Reading Mode - Questions

Mathematics QUESTION #6928

If $\displaystyle\int_0^{\pi/3}\dfrac{\tan\theta}{\sqrt{2k\sec\theta}}\,d\theta = 1-\dfrac{1}{\sqrt{2}}$ for $k>0$, find $k$.

4
$\dfrac{1}{2}$
1
2✔️

Correct Answer Logic:

$\displaystyle\int_0^{\pi/3}\dfrac{\tan\theta}{\sqrt{2k}\cdot\sqrt{\sec\theta}}\,d\theta = \dfrac{1}{\sqrt{2k}}\int_0^{\pi/3}\dfrac{\sin\theta}{\cos\theta}\cdot\sqrt{\cos\theta}\,d\theta=\dfrac{1}{\sqrt{2k}}\int_0^{\pi/3}\sin\theta\cdot(\cos\theta)^{-1/2}d\theta$

Let $u=\cos\theta$, $du=-\sin\theta\,d\theta$; limits: $1$ to $1/2$:

$=\dfrac{1}{\sqrt{2k}}\int_1^{1/2}(-u^{-1/2})du=\dfrac{1}{\sqrt{2k}}\left[2\sqrt{u}\right]_1^{1/2}... $ Wait: $\int_1^{1/2}(-u^{-1/2})du=\int_{1/2}^1 u^{-1/2}du=[2\sqrt{u}]_{1/2}^1=2-\sqrt{2}=2(1-1/\sqrt{2})$

$\dfrac{2(1-1/\sqrt{2})}{\sqrt{2k}}=1-\dfrac{1}{\sqrt{2}} \Rightarrow \dfrac{2}{\sqrt{2k}}=1 \Rightarrow \sqrt{2k}=2 \Rightarrow 2k=4 \Rightarrow k=\mathbf{2}$

Uploaded by: Fani Warraich

Biomedical Sciences QUESTION #3804

Question 4342

What is the primary physiological action of antidiuretic hormone (vasopressin) in the kidneys?

To increase blood pressure, increasing formation of nephric filtrate
To cause active transport of urea and uric acid from renal blood into tubules
To inhibit aldosterone action
To cause reabsorption of water✔️

Correct Answer Logic:

Vasopressin (ADH) acts on collecting duct principal cells to increase water permeability via aquaporin-2 channels, promoting water reabsorption and reducing urine volume.

Uploaded by: Fani Warraich

Tourism & Hospitality Management QUESTION #1610

Question 4343

In the Front Office Operations course, 'overbooking' is discussed as a front office practice. Which management strategy best justifies its controlled use?

To maximize staff utilization during quiet periods
To offset anticipated no-shows and cancellations, ensuring maximum occupancy and revenue while managing the risk of walking guests✔️
To provide discounted rooms to loyal customers
To manage tour group bookings separately from individual reservations

Correct Answer Logic:

Overbooking is addressed in Module 3 (Reservations and Check-in) of the Front Office Operations course. When practiced strategically, it is used to offset predictable no-show rates and last-minute cancellations — maximizing occupancy. The course covers its relationship with yield management and the front office procedures for managing 'walked' guests when overbooking results in excess arrivals.

Uploaded by: Fani Warraich

Law QUESTION #9512

Question 4344

A District Court transfers a suit to itself from a subordinate Court. The transferred suit is tried by the District Court and a decree is passed. The losing party B appeals. B contends the District Court lacked jurisdiction to try the suit originally since it should be tried by the subordinate Court. What should the appellate Court do?

Refer the question of jurisdiction to the High Court
Dismiss B's appeal; under Section 24(4) CPC, a Court trying a suit transferred or withdrawn under Section 24 has the same powers as the original Court, and an order of transfer by the District Court of its own motion is valid✔️
Send the matter back for retrial to the subordinate Court
Set aside the decree since the District Court should not have tried it

Correct Answer Logic:

Section 24(1) CPC empowers the District Court to withdraw any suit from a subordinate Court and try it itself. Section 24(2) provides that such Court may retry or continue from where it was transferred. The transfer is lawful, and the decree of the District Court in a transferred suit is as valid as if it had originally had jurisdiction.

Uploaded by: Fani Warraich

Paper-I (Anatomy/Physiology and Biochemistry/Microbiology) QUESTION #3395

Question 4345

'Co-enzymes' are often derived from:

Minerals
Vitamins✔️
Carbohydrates
Fats

Correct Answer Logic:

Many B-complex vitamins serve as precursors for essential co-enzymes (like $NAD^+$).

Uploaded by: Fani Warraich

Paper-I (Anatomy/Physiology and Biochemistry/Microbiology) QUESTION #3273

Question 4346

Which scientist is known as the 'Father of Microbiology' for his work with microscopes?

