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Mathematics QUESTION #4121

Question 1

By Mean Value Theorem on $f(x) = e^x$, for $x > 0$, there exists $c \in (0, x)$ such that:

$e^x - 1 = e^c \cdot x$✔️
$e^x - 1 = x$
$e^x = 1 + cx$
$\frac{e^x - 1}{x} = c$

Correct Answer Logic:

MVT: $\frac{f(x) - f(0)}{x - 0} = f'(c) = e^c$. So $\frac{e^x - 1}{x} = e^c$, giving $e^x - 1 = xe^c$.

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Islamic Studies QUESTION #8195

Question 2

"And thou do see the people enter ALLAH's religion in crowds". This is the translation of a Quranic verse. It is included in Surah:

Qadr
Kafrun
Fatiha
Nasr✔️

Correct Answer Logic:

This verse is from Surah An-Nasr (110:2), which was one of the last Surahs revealed. It consists of 3 verses announcing the completion of the Prophet's mission: when Allah's help comes and victory (conquest of Makkah), and people enter Islam in multitudes, the Prophet should glorify Allah's praise and seek His forgiveness. According to Hazrat Ayesha (RA), after this Surah's revelation, the Prophet (PBUH) frequently recited 'SubhanAllahi wa bihamdihi, Astaghfirullaha wa atubu ilayh.'

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Nursing QUESTION #9188

Question 3

A Head Nurse is reviewing a study that reports: p = 0.03 with a significance level set at $\alpha = 0.05$. Which conclusion is correct?

Fail to reject the null hypothesis; the result is not significant
Reject the null hypothesis; the result is statistically significant✔️
Accept the null hypothesis unconditionally
The result is clinically significant but not statistically significant

Correct Answer Logic:

Correct Answer: B

Decision rule for hypothesis testing:

If $p \leq \alpha$: Reject the null hypothesis $(H_0)$
If $p > \alpha$: Fail to reject the null hypothesis

Here, $p = 0.03 \leq \alpha = 0.05$, so we reject $H_0$.

Important note: Statistical significance does not automatically mean clinical significance. A nurse must also evaluate effect size and practical relevance. Saying 'accept the null hypothesis' is incorrect terminology in research — we only ever reject or fail to reject it.

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Mathematics QUESTION #6986

Question 4

Five observations have mean $= 4$ and variance $= 5.2$. Three of the observations are $3, 4, 4$. Find the absolute difference between the remaining two observations.

7✔️
5
1
3

Correct Answer Logic:

Step 1 — Find the sum: $\sum x_i = 5\times4=20$. Known three: $3+4+4=11$. So $x_4+x_5=9$.

Step 2 — Find sum of squares: Variance $=\frac{\sum x_i^2}{n}-\bar{x}^2 \Rightarrow \frac{\sum x_i^2}{5}-16=5.2 \Rightarrow \sum x_i^2=106$.

Known: $3^2+4^2+4^2=9+16+16=41$. So $x_4^2+x_5^2=65$.

Step 3 — Solve: $x_4+x_5=9$ and $x_4^2+x_5^2=65$.

$(x_4+x_5)^2=81 \Rightarrow 2x_4x_5=81-65=16 \Rightarrow x_4x_5=8$.

$(x_4-x_5)^2=(x_4+x_5)^2-4x_4x_5=81-32=49$

$|x_4-x_5|=\mathbf{7}$

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Education QUESTION #6893

Question 5

Which of the following classroom configurations would BEST support a lesson designed around Socratic discussion and collaborative meaning-making?

Individual desks arranged in rows facing the board
A U-shaped or circular seating arrangement✔️
A laboratory-style arrangement with side-by-side benches
A cluster arrangement of groups of four desks

Correct Answer Logic:

For whole-group discussion requiring all students to see and respond to each other — as in Socratic seminars — a circular or U-shaped arrangement is most effective. It breaks the traditional teacher-centered hierarchy, enables eye contact between all participants, and signals a collaborative rather than receptive mode of interaction.

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Journalism / Mass Communication QUESTION #6376

Question 6

The IFJ (International Federation of Journalists) Declaration of Principles on the Conduct of Journalists, adopted at Bordeaux in 1954, lists several grave professional offences. Which of the following is NOT listed as a grave professional offence under this declaration?

