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Mathematics QUESTION #7486

If the function $f: \mathbb{R} - \{1,-1\} \to A$ defined by $f(x) = \frac{x^2}{1-x^2}$ is surjective, then A is equal to:

$\mathbb{R} - \{-1\}$
$[0,\infty)$
$\mathbb{R} - [-1,0)$✔️
$\mathbb{R} - (-1,0)$

Correct Answer Logic:

To find the range, let $y = \frac{x^2}{1-x^2}$. Solving for $x^2$: $y(1-x^2) = x^2$, so $y = x^2 + yx^2 = x^2(1+y)$, giving $x^2 = \frac{y}{1+y}$. For real x, we need $\frac{y}{1+y} \geq 0$. This holds when $y \geq 0$ and $1+y > 0$ (i.e., $y > -1$), or $y < 0$ and $1+y < 0$ (i.e., $y < -1$). Combining: $y \in (-\infty, -1) \cup [0, \infty) = \mathbb{R} - [-1,0)$. So A = $\mathbb{R} - [-1,0)$.

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Civil / Architecture QUESTION #2347

Question 1802

Sound Pressure Level (SPL) $L_p$ in decibels relative to reference pressure $p_0 = 20\,\mu\text{Pa}$ is defined as:

$L_p = 10\log_{10}\!\left(\dfrac{p}{p_0}\right) \text{ dB}$
$L_p = 20\log_{10}\!\left(\dfrac{p}{p_0}\right) \text{ dB}$✔️
$L_p = 10\log_{10}\!\left(\dfrac{I}{I_0}\right) \text{ dB where } I_0 = 10^{-12}\,\text{W/m}^2$
$L_p = 20\log_{10}\!\left(\dfrac{p_0}{p}\right) \text{ dB}$

Correct Answer Logic:

SPL is defined as $L_p = 20\log_{10}\!\left(\dfrac{p}{p_0}\right)$ dB, since pressure is an amplitude (not power) quantity. Note that Option C defines Sound Intensity Level $L_I = 10\log_{10}(I/I_0)$, which numerically equals SPL in a free field for plane waves. Options A would be correct for power ratios. Option D is inverted and gives negative values.

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Boilers Mechanical Engineering QUESTION #2404

Question 1803

The Euler number (pressure coefficient) represents the ratio of:

Inertial forces to gravity forces $= V^2/(gL)$
Pressure forces to inertial forces: $Eu = p/(\rho V^2)$✔️
Viscous forces to inertial forces
Surface tension to inertial forces

Correct Answer Logic:

Euler number: $Eu=p/(\rho V^2)$, the ratio of pressure forces to inertial forces. Important in cavitation analysis.

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Islamic Studies QUESTION #351

Question 1804

Jerusalem was conquered in the period of:

Hazrat Abu Bakr (RA)
Hazrat Umar (RA)✔️
Hazrat Usman (RA)
Hazrat Ali (RA)

Correct Answer Logic:

Jerusalem was surrendered to Caliph Hazrat Umar (RA) in 637 AD.

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Planning QUESTION #4942

Question 1805

Which type of housing layout maximizes privacy?

Linear pattern
Cluster pattern
Courtyard pattern✔️
Grid pattern

Correct Answer Logic:

Courtyard pattern (houses oriented around shared courts) maximizes privacy by separating public and private spaces, creating protected outdoor areas while maintaining community interaction.

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Physics QUESTION #369

Question 1806

If the mass of the bob of a pendulum is doubled its time period is:

Halved
Doubled
Unchanged✔️
Increases four times

Correct Answer Logic:

Time period of a pendulum is independent of mass

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Boilers Mechanical Engineering QUESTION #2496

Question 1807

The flexure (bending stress) formula for a beam subjected to bending moment $M$ gives stress $\sigma$ at distance $y$ from the neutral axis as:

$\sigma = \frac{My}{I}$✔️
$\sigma = \frac{MI}{y}$
$\sigma = \frac{M}{yI}$
$\sigma = \frac{y}{MI}$

Correct Answer Logic:

Derived from pure bending theory (Euler-Bernoulli beam), $\sigma = -My/I$. Maximum bending stress occurs at $y = c$ (outermost fiber): $\sigma_{max} = Mc/I = M/Z$, where $Z = I/c$ is the section modulus.

