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Shape factor $f = \dfrac{M_p}{M_y} = \dfrac{Z_p}{Z_e}$, where $Z_p$ = plastic section modulus and $Z_e$ = elastic section modulus. For a rectangle: $Z_p = \dfrac{bd^2}{4}$ and $Z_e = \dfrac{bd^2}{6}$. Therefore $f = \dfrac{bd^2/4}{bd^2/6} = \dfrac{6}{4} = 1.5$. For I-sections, $f \approx 1.12$. The shape factor quantifies the reserve strength beyond first yield — the basis of plastic design.

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English QUESTION #7633

Question 4

What is the underlined part of the sentence? Several ducks had dark green heads.

Subject
Adjective✔️
Conjunction
None of these

Correct Answer Logic:

In the sentence, 'dark green' describes the noun 'heads' and functions as an adjective. Adjectives modify nouns and provide descriptive information about color, size, shape, or other qualities.

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General Abilities QUESTION #2856

Question 5

Factorize: $x^2 - 5x + 6$

$(x-2)(x-3)$✔️
$(x+2)(x+3)$
$(x-1)(x-6)$
$(x-2)(x+3)$

Correct Answer Logic:

We need two numbers that multiply to 6 and add to $-5$: those are $-2$ and $-3$. So $x^2 - 5x + 6 = (x-2)(x-3)$.

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Mathematics QUESTION #6939

Question 6

Let $S_n = 1+q+q^2+\cdots+q^n$ and $T_n = 1+\dfrac{q+1}{2}+\left(\dfrac{q+1}{2}\right)^2+\cdots+\left(\dfrac{q+1}{2}\right)^n$, where $q \in \mathbb{R},\ q\neq 1$. If ${}^{101}C_1 + {}^{101}C_2\cdot S_1 + \cdots + {}^{101}C_{101}\cdot S_{100} = \alpha\, T_{100}$, find $\alpha$.

$2^{99}$
202
200
$2^{100}$✔️

Correct Answer Logic:

$S_n = \dfrac{q^{n+1}-1}{q-1}$. The LHS sum involves $\sum_{k=1}^{101}\binom{101}{k}S_{k-1}$.

After substituting and applying binomial theorem: the sum simplifies using $\sum \binom{101}{k}\frac{q^k-1}{q-1}$.

The result evaluates to $\alpha T_{100}$ where $\alpha = 2^{100}$.

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Paper-II (Pharmacognosy and Pharmaceutics-I) QUESTION #2955

Question 7

Which part of the prescription contains the names and quantities of the prescribed ingredients?

Superscription
Inscription✔️
Subscription
Transcription

Correct Answer Logic:

The Inscription is the main body of the prescription containing the names and quantities of the drugs.

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Egnlish QUESTION #697

Question 8

The character "Big Brother" is a symbol of:

Guidance
Totalitarianism✔️
Brotherhood
None of these

Correct Answer Logic:

He represents the all-seeing, oppressive state that demands total obedience in Orwell's 1984.

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English QUESTION #2794

Question 9

Choose the word that BEST COMPLETES the sentence: 'Neither Ali nor his brothers ___ present at the function.'

was
is
were✔️
has been

Correct Answer Logic:

With 'neither...nor', the verb agrees with the subject nearest to it. 'Brothers' is plural, so the plural verb 'were' is correct.

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Administration QUESTION #9556

Question 10

The National Economic Council (NEC) and National Finance Commission (NFC) are both constitutional bodies. What is the fundamental difference in their scope and functions?

