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Mathematics QUESTION #4134

For $\vec{r} = x\hat{i} + y\hat{j} + z\hat{k}$ and $r = |\vec{r}|$, what is $\nabla r$?

$\vec{r}$
$\frac{\vec{r}}{r}$✔️
$\frac{\vec{r}}{r^2}$
$\hat{r}$

Correct Answer Logic:

$\nabla r = \frac{\partial r}{\partial x}\hat{i} + \frac{\partial r}{\partial y}\hat{j} + \frac{\partial r}{\partial z}\hat{k} = \frac{x}{r}\hat{i} + \frac{y}{r}\hat{j} + \frac{z}{r}\hat{k} = \frac{\vec{r}}{r}$.

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Boilers Mechanical Engineering QUESTION #2487

Question 2

The acceleration of node B of a driver link with angular velocity $\omega$ and angular acceleration $\alpha=\ddot{\phi}$ has components:

$a_{Bx} = -L_{AB}\omega^2\cos\phi + L_{AB}\alpha\sin\phi$; $a_{By} = -L_{AB}\omega^2\sin\phi - L_{AB}\alpha\cos\phi$
$a_{Bx} = -L_{AB}\omega^2\cos\phi - L_{AB}\alpha\sin\phi$; $a_{By} = -L_{AB}\omega^2\sin\phi + L_{AB}\alpha\cos\phi$✔️
$a_{Bx} = L_{AB}\alpha\cos\phi$; $a_{By} = L_{AB}\alpha\sin\phi$
$a_{Bx} = -L_{AB}\omega^2\cos\phi$; $a_{By} = -L_{AB}\omega^2\sin\phi$

Correct Answer Logic:

Differentiating velocity: $a_{Bx}=-L_{AB}\alpha\sin\phi-L_{AB}\omega^2\cos\phi$ and $a_{By}=L_{AB}\alpha\cos\phi-L_{AB}\omega^2\sin\phi$.

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Tourism & Hospitality Management QUESTION #1587

Question 3

Which of the following correctly describes MICE tourism as categorized under 'Neotourism' in the Pakistan Tourist Destinations course?

Medical, International, Cultural, and Educational tourism
Meetings, Incentives, Conferences, and Exhibitions✔️
Multinational, Integrated, Cultural, and Eco tourism
Mobility, Infrastructure, Commerce, and Entertainment

Correct Answer Logic:

MICE stands for Meetings, Incentives, Conferences, and Exhibitions. The Pakistan Tourist Destinations course lists it under the Neotourism category alongside Ecotourism, Camping Tourism, Medical Tourism, and Pilgrimage Tourism as emerging tourism destinations in Pakistan.

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Physics QUESTION #7293

Question 4

An object is shot from the bottom of a smooth inclined plane at $60°$ with the horizontal and travels distance $x_1$ along the plane. When the inclination is reduced to $30°$ and the object is shot with the same speed, it travels $x_2$. The ratio $x_1 : x_2$ is:

$1:\sqrt{2}$
$\sqrt{2}:1$
$1:\sqrt{3}$✔️
$1:2\sqrt{3}$

Correct Answer Logic:

For a projectile launched along a smooth inclined plane, the range along the incline is: $x = \dfrac{2u^2\sin(\theta-\alpha)\cos\theta}{g\cos^2\alpha}$, where $\alpha$ is the incline angle and $\theta$ the launch angle from horizontal.

When the projectile is fired along the incline: $\theta = \alpha$, so $\sin(\theta-\alpha) = 0$... Using the general formula and applying both cases gives $x_1 : x_2 = \mathbf{1:\sqrt{3}}$.

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English QUESTION #8463

Question 5

Regular exercise is beneficial _______ health.

with
for
to✔️
of

Correct Answer Logic:

'Beneficial to' is the correct preposition.

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Urdu QUESTION #5260

Question 6

فورٹ ولیم کالج کب بنا؟

1500
1600
1700
1800✔️

Correct Answer Logic:

فورٹ ولیم کالج کلکتہ میں 1800ء میں قائم ہوا جہاں اردو نثر کو بہت فروغ ملا۔

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Islamic Studies QUESTION #341

Question 7

Imam Muslim Bin Hijaj Qusheri (author of Sahih Muslim) died in:

260 AH
261 AH✔️
262 AH
263 AH

Correct Answer Logic:

He passed away in 261 AH in Nishapur.

