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Mathematics QUESTION #6938

If $\displaystyle\sum_{r=0}^{25}\left\{{}^{50}C_r \cdot {}^{50-r}C_{25-r}\right\} = K\binom{50}{25}$, find the value of $K$.

$(25)^2$
$2^{25}-1$
$2^{24}$
$2^{25}$✔️

Correct Answer Logic:

Note: ${}^{50}C_r \cdot {}^{50-r}C_{25-r} = \dfrac{50!}{r!(50-r)!} \cdot \dfrac{(50-r)!}{(25-r)!(25)!} = \dfrac{50!}{r!(25-r)!25!} = {}^{50}C_{25}\cdot{}^{25}C_r$

So the sum $= {}^{50}C_{25}\displaystyle\sum_{r=0}^{25}{}^{25}C_r = {}^{50}C_{25}\cdot 2^{25}$

Therefore $K = \mathbf{2^{25}}$.

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Chemistry QUESTION #7390

Question 2

For the electron affinity (EA) of halogens, which order is correct?

$\text{Br} > \text{F}$
$\text{F} > \text{Cl}$
$\text{Br} > \text{Cl}$
$\text{F} > \text{I}$✔️

Correct Answer Logic:

Electron affinity trend in halogens:
Expected trend: EA increases up the group (smaller atom = stronger attraction for incoming electron). However, F is an exception — its very small size causes high electron–electron repulsion in the compact 2p subshell, reducing its EA.

Actual order: Cl > F > Br > I

$\text{F} > \text{I}$ is correct ✓. The correct option here is (4): F > I.

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Dairy Food Science and Technology QUESTION #5982

Question 3

In the production of WPC (Whey Protein Concentrate), the MWCO of UF membranes used is typically:

$100\text{–}200\;\text{Da}$ (nanofiltration range)
$5{,}000\text{–}30{,}000\;\text{Da}$ (retains whey proteins; $\beta$-Lg MW $= 18{,}300\;\text{Da}$; $\alpha$-La MW $= 14{,}000\;\text{Da}$)✔️
$100{,}000\;\text{Da}$ (retains only casein micelles)
$1{,}000{,}000\;\text{Da}$ (retains only fat globules)

Correct Answer Logic:

UF membranes with $5{,}000\text{–}30{,}000\;\text{Da}$ MWCO are used for WPC/WPI production. They retain whey proteins ($\beta$-Lg MW $\approx 18{,}300\;\text{Da}$, $\alpha$-La MW $\approx 14{,}000\;\text{Da}$, BSA $\approx 67{,}000\;\text{Da}$) while allowing lactose ($342\;\text{Da}$), minerals, and water to permeate.

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Dairy Food Science and Technology QUESTION #5942

Question 4

In yoghurt production, the typical inoculation rate of starter culture is:

$0.1\text{–}0.5\%$
$2\text{–}3\%$✔️
$10\text{–}15\%$
$0.01\%$

Correct Answer Logic:

Standard inoculation rate for yoghurt is $2\text{–}3\%$ (v/v) of a working starter culture. Higher rates produce faster acidification but may result in excessive post-acidification. Lower rates result in inadequate acidification.

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Ability / HR / Governance / Special Education QUESTION #1857

Question 5

Under Rule 8-B(1), on what basis can the most senior eligible civil servant be appointed if he lacks the specified length of service?

Regular promotion
Contract basis
Acting charge basis✔️
Ad hoc basis

Correct Answer Logic:

Rule 8-B(1) states the authority may appoint the most senior civil servant on acting charge basis if he does not possess the specified length of service but is otherwise eligible.

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Urdu QUESTION #5221

Question 6

مشہور نظم 'طلوعِ اسلام' کے شاعر کون ہیں؟

حفیظ جالندھری
احسان دانش
علامہ اقبال✔️
الطاف حسین حالی

Correct Answer Logic:

طلوعِ اسلام علامہ اقبال کی مشہور نظم ہے جو بانگِ درا میں شامل ہے۔

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Paper-II (Pharmacognosy and Pharmaceutics-I) QUESTION #3035

Question 7

'Dusting Powders' are intended for:

Internal use
External application to the skin✔️
Sterile injection
Inhalation

Correct Answer Logic:

Dusting powders are fine medicinal powders used externally on the skin.

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Chemistry QUESTION #464

Question 8

The amount of heat absorbed by one mole of solid at 1 atm when it melts into liquid form is denoted by __________

?H?
?Hf✔️
?H?
?H?

Correct Answer Logic:

?Hf is heat of fusion

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Math Physics Chemistry Biology QUESTION #817

Question 9

The reactivity order of alkyl halides for a particular alkyl group is:

$\text{F} > \text{Cl} > \text{Br} > \text{I}$
$\text{I} > \text{Br} > \text{Cl} > \text{F}$✔️
$\text{Cl} > \text{Br} > \text{F} > \text{I}$
$\text{Br} > \text{I} > \text{Cl} > \text{F}$

Correct Answer Logic:

Reactivity of alkyl halides in nucleophilic substitution follows bond strength (C–X bond): C–I is weakest so iodide is most reactive. Order: $\text{I} > \text{Br} > \text{Cl} > \text{F}$.