NEC decides how federal taxes are distributed between federation and provinces; NFC formulates long-term economic plans for national development
NEC reviews overall economic conditions and formulates financial, commercial and social policy frameworks; NFC decides criteria for distributing tax revenues between federal and provincial governments✔️
NEC supervises the Planning Commission and approves development projects above Rs. 40 million; NFC ensures audit compliance across all government tiers
NEC is a permanent body chaired by the Prime Minister; NFC is a temporary body constituted every five years — both perform identical functions of resource allocation

Correct Answer Logic:

NEC (Article 156) is the apex economic policy body — it formulates the macro-framework for financial, commercial, social and economic policy, chaired by the PM. NFC (Article 160) is a constituted body (every 5 years) with the specific technical function of determining how taxes in the 'divisible pool' are distributed between federation and the four provinces. They operate at different levels: policy framework vs. fiscal distribution formula.

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Economics QUESTION #1703

Question 11

Structural analysis of Pakistan's persistent current account and balance of payments deficits most consistently points to which underlying root cause?

Excessive dependence on workers' remittances as the primary revenue source
Narrow export base concentrated in low-value-added commodities with poor global competitiveness✔️
Chronically inadequate inflows of foreign direct investment
None of these

Correct Answer Logic:

Pakistan's balance of payments crises are structurally rooted in its narrow, undiversified export base — heavily concentrated in low-value textiles and agricultural commodities — and weak global competitiveness. This structural weakness means imports consistently outpace exports, creating persistent current account deficits. While FDI shortfalls and remittance dependence are also issues, the IMF and World Bank consistently identify low export diversification and competitiveness as the most fundamental structural constraint.

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General Abilities QUESTION #2812

Question 12

A population increased from 50,000 to 65,000. What is the percentage increase?

20%
25%
30%✔️
35%

Correct Answer Logic:

Increase $= 65000 - 50000 = 15000$. Percentage increase $= \dfrac{15000}{50000} \times 100 = 30\%$.

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General Knowledge QUESTION #8908

Question 13

The word 'Archipelago' means:

A cluster of islands✔️
A cluster of small states
Rocks under the sea
A cluster of stars

Correct Answer Logic:

Archipelago means a group of islands.

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Library Sciences QUESTION #1572

Question 14

In serials management, a 'check-in' record serves which primary function?

Recording the cost of each serial subscription
Systematically tracking the receipt of each issue of a periodical to identify gaps, missing issues, or irregular publication✔️
Binding completed serial volumes
Providing access to serial articles through an index

Correct Answer Logic:

The check-in record (or kardex) is a serials control tool that tracks the arrival of each issue of a periodical subscription. It enables librarians to quickly identify missing or late issues, claim them from vendors, and maintain a complete run — critical for academic and special library serials management.

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Pakistan Affairs QUESTION #9038

Question 15

Which country was the first to recognize Pakistan after its independence in 1947?

Afghanistan
Iran✔️
Saudi Arabia
Egypt

Correct Answer Logic:

Iran was the first country to recognize Pakistan.

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Agronomy QUESTION #2054

Question 16

Which of the following statements about zero tillage (direct seeding) in the rice–wheat cropping system of South Asia is MOST agronomically accurate?

Zero tillage increases soil compaction, always reducing wheat yields below conventionally tilled wheat
Zero tillage allows timely wheat planting after rice harvest, reducing the turnaround period, conserving soil moisture, lowering production costs, and achieving equal or higher yields compared to conventional tillage when managed correctly✔️
Zero tillage is only beneficial in light sandy soils and fails in clay loam soils typical of rice–wheat zones
Zero tillage eliminates the need for all herbicide application in wheat

Correct Answer Logic:

In the rice–wheat system, delayed wheat planting after rice harvest is a major yield constraint. Zero tillage (using zero-till drills) reduces the turnaround period by 10–15 days, conserves residual soil moisture, reduces diesel use by 60–70%, and achieves comparable or higher yields than conventional tillage — demonstrated across millions of hectares in Pakistan, India, and Bangladesh.

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Accounting & Finance QUESTION #6153

Question 17

Units produced and sold: 48,000; Direct materials ($3/kg): $298,000; Direct labour ($4/hr): $240,000; Fixed selling costs: $150,000; Variable selling costs: $24,000. Fixed production overheads absorbed at $10 per labour hour. What is the total absorption cost per unit?