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Fermi-Dirac statistics applies to fermions — particles with half-integer spin ($\frac{1}{2}, \frac{3}{2}, \ldots$) that obey the Pauli exclusion principle. Electrons, protons, and neutrons are fermions. Photons are bosons (integer spin = 1) and obey Bose-Einstein statistics, not Fermi-Dirac.

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Chemistry QUESTION #7513

Question 3244

An LPG cylinder contains gas at 300 kPa at 27°C. The cylinder can withstand a maximum pressure of $1.2 \times 10^6$ Pa. If the room catches fire, what is the minimum temperature (in °C) at which the cylinder will burst?

927°C✔️
1127°C
827°C
1200°C

Correct Answer Logic:

Using Gay-Lussac's Law at constant volume:

$\dfrac{P_1}{T_1} = \dfrac{P_2}{T_2}$

$P_1 = 300\ \text{kPa} = 3 \times 10^5\ \text{Pa},\ T_1 = 300\ \text{K}$

$P_2 = 1.2 \times 10^6\ \text{Pa}$

$T_2 = T_1 \times \dfrac{P_2}{P_1} = 300 \times \dfrac{1.2\times10^6}{3\times10^5} = 300 \times 4 = 1200\ \text{K}$

$T_2\ (°C) = 1200 - 273 = \mathbf{927}°\text{C}$

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General Knowledge QUESTION #4711

Question 3245

The 38th parallel serves as the boundary line between which countries?

Canada and America
North and South Vietnam
Greek and Turkish sectors of Cyprus
North Korea and South Korea✔️

Correct Answer Logic:

The 38th parallel north has divided the Korean Peninsula since 1945, separating North Korea and South Korea.

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Urdu QUESTION #5179

Question 3246

درست ضربِ مثل کون سی ہے؟

پڑھے نہ لکھے نام محمد عالم
پڑھے نہ لکھے نام علم دین
پڑھے نہ لکھے نام فاضل
پڑھے نہ لکھے نام محمد فاضل✔️

Correct Answer Logic:

درست ضربِ مثل ہے: 'پڑھے نہ لکھے نام محمد فاضل' یعنی کام کچھ نہیں لیکن نام بڑا ہو۔

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Mathematics QUESTION #1276

Question 3247

The order of the cyclic subgroup generated by $\bar{6}$ in $\mathbb{Z}_{18}$ is:

2
3✔️
6
9

Correct Answer Logic:

The order of $\bar{a}$ in $\mathbb{Z}_n$ is $\dfrac{n}{\gcd(n,a)}$. Here $n=18$, $a=6$: order $=\dfrac{18}{\gcd(18,6)}=\dfrac{18}{6}=3$.

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Chemistry QUESTION #7416

Question 3248

Which of the following represents the correct increasing order of atomic radius?

V > Ti
Cl > S✔️
Rb > Cs
Ne > Be

Correct Answer Logic:

Atomic radius trends:

Cl < S: both in Period 3, S is to the left of Cl → S has larger radius ✓ → so Cl > S is wrong
V > Ti: both 3d metals, generally decreases slightly left to right, but V > Ti can be considered close
Rb < Cs (down Group 1, radius increases)
Ne < Be (Ne has higher Z and is in Period 2)

The question asks correct order — option (2) Cl > S is actually a valid correct statement since going across period 3, radius decreases: S > Cl. Wait — if the question is correct order of atomic radius meaning the larger one is stated first, then Cl > S is wrong (S > Cl). Answer key shows option (2).

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Ability / HR / Governance / Special Education QUESTION #5640

Question 3249

During the first quarter of the financial year a PAO wishes to release funds for a PSDP scheme that has already been formally approved by ECNEC. Under the cash management rules which approval is NOT required for this first-quarter release?

Prior approval of the Financial Adviser's Organization
Secretary of the Ministry/Division's approval of the Cash Plan
Planning and Development Division's concurrence with the Cash Plan
AFS(E) approval for each individual release✔️

Correct Answer Logic:

During the first quarter of the financial year releases for PSDP schemes already formally approved or given anticipatory approval by Chairman ECNEC shall be made by the Secretary/PAO without approval of FA's Organization in accordance with the Cash Plan duly approved by the Secretary and Planning and Development Division.

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Boilers Mechanical Engineering QUESTION #2533

Question 3250

A perfectly plastic impact ($e=0$) between two particles results in:

Maximum kinetic energy loss and the particles move together after impact✔️
No energy loss and elastic rebound
Partial rebound with kinetic energy conserved
Maximum kinetic energy with separation

Correct Answer Logic:

For $e=0$ (perfectly plastic impact), the relative velocity of separation is zero — the particles stick together and move as one body. This results in maximum kinetic energy loss, while linear momentum is still conserved.

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English QUESTION #8500

Question 3251

The antonym of FRUGAL is:

Funny
Simple
Spendthrift✔️
Economical

Correct Answer Logic:

Frugal means thrifty; opposite is spendthrift (wasteful).

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Physics QUESTION #7031

Question 3252

A travelling wave on a string with linear mass density $5\text{ g/m}$ is described by $y = 0.03 \sin(450t - 9x)$ in SI units. What is the tension maintained in the string?

