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Maths QUESTION #4516

Question 4101

Simplify: $\frac{3^8}{3^5}$

$3^{40}$
$3^3$✔️
$3^{13}$
$1$

Correct Answer Logic:

Using law of exponents: $\frac{b^m}{b^n} = b^{m-n}$. So $\frac{3^8}{3^5} = 3^{8-5} = 3^3$

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Dairy Food Science and Technology QUESTION #5936

Question 4102

The purpose of 'aging' (tempering) cream at $8\text{–}13^{\circ}\text{C}$ before churning in butter production is to:

Increase the cream's water content
Promote partial crystallization of fat into stable polymorphic crystal forms ($\beta'$) to facilitate efficient churning and improve butter texture✔️
Lower the cream's viscosity for better separation
Allow lactose to ferment producing diacetyl

Correct Answer Logic:

Cream tempering involves temperature cycling to promote formation of stable $\beta'$ and $\beta$ polymorphic crystal forms of triglycerides. Properly crystallized fat churns efficiently and produces butter with good texture, spreadability, and body.

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Law QUESTION #9502

Question 4103

A plaintiff sues on a bond. The defendant pleads payment. The Court holds that payment has been proved and dismisses the suit. The plaintiff appeals. The appellate Court, without additional evidence, reverses the trial Court and decrees the suit. The defendant files a second appeal. Is the second appeal competent?

No; second appeals on questions of fact are generally not entertained
Yes; a second appeal lies only if the High Court is satisfied that the case involves a substantial question of law, such as improper appreciation of evidence to the point of legal error, or if the appellate Court reversed findings without lawful basis✔️
No; second appeals are never maintainable in money suits
Yes; any party aggrieved by an appellate decree can file a second appeal

Correct Answer Logic:

Section 100 CPC provides that a second appeal lies only on a substantial question of law. However, if the first appellate Court misapplied legal principles in appreciating evidence or reversed findings of fact without reasoning, that can itself constitute a substantial question of law. The second appeal is competent if such a question is involved.

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Law QUESTION #9518

Question 4104

A interpleader suit is filed by a stakeholder who holds money to which both B and C lay claims. B argues that only B and the stakeholder have a dispute, not B and C. Is B's argument a ground to reject the interpleader suit?

No; but only the High Court can entertain interpleader suits
Yes; an interpleader suit requires a direct dispute between B and C
No; Section 88 CPC requires only that the stakeholder holds money or property and two or more persons make adverse claims to it; the stakeholder's own interest is in having the Court determine the competing claims so as to be protected from multiple liabilities; a dispute between B and C inter se is not required✔️
Yes; interpleader suits are only for moveable property

Correct Answer Logic:

Section 88 CPC provides that where two or more persons claim adversely to one another the same debt, sum of money, or other property from a person who has no interest in the matter other than the charges, an interpleader suit may be filed. The essence is adverse claims against the stakeholder, not necessarily a direct dispute between the claimants inter se.

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Accounting & Finance QUESTION #9651

Question 4105

In an Independent Branch reconciliation, which of the following is a reason for the difference between the Head Office Account balance in branch books and the Branch Account balance in HO books?

Different depreciation rates applied
Goods in transit from HO to branch✔️
Different accounting policies
Year-end accruals at the branch

Correct Answer Logic:

The two balances may differ due to: (1) cash in transit, (2) goods in transit, and (3) mistakes committed by either party. Goods dispatched by HO but not yet received at branch create a timing difference, causing a temporary mismatch in both parties' books.

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Ability / HR / Governance / Special Education QUESTION #1798

Question 4106

Rule 42(b) on 'request for quotations' requires a minimum of how many quotations, and from which category of firms?

Two quotations from any registered firms
Three quotations from GST registered firms, original equipment manufacturers or authorized dealers✔️
Four quotations from SECP registered companies
Three quotations from any suppliers regardless of registration

Correct Answer Logic:

Rule 42(b)(i) and (iii) together require that at least three quotations be obtained from GST registered firms, original equipment manufacturers, or authorized dealers when procurement value exceeds PKR 100,000 but does not exceed PKR 500,000.

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Maths QUESTION #7652

Question 4107

Three years ago, the age of a father was three times the age of his son. If the sum of their current ages is 70 years, what is the present age of the son?

$20$ years
$25$ years
$21$ years
None of these✔️

Correct Answer Logic:

Let current age of son = $x$ and father = $y$. Given: $x + y = 70$. Three years ago: $(y-3) = 3(x-3)$. Expanding: $y - 3 = 3x - 9$, so $y = 3x - 6$. Substituting in first equation: $x + 3x - 6 = 70$, giving $4x = 76$, so $x = 19$ years. The answer should be 19 years, but this doesn't match the options, suggesting 'None of these' is correct.

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Physics QUESTION #7065

Question 4108

Consider an n-type semiconductor where the electron density is $10^{19} \text{ m}^{-3}$ and the electron mobility is $1.6 \text{ m}^2/(\text{V}\cdot\text{s})$. If we neglect the contribution of holes, what is the approximate resistivity of this semiconductor?

$2 \ \Omega\text{m}$
$4 \ \Omega\text{m}$
$0.4 \ \Omega\text{m}$✔️
$0.2 \ \Omega\text{m}$

Correct Answer Logic:

Resistivity ($\rho$) is the reciprocal of conductivity ($\sigma$).

$\sigma = ne\mu_e$

Given: $n = 10^{19} \text{ m}^{-3}$, $\mu_e = 1.6 \text{ m}^2/\text{Vs}$, and $e = 1.6 \times 10^{-19} \text{ C}$.

