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Statistics QUESTION #1984

If a population has mean $\mu$ and variance $\sigma^2$, the variance of the sample mean $\bar{X}$ for samples of size $n$ drawn WITHOUT replacement from a finite population of size $N$ is:

$\dfrac{\sigma^2}{n}$
$\dfrac{\sigma^2}{n} \cdot \dfrac{N-n}{N-1}$✔️
$\dfrac{\sigma^2}{n} \cdot \dfrac{N-n}{N}$
$\dfrac{\sigma^2}{N}$

Correct Answer Logic:

For sampling without replacement from a finite population, $Var(\bar{X}) = \dfrac{\sigma^2}{n} \cdot \dfrac{N-n}{N-1}$, where $\dfrac{N-n}{N-1}$ is the finite population correction (fpc) factor. It reduces variance compared to sampling with replacement.

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Mathematics QUESTION #4092

Question 1262

The solution set of the inequality $x^2+x>2$ is:

$(-2,1)$
$(-\infty,-2)\cup(1,\infty)$✔️
$[-2,1]$
$(-1,2)$

Correct Answer Logic:

Factor: $x^2+x-2=(x+2)(x-1)>0$. Product of two factors is positive when both are positive ($x>1$) or both are negative ($x<-2$). Solution: $(-\infty,-2)\cup(1,\infty)$.

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Mathematics QUESTION #975

Question 1263

The perpendicular distance of the line $\dfrac{x-1}{2}=\dfrac{y+2}{-1}=\dfrac{z+3}{2}$ from the point $P(2,-10,1)$ is:

6
$5\sqrt{2}$
$4\sqrt{3}$
$3\sqrt{5}$✔️

Correct Answer Logic:

Direction vector $\vec{d}=(2,-1,2)$. Point on line $A=(1,-2,-3)$. $\vec{AP}=(1,-8,4)$. $|\vec{AP}|^2=1+64+16=81$. $\vec{AP}\cdot\vec{d}=2+8+8=18$. $|\vec{d}|^2=9$. Distance$^2=81-\frac{324}{9}=81-36=45$. Distance$=\sqrt{45}=3\sqrt{5}$.

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Biology QUESTION #4267

Question 1264

Which part of the brain contains central chemoreceptors that monitor $CO_2$ levels in blood?

Pons
Midbrain
Hypothalamus
Medulla oblongata✔️

Correct Answer Logic:

The medulla oblongata contains central chemoreceptors that detect changes in $CO_2$ and pH of cerebrospinal fluid, regulating the breathing rate.

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Mathematics QUESTION #4157

Question 1265

For the Fourier series of an even function $f(x)$ on $[-L, L]$, which coefficients are zero?

All $a_n$
All $b_n$✔️
All $a_n$ and $b_n$
None

Correct Answer Logic:

For even functions, $f(-x) = f(x)$, so $b_n = \frac{1}{L}\int_{-L}^{L} f(x)\sin(\frac{n\pi x}{L})dx = 0$ since integrand is odd. Only cosine terms ($a_n$) remain.

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Library Sciences QUESTION #1543

Question 1266

According to Stueart and Moran (2007), 'coordination' as a management function in libraries is best described as:

The process of hiring and training new library staff
Synchronizing the activities and efforts of different departments and personnel to achieve organizational goals efficiently✔️
Preparing the annual budget report for the governing board
Evaluating the performance of individual library employees

Correct Answer Logic:

Coordination involves synchronizing the work of different units, departments, and individuals so their efforts align toward common organizational goals. In libraries, this is critical given the interdependence of technical services, public services, and administrative units.

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Mathematics QUESTION #4142

Question 1267

At the point $(0, b)$ on the ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$, what is the radius of curvature $\rho$?

$\frac{a^2}{b}$✔️
$\frac{b^2}{a}$
$\frac{a}{b}$
$\frac{b}{a}$

Correct Answer Logic:

For ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$, radius of curvature at $(0,b)$ (vertex on minor axis) is $\rho = \frac{a^2}{b}$.

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Paper-I (Anatomy/Physiology and Biochemistry/Microbiology) QUESTION #3137

Question 1268

The 'Pituitary Gland' is often called the 'Master Gland' because it is controlled by the:

Thalamus
Hypothalamus✔️
Pineal gland
Thyroid gland

Correct Answer Logic:

The hypothalamus tells the pituitary which hormones to release.

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Urdu QUESTION #5259

Question 1269

Idiom Through Thick and Thin کا درست مطلب:

ہر مشکل میں
اچھے برے وقت میں✔️
ہر حال میں
چھوٹی بڑی باتیں

Correct Answer Logic:

Through thick and thin کا مطلب ہے ہر اچھے اور برے وقت میں ساتھ دینا۔

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Mechanical Engineering QUESTION #2467

Question 1270

The base circle diameter $d_b$ of a gear with pitch diameter $d$ and pressure angle $\phi$ is:

$d_b = d / \cos\phi$
$d_b = d \cdot \tan\phi$
$d_b = d \cdot \cos\phi$✔️
$d_b = d \cdot \sin\phi$

Correct Answer Logic:

The base circle radius is related to the pitch circle radius by $r_b = r\cos\phi$, hence $d_b = d\cos\phi$.

