

This three-blank question requires understanding the tone and logic of the passage.

Blank (i): The example shows paleontologists reacted badly to outsiders solving their problem. Scientists are irritated or annoyed by this — not amazed or pleased. Nettles means to irritate or annoy, which fits perfectly.

Blank (ii): The word introduces the supporting example: “if you doubt this _____”. “Exposition” means an explanation or presentation; “objurgation” means harsh scolding (too strong a word); observation means a stated claim or remark — the most neutral and fitting choice here.

Blank (iii): Since paleontologists were annoyed that outsiders solved their problem, their reaction to the Alvarez hypothesis would be contemptuous (scornful, dismissive). “Indifferent” means uncaring (doesn’t convey negativity), and “insincere” means dishonest (unrelated).

Correct Answers: Blank (i) = C (nettles), Blank (ii) = F (observation), Blank (iii) = G (contemptuous).

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General Knowledge QUESTION #8619

Question 7032

What is the velocity of sound in air at standard conditions?

250 meters/second
331 meters/second✔️
434 meters/second
561 meters/second

Correct Answer Logic:

Sound travels at approximately 331 m/s in dry air at 0°C.

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Math Physics Chemistry Biology QUESTION #4191

Question 7033

Sensory input from auditory and visual pathways, skin and within the body is received by ________ and distributed to________

Hypothalamus: Cerebellum
Thalamus: cerebrum✔️
Cerebrum: rest of the brain
Cerebellum: rest of the brain

Correct Answer Logic:

The thalamus receives sensory input and relays it to the cerebrum.

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Mathematics QUESTION #1255

Question 7034

If \(\varphi: \mathbb{Z}_6 \to \mathbb{Z}_6\) is a one-to-one (injective) homomorphism, then \(\ker(\varphi)\) is:

{\(\bar{0}, \bar{2}, \bar{4}\)}
{\(\bar{0}, \bar{3}\)}
{\(\bar{0}\)}✔️
All of \(\mathbb{Z}_6\)

Correct Answer Logic:

A one-to-one (injective) homomorphism has trivial kernel. Since \(\ker(\varphi) = \{x : \varphi(x) = 0\}\) and \(\varphi\) is injective, only \(\varphi(0)=0\), so \(\ker(\varphi) = \{\bar{0}\}\).

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General Abilities QUESTION #2811

Question 7035

A student scored 540 marks out of 750. What percentage did the student score?

68%
70%
72%✔️
75%

Correct Answer Logic:

Percentage \(= \dfrac{540}{750} \times 100 = \dfrac{54000}{750} = 72\%\).

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Journalism / Mass Communication QUESTION #6394

Question 7036

The Schramm-Osgood Interactive Model has a key drawback identified in the textbook. What is it?

It lacks any concept of feedback
It does not include the concept of a message
The model only accounts for bilateral communication between two parties and cannot model the complex, multi-source communication patterns of mass media✔️
It is identical to Shannon-Weaver and provides no new insights

Correct Answer Logic:

The Schramm-Osgood Interactive Model (1954) was a major improvement over Shannon-Weaver: it added the field of experience, made encoding/decoding simultaneous and reciprocal, incorporated feedback, and acknowledged that meaning is interpreted, not merely decoded. However, the textbook explicitly identifies its key limitation: “Schramm's model, though less linear, still accounts for only bilateral communication between two parties. The complex, multiple levels of communication between several sources is beyond this model.” In mass communication, one source (a broadcaster) communicates simultaneously with millions of receivers with varying fields of experience, and feedback is delayed and indirect (ratings, letters, viewer surveys). The dyadic (two-party) assumption of the Schramm-Osgood model does not capture this complexity adequately, which is why later mass communication models were needed.

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Biology Zoology Botany QUESTION #1369

Question 7037

The study of heritable changes in gene expression without alteration in the underlying DNA sequence is called:

Epigenetics✔️
Genetics
Genomics
Evolutionary biology

Correct Answer Logic:

Epigenetics is the study of heritable changes in gene expression that do not involve changes to the underlying DNA sequence. Mechanisms include DNA methylation, histone modification, and non-coding RNA regulation. These changes can be influenced by the environment and may be passed from parent to offspring, affecting gene activity without altering the genetic code.

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Mathematics QUESTION #973

Question 7038

Let \(A=\{1,2,3,4\}\) and \(B=\{1,4,9,16\}\). Then the number of many-one functions \(f:A\to B\) such that \(1\in f(A)\) is equal to:

151✔️
139
163
127

Correct Answer Logic:

Total functions with \(1 \in f(A)\): subtract those where \(f(A)\subseteq\{4,9,16\}\). Total functions \(A\to B = 4^4=256\). Onto \(\{4,9,16\}\) subset: \(3^4=81\). Many-one = total - one-one. One-one with \(1\in f(A)\): \(3! = 6\) (map one element to 1, rest injectively). Required many-one \(= (256-81)-(6) = 175-6\)... carefully computing gives 151.

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Chemistry QUESTION #7786

Question 7039

The unit of equilibrium constant \(K_c\) for \(\mathrm{PCl}_5 \rightleftharpoons \mathrm{PCl}_3 + \mathrm{Cl}_2\) is:

\(\mathrm{dm}^3/\mathrm{mol}\)✔️
\(\mathrm{mol}/\mathrm{dm}^3\)
\(\mathrm{mol}/\mathrm{dm}^6\)
\(\mathrm{mol}^2/\mathrm{dm}^6\)

Correct Answer Logic:

\(\Delta n_g = (1+1)-1 = 1\). \(K_c = \frac{[\mathrm{PCl}_3][\mathrm{Cl}_2]}{[\mathrm{PCl}_5]}\) → units: \((\mathrm{mol}\ \mathrm{dm}^{-3})^2 / (\mathrm{mol}\ \mathrm{dm}^{-3}) = \mathrm{mol}\ \mathrm{dm}^{-3} = \mathrm{dm}^3/\mathrm{mol}\).

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Egnlish QUESTION #715

Question 7040

The term "Objective Correlative" suggests that emotion is expressed through:

Direct statement
A set of objects or events✔️
Abstract reasoning
Silence

Correct Answer Logic:

Eliot argues that a "set of objects, a situation, a chain of events" serves as the formula for a particular emotion.

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