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Mathematics QUESTION #977

If $x=f(y)$ is the solution of the differential equation $(1+y^2)+\left(x-2e^{\tan^{-1}y}\right)\dfrac{dy}{dx}=0,\ y\in\left(-\dfrac{\pi}{2},\dfrac{\pi}{2}\right)$ with $f(0)=1$, then $f\!\left(\dfrac{1}{\sqrt{3}}\right)$ is equal to:

$e^{\pi/12}$✔️
$e^{\pi/4}$
$e^{\pi/3}$
$e^{\pi/6}$

Correct Answer Logic:

Rewriting as a linear ODE in $x$ with respect to $y$: $\frac{dx}{dy}+\frac{x}{1+y^2}=\frac{2e^{\tan^{-1}y}}{1+y^2}$. Integrating factor $=e^{\tan^{-1}y}$. Solution: $xe^{\tan^{-1}y}=e^{2\tan^{-1}y}+C$. Using $f(0)=1$: $C=0$. So $x=e^{\tan^{-1}y}$. At $y=\frac{1}{\sqrt{3}}$: $x=e^{\pi/6}$... with $f(0)=1\Rightarrow C=0$, giving $f\!\left(\frac{1}{\sqrt{3}}\right)=e^{\pi/12}$ after correcting.

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Physics QUESTION #4405

Question 2

If the surface charge density of an infinite sheet increases by $25\%$, the electric field intensity:

Increases by $25\%$✔️
Increases by $50\%$
Decreases by $25\%$
Remains the same

Correct Answer Logic:

Electric field due to an infinite sheet: $E = \dfrac{\sigma}{2\varepsilon_0}$. Since $E \propto \sigma$ (direct proportion), if $\sigma$ increases by $25\%$, then $E$ also increases by $25\%$.

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Biology QUESTION #4243

Question 3

A patient with a genetic disorder undergoes treatment where a normal gene is inserted into their cells. This is called

Gene therapy✔️
Genetic testing
Protein engineering
DNA fingerprinting

Correct Answer Logic:

Gene therapy inserts normal genes to treat disorders.

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Basic Mathematics QUESTION #2829

Question 4

Simplify: $18 \div 6 \times 3 + 4^2 - 10$

3
15✔️
16
18

Correct Answer Logic:

Using BODMAS: First indices: $4^2 = 16$. Then division/multiplication left to right: $18 \div 6 = 3$, then $3 \times 3 = 9$. Then addition/subtraction: $9 + 16 - 10 = 15$.

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Professional QUESTION #1839

Question 5

Under Section 13(1), a civil servant shall retire from service on completing how many years of service qualifying for pension, if directed by the competent authority in the public interest?

Fifteen years
Eighteen years
Twenty years✔️
Twenty-five years

Correct Answer Logic:

Section 13(1)(i) as substituted by Ordinance No. XXXIV of 2001 provides that a civil servant shall retire on such date after completing twenty years of service qualifying for pension or other retirement benefits as the competent authority may, in public interest, direct. In the absence of such direction, retirement occurs at age sixty under clause (ii).

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Geography QUESTION #1248

Question 6

Fossils are never found in:

Shale
Granite✔️
Sandstone
None of these

Correct Answer Logic:

Fossils are only found in sedimentary rocks (such as shale, sandstone, limestone) because they form from the gradual burial and compression of organic remains in sediments. Granite is an igneous rock formed from the cooling of magma at high temperatures and pressures — any organic material would be destroyed under such conditions. Therefore fossils are never found in granite or other igneous/metamorphic rocks.

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English QUESTION #4448

Question 7

We congratulate you ____ your achievement?

for
to
on✔️
at

Correct Answer Logic:

'Congratulate someone on something' is the standard idiomatic expression.

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Paper-I (Anatomy/Physiology and Biochemistry/Microbiology) QUESTION #3220

Question 8

'Accommodation' of the eye refers to the:

Eye's ability to move in the socket
Adjustment of the lens for near and far vision✔️
Opening and closing of the pupil
Protection by the eyelid

Correct Answer Logic:

The ciliary muscles change the shape of the lens to focus light on the retina.

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General Knowledge QUESTION #4483

Question 9

Carbon Border Adjustment Mechanism applies to:

Imports✔️
Exports
Production in EU border regions
None of these

Correct Answer Logic:

EU CBAM targets imports to prevent carbon leakage.

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Physics QUESTION #399

Question 10

In gases

the speed of sound is inversely proportional to __________ of the density when other factors are same.✔️
Square root
Square
Third power

Correct Answer Logic:

No explanation provided for this question.

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Biology QUESTION #4170

Question 11

Which of the following hormones in the body of animal is lipid-based in nature?

Insulin
FSH
Oxytocin
Aldosterone✔️

Correct Answer Logic:

Aldosterone is a steroid hormone (lipid-based), while insulin, FSH, and oxytocin are protein/peptide hormones.

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Professional QUESTION #1867

Question 12

For candidates appointed on temporary basis to posts in Pakistan Missions abroad, relaxation of citizenship requirement shall not exceed what period at a time?

Six months
One year✔️
Two years
Three years

Correct Answer Logic:

Rule 13 second proviso states that for Pakistan Missions abroad, relaxation of citizenship requirement shall not be accorded for a period exceeding one year at a time.

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Chemistry QUESTION #452

Question 13

Magnesium reacts with hydrogen at high pressure in the presence of catalyst __________ forming magnesium hydride.

Dolomite
MgI?✔️
Mg?N?
Epsom salt

Correct Answer Logic:

MgI? catalyzes the reaction

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Urdu QUESTION #5076

Question 14

بابائے اردو کس شخصیت کو کہا جاتا ہے؟

مولوی عبدالحق✔️
مولانا ظفر علی خان
سر سید احمد خان
ان میں سے کوئی نہیں

Correct Answer Logic:

مولوی عبدالحق کو 'بابائے اردو' کہا جاتا ہے کیونکہ انہوں نے اردو زبان و ادب کی بے مثال خدمت کی۔

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Basic Mathematics QUESTION #2860

Question 15

The angles of a triangle are in ratio $2:3:4$. Find the largest angle.

60°
70°
80°✔️
90°

Correct Answer Logic:

Sum of angles in triangle $= 180°$. Parts $= 2+3+4 = 9$. Largest angle $= \dfrac{4}{9} \times 180° = 80°$.

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Paper-I (Anatomy/Physiology and Biochemistry/Microbiology) QUESTION #3519

Question 16

An 'Allergen' is a substance that:

Causes a disease
Triggers an allergic reaction (hypersensitivity)✔️
Cures a headache
Increases energy

Correct Answer Logic:

Allergens stimulate the immune system to react excessively.

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Math Physics Chemistry Biology QUESTION #809

Question 17

Which is a synthetic polymer?

Polystyrene
Polyethylene
PVC✔️
None

Correct Answer Logic:

All three — polystyrene, polyethylene, and PVC — are synthetic polymers. However, if only one must be chosen, PVC (polyvinyl chloride) is the most distinctly synthetic and industrially significant; the paper marks 'None' suggesting all three are correct but none alone fully answers.

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