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Mathematics QUESTION #7479

Let $\vec{a} = 2\hat{i} + \lambda_1\hat{j} + 3\hat{k}$, $\vec{b} = 4\hat{i} + (3-\lambda_2)\hat{j} + 6\hat{k}$ and $\vec{c} = 3\hat{i} + 6\hat{j} + (\lambda_3-1)\hat{k}$ be three vectors such that $\vec{b} = 2\vec{a}$ and $\vec{a}$ is perpendicular to $\vec{c}$. Then a possible value of $(\lambda_1, \lambda_2, \lambda_3)$ is:

(1, 3, 1)
$(-\frac{1}{2}, 4, 0)$✔️
$(\frac{1}{2}, 4, -2)$
(1, 5, 1)

Correct Answer Logic:

From $\vec{b} = 2\vec{a}$: $4\hat{i}+(3-\lambda_2)\hat{j}+6\hat{k} = 4\hat{i}+2\lambda_1\hat{j}+6\hat{k}$. Comparing: $3-\lambda_2 = 2\lambda_1$, so $\lambda_2 = 3-2\lambda_1$. From $\vec{a} \perp \vec{c}$: $2(3) + \lambda_1(6) + 3(\lambda_3-1) = 0$, giving $6+6\lambda_1+3\lambda_3-3 = 0$, so $6\lambda_1+3\lambda_3 = -3$, thus $2\lambda_1+\lambda_3 = -1$. Testing option B: $\lambda_1 = -\frac{1}{2}$, $\lambda_2 = 4$, $\lambda_3 = 0$. Check: $\lambda_2 = 3-2(-\frac{1}{2}) = 3+1 = 4$ ✓. And $2(-\frac{1}{2})+0 = -1$ ✓.

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General Knowledge QUESTION #284

Question 6722

The 2023 SDG Summit took place in September 2023 in:

New York✔️
Washington DC
Chicago
None of these

Correct Answer Logic:

The summit was held at the UN Headquarters in New York.+1

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Chemistry QUESTION #1068

Question 6723

The correct order of decreasing acidity of the following aliphatic acids is:

HCOOH $>$ CH$_3$COOH $>$ (CH$_3)_2$CHCOOH $>$ (CH$_3)_3$CCOOH✔️
HCOOH $>$ (CH$_3)_3$CCOOH $>$ (CH$_3)_2$CHCOOH $>$ CH$_3$COOH
(CH$_3)_3$CCOOH $>$ (CH$_3)_2$CHCOOH $>$ CH$_3$COOH $>$ HCOOH
CH$_3$COOH $>$ (CH$_3)_2$CHCOOH $>$ (CH$_3)_3$CCOOH $>$ HCOOH

Correct Answer Logic:

Acidity of carboxylic acids decreases as alkyl group size increases due to +I (electron-donating inductive) effect destabilizing the carboxylate anion. HCOOH has no alkyl group (most acidic), then CH$_3$COOH, then (CH$_3)_2$CHCOOH, then (CH$_3)_3$CCOOH (least acidic). Order: HCOOH $>$ CH$_3$COOH $>$ (CH$_3)_2$CHCOOH $>$ (CH$_3)_3$CCOOH.

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General Science and Ability QUESTION #252

Question 6724

The minimum amount of vitamin stored in the human body is of:

Vitamin D
Vitamin C✔️
Vitamin E
Vitamin A

Correct Answer Logic:

Water-soluble vitamins like Vitamin C are not stored in large amounts compared to fat-soluble ones.+2

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General Knowledge QUESTION #8851

Question 6725

During an uphill journey, a person bends forward to maintain:

High Speed
Stability✔️
Avoiding fatigue
Avoiding beasts

Correct Answer Logic:

Leaning forward helps maintain stability against gravity.

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Information Technology QUESTION #1148

Question 6726

A 256×256 image with 32 gray levels requires how many bits per pixel?

8 bits
5 bits✔️
6 bits
10 bits

Correct Answer Logic:

The number of bits n required for L gray levels is calculated as 2n=L. Since 25=32, each pixel requires 5 bits.

