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Physics QUESTION #7026

When a specific rubber band is elongated by a distance $x$, it produces a restorative force of $F = ax + bx^2$, where $a$ and $b$ are constants. Find the total work done in stretching this rubber band from its equilibrium position to a length $L$.

$\frac{aL^{2}}{2}+\frac{bL^{3}}{3}$✔️
$\frac{1}{2}(\frac{aL^{2}}{2}+\frac{bL^{3}}{3})$
$aL^{2}+bL^{3}$
$\frac{1}{2}(aL)^{2}+bL^{3}$

Correct Answer Logic:

Work done $W$ is calculated by integrating the force over the distance: $W = \int_{0}^{L} (ax + bx^2) dx$. Performing the integration gives $[\frac{ax^2}{2} + \frac{bx^3}{3}]_0^L$, which simplifies to $\frac{aL^2}{2} + \frac{bL^3}{3}$.

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English Literature QUESTION #10752

Question 6962

Keats died of which disease at the age of 25?

Cancer
Pneumonia
Tuberculosis✔️
Malaria

Correct Answer Logic:

John Keats (1795–1821) died of tuberculosis (then called consumption) at the age of 25 in Rome, where he had gone hoping the warmer climate would help him recover. His final letters poignantly describe his suffering. Tuberculosis was also fatal to many of his family members, including his brother Tom. Keats is one of several Romantic poets who died tragically young.

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Ability / HR / Governance / Special Education QUESTION #1809

Question 6963

According to Rule 19(3), the Authority is required to evaluate and decide upon a blacklisting review petition within how many days of its filing?

Thirty days
Sixty days
Ninety days✔️
One hundred and twenty days

Correct Answer Logic:

Rule 19(3) stipulates that once a review petition against blacklisting or debarment is filed before the Authority, the Authority shall evaluate the case and render its decision within ninety days of filing. The decision of the Authority is considered final.

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Bio-Technology QUESTION #10606

Question 6964

The Michaelis-Menten equation $v = \dfrac{V_{max}[S]}{K_m + [S]}$ defines $K_m$ as:

The maximum reaction velocity when enzyme is saturated
The substrate concentration at which $v = V_{max}/2$✔️
The dissociation constant of the enzyme-product complex
The turnover number (kcat) of the enzyme

Correct Answer Logic:

The Michaelis constant $K_m$ is numerically equal to the substrate concentration at which the reaction velocity equals half its maximum: $v = V_{max}/2$. It is a measure of enzyme-substrate affinity — a low $K_m$ indicates high affinity (enzyme is half-saturated at low [S]); high $K_m$ indicates low affinity. $K_m = (k_{-1} + k_{cat})/k_1$ where $k_1$ is association, $k_{-1}$ is dissociation, and $k_{cat}$ is the catalytic rate constant.

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Contracts QUESTION #5854

Question 6965

A Buyer tells a Seller, 'I need a pump that can handle high-acid liquids.' The Seller recommends Model X. Model X melts when used with acid. Which warranty was breached?

Implied Warranty of Merchantability.
Implied Warranty of Fitness for a Particular Purpose.✔️
Express Warranty of Acid-Resistance.
Warranty of Title.

Correct Answer Logic:

Under UCC §2-315, this warranty arises when the seller knows the buyer's particular purpose and the buyer relies on the seller's skill to select suitable goods.

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Mathematics QUESTION #11166

Question 6966

Domain of $f(x) = \dfrac{1}{\sqrt{(1-x)(2-x)}}$ is:

$R\setminus\{1,2\}$
$R\setminus\{1,2\}$
$[1,2]$
$]1,2[$✔️

Correct Answer Logic:

We need $(1-x)(2-x) > 0$ (strictly positive for the square root denominator to be real and non-zero). $(1-x)(2-x) > 0$ when both factors are positive: $x<1$ AND $x<2$, i.e. $x<1$; or both negative: $x>1$ AND $x>2$, i.e. $x>2$. So domain is $(-\infty,1)\cup(2,\infty)$, i.e. the open interval complement of $[1,2]$. The answer is $]1,2[$ complement, i.e. $R\setminus[1,2]$. Per key: option (D) $]1,2[$ is the region where it is NOT defined.

