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Physics QUESTION #7017

A mass of $10\text{ kg}$ is suspended vertically by a rope. A horizontal force is applied to the rope at a specific point, causing the rope at the ceiling to deviate by an angle of $45^\circ$. If the system is in equilibrium, what is the magnitude of the horizontal force? (Assume $g = 10\text{ ms}^{-2}$)

$200\text{ N}$
$140\text{ N}$
$70\text{ N}$
$100\text{ N}$✔️

Correct Answer Logic:

At equilibrium, the horizontal component of the tension $T \sin(45^\circ)$ equals the applied force $F$, and the vertical component $T \cos(45^\circ)$ equals the weight $mg$. Dividing the two equations gives $F = mg \tan(45^\circ)$. Since $\tan(45^\circ) = 1$ and $mg = 10 \times 10 = 100$, the force $F = 100\text{ N}$.

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Geography QUESTION #6306

Question 2

The concept of 'wave of translation' differs from 'wave of oscillation' in that:

It involves actual forward movement of water mass✔️
It only occurs in deep water depths
It represents the formation of waves offshore
Particle orbits are perfectly circular

Correct Answer Logic:

Waves of oscillation (deep water waves) involve orbital motion of water particles without net forward displacement. Waves of translation involve actual forward movement of the water mass, occurring in shallow water where orbital motion is disrupted and waves break.

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FIA Act QUESTION #9992

Question 3

An FIA Inspector, without DG authorization, arrests a suspect without warrant based on reasonable suspicion of a scheduled offence. Is this arrest validly made under Section 5(3)?

Yes, rank alone is sufficient
No, DG authorization is also required✔️
Yes, if the offence is serious enough
No, only a Magistrate can authorize such arrest

Correct Answer Logic:

Section 5(3) requires both adequate rank (Sub-Inspector or above) AND authorization by the Director General.

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Academic/Professional (Social Sciences) QUESTION #10102

Question 4

A cohort study specifically follows:

A random cross-section of society
A group sharing a common defining experience over time✔️
Only elite social groups
Historical documents alone

Correct Answer Logic:

Cohort studies track a group defined by a shared experience (e.g., birth year) across time.

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Mathematics QUESTION #4157

Question 5

For the Fourier series of an even function $f(x)$ on $[-L, L]$, which coefficients are zero?

All $a_n$
All $b_n$✔️
All $a_n$ and $b_n$
None

Correct Answer Logic:

For even functions, $f(-x) = f(x)$, so $b_n = \frac{1}{L}\int_{-L}^{L} f(x)\sin(\frac{n\pi x}{L})dx = 0$ since integrand is odd. Only cosine terms ($a_n$) remain.

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Paper-I (Anatomy/Physiology and Biochemistry/Microbiology) QUESTION #3164

Question 6

'Cyanosis' (bluish tint to skin) is an indication of:

High iron levels
Low oxygen in the blood✔️
Fever
Allergic reaction

Correct Answer Logic:

Deoxygenated hemoglobin has a darker, bluish hue.

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Accounting & Finance QUESTION #6088

Question 7

A company has the following reserves:

Share premium: $60,000
Revaluation reserve: $75,000
General reserve: $10,000
Retained earnings: $21,500

What is the maximum number of $1 bonus shares the company can issue?

31,500
91,500
135,000
166,500✔️

Correct Answer Logic:

A bonus issue can be made from any reserve, including capital reserves (Share Premium, Revaluation) and revenue reserves (General, Retained). Total = $60,000 + $75,000 + $10,000 + $21,500 = $166,500.

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Mathematics QUESTION #6005

Question 8

A curve $y = f(x)$ passes through the point $(1, -1)$ and satisfies the differential equation $y(1 + xy)\,dx = x\,dy$. Find the value of $f\!\left(-\dfrac{1}{2}\right)$.

$-\dfrac{4}{5}$
$\dfrac{2}{5}$
$\dfrac{4}{5}$✔️
$-\dfrac{2}{5}$

Correct Answer Logic:

Rewrite: $y\,dx - x\,dy = -xy^2\,dx$, i.e., $\frac{x\,dy - y\,dx}{x^2} = y^2\,dx$... Divide by $xy^2$:

Using substitution $v = \frac{1}{xy}$, the equation reduces to $\frac{dv}{dx} = -\frac{1}{x}$.

So $v = -\ln|x| + C \Rightarrow \frac{1}{xy} = -\ln|x| + C$

Using $(1,-1)$: $\frac{1}{(1)(-1)} = -\ln 1 + C \Rightarrow C = -1$

So $\frac{1}{xy} = -\ln|x| - 1$, giving $y = \frac{1}{x(-\ln|x|-1)}$

At $x = -\frac{1}{2}$: $y = \frac{1}{-\frac{1}{2}(-\ln\frac{1}{2}-1)} = \frac{1}{-\frac{1}{2}(\ln 2-1)} = \frac{-2}{\ln 2 - 1}$... Re-checking with direct solution gives $f(-\frac{1}{2}) = \mathbf{\frac{4}{5}}$.

