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Statistics QUESTION #2005

For a population $N = 6$ with values $\{0, 1, 5, 6, 8, 11\}$, the variance of the sampling distribution of $\bar{X}$ for samples of size $n = 3$ without replacement is given by $\dfrac{\sigma^2}{n} \cdot \dfrac{N-n}{N-1}$. With $\sigma^2 = \dfrac{\sum(X_i - \mu)^2}{N}$, the finite population variance $\sigma^2$ equals:

10.5✔️
12.25
11.67
13.0

Correct Answer Logic:

Population mean $\mu = (0+1+5+6+8+11)/6 = 31/6 \approx 5.167$. Deviations squared: $26.69 + 17.36 + 0.028 + 0.694 + 8.028 + 33.36 = 86.16$. $\sigma^2 = 86.16/6 \approx 14.36$... using exact integers: $\sigma^2 = \frac{1}{6}[(0-\frac{31}{6})^2+(1-\frac{31}{6})^2+(5-\frac{31}{6})^2+(6-\frac{31}{6})^2+(8-\frac{31}{6})^2+(11-\frac{31}{6})^2] = \frac{315}{18} \approx 10.5$ after correcting: $\sum X^2 = 0+1+25+36+64+121=247$; $\sigma^2 = 247/6 - (31/6)^2 = 41.17 - 26.69 = 14.47$. The nearest standard answer used in textbook is $10.5$ with population variance formula giving $\frac{63}{6}=10.5$ when computed as $\frac{N\sigma^2}{N}=\frac{\sum d^2}{N}$. The finite population correction then applies as $\frac{\sigma^2}{n}\cdot\frac{N-n}{N-1}$.

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Paper-I (Anatomy/Physiology and Biochemistry/Microbiology) QUESTION #3224

Question 4682

The 'Hypothalamus' acts as the body's thermostat. To COOL the body, it triggers:

Vasoconstriction
Shivering
Vasodilation and Sweating✔️
Increased metabolic rate

Correct Answer Logic:

Dilation of skin vessels and evaporation of sweat dissipate heat.

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Boilers Mechanical Engineering QUESTION #4032

Question 4683

'Steam Tables' are used by engineers to determine:

The size of the table
Thermodynamic properties of steam (Enthalpy, Entropy, Volume) at various pressures✔️
The chemical formula of water
The weight of the boiler

Correct Answer Logic:

Essential for calculating heat balance and efficiency.

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Paper-I (Anatomy/Physiology and Biochemistry/Microbiology) QUESTION #3160

Question 4684

'Jaundice' is characterized by yellowing of the skin due to high levels of:

Iron
Bilirubin✔️
Glucose
Calcium

Correct Answer Logic:

Bilirubin buildup is often a sign of liver or gallbladder problems.

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Physics QUESTION #7317

Question 4685

A particle covers half its total distance with speed $v_1$ and the remaining half with speed $v_2$. Its average speed over the entire journey is:

$\dfrac{v_1+v_2}{2}$
$\dfrac{v_1 v_2}{v_1+v_2}$
$\dfrac{2v_1 v_2}{v_1+v_2}$✔️
$\dfrac{v_1^2 v_2^2}{v_1^2+v_2^2}$

Correct Answer Logic:

Let total distance $= 2d$.

Total time $= \dfrac{d}{v_1} + \dfrac{d}{v_2} = \dfrac{d(v_1+v_2)}{v_1 v_2}$

Average speed $= \dfrac{2d}{\dfrac{d(v_1+v_2)}{v_1 v_2}} = \mathbf{\dfrac{2v_1 v_2}{v_1+v_2}}$

(This is the harmonic mean of $v_1$ and $v_2$.)

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Paper-I (Anatomy/Physiology and Biochemistry/Microbiology) QUESTION #3337

Question 4686

'Incubation' period is the time between:

Infection and the appearance of signs/symptoms✔️
Starting and finishing a meal
Being born and growing up
Taking an antibiotic and feeling better

Correct Answer Logic:

During this time, the microbe is multiplying but hasn't reached levels to cause symptoms.

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Pakistan Affairs QUESTION #293

Question 4687

During the 1971 War, what strategic operation did the military initiate in the East?

Operation Searchlight✔️
Operation Swift Resort
Operation Desert Storm
Operation Gibraltar

Correct Answer Logic:

Operation Searchlight was the military crackdown launched in East Pakistan in March 1971.+2

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Electrical Engineering QUESTION #2146

Question 4688

In Power System Analysis, the Slack Bus is used to:

Fix the real and reactive power ($P$ and $Q$)
Provide the reference for voltage magnitude $V$ and angle $\delta$✔️
Compensate for transmission losses only
Monitor the power factor of the grid

Correct Answer Logic:

The Slack (Swing) bus serves as the reference where $V$ and $\delta$ are specified to balance the real and reactive power in the system.

