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A linear transformation requires $T(c\mathbf{v})=cT(\mathbf{v})$. Check: $T(-1,0,0)=(|-1|,0)=(1,0)$ but $-T(1,0,0)=-(1,0)=(-1,0)$. Since $T(-\mathbf{v})\neq -T(\mathbf{v})$, $T$ is NOT linear. The $|x|$ component violates homogeneity.

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Chemistry QUESTION #1020

Question 744

Arrange $\text{HBr}$, $\text{H}_2\text{S}$, $\text{NF}_3$ and $\text{CHCl}_3$ in increasing order of their dipole moment:

$\text{H}_2\text{S} < \text{HBr} < \text{NF}_3 < \text{CHCl}_3$
$\text{NF}_3 < \text{HBr} < \text{H}_2\text{S} < \text{CHCl}_3$✔️
$\text{HBr} < \text{H}_2\text{S} < \text{NF}_3 < \text{CHCl}_3$
$\text{CHCl}_3 < \text{NF}_3 < \text{HBr} < \text{H}_2\text{S}$

Correct Answer Logic:

Dipole moments (approx): $\text{NF}_3\approx0.24\ \text{D}$ (F pulls away from N lone pair, net dipole is small); $\text{HBr}\approx0.82\ \text{D}$; $\text{H}_2\text{S}\approx0.97\ \text{D}$; $\text{CHCl}_3\approx1.87\ \text{D}$. Increasing order: $\text{NF}_3 < \text{HBr} < \text{H}_2\text{S} < \text{CHCl}_3$.

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Biology QUESTION #4291

Question 745

Which part of the neuron typically receives incoming signals from other neurons?

Axon
Dendrites✔️
Myelin sheath
Synaptic knob

Correct Answer Logic:

Dendrites are the branched extensions of a neuron that receive incoming signals from other neurons and transmit them toward the cell body.

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Chemistry QUESTION #458

Question 746

Al?O?(SiO?).2H?O is called

Clay✔️
Talc
Asbestos
None of these

Correct Answer Logic:

This is the formula for clay

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Urdu QUESTION #5138

Question 747

وہ گھڑی جس کا انتظار تھا، ______ ۔

آن پہنچی✔️
آپہنچی
آن پہنچا
ان میں سے کوئی نہیں

Correct Answer Logic:

درست جملہ ہے: 'آن پہنچی' کیونکہ گھڑی مونث ہے اور آن پہنچی اس کا درست فعل ہے۔

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Urdu QUESTION #5292

Question 748

دامن تر ہونا محاورے کا مفہوم کیا ہے؟

آنسو سے بھیگ جانا
گنہگار ہونا✔️
غم میں شریک ہونا
پیاس بجھانا

Correct Answer Logic:

دامن تر ہونا محاورے کا مطلب ہے گنہگار ہونا یعنی اپنی آستین پر گناہ کے داغ ہونا۔

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Professional QUESTION #1915

Question 749

Under Rule 5(12) if doubt or dispute arises about the interpretation of the Rules or the Division to which a case pertains whose decision is final?

The Establishment Division
The Cabinet
The Cabinet Division✔️
The Prime Minister

Correct Answer Logic:

Rule 5(12) states that such a case shall be referred to the Cabinet Division whose decision shall be final; the Cabinet Division shall obtain orders of the Prime Minister where necessary.

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Basic Mathematics QUESTION #2803

Question 750

Which of the following is a PRIME number?

91
87
97✔️
111

Correct Answer Logic:

A prime number has exactly two factors: 1 and itself. 97 is only divisible by 1 and 97, making it prime. 91 = 7 × 13, 87 = 3 × 29, and 111 = 3 × 37, so they are composite.

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Therapeutics and Patient Care QUESTION #3864

Question 751

What is the accepted therapeutic daily dose range of the thiazide diuretic hydrochlorothiazide in adults?

$0.5$–$1$ mg
$2$–$5$ mg
$6.25$–$25$ mg✔️
$50$–$100$ mg

Correct Answer Logic:

The standard adult daily dose range for hydrochlorothiazide is $6.25$–$25$ mg depending on indication.

