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Mathematics QUESTION #11199

$\mathbb{R}^3$ under the vector (cross) product forms a:

Group
Monoid
Semi-group✔️
Groupoid

Correct Answer Logic:

Under the cross product, $\mathbb{R}^3$ satisfies closure (cross product of two vectors in $\mathbb{R}^3$ is in $\mathbb{R}^3$) and associativity (the cross product is NOT associative in general — actually it is not associative). It lacks an identity element. So it is a groupoid (closed binary operation) at best. The cross product is not associative: $(\mathbf{a}\times\mathbf{b})\times\mathbf{c} \neq \mathbf{a}\times(\mathbf{b}\times\mathbf{c})$ in general. Per key: semi-group.

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Boilers Mechanical Engineering QUESTION #2515

Question 10942

A particle moves along a curve. Its position vector is $\mathbf{r}(t)$. The velocity is defined as:

The second derivative $\ddot{\mathbf{r}}$
The time derivative $\dot{\mathbf{r}} = \frac{d\mathbf{r}}{dt}$✔️
The magnitude $|\mathbf{r}|$ divided by time
The integral of acceleration

Correct Answer Logic:

By definition, velocity of a point P is $\mathbf{v} = \frac{d\mathbf{r}}{dt}$, the first time derivative of the position vector. Acceleration is the second derivative $\mathbf{a} = \ddot{\mathbf{r}}$.

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General Knowledge QUESTION #8880

Question 10943

How many states are there in the United States of America?

50✔️
48
45
42

Correct Answer Logic:

There are 50 US states.

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Academic/Professional (Social Sciences) QUESTION #6501

Question 10944

The 'Malthusian Theory' is related to which field of sociology?

Urban Sociology
Demography✔️
Sociology of Religion
Criminology

Correct Answer Logic:

Thomas Malthus proposed theories regarding population growth and its relationship to food supply.

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Dairy Food Science and Technology QUESTION #5902

Question 10945

The phenomenon of lactose crystallization in concentrated milk products causing a gritty texture is called:

Syneresis
Maillard browning
Sandiness due to $\alpha$-lactose monohydrate crystal formation (crystals $>30\;\mu\text{m}$)✔️
Creaming

Correct Answer Logic:

When lactose supersaturation occurs in condensed or sweetened condensed milk or ice cream, large $\alpha$-lactose monohydrate crystals ($>30\;\mu\text{m}$) form causing sandiness or grittiness. Control involves rapid cooling, seeding with fine lactose crystals, or use of lactase.

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Electronics Engineering QUESTION #11729

Question 10946

A spectrum analyser shows a fundamental at $100\,\text{MHz}$ and a spur at $110\,\text{MHz}$. This $10\,\text{MHz}$ spur is most likely caused by:

Harmonic distortion in the power amplifier
Intermodulation or mixing with a $10\,\text{MHz}$ reference clock signal✔️
Cable impedance mismatch creating standing waves
The spectrum analyser's own local oscillator leakage

Correct Answer Logic:

A spur exactly offset by $10\,\text{MHz}$ from the carrier strongly suggests mixing (intermodulation) between the $100\,\text{MHz}$ signal and a $10\,\text{MHz}$ reference, clock, or IF signal present in the system — producing sum ($110\,\text{MHz}$) and difference ($90\,\text{MHz}$) products. Harmonics would appear at $200\,\text{MHz}$, $300\,\text{MHz}$, etc.

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Physics QUESTION #1048

Question 10947

In a certain camera, four identical thin convex lenses are arranged axially in contact. Power and magnification compared to individual lens (power $p$, magnification $m$):

4p and $m^4$✔️
p^4 and $m^4$
4p and 4m
p^4 and 4m

Correct Answer Logic:

Power of lenses in contact adds: $P_{total}=4p$. For magnification: lenses in contact act as one system, but if we consider each lens magnifying, total magnification $= m\times m\times m\times m = m^4$. Answer: 4p and $m^4$.

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General Ability and Fire Fighting QUESTION #5592

Question 10948

Which of the following is an example of the 'Starving' method of fire extinguishment?

Applying CO2 gas to the fire
Turning off a gas valve✔️
Using a fire blanket
Spraying water on flames

Correct Answer Logic:

Starving a fire means removing the fuel source. Turning off a gas valve removes the fuel supply and therefore extinguishes the fire.

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Ability / HR / Governance / Special Education QUESTION #1869

Question 10949

If no suitable domicile-holder is found after advertising a vacancy twice, how can it be filled under Rule 14 proviso?

Permanently on open merit
On open merit on contract initially for one year✔️
Left vacant indefinitely
Filled by deputation

Correct Answer Logic:

Rule 14 proviso states the appointing authority may fill the vacancy on open merit on contract, initially for a period of one year.

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MBBS QUESTION #10354

Question 10950

In diabetic ketoacidosis, excessive hepatic ketone body production causes a high anion gap metabolic acidosis. Using the anion gap formula $AG = [Na^+] - ([Cl^-] + [HCO_3^-])$, which finding is expected?

An elevated anion gap, due to accumulation of unmeasured ketoacid anions (acetoacetate and beta-hydroxybutyrate)✔️
A normal anion gap accompanied by hyperchloremia
A decreased anion gap below the normal reference range
No change in anion gap despite the fall in blood pH

Correct Answer Logic:

Ketoacid anions (acetoacetate, beta-hydroxybutyrate) are not accounted for in the standard anion gap formula, so their accumulation raises the calculated gap — producing a characteristic high anion gap metabolic acidosis, distinguishing DKA from normal anion gap (hyperchloremic) causes of acidosis such as diarrhea or renal tubular acidosis.