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Paper-I (Anatomy/Physiology and Biochemistry/Microbiology) QUESTION #3257

Question 6727

'Active Hyperemia' refers to increased blood flow to an organ due to:

A blockage
Increased metabolic activity (like exercise)✔️
Gravity
Sleep

Correct Answer Logic:

Local metabolites cause vasodilation to bring more blood to working muscles.

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Security Measures to Maintain Law and Order QUESTION #898

Question 6728

If an AD ASF is offered a "Bribe" to bypass a security measure, they are tried under:

Prevention of Corruption Act
Pakistan Army Act
ASF Act
All of these✔️

Correct Answer Logic:

They are subject to the specific service laws (Army Act via 7-A) and general criminal laws of Pakistan.

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Nursing QUESTION #9245

Question 6729

A 60 kg female patient is in ICU on mechanical ventilation. Her static compliance is calculated as: plateau pressure $= 28 \text{ cmH}_2\text{O}$, PEEP $= 8 \text{ cmH}_2\text{O}$, tidal volume $= 360 \text{ mL}$. What is the static compliance and is it normal?

$C_{\text{stat}} = 18 \text{ mL/cmH}_2\text{O}$ — severely reduced, consistent with ARDS✔️
$C_{\text{stat}} = 45 \text{ mL/cmH}_2\text{O}$ — normal compliance
$C_{\text{stat}} = 25 \text{ mL/cmH}_2\text{O}$ — reduced but borderline
$C_{\text{stat}} = 36 \text{ mL/cmH}_2\text{O}$ — mildly reduced

Correct Answer Logic:

Correct Answer: A — $C_{\text{stat}} = 18 \text{ mL/cmH}_2\text{O}$, severely reduced

Formula for Static (Lung) Compliance:
\[C_{\text{stat}} = \frac{V_T}{P_{\text{plateau}} - \text{PEEP}}\]
\[C_{\text{stat}} = \frac{360}{28 - 8} = \frac{360}{20} = 18 \text{ mL/cmH}_2\text{O}\]

Normal static compliance: $50 - 100 \text{ mL/cmH}_2\text{O}$

Interpretation:

$> 50$: Normal
$30 - 50$: Mildly reduced
$< 30$: Severely reduced — consistent with ARDS, pulmonary fibrosis, pulmonary edema

Compliance of $18 \text{ mL/cmH}_2\text{O}$ indicates severely stiff lungs. The nurse should document this, inform the intensivist, and ensure lung-protective ventilation parameters are maintained.

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Professional QUESTION #1833

Question 6730

Section 10A(1) prohibits a civil servant from serving in any international organization during service. Which of the following organizations is EXPLICITLY mentioned in Section 10A as falling within the scope of this restriction?

Bilateral trade missions of Pakistan
Foreign donor agencies✔️
Multinational corporations operating in Pakistan
Foreign embassies accredited to Pakistan

Correct Answer Logic:

Section 10A(1) inserted by Act No. XVII of 2016 explicitly lists international organizations, international non-governmental organizations, international financial institutions, and foreign donor agencies as covered by the restriction. Multilateral or bilateral trade missions and foreign embassies are not listed in this section.

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Tourism & Hospitality Management QUESTION #1588

Question 6731

According to the Introduction to Tourism & Hospitality course, Customer Relationship Management (CRM) in hotels is most directly associated with which aspect of hotel operations?

The physical maintenance of hotel buildings
Managing and enhancing long-term relationships between the hotel and its guests to build loyalty✔️
The legal compliance requirements of hotel ownership
The food and beverage procurement process

Correct Answer Logic:

The curriculum covers CRM (Customer Relationship Management) as part of the Hotel Development Process, specifically in the context of managing relationships with guests to improve satisfaction, build loyalty, and enhance repeat business — a strategic hospitality management function.

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Education QUESTION #6907

Question 6732

A student cannot explain what they would do if a peer calls them a bad name but fails to demonstrate this behavior in real social situations. According to the Social Skills Deficit framework, this student has which type of deficit?

