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Mathematics QUESTION #4129

Question 1941

Find the Maclaurin series for $f(z) = z^2 e^{3z}$. What is the coefficient of $z^5$?

$\frac{9}{2}$✔️
$\frac{27}{40}$
$\frac{81}{40}$
$\frac{27}{8}$

Correct Answer Logic:

$e^{3z} = \sum_{n=0}^{\infty} \frac{(3z)^n}{n!} = \sum_{n=0}^{\infty} \frac{3^n z^n}{n!}$. So $z^2 e^{3z} = \sum_{n=0}^{\infty} \frac{3^n z^{n+2}}{n!}$. For $z^5$: $n + 2 = 5$, so $n = 3$. Coefficient: $\frac{3^3}{3!} = \frac{27}{6} = \frac{9}{2}$.

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Home Economics QUESTION #6268

Question 1942

Which food preservation method uses 'Ionizing Radiation' to destroy microorganisms without heating?

Food Irradiation✔️
Lyophilization
Pasteurization
Appertization

Correct Answer Logic:

Food irradiation (cold pasteurization) uses gamma rays or X-rays to extend shelf life and kill pests.

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General Knowledge QUESTION #177

Question 1943

Saudi Arabia re-established diplomatic relations with Iran on:

Dec 10, 2023
May 10, 2023
March 10, 2023✔️
None of these

Correct Answer Logic:

The China-brokered deal was announced on March 10, 2023.

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Reading and Writing (Module-1) QUESTION #5366

Question 1944

Julia Alvarez's 1994 novel In the Time of the Butterflies, a fictionalized account of the lives of the Mirabal ______ can serve as a starting point for those wanting to explore how the rule of dictator Rafael Trujillo has been represented in Dominican American literature. Which choice completes the text so that it conforms to the conventions of Standard English?

sisters, and
sisters and
sisters,✔️
sisters

Correct Answer Logic:

A comma is needed after 'sisters' to close the appositive phrase that began after 'Butterflies.'

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Physics QUESTION #7079

Question 1945

Determine the pressure required at the ends of a steel wire (length $10\text{ cm}$) to maintain a constant length when the temperature is increased by $100^{\circ}\text{C}$. (Given: Steel Young's modulus $Y = 2 \times 10^{11}\text{ Nm}^{-2}$ and coefficient of thermal expansion $\alpha = 1.1 \times 10^{-5}\text{ K}^{-1}$)

$2.2 \times 10^{7}\text{ Pa}$
$2.2 \times 10^{6}\text{ Pa}$
$2.2 \times 10^{8}\text{ Pa}$✔️
$2.2 \times 10^{9}\text{ Pa}$

Correct Answer Logic:

The thermal stress required to keep the length constant is given by the formula:

$\text{Stress} = Y \alpha \Delta T$
Substituting the values: $\text{Stress} = (2 \times 10^{11}) \times (1.1 \times 10^{-5}) \times 100$
$\text{Stress} = 2.2 \times 10^{8}\text{ Pa}$

Pressure is equivalent to the stress applied at the ends.

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Constitutional Law QUESTION #5837

Question 1946

Congress passes a law that prevents the Supreme Court from hearing any case that challenges the 'Don't Ask, Don't Tell' policy for the military. Is this law valid?

Yes, under the 'Exceptions and Regulations' clause of Article III.✔️
Yes, because it involves a 'political question' regarding military affairs.
No, because Congress cannot strip the court of jurisdiction over cases already in progress.
No, because it violates the due process rights of litigants to have a neutral forum.

Correct Answer Logic:

This is another application of the 'Exceptions Clause' (Article III, Section 2). Congress has broad authority to limit the appellate jurisdiction of the Supreme Court, though it cannot use this power to violate other constitutional provisions (like the Bill of Rights).

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Physics QUESTION #7023

Question 1947

Unpolarized light passes through polarizer A, then B, resulting in half the initial intensity. If a third polarizer C is placed between them, the final intensity drops to $\frac{1}{8}$ of the original. What is the angle between polarizer A and C?

$45^\circ$✔️
$60^\circ$
$0^\circ$
$30^\circ$

Correct Answer Logic:

Initial intensity $I$. After A, $I_A = I/2$. Since $I_B$ is also $I/2$, axes of A and B are parallel ($\theta_{AB} = 0$).

Insert C at angle $\phi$ to A. Then angle between C and B is also $\phi$.

Final intensity $I' = I_A \cos^2 \phi \cos^2 \phi = \frac{I}{2} \cos^4 \phi$.

Given $\frac{I}{2} \cos^4 \phi = \frac{I}{8} \implies \cos^4 \phi = \frac{1}{4} \implies \cos^2 \phi = \frac{1}{2}$.

Thus, $\cos \phi = \frac{1}{\sqrt{2}} \implies \phi = 45^\circ$.

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Pakistan Affairs QUESTION #152

Question 1948

From whom did Gandhi draw inspiration regarding the village as the ideal unit for "loving thy neighbour"?

Rabindranath Tagore
Leo Tolstoy
John Ruskin✔️
None of these

Correct Answer Logic:

Gandhi was deeply influenced by Ruskin's 'Unto This Last' regarding agrarian and community living.

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Physics and Math QUESTION #78

Question 1949

Asim is now three times as old as Irfan. After 10 years, Asim will be twice as old as Irfan. Asim’s at this time is:

40
30✔️
20
10

Correct Answer Logic:

Asim’s current age = 30 years.

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General Abilities QUESTION #7984

Question 1950

What is the set of all prime numbers from 60 to 80?