Plagiarism and malicious misrepresentation
Calumny, slander, libel, and unfounded accusations
Accepting a bribe in consideration of either publication or suppression of information
Expressing personal political opinions in editorial content✔️

Correct Answer Logic:

The IFJ Declaration of Principles (adopted 1954, amended 1986 in Helsingör) specifically defines the following as grave professional offences for journalists:

Plagiarism
Malicious misrepresentation
Calumny, slander, libel, and unfounded accusations
Acceptance of a bribe in any form in consideration of either publication or suppression of information

Expressing personal political opinions in editorial content is not listed as a grave professional offence in this declaration. The declaration also requires journalists to: respect truth, defend freedom of information, report only facts of known origin, use only fair methods to obtain news, rectify inaccurate information, observe professional secrecy regarding sources, and be aware of discrimination. The code emphasises that journalists should recognise “in professional matters the jurisdiction of colleagues only, to the exclusion of every kind of interference by governments or others.”

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Math Physics Chemistry Biology QUESTION #11393

Question 7

Joints in the past a:

Vagina
Ovotid
Urethra
Cervix✔️

Correct Answer Logic:

The cervix is the lower, narrow portion of the uterus that connects the uterus to the vagina. It plays a role in directing sperm into the uterus and dilates during childbirth. (Note: this question as printed appears to have a transcription issue in the original paper; cervix is the standard anatomical answer for this structure.)

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Mathematics QUESTION #4160

Question 8

For the heat equation $u_t = k u_{xx}$ on a rod of length $L$ with insulated ends ($u_x(0,t) = u_x(L,t) = 0$), what are the eigenfunctions?

$\sin(\frac{n\pi x}{L})$
$\cos(\frac{n\pi x}{L})$✔️
$e^{\frac{n\pi x}{L}}$
$\sin(\frac{(2n+1)\pi x}{2L})$

Correct Answer Logic:

Insulated ends (Neumann BCs) $u_x = 0$ at $x = 0, L$ give eigenfunctions $\cos(\frac{n\pi x}{L})$ for $n = 0, 1, 2, ...$

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Biology QUESTION #11103

Question 9

Which gland secretes the hormone glucagon?

Thyroid gland
Pituitary gland
Liver
Pancreas✔️

Correct Answer Logic:

Glucagon is secreted by the alpha (α) cells of the islets of Langerhans in the pancreas. It is released when blood glucose falls below normal (hypoglycaemia) and acts primarily on the liver to: (1) stimulate glycogenolysis (glycogen → glucose), (2) stimulate gluconeogenesis (amino acids/lactate → glucose), and (3) inhibit glycolysis. Glucagon is the primary counter-regulatory hormone to insulin, maintaining glucose homeostasis.

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The Constitution of Pakistan QUESTION #9342

Question 10

Under Article 48(1) as amended, the President is required to return advice for reconsideration within what period, and must act on the reconsidered advice within what period?

Seven days; five days
Fifteen days; ten days✔️
Ten days; fifteen days
Thirty days; ten days

Correct Answer Logic:

Article 48(1) proviso, as amended by the 18th Amendment, sets a 15-day window within which the President may require reconsideration, and then a 10-day window within which the President must act on the advice rendered after reconsideration. The sequence and asymmetry of these periods is frequently tested.

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Pakistan Affairs QUESTION #126

Question 11

What is the total length of Pakistan's coastline?

758 km
1058 km✔️
1258 km
990 km

Correct Answer Logic:

The coastline of Pakistan is approximately 1058 km (sometimes cited as 1046 km) along the Arabian Sea.

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General Knowledge QUESTION #8656

Question 12

What is a 'casting vote'?

Deciding vote
Vote cast in case of a tie✔️
Both a and b
None of above

Correct Answer Logic:

A casting vote is used to break a tie.

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Paper-I (Anatomy/Physiology and Biochemistry/Microbiology) QUESTION #3406

Question 13

'Glycolysis' occurs in which part of the cell?

Mitochondria
Nucleus
Cytoplasm✔️
Ribosome

Correct Answer Logic:

Glycolysis breaks down glucose into pyruvate in the cytosol.

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Chemistry QUESTION #1073

Question 14

Which of the following aqueous solutions will exhibit the highest boiling point?