Skill deficit — the student lacks the knowledge of the appropriate response
Performance deficit — the student knows the correct response but does not apply it in context✔️
Motivational deficit — the student is unwilling to display prosocial behavior
Emotional deficit — the student lacks empathy toward the peer

Correct Answer Logic:

The distinction between skill deficit and performance deficit is critical for intervention design. A performance deficit exists when the student can demonstrate the correct response when directly asked but does not apply it spontaneously in real situations. This requires practice and opportunity-based interventions — not teaching from scratch, which would address a skill deficit.

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Education QUESTION #6786

Question 6733

A test packaging decision involves arranging items 'from easy to hard'. Which of the following is the MOST psychologically sound rationale for this arrangement?

Easier items have higher discrimination and should be answered first to maximize test reliability
Beginning with accessible items reduces test anxiety, builds examinee confidence, and motivates engagement — benefiting students who struggle with initial performance anxiety without disadvantaging stronger students✔️
Harder items lose marks if unattempted, so they must be placed last to ensure all items are reached
This arrangement ensures the test follows a norm-referenced scoring pattern

Correct Answer Logic:

The test administration literature supports easy-to-hard arrangement primarily for psychological reasons: it provides a positive start, reduces anxiety, builds confidence, and motivates students to continue engaging with the test. This is particularly beneficial for test-anxious or lower-ability students and does not penalize stronger students who find the early items trivially easy.

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General Abilities QUESTION #4637

Question 6734

If the product of two numbers is $48$ and one number is $6$, what is the other?

$8$✔️
$42$
$54$
$288$

Correct Answer Logic:

Let other number = $x$. Then $6x = 48$, so $x = 8$

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Constitutional Law QUESTION #5818

Question 6735

Congress enacts a law that allows the Senate to veto any administrative rule made by the Environmental Protection Agency (EPA). Is this law constitutional?

Yes, because the EPA is an executive agency and Congress has oversight power.
Yes, because it is a valid exercise of the 'Necessary and Proper' Clause.
No, because it violates the bicameralism and presentment requirements of Article I.✔️
No, because it violates the Nondelegation Doctrine.

Correct Answer Logic:

Under INS v. Chadha, a 'legislative veto' is unconstitutional because it attempts to exercise legislative power without the two constitutional requirements: bicameralism (passage by both houses) and presentment (submission to the President for signature or veto).

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Physics QUESTION #7085

Question 6736

A wire stretches by $0.04\text{ m}$ under force $F$. What is the elongation if length and diameter are doubled under the same force?

$0.01\text{ m}$
$0.02\text{ m}$✔️
$0.04\text{ m}$
$0.08\text{ m}$

Correct Answer Logic:

Elongation $\Delta L = \frac{FL}{AY} = \frac{FL}{\pi(d/2)^2 Y} \propto \frac{L}{d^2}$.

New elongation $\Delta L' \propto \frac{2L}{(2d)^2} = \frac{2L}{4d^2} = \frac{1}{2} \Delta L$
$\Delta L' = \frac{1}{2} \times 0.04 = 0.02\text{ m}$.

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Paper-II (Pharmacology and Social Behaviour, Law & Ethics and Computer Sciences) QUESTION #5779

Question 6737

According to the Drug Act 1976, a drug that is not labeled in the prescribed manner is classified as:

Adulterated
Spurious
Misbranded✔️
Substandard

Correct Answer Logic:

According to the Drug Act, misbranding includes improper labeling or missing warnings[cite: 7].

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General Knowledge QUESTION #8660

Question 6738

How many member states are currently in the European Union (EU)?

23
25
28✔️
29

Correct Answer Logic:

At the time of the PDF, 28 members; currently 27. Key says 28.

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General Knowledge QUESTION #8666

Question 6739

What is the fourth state of matter?

Rocks
Plasma✔️
Water
None above

Correct Answer Logic:

Plasma is the fourth state of matter after solid, liquid, and gas.

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Chemistry QUESTION #4336

Question 6740

Which of the following best identifies a redox reaction?

Transfer of proton
Transfer of electron✔️
Absorption of light
Exchange of ions

Correct Answer Logic:

A redox (reduction-oxidation) reaction involves the transfer of electrons between species. Oxidation is loss of electrons and reduction is gain of electrons: $OIL\ RIG$.

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