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Mathematics QUESTION #1256

Let $N$ be a normal subgroup of $G$ and $H$ a subgroup of $G$. Which of the following is a subgroup of $G$?

$N \cap H$
$N \cup H$
$NH = \{nh : n\in N, h\in H\}$
Both (A) and (C)✔️

Correct Answer Logic:

Both $N\cap H$ (intersection of subgroups) and $NH$ (product set when $N$ is normal) are subgroups of $G$. The union $N\cup H$ is generally NOT a subgroup. Since the question asks which one from the listed options forms a subgroup, and option (D) correctly identifies both valid subgroup constructions, (D) is the complete answer.

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Administration QUESTION #9593

Question 5202

The yield curve inverts (short-term interest rates exceed long-term rates). Which macroeconomic interpretation is most widely accepted, and what is the implication for business investment decisions?

An inverted yield curve signals excess liquidity in the banking system — businesses should accelerate borrowing before rates normalize upward
An inverted yield curve signals market expectations of economic slowdown or recession — investors accept lower long-term yields because they anticipate falling future rates, prompting businesses to defer capital investment and maintain liquidity✔️
An inverted yield curve is caused by central bank intervention in bond markets and has no predictive value for real economic conditions
An inverted yield curve signals inflation expectations — businesses should invest in real assets immediately to hedge against purchasing power erosion

Correct Answer Logic:

An inverted yield curve (short rates > long rates) is the bond market's expression that investors expect future short-term rates to fall — which typically happens when the central bank cuts rates in response to economic weakness or recession. Historically, inversions have preceded recessions with high reliability (US data). For businesses, this signals: reduce capital expenditure, preserve liquidity, defer expansion, and prepare for demand contraction.

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Aptitude QUESTION #11006

Question 5203

Which monument is an example of Indo-Islamic architecture built during the reign of Akbar?

Red Fort
Buland Darwaza✔️
Qutub Minar
Hawa Mahal

Correct Answer Logic:

Buland Darwaza at Fatehpur Sikri was built by Akbar in 1601 to commemorate his victory over Gujarat. It is a masterpiece of Indo-Islamic architecture.

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Pakistan Affairs QUESTION #9105

Question 5204

In which year were non-party elections held in Pakistan?

1985✔️
1995
2008
None of above

Correct Answer Logic:

Non-party based elections were held in 1985.

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General Knowledge QUESTION #8866

Question 5205

What does ATM stand for?

Announcement Time Machine
Automated Teller Machine✔️
Automatic Time Machine
Animated Time Machine

Correct Answer Logic:

ATM stands for Automated Teller Machine.

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General Knowledge QUESTION #11524

Question 5206

Which key takes a snapshot of the entire computer screen and saves it to the clipboard?

Alt Key
Shift Key
Print Screen (PrtScn)✔️
None of these

Correct Answer Logic:

Pressing Print Screen (PrtSc) captures the entire screen and copies it to the Windows Clipboard. Alt + Print Screen captures only the active window. In Windows 10/11, Windows + Shift + S opens the Snipping Tool for selective capture. The image can be pasted (Ctrl+V) into any application.

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Education QUESTION #11651

Question 5207

During a classroom demonstration, the topic should ideally be presented in which style to maximize student engagement?

Suspending style
Problematic style✔️
Debatable style
None of these

Correct Answer Logic:

The problematic style of presentation frames the topic as a problem or challenge to be solved, stimulating curiosity and active thinking. It keeps students engaged and intellectually invested. This approach aligns with inquiry-based and constructivist learning principles.

Correct Answer: B — Problematic style.

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MCQs Section QUESTION #5226

Question 5208

ما وراء کس شاعر کا پہلا مجموعۂ کلام ہے؟

سلیم کوثر
یہاں سے کوثر
این ایم راشد✔️
ان میں سے کوئی نہیں

Correct Answer Logic:

ما وراء این ایم راشد کا پہلا شعری مجموعہ ہے جو 1941ء میں شائع ہوا۔

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Library Sciences QUESTION #1495

Question 5209

Which of the following best describes a 'surrogate record' in the context of information organization?

The original document stored in a library
A metadata record that represents and provides access to an information resource✔️
A backup copy of a digital file
A printed index of journal articles

Correct Answer Logic:

A surrogate record (also called a metadata record) is a representation of an information resource — not the item itself — that enables description and access. It includes bibliographic details, subject headings, and classification numbers.

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Electronics Engineering QUESTION #11737

Question 5210

The polarisation index (PI) of a motor winding insulation is defined as:

$\text{PI} = R_{10\,\text{min}} / R_{1\,\text{min}}$✔️
$\text{PI} = R_{1\,\text{min}} / R_{10\,\text{min}}$
$\text{PI} = R_{10\,\text{min}} \times R_{1\,\text{min}}$
$\text{PI} = (R_{10} - R_1) / R_1$

Correct Answer Logic:

$\text{PI} = \dfrac{R_{10\,\text{min}}}{R_{1\,\text{min}}}$ — the ratio of insulation resistance at 10 minutes to 1 minute of applied test voltage. Good, dry insulation absorbs charge over time (polarisation current decreases), giving PI > 2. Contaminated or wet insulation has low PI (~1). Per IEEE 43, PI < 1.0 is dangerous; 1.0–2.0 is questionable; > 2.0 is good.