Louis Pasteur
Antonie van Leeuwenhoek✔️
Robert Koch
Alexander Fleming

Correct Answer Logic:

Leeuwenhoek was the first to observe 'animalcules' (bacteria and protozoa) using handcrafted lenses.

Uploaded by: Fani Warraich

Paper-I (Anatomy/Physiology and Biochemistry/Microbiology) QUESTION #3228

Question 4347

'Metabolic Acidosis' occurs when the blood $pH$ falls below:

$7.45$
$7.35$✔️
$7.0$
$8.0$

Correct Answer Logic:

Acidosis is defined as $pH < 7.35$.

Uploaded by: Fani Warraich

MCQs Section QUESTION #5075

Question 4348

فصیلِ شب کس شاعر کی تحریر ہے؟

حفیظ جالندھری
محمد حسین آزاد
علامہ اقبال
مرزا ادیب✔️

Correct Answer Logic:

فصیلِ شب مرزا ادیب کی مشہور ادبی تصنیف ہے۔

Uploaded by: Fani Warraich

Accounting & Finance QUESTION #1195

Question 4349

Accounting information is said to be relevant when it:

Is free from material error.
Influences the decision-making of users.✔️
Can be compared across entities.
Is supported by evidence from independent sources.

Correct Answer Logic:

Relevance is a fundamental qualitative characteristic of useful financial information (per IASB Conceptual Framework). Information is relevant if it is capable of making a difference in the decisions made by users — it has predictive value, confirmatory value, or both. Being free from error refers to faithful representation, not relevance.

Uploaded by: Fani Warraich

English QUESTION #8312

Question 4350

One who cannot die is called _______.

Stable
Immortal✔️
Perpetual
Perennial

Correct Answer Logic:

'Immortal' means not subject to death.

Uploaded by: Fani Warraich

Boilers Mechanical Engineering QUESTION #2446

Question 4351

In free vibrations with Coulomb (dry) damping, the amplitude of successive oscillation cycles decreases by a constant amount per half-cycle of:

$\Delta x = \mu m g / k = x_s$ per HALF-cycle (linear decay)✔️
$\Delta x = e^{-\zeta\omega_n T}$ (exponential decay)
The amplitude increases due to friction
The amplitude decreases only when velocity is negative

Correct Answer Logic:

With Coulomb damping, the amplitude decreases LINEARLY by $4x_s=4\mu mg/k$ per full cycle. This contrasts with viscous damping where the decay is exponential.

Uploaded by: Fani Warraich

FIA Act QUESTION #9986

Question 4352

Upon repeal of the 1948 Ordinance, members of the Special Police:

Lost their jobs immediately
Stood transferred to the Agency✔️
Were transferred to Provincial Police
Had to reapply for FIA posts

Correct Answer Logic:

All Special Police members, including specified persons, stood transferred to the Agency.

Uploaded by: Fani Warraich

MCQs Section QUESTION #5030

Question 4353

غلط املا کا انتخاب کریں۔

جنہوں✔️
تمہیں
انہوں
ان میں سے کوئی نہیں

Correct Answer Logic:

درست املا 'جنھوں' ہے، 'جنہوں' غلط ہے۔ 'انھوں' اور 'تمھیں' درست ہیں۔

Uploaded by: Fani Warraich

Maths QUESTION #4574

Question 4354

If $\frac{x}{4} = \frac{15}{6}$, what is $x$?

$10$✔️
$5$
$22.5$
$36$

Correct Answer Logic:

Cross-multiply: $6x = 60$, so $x = 10$

Uploaded by: Fani Warraich

Statistics QUESTION #2005

Question 4355

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 $\frac{\sigma^2}{n}\cdot\frac{N-n}{N-1}$.

Uploaded by: Fani Warraich

Electrical Engineering QUESTION #2154

Question 4356

The Routh-Hurwitz criterion is used to determine the:

Exact roots of a characteristic equation
Relative stability of a system
Absolute stability of a linear time-invariant system✔️
Steady-state error of a system

Correct Answer Logic:

Routh-Hurwitz determines if any roots of the characteristic equation lie in the right half of the $s$-plane, thus establishing absolute stability.

Uploaded by: Fani Warraich

Therapeutics and Patient Care QUESTION #3890

Question 4357

Which medication among those listed would require the least dose modification in a patient with significantly reduced kidney function?

Haloperidol✔️
Metformin
Digoxin
Tobramycin

Correct Answer Logic:

Haloperidol is predominantly hepatically metabolised and minimally renally excreted, making dose adjustment for renal impairment the least critical of the options listed.

Uploaded by: Fani Warraich