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Mathematics QUESTION #6028

Let $S=\left\{t\in\mathbb{R}: f(x)=|x-\pi|\cdot(e^{|x|}-1)\sin|x|\right.$ is not differentiable at $t\}$. Find $S$.

$\{\pi\}$
$\{0,\pi\}$
$\emptyset$ (empty set)✔️
$\{0\}$

Correct Answer Logic:

Check $x=0$: $f(x)=|x-\pi|(e^{|x|}-1)\sin|x|$. Near $x=0$, both $(e^{|x|}-1)$ and $\sin|x|$ have factors of $|x|$, so $f(x)\approx |x-\pi|\cdot|x|^2$ near 0, which is differentiable at 0.

Check $x=\pi$: near $\pi$, $(e^{|x|}-1)\sin|x|$ is smooth and non-zero ($e^\pi\sin\pi=0$!). Since $\sin\pi=0$, the product $(e^{|x|}-1)\sin|x|$ vanishes at $\pi$, making $f(x)=0$ near $\pi$ — wait, $\sin\pi=0$, so $f(\pi)=0$. Checking differentiability more carefully shows $f$ is differentiable at $\pi$ too.

Therefore $S=\boldsymbol{\emptyset}$.

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English QUESTION #2761

Question 2

Which sentence uses the SEMICOLON correctly?

She was tired; but she kept working.
She was tired; she kept working.✔️
She was tired; and she kept working.
She was tired; to keep working.

Correct Answer Logic:

A semicolon is used to join two independent (complete) clauses without a conjunction. 'She was tired; she kept working' correctly joins two complete sentences. A semicolon should not be used before conjunctions like 'but' or 'and'.

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Reading and Writing (Module-1) QUESTION #10379

Question 3

Despite the coach's repeated warnings, the team's performance remained -------, oscillating wildly between brilliant victories and dismal defeats.

consistent
erratic✔️
commendable
predictable

Correct Answer Logic:

The contrast set up by 'despite the coach's warnings' and 'oscillating wildly' signals inconsistency, matching 'erratic.'

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Civil / Architecture QUESTION #2369

Question 4

In the Slope-Deflection Method for analysis of indeterminate beams and frames, the slope-deflection equation for the near-end moment $M_{AB}$ of member $AB$ with near-end rotation $\theta_A$, far-end rotation $\theta_B$, chord rotation $\psi = \Delta/L$, and Fixed-End Moment $FEM_{AB}$ is:

$M_{AB} = \dfrac{2EI}{L}(2\theta_A + \theta_B - 3\psi) + FEM_{AB}$✔️
$M_{AB} = \dfrac{EI}{L}(4\theta_A + 2\theta_B - 6\psi) + FEM_{AB}$
$M_{AB} = \dfrac{2EI}{L}(\theta_A + 2\theta_B - 3\psi) + FEM_{AB}$
$M_{AB} = \dfrac{4EI}{L}(\theta_A - \theta_B) + FEM_{AB}$

Correct Answer Logic:

The slope-deflection equation is $M_{AB} = \dfrac{2EI}{L}(2\theta_A + \theta_B - 3\psi) + FEM_{AB}$, where $\theta_A$ is near-end rotation, $\theta_B$ is far-end rotation, and $\psi = \Delta/L$ is the chord rotation due to relative settlement or sway. The near-end joint rotation carries a coefficient twice that of the far-end (reflecting the carry-over factor of 1/2). The chord rotation term $-3\psi$ accounts for sidesway. This equation is the foundation of the Slope-Deflection Method for all prismatic members.

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Accounting & Finance QUESTION #9648

Question 5

Under the Stock and Debtors system of Branch Accounting, the Branch Stock Account is maintained at:

Cost price throughout
Selling price for sales and returns; pro-forma invoice price for all other entries✔️
Pro-forma invoice price for all entries
Cost price for opening and closing stock; selling price for goods sent

Correct Answer Logic:

Under the Stock and Debtors system, branch stock account records sales to customers and sales returns at selling price, while all other entries (opening/closing stock, goods sent, goods returned to HO) are recorded at pro-forma invoice price.

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Reading and Writing (Module-1) QUESTION #10413

Question 6

The judge's ruling was notably ------- , showing no favoritism toward either the plaintiff or the defendant.

biased
evenhanded✔️
partisan
prejudiced

Correct Answer Logic:

Showing 'no favoritism toward either side' describes a ruling that is 'evenhanded.'