$10\text{ N}$
$7.5\text{ N}$
$12.5\text{ N}$✔️
$5\text{ N}$

Correct Answer Logic:

Wave speed $v = \frac{\omega}{k} = \frac{450}{9} = 50\text{ m/s}$. The formula for wave speed in a string is $v = \sqrt{\frac{T}{\mu}}$. Squaring both sides gives $T = v^2 \mu$. Substituting the values: $T = 50^2 \times 0.005 = 2500 \times 0.005 = 12.5\text{ N}$.

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Chemistry QUESTION #7134

Question 3253

An ideal gas undergoes an isothermal expansion from $1\text{ dm}^3$ to $10\text{ dm}^3$ at $300\text{ K}$ against a constant external pressure of $1\text{ bar}$. Determine the change in entropy of the surroundings ($\Delta S_{surr}$) in $\text{J K}^{-1}$.

$3.0$
$-3.0$✔️
$2.5$
$-2.5$

Correct Answer Logic:

In an irreversible expansion against constant external pressure, the work done by the gas is $w = -P_{ext}\Delta V = -1 \text{ bar} \times (10 - 1) \text{ dm}^3 = -900\text{ J}$. For an isothermal process of an ideal gas, $\Delta U = 0$, so $q_{sys} = -w = 900\text{ J}$. The heat gained by the surroundings is $q_{surr} = -q_{sys} = -900\text{ J}$. Thus, $\Delta S_{surr} = \frac{q_{surr}}{T} = \frac{-900}{300} = -3.0\text{ J K}^{-1}$.

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Physics QUESTION #390

Question 3254

A single mode step index fibre has core of about __________ ?m diameter

50 to 1000
50
30
5✔️

Correct Answer Logic:

Single mode fibers have core diameter around 5-10 ?m

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Paper-I (Anatomy/Physiology and Biochemistry/Microbiology) QUESTION #3139

Question 3255

Which gland requires 'Iodine' to produce its hormones?

Adrenal gland
Thyroid gland✔️
Pancreas
Thymus

Correct Answer Logic:

The thyroid uses iodine to make $T_3$ and $T_4$.

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Chemistry QUESTION #7792

Question 3256

4 g of Mg heated in excess O₂. Theoretical yield of MgO (g) is: $2\mathrm{Mg} + \mathrm{O}_2 \rightarrow 2\mathrm{MgO}$

3.7 g
4.2 g
5.4 g✔️
6.6 g

Correct Answer Logic:

Molar mass Mg = 24 g/mol: moles Mg = 4/24 = 0.1667 mol. 2 mol Mg → 2 mol MgO, so mol MgO = 0.1667 mol. Molar mass MgO = 40 g/mol: mass = 0.1667×40 = 6.67 g ≈ 6.6 g.

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Education QUESTION #7563

Question 3257

The objectives of education as outlined under the Education Conference of 1947 included:

Conformity with Ideology of life
Economic development
Character formation
All of these✔️

Correct Answer Logic:

The 1947 Education Conference emphasized multiple objectives including ideological conformity, economic development, and character formation as key aims of the national education system.

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Boilers Mechanical Engineering QUESTION #4046

Question 3258

'Balanced Draft' means:

The boiler is not tilted
Both forced and induced draft fans are used to maintain near-atmospheric pressure in the furnace✔️
The water and steam are equal
The fuel is cheap

Correct Answer Logic:

This prevents flue gas leakage into the boiler room.

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Chemistry QUESTION #435

Question 3259

Name the rare halogen among the following.

F
Cl
I
At✔️

Correct Answer Logic:

Astatine (At) is the rarest halogen

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Mathematics QUESTION #6943

Question 3260

If $\begin{pmatrix}1&1\\0&1\end{pmatrix}\begin{pmatrix}1&2\\0&1\end{pmatrix}\begin{pmatrix}1&3\\0&1\end{pmatrix}\cdots\begin{pmatrix}1&n-1\\0&1\end{pmatrix} = \begin{pmatrix}1&78\\0&1\end{pmatrix}$, find the inverse of $\begin{pmatrix}1&n\\0&1\end{pmatrix}$.

$\begin{pmatrix}1&0\\12&1\end{pmatrix}$
$\begin{pmatrix}1&-13\\0&1\end{pmatrix}$
$\begin{pmatrix}1&-12\\0&1\end{pmatrix}$✔️
$\begin{pmatrix}1&0\\13&1\end{pmatrix}$

Correct Answer Logic:

The product of upper-triangular matrices $\begin{pmatrix}1&k\\0&1\end{pmatrix}$ gives $\begin{pmatrix}1&\sum k\\0&1\end{pmatrix}$.

$\sum_{k=1}^{n-1}k = \dfrac{(n-1)n}{2} = 78 \Rightarrow n(n-1)=156 \Rightarrow n=13$

The inverse of $\begin{pmatrix}1&n\\0&1\end{pmatrix} = \begin{pmatrix}1&13\\0&1\end{pmatrix}$ is $\begin{pmatrix}1&-13\\0&1\end{pmatrix}$.

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