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Physics QUESTION #7324

Question 5211

A particle is projected vertically upward with $u = 10\text{ m/s}$. Air exerts a resistive force $F = -0.2v^2$ on it ($m = 2\text{ kg}$, $g = 10\text{ m/s}^2$). The maximum height attained is:

$5\ln 2$✔️
$3\ln 2$
$2\ln 2$
$10\ln 2$

Correct Answer Logic:

Net force (taking up as positive): $F_{net} = -mg - 0.2v^2 = -20 - 0.2v^2$

Using $ma = v\dfrac{dv}{dx}$: $2v\dfrac{dv}{dx} = -20 - 0.2v^2$

Separating variables: $\dfrac{v\,dv}{20+0.2v^2} = -\dfrac{dx}{2}$

Integrating from $v = 10$ to $v = 0$: let $k = 20 + 0.2v^2$, $dk = 0.4v\,dv$

$\dfrac{1}{0.4}\big[\ln(20) - \ln(40)\big] = -\dfrac{H}{2} \Rightarrow H = \dfrac{2\ln 2}{0.4} = \mathbf{5\ln 2}$

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Security Measures to Maintain Law and Order QUESTION #938

Question 5212

What does the term 'Landside' refer to in airport security?

The runway and taxiway
Areas accessible to the non-traveling public✔️
The inside of the airplane
The cargo loading zone

Correct Answer Logic:

Landside includes check-in areas and parking lots where security measures are different from the 'Airside'.

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General Knowledge QUESTION #8951

Question 5213

In which country was a 240-year-old monarchy abolished in 2008?

Sweden
Brunei
Bhutan
Nepal✔️

Correct Answer Logic:

Nepal abolished its monarchy in 2008.

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Pakistan Affairs QUESTION #613

Question 5214

What principle was supported by Bengali politicians for representation in the legislature and executive?

Population✔️
Area
Revenue
None of these

Correct Answer Logic:

Bengal, being the most populous province, advocated for representation based on population .

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Political Science QUESTION #6685

Question 5215

Which institution is responsible for interpreting the Constitution in Pakistan?

Parliament
Supreme Court✔️
President
None of these

Correct Answer Logic:

The Supreme Court of Pakistan is the final arbiter and interpreter of the Constitution.

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Accounting & Finance QUESTION #9635

Question 5216

Interest on a loan taken specifically to construct a building is normally treated as:

Revenue expenditure, charged to P&L in the year incurred
Capital expenditure, added to the cost of the building until it is completed and ready for use✔️
Financial expenditure, shown separately in P&L under financial charges throughout the loan period
Deferred expenditure, spread over the life of the building

Correct Answer Logic:

Interest on a loan taken to purchase or construct an asset is an exception to the general rule. Such interest is capitalized (added to the cost of the asset) up to the date the asset is brought into use. This is consistent with the principle that all costs incurred to bring an asset to its intended use are part of its cost. After the asset is ready, subsequent interest is treated as a revenue expense.

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The Constitution of Pakistan QUESTION #9397

Question 5217

Under Article 19A, the right to information extends to matters of public importance subject to:

Absolute disclosure without restriction
Regulation and reasonable restrictions imposed by law✔️
A presidential declaration of what is public
Parliamentary approval for each disclosure request

Correct Answer Logic:

Article 19A, inserted by the 18th Amendment, provides: 'Every citizen shall have the right to have access to information in all matters of public importance subject to regulation and reasonable restrictions imposed by law.' The right is broad but subject to lawful regulation — balancing transparency with legitimate confidentiality interests.

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Maths QUESTION #4528

Question 5218

What is $\sqrt{(-5)^2}$?

$-5$
$5$✔️
$\pm 5$
$25$

Correct Answer Logic:

$\sqrt{a^2} = |a|$, the absolute value. So $\sqrt{(-5)^2} = \sqrt{25} = 5$

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English QUESTION #8453

Question 5219

NETTLED means:

displeased
Agreed
Annoyed✔️
None of these

Correct Answer Logic:

Nettled means irritated or annoyed.

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Molecular Biology / Bioinformatics / Biochemistry QUESTION #11092

Question 5220

Which enzyme joins (forms covalent bonds between) restriction fragments during DNA cloning?

DNA primase
DNA helicase
DNA polymerase
DNA ligase✔️

Correct Answer Logic:

DNA ligase is the enzyme that forms covalent phosphodiester bonds between adjacent nucleotides, joining restriction fragments or Okazaki fragments. In recombinant DNA technology, after restriction endonucleases cut DNA and the insert is placed into the vector, DNA ligase seals the nicks by connecting the 3′-OH of one fragment to the 5′-phosphate of the adjacent fragment, using ATP or NAD⁺ as a cofactor. Without ligase, the recombinant DNA molecule would not be covalently sealed.

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