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Accounting & Finance QUESTION #6103

Question 7

Which statements about capital income and revenue income are correct?

Revenue income includes amounts received from renting out part of business premises.
Capital income includes amounts received from the sale of non-current assets.
Capital income includes loans taken by a business.

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

Correct Answer Logic:

Option B (1 and 2 only) is correct.

Statement 1 (True): Rental income is regular and recurring — revenue income.
Statement 2 (True): Proceeds from selling a non-current asset are a one-off receipt — capital income.
Statement 3 (False): Loans are liabilities, not capital income.

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Accounting & Finance QUESTION #6219

Question 8

In an 'Operational Audit', the auditor focuses on 'Efficiency' and 'Effectiveness'. These criteria are often considered:

Clearly defined by International Financial Reporting Standards (IFRS)
Subjective and difficult to evaluate objectively✔️
Strictly limited to accounting and financial records
Mandated by the Companies Ordinance 1984 for all firms

Correct Answer Logic:

Efficiency and effectiveness are more difficult to evaluate objectively than compliance or financial presentation, making operational auditing more like management consulting.

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Mathematics QUESTION #6967

Question 9

Evaluate $\sin^{-1}\!\left(\dfrac{12}{13}\right)-\sin^{-1}\!\left(\dfrac{3}{5}\right)$.

$\pi-\sin^{-1}\!\left(\dfrac{63}{65}\right)$
$\dfrac{\pi}{2}-\sin^{-1}\!\left(\dfrac{56}{65}\right)$✔️
$\dfrac{\pi}{2}-\cos^{-1}\!\left(\dfrac{9}{65}\right)$
$\pi-\cos^{-1}\!\left(\dfrac{33}{65}\right)$

Correct Answer Logic:

Let $A=\sin^{-1}(12/13)$: $\sin A=12/13,\ \cos A=5/13$.

Let $B=\sin^{-1}(3/5)$: $\sin B=3/5,\ \cos B=4/5$.

$\sin(A-B)=\sin A\cos B-\cos A\sin B=\dfrac{12}{13}\cdot\dfrac{4}{5}-\dfrac{5}{13}\cdot\dfrac{3}{5}=\dfrac{48}{65}-\dfrac{15}{65}=\dfrac{33}{65}$... Hmm, but let me check $\cos(A-B)$: $=\cos A\cos B+\sin A\sin B=\dfrac{5}{13}\cdot\dfrac{4}{5}+\dfrac{12}{13}\cdot\dfrac{3}{5}=\dfrac{20+36}{65}=\dfrac{56}{65}$.

So $A-B=\cos^{-1}(56/65)=\pi/2-\sin^{-1}(56/65)$. Answer: $\dfrac{\pi}{2}-\sin^{-1}\!\left(\dfrac{56}{65}\right)$.

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Paper-I (Anatomy/Physiology and Biochemistry/Microbiology) QUESTION #3250

Question 10

'Bilirubin' is a waste product derived from the breakdown of:

Muscle protein
Hemoglobin✔️
Fatty acids
DNA

Correct Answer Logic:

When RBCs are destroyed, the heme part is converted to bilirubin.

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MCQs Section QUESTION #4840

Question 11

Pick the word nearly similar in meaning to "SEQUESTER"

Eliminate
Finalize
Sedate
Isolate✔️

Correct Answer Logic:

To sequester means to isolate or set apart from others, or to take legal possession of assets. Isolate is its closest synonym.

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Chemistry QUESTION #7387

Question 12

Among the isoelectronic species $\text{O}^{2-}$, $\text{F}^-$, $\text{Na}^+$, $\text{Mg}^{2+}$ and $\text{Al}^{3+}$, their ionic radii show which trend?

An increase from $\text{O}^{2-}$ to $\text{F}^-$ then decrease from $\text{Na}^+$ to $\text{Al}^{3+}$
A decrease from $\text{O}^{2-}$ to $\text{F}^-$ then increase from $\text{Na}^+$ to $\text{Al}^{3+}$
A significant overall increase from $\text{O}^{2-}$ to $\text{Al}^{3+}$
A significant overall decrease from $\text{O}^{2-}$ to $\text{Al}^{3+}$✔️

Correct Answer Logic:

Isoelectronic species all have 10 electrons. Their size depends on nuclear charge:

$\text{O}^{2-}(Z=8) > \text{F}^-(Z=9) > \text{Na}^+(Z=11) > \text{Mg}^{2+}(Z=12) > \text{Al}^{3+}(Z=13)$

More protons = stronger pull on same electron cloud = smaller radius. There is a steady significant decrease across the series. No increase occurs — all species have the same number of electrons but increasing nuclear charge.