$\sigma = 10^{19} \times (1.6 \times 10^{-19}) \times 1.6 = 1.6 \times 1.6 = 2.56 \ \Omega^{-1}\text{m}^{-1}$.

$\rho = \frac{1}{\sigma} = \frac{1}{2.56} \approx 0.39 \ \Omega\text{m}$.

The closest value provided is $0.4 \ \Omega\text{m}$.

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Paper-I (Anatomy/Physiology and Biochemistry/Microbiology) QUESTION #3133

Question 4109

Which cranial nerve is responsible for the sense of smell?

Optic nerve (II)
Oculomotor nerve (III)
Olfactory nerve (I)✔️
Vagus nerve (X)

Correct Answer Logic:

Cranial nerve I is dedicated to olfaction.

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Mathematics QUESTION #6963

Question 4110

Find all $x$ satisfying $(\cot^{-1}x)^2 - 7(\cot^{-1}x)+10>0$.

$(-\infty,\cot5)\cup(\cot4,\cot2)$
$(\cot2,\infty)$
$(-\infty,\cot5)\cup(\cot2,\infty)$✔️
$(\cot5,\cot4)$

Correct Answer Logic:

Let $u=\cot^{-1}x$. Solve $u^2-7u+10>0$, i.e., $(u-2)(u-5)>0$.

This gives $u<2$ or $u>5$.

Since $\cot^{-1}x$ is a decreasing function with range $(0,\pi)$:

$u<2 \Rightarrow \cot^{-1}x<2 \Rightarrow x>\cot2$ (decreasing function reverses inequality)
$u>5 \Rightarrow \cot^{-1}x>5 \Rightarrow x<\cot5$

Solution: $x\in(-\infty,\cot5)\cup(\cot2,\infty)$

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Pakistan Affairs QUESTION #4678

Question 4111

The Diamer-Bhasha Dam in Pakistan has been planned on which river?

Jhelum
Chenab
Indus✔️
Kabul

Correct Answer Logic:

The Diamer-Bhasha Dam is a gravity dam being constructed on the Indus River in the Gilgit-Baltistan region of Pakistan. It will be one of the largest dams in the world when completed.

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Paper-I (Anatomy/Physiology and Biochemistry/Microbiology) QUESTION #3136

Question 4112

The 'Myelin Sheath' serves to:

Protect the neuron from infection
Slow down nerve impulses
Increase the speed of nerve impulse transmission✔️
Produce neurotransmitters

Correct Answer Logic:

Myelin acts as insulation for rapid signal 'jumping' (saltatory conduction).

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Dairy Food Science and Technology QUESTION #5897

Question 4113

In CIP (Cleaning-In-Place) of dairy equipment, the correct sequence of steps is:

Hot water rinse $\rightarrow$ caustic wash $\rightarrow$ acid wash $\rightarrow$ sanitizer $\rightarrow$ final rinse
Pre-rinse (warm water $35\text{–}40^{\circ}\text{C}$) $\rightarrow$ caustic wash (NaOH $1\text{–}2\%$, $70\text{–}80^{\circ}\text{C}$) $\rightarrow$ intermediate rinse $\rightarrow$ acid wash $\rightarrow$ final rinse $\rightarrow$ sanitizer✔️
Acid wash $\rightarrow$ caustic wash $\rightarrow$ pre-rinse $\rightarrow$ sanitizer
Sanitizer $\rightarrow$ caustic wash $\rightarrow$ acid wash $\rightarrow$ water rinse

Correct Answer Logic:

Standard CIP sequence: (1) Pre-rinse with warm water ($35\text{–}40^{\circ}\text{C}$); (2) Alkaline wash (NaOH $1\text{–}2\%$ at $70\text{–}80^{\circ}\text{C}$) to remove proteins and fats; (3) Intermediate water rinse; (4) Acid wash ($\text{HNO}_3$ or $\text{H}_3\text{PO}_4$ $0.5\text{–}1\%$) to remove milkstone; (5) Final water rinse; (6) Sanitizer before use.

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Library Sciences QUESTION #1566

Question 4114

An Integrated Library System (ILS) typically includes which set of core functional modules?

Acquisitions, Cataloguing, Circulation, Serials Management, and OPAC✔️
Acquisitions, Binding, Photocopying, Printing, and Accounting
Cataloguing, Housekeeping, Archiving, Scanning, and Emailing
Circulation, Website Design, Social Media, Budgeting, and Staffing

Correct Answer Logic:

A standard ILS integrates core library functions into a unified system: Acquisitions (ordering and receiving), Cataloguing (bibliographic records), Circulation (loans and returns), Serials Management (periodicals), and an OPAC (Online Public Access Catalogue) for user searching.

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Mathematics QUESTION #4124

Question 4115

The polar curve $r = 2\cos(\theta)$ represents which conic section?

Circle with center at origin, radius $2$
Circle with center at $(1, 0)$, radius $1$✔️
Circle with center at $(0, 1)$, radius $1$
Ellipse with semi-major axis $2$

Correct Answer Logic:

$r = 2\cos(\theta) \Rightarrow r^2 = 2r\cos(\theta) \Rightarrow x^2 + y^2 = 2x \Rightarrow (x-1)^2 + y^2 = 1$. Circle center $(1,0)$, radius $1$.

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Education QUESTION #6737

Question 4116

When students work collaboratively and construct knowledge through social interaction, this reflects principles of:

Behaviorism
Social constructivism✔️
Direct instruction
Individual learning theory

Correct Answer Logic:

Social constructivism (Vygotsky) emphasizes that learning occurs through social interaction and collaborative knowledge construction. Understanding develops through dialogue, shared activity, and cultural tools—not just individual cognition.

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