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Urdu QUESTION #5236

Question 8

سخن آباد کس شاعر کے کلیات ہیں؟

نصیر ہاشمی
عرفان صدیقی✔️
میر تقی میر
ان میں سے کوئی نہیں

Correct Answer Logic:

سخن آباد عرفان صدیقی کے کلیات ہیں۔

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Paper-II (Pharmacognosy and Pharmaceutics-I) QUESTION #2985

Question 9

A $1:500$ (w/v) solution is equivalent to what percentage concentration?

$0.02\%$
$0.2\%$✔️
$2\%$
$0.5\%$

Correct Answer Logic:

$1/500 = 0.002$. Multiplying by $100$ gives $0.2\%$.

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Library Sciences QUESTION #1574

Question 10

According to standard library procedures, 'write-off' of library material is most appropriately initiated when an item meets which condition?

The item has been on loan for more than two weeks
The item is lost, permanently damaged beyond repair, stolen and unrecoverable, or obsolete and beyond economic repair after following due process✔️
The item has not been circulated for one year
The item's subject matter is no longer taught in the curriculum

Correct Answer Logic:

Write-off (stock withdrawal) is a formal administrative procedure initiated when materials are lost, irreparably damaged, stolen, or obsolete. It requires documentation, approval from competent authority, and removal from the catalogue and inventory records — following institutional rules and audit requirements.

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General Knowledge QUESTION #4477

Question 11

The central idea of Anatol Lieven’s book “Pakistan: A Hard Country” is:

Pakistan is undefeatable
Pakistan is hard-wired
Society is extraordinarily resilient✔️
None of these

Correct Answer Logic:

Lieven argues Pakistan’s society is resilient despite political instability.

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Paper-II (Pharmacognosy and Pharmaceutics-I) QUESTION #3063

Question 12

A 'Biphasic' dosage form refers to:

Tablets and capsules
Emulsions and suspensions✔️
Syrups and elixirs
Ointments and pastes

Correct Answer Logic:

Biphasic forms contain two distinct phases (e.g., oil/water or solid/liquid).

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Geography QUESTION #6311

Question 13

Which linguistic family has the greatest number of native speakers globally but is geographically concentrated primarily in one region?

Indo-European family
Sino-Tibetan family✔️
Afro-Asiatic family
Niger-Congo family

Correct Answer Logic:

The Sino-Tibetan family (primarily Mandarin Chinese) has ~1.3 billion native speakers but is geographically concentrated in East and Southeast Asia, unlike Indo-European which spans multiple continents.

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Agronomy QUESTION #2045

Question 14

The 'critical concentration' of a nutrient in plant tissue is defined as:

The concentration above which toxicity symptoms appear
The tissue concentration below which yield is reduced by 10% relative to maximum yield, used to diagnose deficiency and calibrate fertilizer recommendations✔️
The minimum concentration detectable by laboratory analysis
The concentration at which a nutrient first becomes visible in a spectroscopic analysis

Correct Answer Logic:

Critical concentration (or critical level) is the tissue nutrient concentration below which a 10% yield reduction occurs (some definitions use 5%). It is determined through nutrient response experiments and tissue analysis. It forms the basis for plant tissue testing diagnostic programs and fertilizer recommendations in modern agronomy.

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Urdu QUESTION #5234

Question 15

موسیٰ کا لفظی مطلب کیا ہے؟

پانی سے نکلا ہوا✔️
پاک
کلام کرنے والا
معزز

Correct Answer Logic:

موسیٰ قبطی زبان کا لفظ ہے جس کے معنی ہیں پانی سے نکلا ہوا۔

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English QUESTION #2774

Question 16

Which ONE WORD means: 'A doctor who treats diseases of the mind'?

Physician
Cardiologist
Neurologist
Psychiatrist✔️

Correct Answer Logic:

A 'Psychiatrist' is a medical doctor who specializes in the diagnosis and treatment of mental disorders. A Physician is a general doctor; Cardiologist treats heart diseases; Neurologist treats nervous system disorders.

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