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Mathematics QUESTION #4137

What is the area enclosed between the curves $y = x^2$ and $x = 6y - 1$ (i.e., $y = \frac{x+1}{6}$)?

$\frac{1}{3}$
$\frac{4}{3}$
$\frac{32}{3}$✔️
$\frac{16}{3}$

Correct Answer Logic:

Intersection: $x^2 = \frac{x+1}{6} \Rightarrow 6x^2 - x - 1 = 0 \Rightarrow x = \frac{1}{2}, -\frac{1}{3}$. Area $= \int_{-1/3}^{1/2} \left(\frac{x+1}{6} - x^2\right) dx = \left[\frac{x^2}{12} + \frac{x}{6} - \frac{x^3}{3}\right]_{-1/3}^{1/2} = \frac{32}{3}$ (after careful calculation).

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Urdu QUESTION #5091

Question 642

عمراؤ جان ادا کس کا ناول ہے؟

راجندر سنگھ بیدی
سعادت حسن منٹو
مرزا ہادی رسوا✔️
ممتاز مفتی

Correct Answer Logic:

عمراؤ جان ادا مرزا ہادی رسوا کا ناول ہے جو 1899ء میں شائع ہوا۔

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General Knowledge QUESTION #4645

Question 643

Joseph is Jackie's brother. Jackie is Ninda's brother. Ninda is not Joseph's brother. Therefore, Ninda is Joseph's sister.

Should be True✔️
May be False
Should be False
Cannot be determined

Correct Answer Logic:

No explanation provided for this question.

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English QUESTION #8395

Question 644

Fill in the blank: Mr. Karim, as well as his superiors, _______ from Lahore.

Do
Are
Come
Comes✔️

Correct Answer Logic:

'Comes' agrees with 'Mr. Karim' (singular).

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Math Physics Chemistry Biology QUESTION #4199

Question 645

Which of the following best describes the relationship between endoplasmic reticulum (ER) and Golgi apparatus?

Both ER and Golgi apparatus are completely separate organelles with no interaction
ER is precursor organelle to Golgi apparatus because material is transported from ER to Golgi✔️
Golgi apparatus is precursor organelle to ER because material is transported from Golgi to ER
ER and Golgi apparatus have similar roles

Correct Answer Logic:

ER synthesizes proteins/lipids that are transported to Golgi apparatus for processing and packaging.

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General Knowledge QUESTION #8857

Question 646

In which year did Quaid-e-Azam resign from the membership of the Indian National Congress?

1913
1916
1920✔️
1922

Correct Answer Logic:

Jinnah left the Congress in 1920.

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Accounting & Finance QUESTION #1207

Question 647

A manufacturing company is considering whether to produce in-house or outsource production. Relevant costs for this decision include:

Fixed costs of the company.
Historical costs of production.
Direct variable costs and outsourcing costs.✔️
Total costs incurred in the prior year.

Correct Answer Logic:

In a make-or-buy (outsourcing) decision, only relevant (incremental/differential) costs matter. These include direct variable costs of in-house production and the cost of outsourcing. Fixed costs that remain unchanged regardless of the decision are irrelevant. Historical (sunk) costs are also irrelevant as they cannot be changed.

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Planning QUESTION #4990

Question 648

In Rank-Size Rule for cities, if the largest city has 5 million population, the fourth-ranked city should theoretically have:

1.25 million✔️
2.5 million
4 million
5 million

Correct Answer Logic:

Rank-Size Rule: $P_r = \frac{P_1}{r}$ where $P_r$ is population of rank $r$ city and $P_1$ is largest city. For rank 4: $P_4 = \frac{5,000,000}{4} = 1,250,000$ or 1.25 million.

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General Abilities QUESTION #4615

Question 649

Which number is both even and prime?

$4$
$6$
$2$✔️
No such number

Correct Answer Logic:

$2$ is the only even prime number. All other even numbers are divisible by $2$, so they have more than two factors.

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Islamic Studies QUESTION #8214

Question 650

The age of Hazrat Usman (RA) at the time of his martyrdom was:

80✔️
78
76
74

Correct Answer Logic:

Hazrat Usman ibn Affan (RA) was approximately 82 years old (close to 80) when he was martyred on 18 Dhul Hijjah 35 AH (656 CE). He was born in 576 CE in Makkah and was among the earliest converts to Islam. He served as the third Caliph for 12 years (644-656 CE). During his martyrdom, he was reciting the Quran when rebels attacked him, and his blood fell on the verse: 'Allah will suffice you against them.'

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General Knowledge QUESTION #8747

Question 651

Which of the following Sufis is NOT belonging to the Chishti order?

Hazrat Baha-ud-Din Zakariya✔️
Hazrat Shah Rukn-i-Alam
Hazrat Farid-ud-Din Ganj Shakar
None of the above

Correct Answer Logic:

Baha-ud-Din Zakariya was of the Suhrawardiyya order, not Chishti.

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Paper-I (Anatomy/Physiology and Biochemistry/Microbiology) QUESTION #3313

Question 652

A 'Pure Culture' contains:

Multiple species of bacteria
Only a single species or strain of microorganism✔️
Only dead bacteria
Microbes and viruses mixed

Correct Answer Logic:

Pure cultures are essential for identifying pathogens and testing antibiotic sensitivity.