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MCQs Section QUESTION #4883

Question 1808

Which word is similar to "ESSAY"

Direct
Compose
Attempt✔️
Suppose

Correct Answer Logic:

Essay as a verb means to attempt or try something. Attempt is its closest synonym in this context.

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Math (Module-1) QUESTION #5389

Question 1809

A line in the $xy$-plane passes through the origin $(0, 0)$ and has a slope of $\frac{1}{7}$. Which of the following equations represents this line?

$y = x + 7$
$y = 7x$
$y = \frac{1}{7}x$✔️
$y = x + \frac{1}{7}$

Correct Answer Logic:

The slope-intercept form is $y = mx + b$. Here, $m = \frac{1}{7}$ and $b = 0$ (since it passes through the origin), giving $y = \frac{1}{7}x$.

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Nursing QUESTION #9266

Question 1810

A 3-year-old child is admitted with sudden onset of high fever, drooling, muffled voice, and sitting in a 'tripod/sniffing position'. The child appears toxic and anxious. The nurse's FIRST priority action is:

Insert a tongue depressor to examine the throat
Start IV antibiotics immediately
Do NOT examine the throat; keep child calm, call physician immediately, and prepare for emergency airway management✔️
Place child supine and administer O₂ via face mask

Correct Answer Logic:

Acute Epiglottitis — a life-threatening supraglottic infection (typically Haemophilus influenzae type b in unvaccinated children).

Classic presentation:

Sudden high fever, toxic appearance
Drooling (inability to swallow secretions)
Muffled 'hot potato' voice
Tripod/sniffing position: leaning forward, neck extended, supporting on hands — maximizes airway opening
Stridor (late, ominous sign)
Anxiety, refuses to lie down

CRITICAL NURSING RULE:

NEVER examine the throat with tongue depressor, attempt IV access, take blood, agitate the child, or lay the child supine — ANY stimulation can cause complete airway obstruction.

Priority actions:

Keep child calm, upright (let child maintain own position)
Administer humidified O₂ gently
Notify physician and anesthesiologist IMMEDIATELY
Prepare for emergency intubation or tracheostomy (bedside)
IV access and antibiotics ONLY after airway is secured

Treatment: Ceftriaxone $100\,\text{mg/kg/day}$ IV after airway secured.

Differentiate from croup: croup has barking cough, subglottic involvement, not toxic, managed with steroids + nebulized epinephrine.

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Logical Reasoning QUESTION #3959

Question 1811

Select the pair with a similar relationship: OBSTRUCTION : BUOY

construction : building✔️
boy : girl
danger : red light
iceberg : titanic

Correct Answer Logic:

2

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Home Economics QUESTION #6265

Question 1812

In therapeutic nutrition, the 'DASH' diet is specifically designed to manage which condition?

Type 1 Diabetes
Hypertension✔️
Phenylketonuria (PKU)
Celiac Disease

Correct Answer Logic:

DASH stands for Dietary Approaches to Stop Hypertension, focusing on reducing sodium and increasing potassium, calcium, and magnesium.

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Chemistry QUESTION #7147

Question 1813

Among the following alkaline earth metal sulfates, which one possesses a hydration enthalpy that is greater than its lattice enthalpy?

$CaSO_{4}$
$BeSO_{4}$✔️
$BaSO_{4}$
$SrSO_{4}$

Correct Answer Logic:

Solubility of sulfates depends on the balance between lattice energy and hydration energy. As we move down the group, both decrease, but lattice energy decreases slowly due to the large size of the sulfate ion. However, $Be^{2+}$ is exceptionally small, giving it a very high hydration enthalpy that exceeds its lattice enthalpy, making $BeSO_{4}$ highly soluble.

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Boilers Mechanical Engineering QUESTION #2483

Question 1814

The velocity of a node B of a driver link in rotational motion (angular velocity $\omega = \dot{\phi}$, link length $L_{AB}$) is given by:

$v_{Bx} = -L_{AB}\dot{\phi}\sin\phi,\quad v_{By} = L_{AB}\dot{\phi}\cos\phi$✔️
$v_{Bx} = L_{AB}\dot{\phi}\cos\phi,\quad v_{By} = L_{AB}\dot{\phi}\sin\phi$
$v_{Bx} = L_{AB}\dot{\phi}^2\cos\phi,\quad v_{By} = -L_{AB}\dot{\phi}^2\sin\phi$
$v_{Bx} = -L_{AB}\ddot{\phi}\cos\phi,\quad v_{By} = L_{AB}\ddot{\phi}\sin\phi$

Correct Answer Logic:

Differentiating position equations $x_B=x_A+L_{AB}\cos\phi$ and $y_B=y_A+L_{AB}\sin\phi$ with respect to time: $v_{Bx}=-L_{AB}\dot{\phi}\sin\phi$ and $v_{By}=L_{AB}\dot{\phi}\cos\phi$.

