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Mathematics QUESTION #6003

A manufacturing firm currently produces 2000 items. The rate of change of production $P$ with respect to additional workers $x$ is given by $\frac{dP}{dx} = 100 - 12\sqrt{x}$. If the firm hires 25 additional workers, what will be the new level of production?

2500
3000
3500✔️
4500

Correct Answer Logic:

We integrate $\frac{dP}{dx} = 100 - 12\sqrt{x}$ from $x = 0$ to $x = 25$:

$P = \int_0^{25}(100 - 12\sqrt{x})\,dx = \left[100x - 12 \cdot \frac{2}{3}x^{3/2}\right]_0^{25}$

$= \left[100x - 8x^{3/2}\right]_0^{25} = 100(25) - 8(25)^{3/2} = 2500 - 8(125) = 2500 - 1000 = 1500$

New production $= 2000 + 1500 = \mathbf{3500}$

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Dairy Food Science and Technology QUESTION #5932

Question 1342

Which fatty acid is present in highest concentration in milk fat by weight?

Butyric acid (C4:0)
Oleic acid (C18:1, n-9) — approximately $25\text{–}30\%$ of total fatty acids✔️
Lauric acid (C12:0)
Linoleic acid (C18:2)

Correct Answer Logic:

Oleic acid (C18:1, n-9) is the most abundant fatty acid in bovine milk fat by weight ($\approx 25\text{–}30\%$ of total FA). Butyric acid (C4:0) gives dairy its unique flavor when released by lipolysis but is present at only $\approx 3\text{–}5\%$.

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Psychology QUESTION #9858

Question 1343

The difficulty with type theories of personality is that they are:

Too simple
Too contradictory
Too arbitrary
All of these✔️

Correct Answer Logic:

Type theories face multiple criticisms: too simple (forcing complex personalities into discrete categories), too contradictory (types don't hold across cultures and situations), and too arbitrary (choice of types lacks empirical grounding). All three apply.

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Dairy Food Science and Technology QUESTION #5960

Question 1344

Which type of homogenizer is most commonly used in the dairy industry?

Ultrasonic homogenizer
High-pressure (valve) homogenizer ($2000\text{–}2500\;\text{psi}$)✔️
Microfluidizer
Membrane emulsification homogenizer

Correct Answer Logic:

High-pressure homogenizers (HPH) are the industry standard. Milk is forced through a narrow adjustable valve at $2000\text{–}2500\;\text{psi}$. The pressure drop, turbulence, cavitation, and shear forces reduce fat globule size from $1\text{–}10\;\mu\text{m}$ to $<0.5\text{–}2\;\mu\text{m}$.

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CISA QUESTION #6835

Question 1345

An organization conducts business impact analysis and assigns Recovery Point Objective (RPO) of 1 hour but performs full backups only weekly with no incremental backups. What is the MAXIMUM potential data loss?

1 hour
168 hours (1 week)✔️
24 hours
Unknown

Correct Answer Logic:

RPO defines maximum acceptable data loss, while backup frequency determines actual potential data loss. Weekly backups mean up to 1 week of data could be lost in a disaster. The gap between 1-hour RPO requirement and weekly backup capability represents a critical mismatch between business requirements and technical implementation.

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Statistics QUESTION #1964

Question 1346

Which of the following correctly lists all recognized types of statistical estimates?

Point estimate only
Interval estimate only
Estimation of confidence region only
Point estimate, Interval estimate, and Confidence region✔️

Correct Answer Logic:

Statistical estimation includes point estimates (single value), interval estimates (a range), and confidence regions (multivariate generalizations). All three are valid types of estimates.

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General Knowledge QUESTION #4642

Question 1347

There are 26 steps in a Church. In the time Sandy comes down two steps, Plato goes one step. If they start simultaneously and keep their speed uniform, then at which step from bottom will they meet.

$9^{th}$✔️
$12^{th}$
$13^{th}$
$8^{th}$

Correct Answer Logic:

No explanation provided for this question.

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Home Economics QUESTION #6275

Question 1348

Which fiber is known as the 'Queen of Fibers' due to its luster and strength?

Silk✔️
Linen
Cotton
Wool

Correct Answer Logic:

Silk is highly prized for its natural shine, strength, and smoothness.

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Paper-II (Pharmacognosy and Pharmaceutics-I) QUESTION #3668

Question 1349

'Gelatin' is obtained by the partial hydrolysis of:

Starch
Collagen from animal skin and bones✔️
Cellulose
Fruit pectin

Correct Answer Logic:

Gelatin is used to make capsule shells.

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Boilers Mechanical Engineering QUESTION #2508

Question 1350

The change in shear force from section A to section B of a beam equals:

$V_B - V_A = M_B - M_A$
$V_B - V_A = \int_{x_A}^{x_B} q\,dx$ (area of load diagram)✔️
$V_B - V_A = \frac{dM}{dx}$
$V_B - V_A = w(x_B - x_A)^2/2$

Correct Answer Logic:

From $dV/dx = q$ (load intensity), integrating between A and B: $V_B - V_A = \int_{x_A}^{x_B}q\,dx$, which is the area under the load intensity diagram.

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Pakistan Affairs QUESTION #4659

Question 1351

What percentage of Pakistan's electricity was generated from thermal sources around 2005?