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Security Measures to Maintain Law and Order QUESTION #910

Question 13

The "Permit System" for airport employees is a measure to maintain:

Financial records
Internal Law & Order✔️
Speed of work
Staff attendance

Correct Answer Logic:

By controlling who goes where (Access Control), the permit system prevents unauthorized internal interference.

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Planning QUESTION #4935

Question 14

What is the concept of 'Carrying Capacity' in regional planning?

Maximum building height allowed
Maximum population a region can sustainably support✔️
Maximum traffic volume on roads
Maximum land area for development

Correct Answer Logic:

Carrying Capacity refers to the maximum population size or development intensity that a region's natural resources, infrastructure, and environment can sustainably support without degradation.

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Accounting & Finance QUESTION #6116

Question 15

A company has: Ordinary shares $1.00 each: $200,000; Share premium: $80,000; Revenue reserves: $160,000. Changes in order: (1) One-for-one bonus issue; (2) Rights issue of 100,000 shares at $1.40 each. Company wishes to maximise dividends. What are the resulting balances?

Ordinary share capital $500,000 | Share premium $40,000 | Revenue reserves $40,000✔️
Ordinary share capital $500,000 | Share premium $80,000 | Revenue reserves nil
Ordinary share capital $540,000 | Share premium nil | Revenue reserves $40,000
Ordinary share capital $540,000 | Share premium $40,000 | Revenue reserves $40,000

Correct Answer Logic:

Option A is correct.

Bonus issue (200,000 new shares @ $1): Use share premium $80,000 first, then revenue reserves $120,000.

After: Shares $400,000 | Share premium $0 | Revenue reserves $40,000

Rights issue (100,000 @ $1.40): $100,000 to share capital, $40,000 to share premium.

Final: Shares $500,000 | Share premium $40,000 | Revenue reserves $40,000

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Boilers Mechanical Engineering QUESTION #2427

Question 16

The efficiency $\eta_f$ of a fin is defined as:

Actual fin heat transfer rate divided by the heat transfer if the entire fin were at the base temperature✔️
Fin area divided by base area
$h \cdot A_{fin} / (k \cdot A_c)$
$1 - e^{-mL}$ always

Correct Answer Logic:

Fin efficiency: $\eta_f=q_{fin}/q_{max}$ where $q_{max}=hA_{fin}(T_b-T_\infty)$. For a straight fin with insulated tip: $\eta_f=\tanh(mL)/(mL)$.

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Pakistan Affairs QUESTION #144

Question 17

What is the range of the latest Shaheen-III missile?

3750 km
2750 km✔️
1750 km
2500 km

Correct Answer Logic:

Shaheen-III is a surface-to-surface medium-range ballistic missile with a maximum range of approximately 2,750 km.

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Education QUESTION #6911

Question 18

A student who is aggressive frequently misinterprets neutral social cues as hostile — for example, reading an accidental shoulder bump as an intentional act of aggression. This pattern reflects which documented characteristic of aggressive students?

A performance deficit in social skills due to lack of practice
Deficits in social information processing, leading to systematic misattribution of hostile intent✔️
A conduct disorder that can only be addressed through psychiatric intervention
Deliberate manipulation of social situations for personal gain

Correct Answer Logic:

Research on aggression in school contexts consistently identifies social information processing deficits as a core characteristic of chronically aggressive students. These students are more likely to misread neutral or ambiguous social cues as threatening, especially under stress, which triggers aggressive responses that peers and teachers experience as disproportionate or unprovoked.

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Planning QUESTION #4937

Question 19

What is the main objective of Traffic Calming measures?

To increase vehicle speed
To reduce vehicle speeds and improve safety✔️
To eliminate pedestrian crossings
To maximize road capacity

Correct Answer Logic:

Traffic Calming uses physical design features (speed bumps, chicanes, raised crosswalks) to reduce vehicle speeds, enhance pedestrian safety, and improve quality of life in residential areas.

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Physics QUESTION #365

Question 20

When a helium atom loses an electron

it becomes:✔️
An alpha particle
Proton
A positive helium ion

Correct Answer Logic:

2

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