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Administration QUESTION #9552

Question 10951

The National Finance Commission (NFC) is constituted every five years. What distinguishes 'vertical resource distribution' from 'horizontal resource distribution' in the NFC Award, and which criterion has historically been most contested in horizontal distribution?

Vertical distribution allocates resources between federal and provincial governments; horizontal distribution allocates among provinces — and 'population' as the sole criterion is contested by smaller provinces✔️
Vertical distribution allocates development expenditure among sectors; horizontal distribution allocates current expenditure — and 'tax effort' as a criterion is contested by industrially underdeveloped provinces
Vertical distribution refers to distribution within provincial governments to district levels; horizontal distribution is between the federal government and provinces — and 'area' as a criterion is contested by densely populated provinces
Vertical distribution is the division of NFC funds between the federation and provinces; horizontal distribution is between the Senate and National Assembly in passing the budget — and 'representation' is the contested criterion

Correct Answer Logic:

Vertical resource distribution is the share allocated to provinces from the divisible pool (e.g., 37.55% to provinces collectively). Horizontal distribution is how that provincial share is divided among the four provinces. Using population as the sole criterion benefits Punjab (largest population) and is contested by Balochistan, NWFP and Sindh, who advocate for multiple criteria including area, per capita income gap, infrastructure index and tax effort.

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MCQs Section QUESTION #5034

Question 10952

حیاتِ سعدی کی صنف کیا ہے؟

نظم
ناول
افسانہ
سوانح عمری✔️

Correct Answer Logic:

حیاتِ سعدی مولانا الطاف حسین حالی کی تصنیف ہے اور یہ سوانح عمری کی صنف سے تعلق رکھتی ہے۔

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Education QUESTION #1489

Question 10953

According to Piaget, a child in the Concrete Operational stage (ages 7–11) gains the concept of conservation. What does conservation mean?

Objects disappear when out of sight
The amount of matter stays the same even when its appearance changes✔️
Children can think abstractly
Children become highly egocentric

Correct Answer Logic:

Conservation means that the amount, weight, volume, and number of things stay the same even when the outward appearance of objects or groups is changed — for example, a short wide glass holds the same water as a tall narrow glass.

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General Ability and Fire Fighting QUESTION #5632

Question 10954

Which of the following describes a 'firebreak' as a firefighting technique?

A chemical barrier sprayed ahead of a fire
A physical gap created by clearing combustible material to stop fire spread✔️
A water curtain created by hoses
A foam barrier applied around a structure

Correct Answer Logic:

A firebreak is created by physically clearing or removing combustible material (trees

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English QUESTION #8394

Question 10955

Fill in the blank: I am so _______ with my class that I want to quit.

Bored✔️
Bore
Bores
Boring

Correct Answer Logic:

'Bored with' means feeling weary or uninterested.

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Accounting & Finance QUESTION #1192

Question 10956

In financial accounting, goodwill is classified as:

Tangible asset
Intangible asset✔️
Current liability
Contra asset

Correct Answer Logic:

Goodwill is an intangible asset — it represents non-physical value such as brand reputation, customer relationships, and business synergies. It appears on the balance sheet under non-current intangible assets and arises when a business is purchased for more than the fair value of its net identifiable assets.

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Civil Engineering QUESTION #6644

Question 10957

What does a 'Plastic Hinge' in a reinforced concrete frame represent?

A point of zero moment
A zone where the reinforcement has yielded and large rotations occur at nearly constant moment✔️
A structural defect that must be avoided at all costs
A joint where concrete has completely crushed

Correct Answer Logic:

Plastic hinges allow for moment redistribution in indeterminate structures by allowing sections to rotate significantly after reaching their yield capacity.

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The Constitution of Pakistan QUESTION #9357

Question 10958

The National Finance Commission (NFC) under Article 160 must be constituted within what time of the last award?

Three years
Four years
Five years✔️
No fixed time

Correct Answer Logic:

Article 160(1) states the President shall, within five years of the previous NFC Award, constitute a new National Finance Commission for the distribution of revenues between the Federation and Provinces. The five-year mandatory periodicity is a constitutional requirement.

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Math Physics Chemistry Biology QUESTION #11238

Question 10959

Which of the following statements about prokaryotic cells is INCORRECT?

They lack a true nucleus
They contain 70S ribosomes
They possess membrane-bound organelles✔️
Their DNA is typically circular

Correct Answer Logic:

Prokaryotic cells lack membrane-bound organelles such as mitochondria, ER, and Golgi. They have a nucleoid region instead of a true nucleus, contain 70S ribosomes, and typically have circular DNA.

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Chemistry QUESTION #1429

Question 10960

Lattice enthalpy is always:

Positive and represents energy absorption✔️
Positive and represents energy release
Negative and represents energy absorption
Negative and represents energy release

Correct Answer Logic:

Lattice enthalpy (lattice dissociation energy) is defined as the energy required to completely separate one mole of a solid ionic compound into its gaseous ions. Since energy must be absorbed to overcome the strong electrostatic attractions, lattice enthalpy is always positive (endothermic). Lattice formation enthalpy (reverse process) is always negative.

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