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Mathematics QUESTION #6021

The system $x+ky+3z=0$, $3x+ky-2z=0$, $2x+4y-3z=0$ has a non-zero solution $(x,y,z)$. Find the value of $\dfrac{xz}{y^2}$.

-30
30
-10
10✔️

Correct Answer Logic:

For non-zero solution, $\Delta=0$:

$\begin{vmatrix}1&k&3\\3&k&-2\\2&4&-3\end{vmatrix}=1(−3k+8)−k(−9+4)+3(12−2k)=−3k+8+5k+36−6k=44−4k=0$

So $k=11$.

With $k=11$: from equations 1 and 2: $x+11y+3z=0$ and $3x+11y-2z=0$. Subtracting: $2x-5z=0\Rightarrow x=\frac{5z}{2}$.

Substituting back: $\frac{5z}{2}+11y+3z=0\Rightarrow 11y=-\frac{11z}{2}\Rightarrow y=-\frac{z}{2}$.

$\frac{xz}{y^2}=\frac{\frac{5z}{2}\cdot z}{\frac{z^2}{4}}=\frac{\frac{5z^2}{2}}{\frac{z^2}{4}}=\frac{5}{2}\times4=\mathbf{10}$

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Math Physics Chemistry Biology QUESTION #799

Question 2

The maximum volume of $\text{O}_2$ is at:

HTP
STP✔️
$127°\text{C},\ 1\ \text{atm}$
None

Correct Answer Logic:

At STP (Standard Temperature and Pressure: $0°\text{C},\ 1\ \text{atm}$), gases occupy maximum volume as temperature is lower, keeping more molecules in gaseous phase.

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Biomedical Sciences QUESTION #3814

Question 3

Which endocrine condition is specifically characterised by autoimmune-driven excessive secretion of thyroid hormone?

Addison's disease
Hashimoto thyroiditis
Graves' disease✔️
Wilson's disease

Correct Answer Logic:

Graves' disease is an autoimmune hyperthyroid condition caused by TSH-receptor stimulating antibodies, leading to excessive thyroid hormone production and clinical thyrotoxicosis.

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Urdu QUESTION #5164

Question 4

مشفق خواجہ کس عنوان سے کالم لکھتے رہے ہیں؟

سخن در سخن
خامہ بگوش✔️
حرف و حکایت
ان میں سے کوئی نہیں

Correct Answer Logic:

مشفق خواجہ 'خامہ بگوش' کے عنوان سے کالم لکھتے رہے ہیں۔

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Chemistry QUESTION #7157

Question 5

The significant reducing ability of hypophosphorous acid ($H_{3}PO_{2}$) is primarily due to the presence of:

Two $P-OH$ bonds
One $P-H$ bond
Two $P-H$ bonds✔️
One $P-OH$ bond

Correct Answer Logic:

The reducing character of oxoacids of phosphorus depends on the number of $P-H$ bonds present. In $H_{3}PO_{2}$ (Hypophosphorous acid), the phosphorus atom is bonded to two hydrogen atoms directly ($2 \times P-H$ bonds) and one hydroxyl group ($1 \times P-OH$ bond). These $P-H$ bonds are responsible for its strong reducing property.

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Chemistry QUESTION #442

Question 6

AlI? (Aluminium Iodide) is electrically a __________

Conductor
Non-conductor✔️
Semiconductor
None of these

Correct Answer Logic:

AlI? is covalent and non-conducting in pure form

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HR and Management QUESTION #6471

Question 7

The 'road map' of the HRM course covering 42 modules suggests:

Random collection of HR topics
Systematic, comprehensive coverage from foundations to advanced topics✔️
Focus only on practical skills
Emphasis on legal compliance

Correct Answer Logic:

The 42-module road map progresses systematically from introductory concepts (management basics, organization components) through core functions (planning, recruitment, selection, training, performance, compensation) to advanced topics (international HRM, leadership, conclusion) - providing comprehensive coverage.