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English QUESTION #7552

Question 1815

Translate into English: تمہارے بغیر زندگی ادھوری لگتی ہے۔

Life seems incomplete without you.✔️
Life feels lonely because of you.
Life is incomplete because of you.
Life becomes dark without your presence.

Correct Answer Logic:

The correct translation accurately conveys "seems incomplete" and "without you" in a natural English structure. Option A is the most accurate.

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Planning QUESTION #4932

Question 1816

In transportation engineering, what does LOS stand for?

Level of Service✔️
Length of Segment
Load on Structure
Limit of Speed

Correct Answer Logic:

LOS (Level of Service) is a qualitative measure describing operational conditions within a traffic stream, ranging from A (free flow) to F (forced flow/congestion).

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Pakistan Affairs QUESTION #9123

Question 1817

Who was the first Pakistani climber to summit Mount Everest on May 17, 2000?

Nazir Sabir✔️
Salma Salim
Namira Salim
Ashraf Aman

Correct Answer Logic:

Nazir Sabir was the first Pakistani on Everest.

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Law QUESTION #9489

Question 1818

A files a suit claiming ownership of a well-defined plot. The Court, after hearing both sides, finds in favour of A on all issues but inadvertently omits to grant consequential relief of mesne profits although it was claimed in the plaint. A applies for amendment of the decree. B argues the decree is final and cannot be amended. What should the Court do?

Refuse; a decree once passed is final and cannot be amended
Allow A's application; the Court has power under Section 152 to correct clerical or arithmetical mistakes and accidental omissions in decrees, and under the inherent powers of Section 151 in appropriate cases✔️
Direct A to file a fresh suit for mesne profits
Refer the matter to the High Court

Correct Answer Logic:

Section 152 CPC empowers the Court to correct clerical or arithmetical mistakes in judgments, decrees or orders, or errors arising from accidental slips or omissions. The inadvertent omission of a claimed relief that was argued falls within correctable error. Additionally, Section 151 preserves inherent powers to do justice.

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Journalism / Mass Communication QUESTION #6378

Question 1819

Sweden's Freedom of the Press Act of 1766 is historically significant in the development of press freedom law. Why?

It was the first law to completely ban all forms of censorship globally
It is the world's oldest freedom of information legislation, establishing the principle that citizens have a legal right to access government-held information✔️
It created the first international media regulatory body
It was the first law to require newspapers to reveal their anonymous sources

Correct Answer Logic:

The textbook notes that “over seventy countries around the world have implemented some form of freedom of information legislation… the oldest being Sweden's Freedom of the Press Act of 1766.” This Act is remarkable for its age — it predates the American Bill of Rights (1791) and the French Declaration of the Rights of Man (1789). It established that government documents should be available to the public, laying the philosophical groundwork for what would later be called sunshine laws or open records laws. The core principle it established — that the burden of proof lies on the government to justify withholding information, rather than on the citizen to justify requesting it — became the global standard for freedom of information legislation. In contrast, Article 19 of the Universal Declaration of Human Rights (adopted 1948) globalised this principle at the international level.

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Administration QUESTION #9539

Question 1820

Henri Fayol identified 14 principles of management. A district officer issues orders to a field inspector who simultaneously receives contradictory orders from a divisional director. Which single Fayol principle has been most directly violated, and what is its practical consequence?

Division of work — resulting in role confusion and overlapping responsibilities
Unity of command — resulting in conflict, confusion and erosion of accountability✔️
Scalar chain — resulting in bypassing the line of authority
Esprit de corps — resulting in breakdown of team cohesion

Correct Answer Logic:

Unity of command (Fayol's Principle 4) holds that each employee should receive orders from one superior only. When violated, accountability becomes diffuse, conflict is inevitable, and the employee cannot determine whose instructions take priority — directly undermining organizational discipline.

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