30%
50%
70%
Over 80%✔️

Correct Answer Logic:

Pakistan generated over 70% of its electricity from thermal sources around 2005; the exact figure was higher than the given options, making 'None of these' the technically correct answer.

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Boilers Mechanical Engineering QUESTION #2379

Question 1352

The transfer function of a PID (Proportional-Integral-Derivative) controller is:

$Y(s) = K + K_I s + K_D s^2$
$Y(s) = K + \frac{K_I}{s} + K_D s$✔️
$Y(s) = \frac{K_I}{s} + K_D s$
$Y(s) = K \cdot K_I \cdot K_D \cdot s$

Correct Answer Logic:

The PID controller combines all three actions: $Y(s)=K+\frac{K_I}{s}+K_D s$. P provides immediate response, I eliminates steady-state error, D adds damping and predictive action.

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Administration QUESTION #9574

Question 1353

The 'Government of India Act 1935' introduced two significant provisions relevant to Pakistan's current administrative structure. What were these provisions, and how did they shape the post-independence civil service?

It introduced the provincial civil service and created the post of Governor General — both were retained after independence with minor modifications
It provided security of tenure for civil servants (no dismissal without hearing/right of appeal) and gave the provinces financial autonomy — establishing the principle of civil servant protection that was later codified in Pakistan's Civil Servants Act 1973✔️
It created the Federal Public Service Commission and the first competitive examination system for entry to the Indian Civil Service — the structural predecessor of Pakistan's FPSC
It established the first merit-based promotion system and abolished seniority-based advancement — a principle reversed by subsequent Pakistani governments

Correct Answer Logic:

The Government of India Act 1935 introduced two landmark protections: security of tenure (no dismissal without due process, including right of appeal up to Secretary of State) and provincial financial autonomy. The security of tenure principle became foundational to civil service independence in Pakistan — codified in the Civil Servants Act 1973 — while provincial financial autonomy laid conceptual groundwork for federalism and NFC-type resource-sharing mechanisms.

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Chemistry QUESTION #7349

Question 1354

The energy of the second Bohr orbit of hydrogen atom is $-328$ kJ/mol. Based on this, the energy of the fourth Bohr orbit will be:

$-41$ kJ/mol
$-1312$ kJ/mol
$-164$ kJ/mol
$-82$ kJ/mol✔️

Correct Answer Logic:

Bohr's energy formula: $E_n = \dfrac{E_1}{n^2}$

Given $E_2 = -328$ kJ/mol, so $E_1 = -328 imes 4 = -1312$ kJ/mol.

$E_4 = \dfrac{-1312}{16} = -82$ kJ/mol

Key point: as $n$ increases, energy becomes less negative — outer orbits are less tightly bound.

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Paper-I (Anatomy/Physiology and Biochemistry/Microbiology) QUESTION #3165

Question 1355

'Tachycardia' refers to a heart rate that is:

Too slow
Too fast✔️
Irregular
Non-existent

Correct Answer Logic:

A resting heart rate over $100\text{ bpm}$ is considered tachycardia.

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Psychology QUESTION #9767

Question 1356

In Freudian theory, the component of personality that serves as a buffer between the id and the demands of the external world is the:

Super-ego
Ego✔️
Ego-ideal
None of these

Correct Answer Logic:

The ego operates on the reality principle, mediating between the id's primitive demands and external constraints using rational, logical thinking. The superego represents moral standards; the ego-ideal is part of the superego.

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Pakistan Affairs QUESTION #9033

Question 1357

Which is Pakistan's largest gas-fired power plant?

Uch power plant✔️
Malakand-Dargai power plant
Gomal power plant
Faisalabad Gas Turbine power plant

Correct Answer Logic:

Uch Power Plant is the largest gas-fired facility in Pakistan.

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Disaster Management QUESTION #6562

Question 1358

What makes gender-disaggregated data collection essential for effective DRR rather than just good practice?

International requirements
It reveals differential vulnerabilities, capacities, and needs that would otherwise remain invisible, enabling targeted and effective interventions✔️
Statistical completeness
Donor expectations

Correct Answer Logic:

Section 13.1 emphasizes gender-disaggregated data to identify specific vulnerabilities. Without disaggregated data, DRR interventions risk being designed for 'average' populations, missing critical gender-specific vulnerabilities (GBV risks, caregiving burdens, resource access) that require targeted responses.

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Education QUESTION #7574

Question 1359

The study of 'great books' and enduring works of literature is at the core of which philosophy?

Perennialism✔️
Essentialism
Progressivism
Reconstructionism

Correct Answer Logic:

Perennialism emphasizes timeless ideas and universal truths found in the 'Great Books' of Western civilization, believing these works contain enduring knowledge.

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Biology QUESTION #7241

Question 1360

The bacterium Clostridium botulinum that causes botulism is:

A facultative aerobe
An obligate aerobe
A facultative anaerobe
An obligate anaerobe✔️

Correct Answer Logic:

Clostridium botulinum is an obligate anaerobe — it can survive and grow only in the absence of oxygen. Oxygen is toxic to it. This is why botulism is associated with improperly sealed (anaerobic) canned foods where the bacterium produces its deadly neurotoxin.

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