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Paper-I (Pharmaceutics II (Industrial and Quality Control) and Pharmaceutics III (Hospital and Community Pharmacy)) QUESTION #5688

Question 8

In the preparation of $100 \text{ mL}$ of a $1:500$ solution of Potassium Permanganate ($KMnO_{4}$), what is the weight of the solute required?

$0.2 \text{ g}$✔️
$2.0 \text{ g}$
$0.5 \text{ g}$
$0.02 \text{ g}$

Correct Answer Logic:

Calculation: $1/500 = x/100 \Rightarrow 500x = 100 \Rightarrow x = 0.2 \text{ g}$.

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Tourism & Hospitality Management QUESTION #1631

Question 9

The Travel & Tour Operations course identifies the distinction between a 'wholesale travel agency' and a 'tour operator.' Which of the following best captures this distinction as covered in the curriculum?

A wholesale travel agency sells only airline tickets; a tour operator sells only hotel rooms
A wholesale travel agency acts as an intermediary distributing products created by others, while a tour operator creates, packages, and prices its own tour products by combining transport, accommodation, and services✔️
A wholesale travel agency is government-owned; a tour operator is privately owned
A wholesale travel agency operates internationally; a tour operator operates only domestically

Correct Answer Logic:

The Travel & Tour Operations course (Module 1) specifically addresses the 'Distinction between wholesale travel agency and tour operator business.' A wholesale travel agency distributes and resells tourism products, while a tour operator creates original packaged products by combining and contracting transport, accommodation, meals, and activities — assuming principal liability for the package.

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Accounting & Finance QUESTION #9654

Question 10

An Independent Branch sends a remittance of Rs. 50,000 to the Head Office. By year-end, the cash is still in transit. Which accounting entry should be passed to reconcile the accounts?

Debit Branch Account, Credit Cash in Transit Account in HO books
Debit Cash in Transit Account, Credit Branch Account in HO books✔️
Debit Head Office Account, Credit Cash in Transit Account in Branch books
No entry required until cash is received

Correct Answer Logic:

Since cash was sent by branch but not yet received by HO, from HO perspective the Branch Account is overstated (HO has not yet recorded the receipt). The reconciling entry in HO books is: Debit Cash in Transit A/c, Credit Branch A/c. This brings the Branch Account balance in line with the HO Account in branch books.

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Mathematics QUESTION #1330

Question 11

In the Euler method for $y'=1+y/x$, $y(1)=2$, $h=0.25$, after step 1 we have $y_1\approx2.75$. The function value $f(x_1,y_1)=f(1.25, 2.75)$ equals:

$3.2$✔️
$2.5$
$3.0$
$3.5$

Correct Answer Logic:

$f(1.25,2.75)=1+\dfrac{2.75}{1.25}=1+2.2=3.2$. This is used in the next Euler step: $y_2=2.75+0.25\times3.2=2.75+0.80=3.55$.

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Boilers Mechanical Engineering QUESTION #2409

Question 12

The bulk modulus of elasticity $E$ of a fluid is defined as:

$E = dp/(d\rho/\rho)$
$E = dp/(-dv/v)$ — ratio of pressure increase to fractional volume decrease
$E = \rho c^2$ where $c$ is sound speed
Both options B and C are correct expressions for $E$✔️

Correct Answer Logic:

Bulk modulus $E=-dp/(dV/V)=\rho c^2$. Both definitions are equivalent. For water: $E\approx2.1$ GPa.

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Paper-II (Pharmacognosy and Pharmaceutics-I) QUESTION #2967

Question 13

'Eutectic Mixtures' are substances that:

Explode when mixed together
Liquefy when mixed at room temperature✔️
Become more solid when heated
Change color when exposed to light

Correct Answer Logic:

Eutectic mixtures (e.g., camphor and menthol) have a combined melting point lower than room temperature.