{61}
{61, 41}
{61, 71}
{61, 67, 71}✔️

Correct Answer Logic:

Prime numbers between 60 and 80:

61 ✓ (prime)
67 ✓ (prime)
71 ✓ (prime)
73 ✓ (prime)

The option listing {61, 67, 71} is the closest correct subset. (73 should also be included but is not listed as a distinct option.)

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Physics QUESTION #7868

Question 1951

Speed of sound in ideal gas does NOT depend on:

Density
Moisture
Pressure✔️
Temperature

Correct Answer Logic:

For ideal gas, v = √(γRT/M). Pressure has no effect at constant temperature; moisture slightly affects density but the question says ideal gas: strictly, pressure independent.

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Egnlish QUESTION #713

Question 1952

Which character in "Hamlet" says, "To thine own self be true"?

Hamlet
Polonius✔️
Horatio
Laertes

Correct Answer Logic:

Polonius gives this advice to his son Laertes before he leaves for France.

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Ability / HR / Governance / Special Education QUESTION #1802

Question 1953

Under the two-stage bidding procedure in Rule 36(c), the minimum time allowed to bidders for national competitive bidding between first and second stage submissions is:

Seven days
Ten days
Fifteen days✔️
Thirty days

Correct Answer Logic:

Rule 36(c)(iv) provides that sufficient time must be allowed to bidders to prepare revised bids, and the proviso specifies this allowance shall not be less than fifteen days in the case of national competitive bidding and thirty days for international competitive bidding.

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Dairy Food Science and Technology QUESTION #5882

Question 1954

In cheese making, coagulation of milk by rennet involves:

Reduction of pH by lactic acid bacteria
Proteolytic cleavage of $\kappa$-casein by chymosin at the $\text{Phe}_{105}\text{–Met}_{106}$ bond✔️
Calcium precipitation of whey proteins
Denaturation of $\beta$-lactoglobulin by heat

Correct Answer Logic:

Chymosin specifically cleaves $\kappa$-casein at the $\text{Phe}_{105}\text{–Met}_{106}$ peptide bond, releasing the hydrophilic glycomacropeptide (GMP) into whey. This removes steric stabilization of casein micelles, allowing calcium-mediated aggregation and gel formation.

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Urdu QUESTION #5076

Question 1955

بابائے اردو کس شخصیت کو کہا جاتا ہے؟

مولوی عبدالحق✔️
مولانا ظفر علی خان
سر سید احمد خان
ان میں سے کوئی نہیں

Correct Answer Logic:

مولوی عبدالحق کو 'بابائے اردو' کہا جاتا ہے کیونکہ انہوں نے اردو زبان و ادب کی بے مثال خدمت کی۔

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Accounting & Finance QUESTION #6149

Question 1956

Total cost data: 600 units = $4,200; 800 units = $5,200. What is the fixed cost per unit at each level?

Option	For 600 units ($)	For 800 units ($)
A	2.00	1.50
B	2.00	2.00
C	5.00	5.00
D	6.50	7.00

Option A✔️
Option B
Option C
Option D

Correct Answer Logic:

Option A is correct.

Variable cost per unit = ($5,200 − $4,200) ÷ 200 = $5

Fixed costs = $4,200 − (600 × $5) = $1,200

At 600 units: $1,200 ÷ 600 = $2.00; At 800 units: $1,200 ÷ 800 = $1.50

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Paper-II (Pharmacognosy and Pharmaceutics-I) QUESTION #2989

Question 1957

Calculate the displacement value of a drug if $10$ suppositories contain $2\text{ g}$ of drug and weigh $11\text{ g}$ (base density is $1\text{ g/ml}$).

$1.0$
$2.0$✔️
$0.5$
$1.5$

Correct Answer Logic:

Disp. Value $=$ (Weight of drug) / (Weight of base displaced). Calculated as $2 / (10-9) = 2$.

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Biology Zoology Botany QUESTION #1337

Question 1958

__________ is the lag between the creation of the habitat fragment and the decrease in species richness to the equilibrium level.

Fragment destruction
Relaxation time✔️
Retention time
None of these

Correct Answer Logic:

Relaxation time (also called extinction debt) is the time lag between habitat fragmentation and the eventual decline of species richness to the new equilibrium level. After a habitat is fragmented, species do not go extinct immediately — the population decline takes time, creating a period where more species exist than the fragment can sustain long-term.

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CISA QUESTION #1728

Question 1959

On what basis should an IS auditor formulate and communicate a final audit opinion?

Based on the objectives stated and verbal representations made by management.
Derived from an understanding of the outcome that management is expecting.
Based on the specifications and directives provided by the audit committee.
Grounded in the evidence collected and the results of testing performed during the audit.✔️

Correct Answer Logic:

The cornerstone of audit integrity is that the auditor's final opinion must be grounded in independently gathered evidence and the results of testing — not in management's assertions, desired outcomes, or committee directives. The auditor's role is to professionally challenge management's claims and render an evidence-based independent judgment. Any opinion not rooted in objective evidence and testing lacks credibility and professional validity.

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Disaster Management QUESTION #6547

Question 1960

What makes the localization of DRR more effective than purely top-down approaches?

It's cheaper
Local actors have contextual knowledge, community trust, and ability to tailor solutions to specific vulnerabilities and capacities✔️
It requires less coordination
It reduces government responsibility

Correct Answer Logic:

Section 13.4 emphasizes that local actors (communities, district authorities, CBOs) understand local risks, have community trust, and can implement context-specific solutions. Effective DRR combines local knowledge and ownership with technical and financial support from higher levels.

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