$0.01\text{M}\ \text{Na}_2\text{SO}_4$✔️
$0.015\text{M}\ \text{C}_6\text{H}_{12}\text{O}_6$
$0.01\text{M}\ \text{Urea}$
$0.01\text{M}\ \text{KNO}_3$

Correct Answer Logic:

Boiling point elevation $\propto i \times m$ (van't Hoff factor $\times$ molality). Na$_2$SO$_4$: $i=3$, effective molality $=0.03$. Glucose: $i=1$, $=0.015$. Urea: $i=1$, $=0.01$. KNO$_3$: $i=2$, $=0.02$. Highest: $0.01\text{M}\ \text{Na}_2\text{SO}_4$ with effective particles $=0.03$.

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Chemistry QUESTION #7183

Question 15

How much water (in litres) must be added to $1 \text{ L}$ of an aqueous $HCl$ solution with a $pH$ of $1$ to result in a final solution with a $pH$ of $2$?

$0.1 \text{ L}$
$0.9 \text{ L}$
$2.0 \text{ L}$
$9.0 \text{ L}$✔️

Correct Answer Logic:

Using the definition of $pH = -\log[H^{+}]$:

Initial $[H^{+}] = 10^{-1} = 0.1 \text{ M}$.
Final $[H^{+}] = 10^{-2} = 0.01 \text{ M}$.
Using dilution formula $M_{1}V_{1} = M_{2}V_{2}$:
$0.1 \times 1 = 0.01 \times V_{2} \implies V_{2} = 10 \text{ L}$.
Volume to be added = $V_{2} - V_{1} = 10 - 1 = 9 \text{ L}$.

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Geology QUESTION #10685

Question 16

Which of the following are recognised agents of metamorphism responsible for transforming pre-existing rocks?

Fluid (chemically active pore fluids)
Heat and elevated temperature
Pressure (confining and directed stress)
All of these✔️

Correct Answer Logic:

Three principal agents of metamorphism are:

Heat (temperature): drives recrystallisation and mineral reactions; increases with burial depth and proximity to magma
Pressure: confining pressure (lithostatic) increases with depth; directed pressure (stress) causes foliation and lineation
Chemically active fluids: water, CO₂, and dissolved ions catalyse mineral reactions, enable mass transfer, and are essential for many metamorphic reactions

All three act together during regional and contact metamorphism.

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Mathematics QUESTION #4133

Question 17

What is the area enclosed by the polar curve $r = 2\cos(\theta)$?

$\pi$✔️
$2\pi$
$4\pi$
$\frac{\pi}{2}$

Correct Answer Logic:

Circle with radius $1$ has area $\pi(1)^2 = \pi$. Or by integration: $A = \frac{1}{2} \int_{-\pi/2}^{\pi/2} (2\cos(\theta))^2 d\theta = 2\int_{-\pi/2}^{\pi/2} \cos^2(\theta) d\theta = \pi$.

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Boilers Mechanical Engineering QUESTION #4057

Question 18

'Thermal Lagging' (Insulation) is applied to steam pipes to:

Make them look thick
Reduce heat loss to the atmosphere✔️
Prevent the pipes from rusting
Increase the noise

Correct Answer Logic:

Insulation keeps the steam hot and prevents it from turning into water during transport.

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Ability / HR / Governance / Special Education QUESTION #1923

Question 19

Under Rule 15(1) a case submitted to the Prime Minister for his orders shall include what type of document?

A printed booklet with full background details
A self-contained concise and objective summary prepared on the same lines as for Cabinet summaries except that only one copy is required which may not be printed✔️
A certified copy of all inter-Division correspondence
A detailed note by the Secretary only without the Minister's recommendations

Correct Answer Logic:

Rule 15(2) precisely prescribes a self-contained concise and objective summary on the same lines as a Cabinet summary except that only one copy is required and it need not be printed — and it must include the Minister-in-Charge's specific recommendations.

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Paper-I (Anatomy/Physiology and Biochemistry/Microbiology) QUESTION #3174

Question 20

The 'Sodium-Potassium Pump' ($Na^+/K^+$ ATPase) is a classic example of:

Facilitated Diffusion
Primary Active Transport✔️
Osmosis
Secondary Active Transport

Correct Answer Logic:

The pump uses ATP directly to move $3~Na^+$ out and $2~K^+$ into the cell against their gradients.

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