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General Knowledge QUESTION #8678

Question 14

What does the term 'mantra' originally mean?

A word with spiritual power✔️
Term in stock exchange
Science of lower species
None of above

Correct Answer Logic:

Mantra is a sacred utterance in Hinduism/Buddhism.

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English QUESTION #2745

Question 15

Identify the ERROR in: 'She is more smarter than her sister.'

She
is
more
smarter✔️

Correct Answer Logic:

'Smarter' is already a comparative adjective. Adding 'more' creates a double comparative, which is grammatically incorrect. It should be either 'smarter' or 'more smart'.

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Paper-I (Anatomy/Physiology and Biochemistry/Microbiology) QUESTION #3494

Question 16

Volatile oils are also known as 'Essential Oils' because:

They are essential for life
They possess the 'essence' or odor of the plant✔️
They are made of proteins
They never evaporate

Correct Answer Logic:

They are volatile in steam and provide the characteristic aroma of the plant.

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Accounting Finance and Punjab Sales Tax on Services QUESTION #2582

Question 17

Under section 5(2) of the Act, a notification issued by the Government amending the Second Schedule (adding, modifying or deleting any entry regarding taxable services or rates) shall be effective from what date?

Three months before the date of notification
The date of approval by the Provincial Assembly
Such date as may be specified in the notification, but not prior to the date on which the notification is PUBLISHED in the Official Gazette✔️
The first day of the next financial year

Correct Answer Logic:

Section 5(2) provides a strict rule: the notification shall be effective from such date as may be specified therein, but SUCH DATE SHALL NOT BE PRIOR TO THE DATE ON WHICH THE NOTIFICATION IS PUBLISHED in the official Gazette — preventing retrospective taxation through subordinate legislation.

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Mathematics QUESTION #970

Question 18

Let $P(4, 4\sqrt{3})$ be a point on the parabola $y^2=4ax$ and $PQ$ be a focal chord. If $M$ and $N$ are the feet of perpendiculars drawn from $P$ and $Q$ respectively on the directrix, then the area of quadrilateral $PQMN$ is equal to:

$17\sqrt{3}$
$\dfrac{263\sqrt{3}}{8}$
$\dfrac{34\sqrt{3}}{3}$
$\dfrac{343\sqrt{3}}{8}$✔️

Correct Answer Logic:

From $P(4,4\sqrt{3})$ on $y^2=4ax$: $(4\sqrt{3})^2=4a\cdot4 \Rightarrow a=3$. So directrix is $x=-3$. Using focal chord properties, find $Q$, then compute the trapezium area $PQMN = \frac{1}{2}(PM+QN)\cdot PQ_x$-component, giving $\frac{343\sqrt{3}}{8}$.

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Boilers Mechanical Engineering QUESTION #4072

Question 19

'Purging' the furnace before ignition is done to:

Clean the dust
Remove any unburnt fuel/gases to prevent an explosion (mishap)✔️
Heat the furnace
Cool the burner

Correct Answer Logic:

A high-volume air purge is the first step in any safe burner start-up sequence.

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Chemistry QUESTION #5532

Question 20

For a reaction following the Arrhenius equation, the plot of $\ln k$ vs $\frac{1}{RT}$ gives a straight line with slope $(-y)$ units. The activation energy of the reaction is:

$y/R$ units
$y$ units✔️
$yR$ units
$-y$ units

Correct Answer Logic:

Arrhenius equation: $\ln k = \ln A - \frac{E_a}{RT}$. Plotting $\ln k$ vs $\frac{1}{RT}$, the slope = $-E_a$. Given slope = $-y$, therefore $E_a = y$ units. (Note: if plotted against $\frac{1}{T}$, slope = $-E_a/R$, but here the x-axis is $\frac{1}{RT}$, so the R is already incorporated into the x-axis, making the slope directly equal to $-E_a$.)

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