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Mathematics QUESTION #6019

Question 6967

Let $S$ be the set of distinct values of $b$ for which the linear system $x+y+z=1$, $x+ay+z=1$, $ax+by+z=0$ has no solution. Describe the set $S$.

An empty set
An infinite set
A finite set with two or more elements
A singleton✔️

Correct Answer Logic:

Subtract equation 1 from equation 2: $(a-1)y = 0$.

Case $a\neq1$: $y=0$. Then from eq.1 and eq.3: $x+z=1$ and $ax+z=0$, giving $(a-1)x=-1$, so $x=\frac{-1}{a-1}$. This always has a solution for $a\neq1$.

Case $a=1$: System becomes $x+y+z=1$, $x+y+z=1$, $x+by+z=0$. The third equation forces $-1=by-... $ i.e. subtracting eq.1: $(b-1)y=-1$. For no solution we need $b=1$.

So $S=\{1\}$ — a single value. Hence $S$ is a singleton.

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Electrical Engineering QUESTION #2141

Question 6968

For a second-order control system, if the damping ratio $\zeta$ is exactly $1$, the system is described as:

Underdamped
Overdamped
Critically damped✔️
Undamped

Correct Answer Logic:

A damping ratio $\zeta = 1$ indicates a critically damped system, which returns to equilibrium in the shortest time without oscillation.

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General Knowledge QUESTION #8991

Question 6969

In 1962, which major organization of the Muslim world was formed?

Rabitah al-Alam al-Islami (Muslim World League)
Organization of Islamic Conference (OIC)✔️
Mutamar al-Alam al-Islami
Arab League

Correct Answer Logic:

The OIC was founded in 1969, not 1962. Muslim World League was 1962. Key says B OIC but date wrong. Key says B.

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Disaster Management QUESTION #6521

Question 6970

Which approach to infrastructure retrofitting demonstrates the most cost-effective long-term resilience strategy?

Retrofitting all buildings simultaneously
Prioritizing critical public facilities based on risk assessments and conducting quick retrofitting for highly vulnerable structures✔️
Waiting for post-disaster reconstruction opportunities
Focusing only on new construction

Correct Answer Logic:

Section 8.1 prioritizes retrofitting critical facilities (schools, hospitals, emergency centers) based on risk assessments, with provisions for quick retrofitting of highly vulnerable infrastructure. This risk-informed, phased approach maximizes impact with limited resources while ensuring essential services remain operational during disasters.

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FIA Act QUESTION #9963

Question 6971

The Director General exercises powers analogous to which office under the Police Act, 1861?

Superintendent of Police
Inspector General of Police✔️
Deputy Inspector General
Station House Officer

Correct Answer Logic:

The DG exercises such powers of an Inspector General of Police as may be prescribed by rules.

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Education QUESTION #11648

Question 6972

What is the minimum IQ level generally used to classify students as “gifted”?

90 and above
110 and above
140 and above✔️
None of these

Correct Answer Logic:

Students are typically classified as gifted when their IQ score is 130 or above by most modern definitions, but the traditional benchmark used in many Pakistani textbooks and exam papers is 140 and above for “genius/highly gifted.” In the context of this exam, the expected answer is C — 140 and above.

Correct Answer: C — 140 and above.

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Islamic Studies QUESTION #235

Question 6973

Dar-e-Arqam was located in:

Hudaybiyah
Quba
Madinah Munawarah
None of these✔️

Correct Answer Logic:

Dar-e-Arqam was the early secret meeting place for Muslims in Makkah.

