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Mean = Variance = $\lambda$
The distribution is always positively skewed for finite $\lambda$
The mgf is $M(t) = e^{\lambda(e^t - 1)}$
As $\lambda \to \infty$, the Poisson distribution approaches the t-distribution✔️

Correct Answer Logic:

The mean, variance, and mgf statements are all correct properties of the Poisson distribution. As $\lambda \to \infty$, the Poisson distribution approaches the NORMAL distribution (not the t-distribution), by the Central Limit Theorem. This is what makes statement (D) incorrect.

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Pakistan Affairs QUESTION #9090

Question 1231

Afghanistan is located on which border of Pakistan?

Northwest✔️
Southwest
North East
South East

Correct Answer Logic:

Afghanistan is to the northwest of Pakistan.

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Mathematics QUESTION #979

Question 1232

The sum of all values of $\theta\in[0,2\pi]$ satisfying $2\sin^2\theta=\cos 2\theta$ and $2\cos^2\theta=3\sin\theta$ is:

$4\pi$
$\dfrac{5\pi}{6}$
$\pi$✔️
$\dfrac{\pi}{2}$

Correct Answer Logic:

From $2\sin^2\theta=\cos2\theta=1-2\sin^2\theta \Rightarrow 4\sin^2\theta=1 \Rightarrow \sin\theta=\pm\frac{1}{2}$. From $2\cos^2\theta=3\sin\theta \Rightarrow 2(1-\sin^2\theta)=3\sin\theta \Rightarrow 2\sin^2\theta+3\sin\theta-2=0 \Rightarrow \sin\theta=\frac{1}{2}$ (taking positive root). So $\theta=\frac{\pi}{6}$ or $\frac{5\pi}{6}$. Sum$=\frac{\pi}{6}+\frac{5\pi}{6}=\pi$.

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Planning QUESTION #4999

Question 1233

What is the recommended minimum population threshold for supporting a secondary school in neighborhood planning?

2,000-3,000
5,000-7,000
10,000-12,000✔️
15,000-20,000

Correct Answer Logic:

Planning standards typically recommend 10,000-12,000 population to support one secondary school (approximately 800-1,200 students assuming school-age population is 8-10% of total), ensuring viable enrollment and efficient resource utilization.

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Logical Reasoning QUESTION #3945

Question 1234

Select the pair with a similar relationship to IMPLICATE : COMPLICATE

Vitality : Inevitable✔️
Empathy : Sympathy
Importune : Construct
Imply : Simplify

Correct Answer Logic:

3

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Accounting & Finance QUESTION #6182

Question 1235

In FM, why is 'Market Value' preferred over 'Historical Cost' for analysis?

Market value is easier to calculate
Historical cost is always higher✔️
Assets' values are determined by the cash flows they generate today, not past cost
Tax authorities require market value for all reports

Correct Answer Logic:

Lesson 03 explains the FM focus on market value and incremental cash flows to determine the true value of a company.

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General Knowledge QUESTION #4785

Question 1236

Silk Air is an airline based in which country?

Sri Lanka
Switzerland
Singapore✔️
Thailand

Correct Answer Logic:

Silk Air was a regional airline and a wholly owned subsidiary of Singapore Airlines, headquartered in Singapore. It was merged into Singapore Airlines in 2021.

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Chemistry QUESTION #431

Question 1237

__________ is used as catalyst in Haber's process for NH? gas manufacture.

Iron✔️
Carbon
Copper
Silver

Correct Answer Logic:

Iron is the catalyst in Haber process

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General Ability and Fire Fighting QUESTION #5627

Question 1238

Which of the following statements about Class D fires is TRUE?

They can be safely extinguished with water
They require wet chemical agents
They involve combustible metals and need specialized dry powder✔️
They are the same as Class B fires

Correct Answer Logic:

Class D fires involve combustible metals like magnesium and potassium. Many of these metals react violently with water

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General Knowledge QUESTION #8959

Question 1239

What does the term 'Intifada' mean?

Reconciliation
Uprising✔️
Offence
Negotiation

Correct Answer Logic:

Intifada means 'shaking off' or uprising in Arabic.

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Law QUESTION #9504

Question 1240

A sues B for damages arising from a road accident. A resides in Islamabad. The accident occurred in Peshawar. B resides in Lahore and carries on business in Quetta. A chooses to file the suit in the Lahore Civil Court. Can A validly institute the suit in Lahore?

Yes; under Section 19 CPC for a suit for compensation for wrong to the person, A may sue either where the wrong was done (Peshawar) or where B resides or carries on business (Lahore or Quetta); Lahore is a valid forum✔️
No; A must sue in Islamabad since A resides there
No; only Peshawar, where the accident occurred, is the proper forum
Yes; A can choose any Court in Pakistan

Correct Answer Logic:

Section 19 CPC provides that for suits for compensation for wrong to the person or moveable property, the plaintiff may institute the suit either where the wrong was done or where the defendant resides or carries on business. B resides in Lahore, making Lahore a valid forum at A's option.

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