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Paper-II (Pharmacognosy and Pharmaceutics-I) QUESTION #3036

Question 10

'Geometric Dilution' is a method used to:

Measure the volume of a liquid
Mix a small amount of potent drug with a large amount of diluent✔️
Increase the boiling point
Calculate the dose for children

Correct Answer Logic:

Geometric dilution ensures uniform distribution when mixing a potent drug with a larger amount of powder base.

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Egnlish QUESTION #670

Question 11

"The Scarlet Letter" is set in:

17th-century Boston✔️
18th-century London
19th-century New York
16th-century Paris

Correct Answer Logic:

Nathaniel Hawthorne's novel is set in the Puritan Massachusetts Bay Colony.

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Boilers Mechanical Engineering QUESTION #2518

Question 12

The principle of work and energy for a particle states that the net work done by all forces equals:

The change in potential energy only
The change in kinetic energy: $U_{1\to2}=\frac{1}{2}mv_2^2 - \frac{1}{2}mv_1^2$✔️
The impulse of the net force
The product of average force and displacement

Correct Answer Logic:

Work-energy theorem: $U_{1\to2}=T_2-T_1$, where $T=\frac{1}{2}mv^2$ is kinetic energy. This is derived by integrating Newton's second law along the path.

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Urdu QUESTION #5163

Question 13

اردو براج بھاشا سے نکلی ہے، یہ کس ادیب سے منسوب ہے؟

مولانا محمد حسین آزاد✔️
مولانا الطاف حسین حالی
مقصود حسین
ان میں سے کوئی نہیں

Correct Answer Logic:

یہ نظریہ مولانا محمد حسین آزاد کے ساتھ منسوب کیا جاتا ہے۔

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General Knowledge QUESTION #4751

Question 14

WAFA is the official news agency of which entity?

Syria
Jordan
Egypt
Palestine✔️

Correct Answer Logic:

WAFA (Wakalat Anba'a Falastiniyya) is the official Palestinian news agency, established in 1972 and operating under the Palestinian Authority.

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Professional QUESTION #1841

Question 15

Section 15A on Declaration of Assets requires civil servants of which Basic Pay Scale and above to digitally file declarations of assets with the Federal Board of Revenue?

BS-16 and above
BS-17 and above✔️
BS-18 and above
BS-19 and above

Correct Answer Logic:

Section 15A inserted by Act No. XX of 2025 requires that the declaration of assets of a civil servant of BS-17 and above, along with assets and liabilities of his spouse and dependent children including domestic and foreign assets, shall be digitally filed with the Federal Board of Revenue and made publicly available.

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Statistics QUESTION #1970

Question 16

Which of the following actions is most effective in reducing sampling error?

Adopting non-probability sampling
Expanding the population size
Decreasing the sample size
Increasing the sample size✔️

Correct Answer Logic:

Sampling error decreases as sample size increases, because larger samples yield better parameter estimates. The standard error $SE = \dfrac{\sigma}{\sqrt{n}}$ decreases as $n$ increases.

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Biology QUESTION #7771

Question 17

The synthesis of ATP using a proton gradient across a membrane is called:

Fermentation
Glycolysis
Oxidative phosphorylation✔️
Pyruvate oxidation

Correct Answer Logic:

Oxidative phosphorylation occurs in the inner mitochondrial membrane (or bacterial plasma membrane) via the electron transport chain and ATP synthase. It couples chemiosmosis with ATP synthesis.

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Biology QUESTION #565

Question 18

Pick the biotic component from the following.

Soil
Water
Atmosphere
Animals✔️

Correct Answer Logic:

Animals are biotic (living) components

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Mathematics QUESTION #6009

Question 19

Let $f:[0,1]\to\mathbb{R}$ satisfy $f(xy)=f(x)\cdot f(y)$ for all $x,y\in[0,1]$ with $f(0)\neq 0$. If $y=y(x)$ solves $\dfrac{dy}{dx} = f(x)$ with $y(0)=1$, find $y\!\left(\dfrac{1}{4}\right)+y\!\left(\dfrac{3}{4}\right)$.

3✔️
4
2
5

Correct Answer Logic:

From the functional equation $f(xy)=f(x)f(y)$ with $f(0)\neq 0$, putting $x=y=0$ gives $f(0)=f(0)^2 \Rightarrow f(0)=1$. Putting $y=0$: $f(0)=f(x)f(0) \Rightarrow f(x)=1$ for all $x$.

So $\frac{dy}{dx}=1$, giving $y=x+C$. With $y(0)=1$: $C=1$, so $y=x+1$.

$y(1/4)+y(3/4)=(1/4+1)+(3/4+1)=5/4+7/4=12/4=\mathbf{3}$

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Urdu QUESTION #5034

Question 20

حیاتِ سعدی کی صنف کیا ہے؟

نظم
ناول
افسانہ
سوانح عمری✔️

Correct Answer Logic:

حیاتِ سعدی مولانا الطاف حسین حالی کی تصنیف ہے اور یہ سوانح عمری کی صنف سے تعلق رکھتی ہے۔

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