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Mathematics QUESTION #967

Question 752

If $\displaystyle\int e^x\!\left(\dfrac{x\sin^{-1}x}{\sqrt{1-x^2}}+\dfrac{\sin^{-1}x}{(1-x^2)^{3/2}}+\dfrac{x}{1-x^2}\right)dx = g(x)+C$, where $C$ is the constant of integration, then $g\!\left(\dfrac{1}{2}\right)$ equals:

$\dfrac{\pi}{4}\sqrt{e^3}$
$\dfrac{\pi}{6}\sqrt{e^3}$✔️
$\dfrac{\pi}{4}\sqrt{e^2}$
$\dfrac{\pi}{6}\sqrt{e^2}$

Correct Answer Logic:

The integrand can be written as $\frac{d}{dx}\!\left[e^x \cdot \frac{x\sin^{-1}x}{\sqrt{1-x^2}}\right]$. So $g(x)=e^x\cdot\frac{x\sin^{-1}x}{\sqrt{1-x^2}}$. At $x=\frac{1}{2}$: $g\!\left(\frac{1}{2}\right)=e^{1/2}\cdot\frac{\frac{1}{2}\cdot\frac{\pi}{6}}{\frac{\sqrt{3}}{2}}=\frac{\pi}{6}\sqrt{e^3}$ after simplification.

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Professional QUESTION #1882

Question 753

Under Rule 4 which penalties disqualify a government servant from future employment?

Both removal and dismissal from service
Only removal from service
Only dismissal from service✔️
Compulsory retirement and dismissal both

Correct Answer Logic:

Rule 4(2) explicitly states: removal from service does NOT disqualify for future employment but dismissal from service DOES disqualify.

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MCQs Section QUESTION #4849

Question 754

Choose the word nearly similar in meaning to "VELD"

Arctic wasteland
European plains
South African grassland✔️
Deep valley

Correct Answer Logic:

Veld (also spelled veldt) refers to the open, uncultivated grasslands or bushland of southern Africa, particularly in South Africa, Zimbabwe, and Namibia.

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Mechanical Engineering QUESTION #2503

Question 755

A simply supported beam with uniformly distributed load $w$ (N/m) over span $L$ has a maximum bending moment of:

$M_{max} = \frac{wL}{8}$
$M_{max} = \frac{wL^2}{4}$
$M_{max} = \frac{wL^2}{8}$✔️
$M_{max} = \frac{wL^2}{2}$

Correct Answer Logic:

For a simply supported beam with UDL $w$ over span $L$: the maximum bending moment occurs at mid-span and equals $M_{max} = wL^2/8$.

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General Knowledge QUESTION #2610

Question 756

Which of the following is NOT a characteristic of 'Open Source' software?

The source code is freely available to view and modify
Other developers can distribute the software for free
The software cannot be used by commercial organizations under any circumstances✔️
Developers can share and improve the software collaboratively

Correct Answer Logic:

Open source means developers will let other developers share, modify, and distribute software for free. However, open source software CAN be used by commercial organizations — many businesses use Linux and other open source tools commercially. The restriction on commercial use is NOT a defining feature of open source.

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Boilers Mechanical Engineering QUESTION #3997

Question 757

Operating a boiler without a 'Valid Certificate' is considered:

A minor oversight
An illegal act subject to penalties and fines✔️
Allowed if the boiler is new
Allowed if no accident happens

Correct Answer Logic:

The law strictly prohibits the use of uncertified boilers to prevent loss of life and property.

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Biology QUESTION #4293

Question 758

Which of the following best highlights the importance of proteins in immunity?

They act as receptors of pathogens
They are long term energy reserves
They act as antibodies
They act as mechanical barrier for pathogens✔️

Correct Answer Logic:

Proteins such as keratin in skin form mechanical barriers that physically prevent pathogens from entering the body, highlighting their protective structural role in immunity.

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