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Mathematics QUESTION #969

Let $f(x) = \displaystyle\int_0^{x^2} \dfrac{t^2-8t+15}{e^t}\,dt,\ x \in \mathbb{R}$. Then the numbers of local maximum and local minimum points of $f$, respectively, are:

2 and 3✔️
2 and 2
3 and 2
1 and 3

Correct Answer Logic:

$f'(x)=\frac{x^4-8x^2+15}{e^{x^2}}\cdot 2x = \frac{2x(x^2-3)(x^2-5)}{e^{x^2}}$. Roots: $x=0, \pm\sqrt{3}, \pm\sqrt{5}$. Analyzing sign changes: 2 local maxima (at $\pm\sqrt{3}$) wait — checking signs carefully gives 2 local maxima and 3 local minima.

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Pakistan Affairs QUESTION #133

Question 4542

The third Khilafat conference was held in 1921 in:

Dhaka
Karachi✔️
Istanbul
Lucknow

Correct Answer Logic:

The Karachi Khilafat Conference of July 1921 was a significant turning point in the movement.

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CISA QUESTION #1721

Question 4543

When considering who should be responsible for issuing and enforcing organisational policies, which of the following options reflects best practice?

Policies should be developed from the bottom up and elevated to the department manager for sign-off.
Auditors should draft policies in line with standards, which are then authorised by senior management.
Policies may be signed and enforced by any level of management deemed appropriate.
Policies must be signed and enforced by the most senior level of management to ensure organisation-wide compliance.✔️

Correct Answer Logic:

Policies derive their authority and enforceability from the level at which they are issued. For a policy to command compliance across the entire organisation, it must originate from — and be visibly backed by — the highest level of management. It is management's responsibility, not the auditor's, to design, implement, and enforce internal controls and governance policies.

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English QUESTION #2733

Question 4544

Which sentence is in the PASSIVE VOICE?

She cleaned the room.
He is writing a letter.
The book was written by him.✔️
They will finish the work.

Correct Answer Logic:

Passive voice uses 'be + past participle'. 'The book was written by him' has 'was written' (was + past participle)

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Mechanical Engineering QUESTION #2470

Question 4545

A helical compression spring has $N_a$ active coils, mean coil diameter $D$, wire diameter $d$, and shear modulus $G$. The spring stiffness (spring rate) $k$ is:

$k = \frac{Gd^4}{8D^3 N_a}$✔️
$k = \frac{Gd^3}{8D^4 N_a}$
$k = \frac{8FD^3 N_a}{Gd^4}$
$k = \frac{Gd^4}{8D^3}$

Correct Answer Logic:

The spring rate: $k=F/\delta=Gd^4/(8D^3N_a)$. Note that $k \propto d^4$ (strong wire diameter dependence) and $k \propto 1/N_a$ (more coils = softer spring).

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Paper-I (Anatomy/Physiology and Biochemistry/Microbiology) QUESTION #3376

Question 4546

Which disaccharide is composed of one molecule of 'Glucose' and one molecule of 'Fructose'?

Maltose
Lactose
Sucrose✔️
Cellulose

Correct Answer Logic:

Sucrose is common table sugar.

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General Ability and Fire Fighting QUESTION #5626

Question 4547

Which firefighting method would be MOST appropriate for a small cooking oil fire on a stove?

Applying water directly to the fire
Covering the pan with a lid to smother it✔️
Using a CO2 extinguisher
Applying dry powder

Correct Answer Logic:

Covering the pan with a lid removes oxygen (smothering)

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Paper-I (Anatomy/Physiology and Biochemistry/Microbiology) QUESTION #3292

Question 4548

Which microorganism is primarily used in the industrial production of 'Penicillin'?

*Saccharomyces cerevisiae*
*Penicillium chrysogenum*✔️
*Bacillus subtilis*
*Escherichia coli*

Correct Answer Logic:

This fungus was discovered by Fleming and later mass-produced for antibiotic therapy.

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Commerce QUESTION #1215

Question 4549

Internal check is carried on by:

Staff specially appointed for the purpose
Internal auditor
Supervisor of the staff
Members of the staff✔️

Correct Answer Logic:

Internal check is a system where the accounting and other operations of a business are so organized that the work of one member of staff is automatically checked by another member in the normal course of their duties. It is carried out by members of the staff themselves as part of their routine work — not by a separately appointed person.

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Mathematics QUESTION #4143

Question 4550

For uniform circular motion with speed $V$ and radius $R$, what is the normal component of acceleration?

$\frac{V}{R}$
$\frac{V^2}{R}$✔️
$\frac{dV}{dt}$
$0$

Correct Answer Logic:

Normal (centripetal) acceleration $a_n = \frac{V^2}{R}$ directed toward the center of curvature.

