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For the most economical trapezoidal section, the condition is $R = y/2$ (hydraulic radius equals half the flow depth). This is equivalent to the condition that the channel can be inscribed in a semicircle of radius $y$. For a rectangular channel, the economical condition $b = 2y$ also yields $R = y/2$.

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Security Measures to Maintain Law and Order QUESTION #837

Question 2565

An AD ASF finds a suspicious bag. Under Section 7, what is the legal requirement before a search?

Written warrant
Judicial permission
Reasonable suspicion✔️
Owner's consent

Correct Answer Logic:

Section 7(1) allows search of persons/baggage based on reasonable suspicion to ensure security.

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General Science and Ability QUESTION #202

Question 2566

The fastest enzyme is:

Pepsin
DNA polymerase
Carbonic anhydrase✔️
None of these

Correct Answer Logic:

Carbonic anhydrase can process up to a million molecules per second.

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Maths QUESTION #7944

Question 2567

The radius of a sphere is increased by 10%. By what percentage does the surface area increase?

21%✔️
31%
41%
None

Correct Answer Logic:

Surface area of a sphere $= 4\pi r^2$.
New radius $= 1.1r$, so new surface area $= 4\pi(1.1r)^2 = 4\pi \times 1.21r^2$.
Increase $= 21\%$.

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Planning QUESTION #4997

Question 2568

What does 'primate city' phenomenon indicate in urban systems?

Equal distribution of city sizes
Dominance of one disproportionately large city✔️
Multiple cities of similar size
Declining urban population

Correct Answer Logic:

A primate city is disproportionately larger (typically 2+ times) than the second-largest city, dominating the urban system economically and politically. Common in developing countries, it often indicates centralized development and regional imbalances.

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Education QUESTION #6768

Question 2569

A teacher constructs a 50-item MCQ test. Items 1–25 cover knowledge-level outcomes (p-values around 0.85–0.90) and items 26–50 cover application-level outcomes (p-values around 0.40–0.55). Which statement about this test's suitability for norm-referenced interpretation is MOST accurate?

Both halves are equally suitable for NRT because they cover all Bloom's levels
The application-level items (items 26–50) are more suitable for NRT because their moderate difficulty creates greater score variance, enabling better discrimination among examinees✔️
The knowledge-level items are better for NRT because easier items reduce test anxiety
NRT requires all items to have the same difficulty level, so the test is unsuitable

Correct Answer Logic:

Norm-referenced tests require substantial score variance to rank examinees accurately. Items with p-values between 0.40 and 0.60 are near optimal for NRT because they generate the widest spread of scores. Items with very high p-values (0.85–0.90) produce ceiling effects and minimal variance, reducing the test's discriminating power — making them less suitable for NRT purposes.

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Physics QUESTION #7829

Question 2570

During isothermal expansion of an ideal gas:

Pressure and temperature increase
Internal energy increases
Temperature remains constant✔️
Work done by gas is zero

Correct Answer Logic:

Isothermal: ΔT=0, so internal energy constant (ideal gas). Gas does work on surroundings.

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Administration QUESTION #2940

Question 2571

What does the "Current Ratio" specifically measure regarding a company's financial health?

Long-term profitability and return on investment
A firm's ability to cover short-term liabilities with short-term assets✔️
The total market value of the company's outstanding shares
None of these

Correct Answer Logic:

The current ratio is a liquidity metric that shows if a company has enough current assets to pay off its debts due within one year.

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The Elections Act 2017 QUESTION #9461

Question 2572

Section 148(6)(a) provides that if an election petition is not decided within the mandatory period, further adjournments may be granted only on payment of special costs. As amended in 2023, the cost range per adjournment is:

Rs. 50,000 to Rs. 100,000
Rs. 5,000 to Rs. 25,000
Rs. 10,000 to Rs. 50,000✔️
Rs. 25,000 to Rs. 75,000

Correct Answer Logic:

Section 148(6)(a) [2023 amendment] states: 'special costs ranging from ten thousand to fifty thousand rupees per adjournment and adjournment shall not be granted for more than three days.'

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Education QUESTION #10845

Question 2573

The most ignored aspect in the field of education is:

Monitoring aspect
Training of teachers
Planning aspect
Research and development✔️

Correct Answer Logic:

Research and development (R&D) is the most neglected area in education, particularly in developing countries. While teaching, curriculum, and administration receive attention, systematic educational research to improve methods, materials, and outcomes is often underfunded and overlooked. R&D provides the evidence base for educational reforms and improvements, yet it receives the least policy attention and budgetary allocation.

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Chemistry QUESTION #432

Question 2574

In many of its properties __________ is quite different from the other alkali metals.

Li✔️
Be
Na
K

Correct Answer Logic:

Lithium shows anomalous behavior among alkali metals

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English QUESTION #8403

Question 2575

He agreed _______ my proposal.

With
For
To✔️
On

Correct Answer Logic:

'Agreed to' a proposal.

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Math Physics Chemistry Biology QUESTION #518

Question 2576

Which bond is the potential source of chemical energy for cellular activities?

C-N✔️
C-O
C-H
H-O

Correct Answer Logic:

Answer key shows A but C-H bonds store most energy

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MCQs Section QUESTION #5237

Question 2577

ہوا کے گھوڑے پر سوار ہونا محاورہ ہے، اس کا کیا مطلب ہے؟

مغرور ہونا
بہت جلدی میں ہونا✔️
کسی کی پروا نہ کرنا
غیر دانشمند ہونا

Correct Answer Logic:

ہوا کے گھوڑے پر سوار ہونا محاورے کا مطلب ہے بہت تیزی اور عجلت میں ہونا۔

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Chemistry QUESTION #7157

Question 2578

The significant reducing ability of hypophosphorous acid ($H_{3}PO_{2}$) is primarily due to the presence of:

Two $P-OH$ bonds
One $P-H$ bond
Two $P-H$ bonds✔️
One $P-OH$ bond

Correct Answer Logic:

The reducing character of oxoacids of phosphorus depends on the number of $P-H$ bonds present. In $H_{3}PO_{2}$ (Hypophosphorous acid), the phosphorus atom is bonded to two hydrogen atoms directly ($2 \times P-H$ bonds) and one hydroxyl group ($1 \times P-OH$ bond). These $P-H$ bonds are responsible for its strong reducing property.

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Biology QUESTION #7237

Question 2579

The thalloid body of a slime mould (Myxomycetes) is known as:

Fruiting body
Mycelium
Protonema
Plasmodium✔️

Correct Answer Logic:

In slime moulds (Myxomycetes), the vegetative body is a plasmodium — a multinucleate, acellular mass of protoplasm that moves and engulfs food. It is not a true mycelium (fungal hyphae network) nor a protonema (moss juvenile stage).

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Civil / Architecture QUESTION #2341

Question 2580

In structural dynamics, the damped natural frequency $\omega_d$ of a SDOF system with critical damping ratio $\xi$ and undamped natural frequency $\omega_n$ is:

$\omega_d = \omega_n (1 + \xi)$
$\omega_d = \omega_n \sqrt{1 - \xi^2}$✔️
$\omega_d = \omega_n \sqrt{1 + \xi^2}$
$\omega_d = \omega_n (1 - \xi)$

Correct Answer Logic:

The damped natural frequency is $\omega_d = \omega_n \sqrt{1 - \xi^2}$. For typical structural damping ($\xi = 0.02$ to $0.05$), $\omega_d \approx \omega_n$. At critical damping ($\xi = 1.0$), $\omega_d = 0$ and the system returns to equilibrium without oscillating.

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