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$e^{3z} = \sum_{n=0}^{\infty} \frac{(3z)^n}{n!} = \sum_{n=0}^{\infty} \frac{3^n z^n}{n!}$. 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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General Knowledge QUESTION #8595

Question 4

Which religion is considered the oldest in the world?

Judaism
Christianity
Buddhism
Hinduism✔️

Correct Answer Logic:

Hinduism has origins dating back thousands of years BCE.

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English Literature QUESTION #676

Question 5

"Beauty is truth, truth beauty" is a famous line from:

Ode to a Nightingale
Ode on a Grecian Urn✔️
To Autumn
Ode on Melancholy

Correct Answer Logic:

These are the concluding lines of John Keats' famous poem.

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Law QUESTION #9501

Question 6

The trial Court in a civil suit, after full trial, passes a judgment. The losing party B files an appeal. The appellate Court, without conducting a hearing on merits, reverses the trial Court's decree only because it disagrees with the trial Court's findings of fact, without identifying any specific perversity or misreading of evidence. Is this valid appellate exercise?

Yes; an appellate Court can freely re-appreciate evidence
No; an appellate Court can reverse only on questions of law
Yes; a first appeal is a rehearing on facts and law
No; while an appellate Court can re-appreciate evidence, reversal requires more than mere disagreement; the appellate Court must assign reasons for disagreeing with the trial Court's findings and identify how the evidence was misread or ignored✔️

Correct Answer Logic:

The CPC and settled principles of appellate jurisprudence require that a first appellate Court, while having jurisdiction to reassess evidence, must not substitute its own findings for those of the trial Court without adequate reasons. Reversal on facts requires the appellate Court to demonstrate perversity, misreading, or improper appreciation of evidence, not mere disagreement.

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Pakistan Affairs QUESTION #323

Question 7

A Supreme Court judge must have been a High Court judge for at least:

Five years✔️
Seven years
Nine years
Fifteen years

Correct Answer Logic:

According to the Constitution, five years of experience as a High Court judge is a prerequisite.

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Chemistry QUESTION #7131

Question 8

Identify the major product obtained when propene reacts with $HBr$ in the presence of organic peroxides.

$1$-bromopropane✔️
$2$-bromopropane
$1,2$-dibromopropane
$2$-bromoprop-1-ene

Correct Answer Logic:

While the addition of $HBr$ to propene normally follows Markovnikov's rule (yielding 2-bromopropane), the presence of peroxides triggers the Kharasch effect (Anti-Markovnikov addition). In this free-radical mechanism, the bromine atom attaches to the terminal carbon, resulting in $1$-bromopropane as the major product.

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Political Science QUESTION #6694

Question 9

The tenure of the US President is:

4 Years✔️
5 Years
6 Years
None of these

Correct Answer Logic:

The US President is elected for a four-year term and can serve a maximum of two terms.

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MCQs Section QUESTION #4839

Question 10

Pick the word nearly similar in meaning to "TOUCHSTONE"

Criterion✔️
Gold
Character
Characteristics

Correct Answer Logic:

A touchstone is a standard or principle by which something is judged or recognized. It originally referred to a stone used to test the purity of gold.

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General Knowledge QUESTION #8728

Question 11

'Miran Shah' is the main town of which FATA agency?

South Waziristan
North Waziristan✔️
Kurram Agency
Khyber Agency

Correct Answer Logic:

Miran Shah is the headquarters of North Waziristan.

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Mathematics QUESTION #6958

Question 12

Evaluate: $\displaystyle\lim_{x\to0}\dfrac{\sin^2 x}{\sqrt{2}-\sqrt{1+\cos x}}$

4✔️
$4\sqrt{2}$
$8\sqrt{2}$
8

Correct Answer Logic:

Rationalise the denominator by multiplying by $\dfrac{\sqrt{2}+\sqrt{1+\cos x}}{\sqrt{2}+\sqrt{1+\cos x}}$:

Denominator becomes $2-(1+\cos x)=1-\cos x$.

$\lim_{x\to0}\dfrac{\sin^2x(\sqrt{2}+\sqrt{1+\cos x})}{1-\cos x}$

Use $\dfrac{\sin^2x}{1-\cos x}=\dfrac{1-\cos^2x}{1-\cos x}=1+\cos x$:

$=\lim_{x\to0}(1+\cos x)(\sqrt{2}+\sqrt{1+\cos x})=(1+1)(\sqrt{2}+\sqrt{2})=2\cdot2\sqrt{2}=\mathbf{4\sqrt{2}}$

Wait: $2\times2\sqrt{2}=4\sqrt{2}$... but option A is 4. Let me recheck: $(2)(\sqrt{2}+\sqrt{2})=2\cdot2\sqrt{2}=4\sqrt{2}$. Answer: $4\sqrt{2}$ is not listed as option A (which is 4). The correct answer is $\mathbf{4\sqrt{2}}$ (index 1).

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Accounting & Finance QUESTION #6157

Question 13

What are the limitations of CVP analysis?

It assumes fixed costs will remain constant.
It cannot be used if multiple products are produced in a constant mix.
It ignores the possibility of semi-variable costs.

1, 2 and 3
1 and 2 only
1 and 3 only✔️
2 and 3 only

Correct Answer Logic:

Option C (1 and 3) is correct.

Statement 1 (True limitation): Fixed costs can change in steps in reality.
Statement 2 (False): CVP can be used with multiple products in a constant mix.
Statement 3 (True limitation): CVP ignores semi-variable costs, treating all costs as purely fixed or variable.

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English QUESTION #8436

Question 14

Identify the incorrectly spelled word:

Tournament
Omniient✔️
Government
Refreshment

Correct Answer Logic:

'Omniient' is misspelled; correct is 'Omniscient'.

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Civil Procedure QUESTION #3706

Question 15

In a diversity case, the federal court must apply a state law that requires a physical examination of the plaintiff. Federal Rule of Civil Procedure 35 also allows for physical examinations but has slightly different procedural requirements regarding notice. Which rule should the federal court follow?

The state law, because physical exams are 'outcome-determinative' under York.
The federal rule, because it is a valid exercise of the Rules Enabling Act and directly conflicts with state law.✔️
Neither; the court should create a 'federal common law' of examinations.
Both; the court must synthesize them to respect state sovereignty.

Correct Answer Logic:

Under Hanna v. Plumer, if a Federal Rule of Civil Procedure (FRCP) is valid and on point, it trumps conflicting state law, even if that state law is substantive in nature or outcome-determinative.

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