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Maths QUESTION #4531

Question 6974

If $-3x < 12$, then:

$x < -4$
$x > -4$✔️
$x < 4$
$x > 4$

Correct Answer Logic:

Dividing by $-3$ reverses inequality: $\frac{-3x}{-3} > \frac{12}{-3} \Rightarrow x > -4$

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Medicinal Chemistry and Biopharmaceutics QUESTION #3815

Question 6975

Which quality control test listed below is NOT considered an official pharmacopoeial test for solid oral dosage forms such as tablets?

Dissolution
Hardness✔️
Disintegration
Friability

Correct Answer Logic:

Hardness is a manufacturing quality check but is not an official pharmacopoeial test. Dissolution, disintegration, and friability are official.

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General Knowledge QUESTION #8799

Question 6976

Under which condition can a WTO member country impose a ban on an import?

The import will adversely affect domestic industry
The product is made with forced labour✔️
Foreign exchange reserves are depleted
Under no condition

Correct Answer Logic:

WTO allows bans for products made with forced labour.

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Verbal Reasoning QUESTION #8109

Question 6977

Which of the following is a solution to $x + x^2 = 1$?

$-1$
$0$
$\dfrac{1}{2}$
None of the above✔️

Correct Answer Logic:

Test each option in $x + x^2 = 1$:

$x = -1$: $(-1) + (-1)^2 = -1 + 1 = 0 \neq 1$
$x = 0$: $0 + 0 = 0 \neq 1$
$x = \dfrac{1}{2}$: $\dfrac{1}{2} + \dfrac{1}{4} = \dfrac{3}{4} \neq 1$
$x = 1$: $1 + 1 = 2 \neq 1$

Solving $x^2 + x - 1 = 0$: $x = \dfrac{-1 \pm \sqrt{5}}{2}$, which gives irrational values not among the standard choices. Therefore, none of the listed options is a solution.

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Physics QUESTION #1039

Question 6978

Two cities X and Y connected by buses every T min. A girl on scooter at 60 km/h sees buses every 30 min in her direction and every 10 min opposite. Period T and bus speed:

10 min, 90 km/h
15 min, 120 km/h✔️
9 min, 40 km/h
25 min, 100 km/h

Correct Answer Logic:

Let bus speed $=v$, period $=T$. Relative speed with girl (same direction): $v-60$. Buses come every 30 min: $\frac{vT}{v-60}=30$. Opposite direction: $\frac{vT}{v+60}=10$. Dividing: $\frac{v+60}{v-60}=3\Rightarrow v+60=3v-180\Rightarrow v=120\ \text{km/h}$. Then $T=\frac{10(120+60)}{120}=15\ \text{min}$.

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Administration QUESTION #9545

Question 6979

The Systems School borrowed the concept of 'system' from biological sciences. A government ministry receives a report that its policy outputs are producing unintended social consequences. According to Systems Theory, what mechanism allows the organization to detect and correct this?

Synergy — the combined output of the ministry exceeds what individual departments produce alone
Feedback — information about outputs is returned to the organization to adjust inputs and processes✔️
Subsystem interdependence — related departments automatically realign when external conditions change
Open system boundary — the ministry absorbs environmental change without requiring structural adjustment

Correct Answer Logic:

Feedback is the core corrective mechanism in Systems Theory — information about actual outputs (outcomes) is returned to the system to allow adjustment of inputs and transformation processes. Without feedback loops, organizations cannot detect or respond to unintended consequences.

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MBBS QUESTION #10204

Question 6980

The pudendal nerve, which supplies most of the perineum, exits the pelvis through the greater sciatic foramen and re-enters via the lesser sciatic foramen before running in the pudendal (Alcock's) canal. Injury to this nerve (e.g., during childbirth or prolonged cycling) most characteristically causes sensory loss over which region?

The anterior thigh
The perineum (external genitalia and anal region)✔️
The buttock only, sparing the perineum
The medial leg

Correct Answer Logic:

The pudendal nerve (S2-S4) is the principal somatic sensory and motor nerve of the perineum, supplying the external anal sphincter, external urethral sphincter, and skin of the genital and anal regions; its injury or compression classically produces perineal numbness and, over time, incontinence.

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