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The Title 28 of the United States Code QUESTION #3738

Question 1271

In a medical malpractice case, the plaintiff's lawyer wants to introduce a page from a standard medical textbook to prove the 'standard of care.' Is this allowed?

No, textbooks are hearsay.
Yes, under the 'Learned Treatises' exception, but only if an expert witness relies on it or it is called to the expert's attention.✔️
Yes, but only if the author of the textbook is present in court.
No, unless the defendant agrees.

Correct Answer Logic:

Rule 803(18) allows statements from learned treatises to be read into evidence if the treatise is established as a reliable authority and an expert witness is on the stand.

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MCQs Section QUESTION #4842

Question 1272

Pick the word nearly opposite in meaning to "DELETERIOUS"

Nourishing✔️
Injurious
Vital
Fatal

Correct Answer Logic:

Deleterious means harmful or damaging to health or wellbeing. Its antonym is 'nourishing,' which means providing nourishment and promoting health and growth.

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Electrical Engineering QUESTION #2149

Question 1273

In a DC machine, the purpose of Interpoles is primarily to:

Increase the main field flux
Reduce the speed of the motor
Improve commutation by neutralizing armature reaction✔️
Decrease the starting torque

Correct Answer Logic:

Interpoles are small poles placed to neutralize the cross-magnetizing effect of armature reaction and reduce sparking at the brushes during commutation.

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Biology QUESTION #4201

Question 1274

The digestive secretions from different parts of GIT have the ability to kill microbe present in the food. Which of the following best describe this role?

Antiseptics
Disinfectants✔️
Chemotherapeutics
Immunosuppressant

Correct Answer Logic:

Digestive secretions act as disinfectants by killing microbes in the digestive tract.

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Pakistan Affairs QUESTION #133

Question 1275

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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Physics QUESTION #1064

Question 1276

Vernier callipers: 10 VSD = 9 MSD, least division = 0.1 cm. Zero of VS at $x=0.1$ cm when closed (zero error = +0.1 cm). Main scale reading M = 5 cm, coinciding vernier division = 8. Measured diameter after zero error correction:

4.98 cm✔️
5.00 cm
5.18 cm
5.08 cm

Correct Answer Logic:

Least count: $\text{LC}=1\ \text{MSD}-1\ \text{VSD}=0.1-0.09=0.01\ \text{cm}$. Reading $= M + n\times LC = 5+8\times0.01=5.08\ \text{cm}$. Zero error $=+0.1\ \text{cm}$ (positive). Corrected reading $=5.08-0.10=4.98\ \text{cm}$.

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Mechanical Engineering QUESTION #2402

Question 1277

The Reynolds number $Re$ is the ratio of inertial forces to viscous forces, defined for pipe flow as:

$Re = \mu V D / \rho$
$Re = \rho V D / \mu = V D / \nu$✔️
$Re = \rho V^2 / \mu$
$Re = \rho g D / \mu V$

Correct Answer Logic:

Reynolds number: $Re=\rho VD/\mu=VD/\nu$. For pipe flow: laminar if $Re<2300$, transitional $23004000$.

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Electrical Engineering QUESTION #2161

Question 1278

Using Norton's theorem, a circuit has $I_N = 4\,\text{A}$ and $R_N = 6\,\Omega$. The maximum power deliverable to a load is:

$24\,\text{W}$✔️
$48\,\text{W}$
$12\,\text{W}$
$96\,\text{W}$

Correct Answer Logic:

Maximum power transfer requires $R_L = R_N = 6\,\Omega$. Thevenin voltage $V_{th} = I_N R_N = 24\,\text{V}$. $P_{max} = \frac{V_{th}^2}{4R_N} = \frac{576}{24} = 24\,\text{W}$.

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Commerce QUESTION #1202

Question 1279

Which financial statement is unique to public sector accounting?

Statement of Financial Performance
Statement of Cash Flows
Appropriation Account✔️
Statement of Changes in Equity

Correct Answer Logic:

The Appropriation Account is unique to public sector (government) accounting. It shows how the government's budget has been allocated and spent across various ministries and departments. It accounts for voted grants and actual expenditures, showing the utilization of appropriated funds.

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Physics QUESTION #4407

Question 1280

In a pipe of varying cross-section, as fluid enters the narrower region, it exhibits:

High velocity, high pressure
High velocity, low pressure✔️
Low velocity, high pressure
Low velocity, low pressure

Correct Answer Logic:

By Bernoulli's principle: $P + \dfrac{1}{2}\rho v^2 + \rho gh = $ constant. In the narrower section, velocity increases (continuity equation), so pressure must decrease. Result: high velocity, low pressure.

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