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Pakistan Affairs QUESTION #287

Question 4551

The Muslim rulers of Delhi in the Pre-Mughal era were called Sultans as they were bound to:

Avoid further expansion
Nominate their successors
Seek recognition from the Caliph after acquiring power✔️
Wage Jihad against the infidels

Correct Answer Logic:

Legally, a Sultan was a representative of the Abbasid Caliph and sought a 'Manshur' (investiture).+1

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English QUESTION #2689

Question 4552

Which modal expresses a 'polite request'?

Must
Could✔️
Should
Shall

Correct Answer Logic:

'Could' is used for making polite requests or seeking permission.

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City and Regional Planning QUESTION #4921

Question 4553

What is the main principle behind Transit-Oriented Development (TOD)?

Maximizing parking facilities
Concentrating development around transit stations✔️
Promoting private vehicle use
Decentralizing urban activities

Correct Answer Logic:

TOD focuses on creating compact, mixed-use development concentrated around public transit stations to reduce car dependency and promote sustainable transportation.

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Mathematics QUESTION #4100

Question 4554

Using partial fractions $\dfrac{5Z-2}{Z(Z-1)}=\dfrac{2}{Z}+\dfrac{3}{Z-1}$, the value of $\displaystyle\oint_{|Z|=2}\dfrac{5Z-2}{Z(Z-1)}\,dZ$ by the Residue Theorem is:

$2\pi i$
$4\pi i$
$10\pi i$✔️
$6\pi i$

Correct Answer Logic:

Both poles $Z=0$ (residue $2$) and $Z=1$ (residue $3$) lie inside $|Z|=2$. By Cauchy's Residue Theorem: $\oint = 2\pi i(\text{Res}_{Z=0}+\text{Res}_{Z=1})=2\pi i(2+3)=10\pi i$.

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Chemistry QUESTION #790

Question 4555

Molarity of heavy water $(\text{D}_2\text{O})$:

55.5 mol dm$^{-3}$
60.5 mol dm$^{-3}$
40.5 mol dm$^{-3}$
50.5 mol dm$^{-3}$✔️

Correct Answer Logic:

Molarity of heavy water $= \dfrac{\text{density} \times 1000}{\text{molar mass}} = \dfrac{1.105 \times 1000}{20} \approx 55.5$ mol dm$^{-3}$. Note: The paper marks 50.5 but the accepted value is ~55.5.

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Urdu QUESTION #5056

Question 4556

ڈرامہ کس زبان کا لفظ ہے؟

یونانی✔️
لاطینی
فارسی
فرانسیسی

Correct Answer Logic:

ڈرامہ یونانی لفظ 'Drao' سے نکلا ہے جس کے معنی عمل یا کام کرنا کے ہیں۔

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Biology Zoology Botany QUESTION #1345

Question 4557

__________ is an important intestinal fluke of large animals.

Fasciola hepatica
Nanophyteus✔️
Schistosoma
None of these

Correct Answer Logic:

Nanophyetus salmincola is a small intestinal fluke that parasitizes fish-eating mammals and is associated with salmon poisoning disease. However, among the common intestinal flukes of large animals (cattle, sheep), Fasciolopsis buski is the classic intestinal fluke. Among the given options, Nanophyteus is listed as an intestinal fluke. Fasciola hepatica is a liver fluke, and Schistosoma is a blood fluke.

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Statistics QUESTION #1974

Question 4558

In an experimental study, the experimental error mainly arises from which source?

Mistakes made by the experimenter
Uncontrolled extraneous (external) factors✔️
Differences in treatment effects
All of the above

Correct Answer Logic:

Experimental error primarily results from extraneous (nuisance) factors not controlled in the experiment. It represents unexplained variability beyond the treatment effects.

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Physics QUESTION #1056

Question 4559

A photon and electron (mass $m$) have same energy $E$. Ratio $\lambda_{photon}/\lambda_{electron}$ is ($c$ = speed of light):

$c\sqrt{\dfrac{2m}{E}}$✔️
$\dfrac{1}{c}\sqrt{\dfrac{E}{2m}}$
$\sqrt{\dfrac{E}{2m}}$
$c\sqrt{2mE}$

Correct Answer Logic:

Photon: $\lambda_{ph}=\frac{hc}{E}$. Electron (non-relativistic): $\lambda_{el}=\frac{h}{\sqrt{2mE}}$. Ratio: $\frac{\lambda_{ph}}{\lambda_{el}}=\frac{hc}{E}\cdot\frac{\sqrt{2mE}}{h}=\frac{c\sqrt{2mE}}{E}=c\sqrt{\frac{2m}{E}}$.

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Paper-I (Anatomy/Physiology and Biochemistry/Microbiology) QUESTION #3291

Question 4560

'Fermentation' is a metabolic process that produces energy (ATP) in the:

Presence of high oxygen
Absence of oxygen (Anaerobic)✔️
Presence of sunlight
Presence of antibiotics

Correct Answer Logic:

Fermentation allows cells to regenerate $NAD^+$ for glycolysis without an electron transport chain.

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