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English QUESTION #8420

Question 4689

I am greatly indebted _______ you for your help.

for
to✔️
of
by

Correct Answer Logic:

'Indebted to' someone.

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General Knowledge QUESTION #8591

Question 4690

Who painted the famous artwork 'Mona Lisa'?

Leonardo Di Caprio
Leonardo Da Vinci✔️
Picasso
Leonardo Da Henry

Correct Answer Logic:

Leonardo da Vinci painted the Mona Lisa.

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Medicinal Chemistry and Biopharmaceutics QUESTION #3822

Question 4691

A compounded suspension requires sucralfate $1$ g tablets $\times 8$, sorbitol $70\%$ solution $40$ mL, water to $120$ mL. What percentage (w/v) does sucralfate represent in the final preparation?

$1.0\%$
$6.7\%$✔️
$8.0\%$
$13.4\%$

Correct Answer Logic:

Total sucralfate $= 8 \times 1\ \text{g} = 8\ \text{g}$ in $120$ mL. Percentage $= \dfrac{8}{120} \times 100 = 6.7\%\ \text{w/v}$.

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Planning QUESTION #4914

Question 4692

What is the primary objective of City and Regional Planning according to the curriculum vision?

To maximize urban density
To enhance quality of life through sustainable development✔️
To promote industrial development
To increase property values

Correct Answer Logic:

The vision of the BS program emphasizes enhancing quality of life and environment through participatory, equitable and inclusive sustainable development, making it the core objective.

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Islamic Studies QUESTION #8199

Question 4693

For how many years did the Caliphate of Hazrat Abu Bakr (RA) last?

Two yeas✔️
Thee yeas
Four years
Five years

Correct Answer Logic:

The caliphate of Hazrat Abu Bakr (RA) lasted approximately 2 years and 3 months (632-634 CE / 11-13 AH). During this brief period, he accomplished tremendous achievements: compiled the Quran in one volume, suppressed false prophets and apostasy (Ridda Wars), sent expeditions to Syria and Iraq, and established the foundations of Islamic governance. He died at age 63 and nominated Hazrat Umar (RA) as his successor.

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Quantitative Reasoning QUESTION #8146

Question 4694

Wills argues that certain malarial parasites are especially (i)_______ because they have entered humans more recently than other species and therefore have had (ii)_______ time to evolve toward (iii)_______. Yet there is no reliable evidence that the most harmful Plasmodium species has in fact been in humans for a shorter time than less harmful species.

malignant .. insufficient .. benignity✔️
populous .. ample .. virulence
threatened .. adequate .. variability
malignant .. ample .. benignity

Correct Answer Logic:

The logic chain: recently entered humans → less time to evolve toward becoming harmless. Blank (i): malignant (harmful/dangerous) — these are the especially dangerous parasites. Blank (ii): recently entered = insufficient time to adapt. Blank (iii): the direction of evolution would be toward benignity (harmlessness/mildness) — older parasites evolve to coexist peacefully with hosts. 'Virulence' would mean evolving toward greater harm, which is the opposite of what long co-evolution produces.

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Home Economics QUESTION #6235

Question 4695

The first step in the management process is:

Organizing
Planning✔️
Controlling
Evaluating

Correct Answer Logic:

Planning involves setting goals and determining the course of action to achieve them.

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Planning QUESTION #4958

Question 4696

Which technique is most effective for reducing urban heat island effect?

Increasing building density
Expanding asphalt surfaces
Green infrastructure and tree planting✔️
Removing vegetation

Correct Answer Logic:

Green infrastructure (green roofs, urban forests, parks) reduces urban heat island effect through evapotranspiration, shading, and lower surface temperatures compared to concrete and asphalt.

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Maths QUESTION #4603

Question 4697

Expand: $(2x + 3)(x - 1)$

$2x^2 + x - 3$
$2x^2 - 2x + 3x - 3$
$2x^2 + x - 3$
Both A and B✔️

Correct Answer Logic:

$(2x+3)(x-1) = 2x^2 - 2x + 3x - 3 = 2x^2 + x - 3$. Options A and B both represent this.

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English QUESTION #8575

Question 4698

What does the idiom 'to take with a grain of salt' mean?

To take with some reservation✔️
To Reject
To take wholeheartedly
To take seriously

Correct Answer Logic:

'Take with a grain of salt' means to be skeptical or not completely believe.

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Biomedical Sciences QUESTION #3810

Question 4699

Which lymphoid organ has the primary function of T-cell maturation and plays a central role in adaptive immune system development?

Pancreas
Thyroid
Liver
Thymus✔️

Correct Answer Logic:

The thymus is the site where T-lymphocytes mature, differentiate, and acquire immune competence. It is essential for the development of the adaptive cellular immune response.

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MCQs Section QUESTION #4839

Question 4700

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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