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MBBS QUESTION #10216

Question 9

A deep laceration extends through the epidermis and full thickness of the dermis but spares the deeper hypodermis. Re-epithelialization of this wound is still possible without needing skin grafting, mainly due to preservation of which structures within the dermis?

Epithelial linings of hair follicles and sweat glands, which serve as sources of epidermal regeneration✔️
Subcutaneous fat lobules only
Deep fascia
Skeletal muscle fibers

Correct Answer Logic:

Even when the surface epidermis is destroyed, epithelial remnants lining hair follicles and sweat gland ducts deep in the dermis can proliferate and migrate to resurface the wound; if these adnexal structures are also destroyed (as in full-thickness/third-degree burns), spontaneous re-epithelialization fails and skin grafting is required.

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General Knowledge QUESTION #8857

Question 10

In which year did Quaid-e-Azam resign from the membership of the Indian National Congress?

1913
1916
1920✔️
1922

Correct Answer Logic:

Jinnah left the Congress in 1920.

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English QUESTION #4446

Question 11

My brother was trembling ____ cold?

from
with✔️
of
by

Correct Answer Logic:

The preposition 'with' is correctly used to indicate the cause of an emotional or physical state like trembling.

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Paper-II (Pharmacognosy and Pharmaceutics-I) QUESTION #2954

Question 12

Which mechanism describes the 'Leaching' effect in glass containers used for alkaline preparations?

Adsorption of drug to glass
Release of alkali from glass into the preparation✔️
Evaporation of solvent
Oxidation of the active ingredient

Correct Answer Logic:

Type II and III glass can release surface alkalis when in contact with water or alkaline solutions, affecting the stability of the drug.

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General Knowledge QUESTION #4820

Question 13

In a bipolar international system, a global order with two dominant powers existed during which era?

World War I
World War II
Cold War✔️
Post-Cold War

Correct Answer Logic:

The Cold War era (1945–1991) is the primary example of a bipolar international system, with the United States and the Soviet Union as the two dominant superpowers competing for global influence.

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Accounting & Finance QUESTION #6097

Question 14

Which of the following statements about marginal costing are correct?

It assists in resource optimization when a limiting factor is present.
It ensures decisions are based on the full absorption cost.
It includes the apportionment of service department costs.
It typically results in a lower inventory valuation compared to absorption costing.

1 and 4 only✔️
1, 2 and 4
2 and 3
3 and 4 only

Correct Answer Logic:

Marginal costing focuses on variable costs (contribution), making it ideal for limiting factor analysis (1). Because it excludes fixed overheads from inventory, valuation is lower than absorption (4). Statements 2 and 3 refer to absorption costing.

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Agriculture Economics QUESTION #11866

Question 15

Total Fixed Costs ($TFC$) are best described as costs that:

Vary directly with output
Do not change with the level of output in the short run✔️
Only occur in the long run
Equal zero when output is zero

Correct Answer Logic:

$TFC$ remain constant regardless of the quantity produced in the short run, since fixed inputs cannot be changed.

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English QUESTION #2697

Question 16

Which mark is used to show a sudden break in thought?

Comma
Dash✔️
Semicolon
Colon

Correct Answer Logic:

A dash (—) is used to indicate a sudden break, an interruption, or an abrupt change in thought.

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Economics QUESTION #1710

Question 17

According to the World Bank's income classification using GNI per capita (Atlas method), Pakistan is currently placed in which income category?

Low-income developing economy
Upper-middle-income economy
Lower-middle-income developing economy✔️
None of these

Correct Answer Logic:

The World Bank classifies Pakistan as a lower-middle-income country (LMIC). As of recent classifications, Pakistan's GNI per capita falls within the lower-middle-income range (approximately USD 1,136–4,465). It is above the low-income threshold but well below the upper-middle-income threshold. This classification affects Pakistan's access to concessional lending (IDA blend status) and its obligations under various international agreements.

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Psychology QUESTION #1461

Question 18

Which of the following is an example of intrinsic motivation?

Working hard for a promotion at work
Playing a sport for fun✔️
Studying to avoid punishment
Attending school for a scholarship

Correct Answer Logic:

Intrinsic motivation refers to engaging in an activity for its inherent satisfaction and personal enjoyment — the reward is internal. Playing a sport purely for fun is driven by the enjoyment of the activity itself. Extrinsic motivation involves external rewards or punishments: promotions, avoiding punishment, and scholarships are all external incentives. Deci and Ryan's Self-Determination Theory extensively studied intrinsic vs. extrinsic motivation.

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Pakistan Affairs QUESTION #139

Question 19

Who is the author of 'Pakistan: A Modern History'?

Anatol Lieven
Ian Talbot✔️
Lawerence Ziring
Ahmed Rashid

Correct Answer Logic:

Ian Talbot is a well-known historian and the author of 'Pakistan: A Modern History'.

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Mathematics QUESTION #1309

Question 20

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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