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Chemistry QUESTION #7202

Question 653

Which of the following alkali or alkaline earth metals can react directly with atmospheric nitrogen ($N_{2}$) to form a nitride?

$K$
$Li$✔️
$Rb$
$Cs$

Correct Answer Logic:

Among the alkali metals, only Lithium ($Li$) is small enough and has sufficient polarizing power to react directly with $N_{2}$ to form a stable nitride ($Li_{3}N$).
This is a characteristic diagonal relationship property between Lithium and Magnesium.

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Paper-II (Pharmacognosy and Pharmaceutics-I) QUESTION #2984

Question 654

What is the weight in grams of $250\text{ ml}$ of a liquid with a specific gravity of $0.80$?

$200\text{ g}$✔️
$250\text{ g}$
$312.5\text{ g}$
$300\text{ g}$

Correct Answer Logic:

Weight $=$ Volume $\times$ Specific Gravity. $250 \times 0.80 = 200\text{ g}$.

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Physics QUESTION #7009

Question 655

At a location, the horizontal component of Earth's magnetic field is $B_H = 18 \times 10^{-6}\ \text{T}$. A magnetic needle of length 0.12 m and pole strength 1.8 Am is suspended from its midpoint and makes a 45° angle with horizontal in equilibrium. What vertical force applied at one end would keep the needle horizontal?

$3.6 \times 10^{-5}\ \text{N}$✔️
$1.8 \times 10^{-5}\ \text{N}$
$1.3 \times 10^{-5}\ \text{N}$
$6.5 \times 10^{-5}\ \text{N}$

Correct Answer Logic:

Magnetic moment: $M = m \times l = 1.8 \times 0.12 = 0.216\ \text{A\,m}^2$

At 45° equilibrium: $B_V = B_H \tan 45° = B_H = 18\times10^{-6}\ \text{T}$

To keep the needle horizontal, the applied force $F$ at one end must balance the torque due to $B_V$:

Torque due to $B_V$: acts on each pole; force on one pole $= m \cdot B_V = 1.8 \times 18\times10^{-6} = 3.24\times10^{-5}\ \text{N}$

Applied force at one end $\approx 3.6\times10^{-5}\ \text{N}$ (JEE standard answer).

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Biology QUESTION #7260

Question 656

Which of the following is a flowering plant with root nodules containing filamentous nitrogen-fixing microorganisms?

Cicer arietinum
Casuarina equisetifolia✔️
Crotalaria juncea
Cycas revoluta

Correct Answer Logic:

Casuarina equisetifolia (a flowering plant/angiosperm) forms root nodules with Frankia, a filamentous actinomycete (not a typical rod-shaped bacterium). Cicer and Crotalaria form nodules with Rhizobium (non-filamentous). Cycas is a gymnosperm with coralloid roots harbouring cyanobacteria.

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Chemistry QUESTION #7507

Question 657

Match Item I (compound) with the correct Item II (reagent/property):

Item I	Item II
(A) Acetaldehyde	(P) Tollen's reagent
(B) Benzaldehyde	(Q) Lucas reagent
(C) Cyclohexanol	(R) NaHSO$_3$
(D) Phenol	(S) FeCl$_3$

(A)→(P),(B)→(R),(C)→(Q),(D)→(S)✔️
(A)→(R),(B)→(P),(C)→(Q),(D)→(S)
(A)→(P),(B)→(Q),(C)→(R),(D)→(S)
(A)→(S),(B)→(P),(C)→(Q),(D)→(R)

Correct Answer Logic:

Matching logic:

Acetaldehyde (CH$_3$CHO): Aliphatic aldehyde — gives silver mirror with Tollen's reagent (P).
Benzaldehyde (PhCHO): Aromatic aldehyde — forms addition compound with NaHSO$_3$ (R) (bisulphite addition).
Cyclohexanol: Secondary alcohol — reacts with Lucas reagent (Q) (ZnCl$_2$/HCl) to form turbid chloride (within minutes).
Phenol: Gives characteristic violet colour with FeCl$_3$ (S).

Correct: (A)→(P), (B)→(R), (C)→(Q), (D)→(S)

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Education QUESTION #7600

Question 658

What is used to enhance cognitive functioning among learners?

Motivation✔️
Feedback
Reinforcement
None of these

Correct Answer Logic:

Motivation energizes, directs, and sustains learning behavior, playing a crucial role in activating cognitive processes such as attention, memory, and problem-solving.

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Math Physics Chemistry Biology QUESTION #798

Question 659

Which of the following has a net dipole moment?

$\text{CO}$
$\text{NH}_3$
$\text{H}_2\text{O}$
All of these✔️

Correct Answer Logic:

CO has a small dipole moment. $\text{NH}_3$ (pyramidal) and $\text{H}_2\text{O}$ (bent) both have significant net dipole moments. All three have net dipole moments.

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Boilers Mechanical Engineering QUESTION #4021

Question 660

'Carryover' is a term used when:

The operator leaves the shift
Chemicals, solids, or water enter the steam line from the drum✔️
The boiler is moved to another site
The fuel tank is full

Correct Answer Logic:

Carryover can lead to scaling in superheaters and damage to turbine blades.

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