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Physics QUESTION #7029

A pipe with a length of $85\text{ cm}$ is closed at one end. Determine the total number of natural oscillations possible for the air column in this pipe that have frequencies below $1250\text{ Hz}$. (Take the speed of sound as $340\text{ m/s}$).

$6$
$4$✔️
$12$
$8$

Correct Answer Logic:

For a closed pipe, the resonance frequencies are $f_n = \frac{(2n-1)v}{4L}$. Here $L = 0.85\text{ m}$ and $v = 340\text{ m/s}$. The fundamental frequency $f_1 = \frac{340}{4 \times 0.85} = 100\text{ Hz}$. The subsequent odd harmonics are $300\text{ Hz}$, $500\text{ Hz}$, $700\text{ Hz}$, $900\text{ Hz}$, and $1100\text{ Hz}$. The next is $1300\text{ Hz}$, which exceeds the limit. Thus, there are $6$ possible oscillations (including fundamental).

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Electrical Engineering QUESTION #2183

Question 8842

In AM with modulation index $\mu = 0.5$, the efficiency (ratio of useful sideband power to total transmitted power) is:

$11.1\%$✔️
$25.0\%$
$33.3\%$
$20.0\%$

Correct Answer Logic:

$\eta = \frac{\mu^2/2}{1+\mu^2/2}\times100 = \frac{0.125}{1.125}\times100 \approx 11.1\%$. At $\mu=1$ (100% modulation), efficiency peaks at only $33.3\%$, illustrating DSB-FC inefficiency.

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Mathematics QUESTION #11147

Question 8843

The radius of convergence of $\displaystyle\sum(3+4i)^n z^n$ is:

$\dfrac{1}{5}$✔️
$5$
$7$
$\infty$

Correct Answer Logic:

For the power series $\sum a_n z^n$ with $a_n = (3+4i)^n$, the radius of convergence is $R = \dfrac{1}{\limsup|a_n|^{1/n}} = \dfrac{1}{|3+4i|} = \dfrac{1}{\sqrt{9+16}} = \dfrac{1}{\sqrt{25}} = \dfrac{1}{5}$.

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Physics QUESTION #982

Question 8844

To obtain the given truth table ($A=0,B=0\to Y=1$; $A=0,B=1\to Y=1$; $A=1,B=0\to Y=0$; $A=1,B=1\to Y=1$), the logic gate placed at G is:

OR Gate
AND Gate✔️
NOR Gate
NAND Gate

Correct Answer Logic:

The circuit has two OR gates feeding into G. Checking the truth table: output is 0 only when $A=1, B=0$. This matches an AND gate at G, as the preceding OR gates produce inputs (1,0) for that row, and $1 \cdot 0 = 0$.

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Bio-Technology QUESTION #10618

Question 8845

ELISA (Enzyme-Linked Immunosorbent Assay) quantifies an antigen by:

Separating antigens by size on polyacrylamide gels
Measuring colour change produced by an enzyme linked to a detection antibody that is proportional to antigen amount✔️
Counting individual antigen molecules using flow cytometry
Agglutinating antigen-coated red blood cells to form visible clumps

Correct Answer Logic:

In a sandwich ELISA: (1) capture antibody is coated on a well, (2) sample antigen binds, (3) a detection antibody conjugated to an enzyme (e.g. HRP, alkaline phosphatase) binds the antigen, (4) enzyme substrate is added, producing a coloured product measured spectrophotometrically. The absorbance is proportional to antigen concentration. ELISA is widely used for diagnostics (HIV, pregnancy tests), food safety testing, and drug monitoring.

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Math Physics Chemistry Biology QUESTION #4295

Question 8846

The following is an example of a globular protein:

Keratin
Collagen
Hemoglobin✔️
Histone

Correct Answer Logic:

Hemoglobin is a classic globular protein — roughly spherical, water-soluble, and has a functional/metabolic role (oxygen transport). Keratin and collagen are fibrous proteins.

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Civil / Architecture QUESTION #2341

Question 8847

In structural dynamics, the damped natural frequency $\omega_d$ of a SDOF system with critical damping ratio $\xi$ and undamped natural frequency $\omega_n$ is:

$\omega_d = \omega_n (1 + \xi)$
$\omega_d = \omega_n \sqrt{1 - \xi^2}$✔️
$\omega_d = \omega_n \sqrt{1 + \xi^2}$
$\omega_d = \omega_n (1 - \xi)$

Correct Answer Logic:

The damped natural frequency is $\omega_d = \omega_n \sqrt{1 - \xi^2}$. For typical structural damping ($\xi = 0.02$ to $0.05$), $\omega_d \approx \omega_n$. At critical damping ($\xi = 1.0$), $\omega_d = 0$ and the system returns to equilibrium without oscillating.

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Boilers Mechanical Engineering QUESTION #2504

Question 8848

The octahedral shear stress theory (von Mises criterion) for yielding states that yielding begins when:

$\sigma_{vm} = \sqrt{\sigma_1^2 + \sigma_2^2 + \sigma_3^2} \geq S_y$
$\sigma_{vm} = \sigma_1 - \sigma_3 \geq S_y$
$\sigma_{vm} = \frac{1}{\sqrt{2}}\sqrt{(\sigma_1-\sigma_2)^2+(\sigma_2-\sigma_3)^2+(\sigma_3-\sigma_1)^2} \geq S_y$✔️
$\sigma_{vm} = \frac{\sigma_1+\sigma_2+\sigma_3}{3} \geq S_y$

Correct Answer Logic:

The von Mises (distortion energy) criterion: $\sigma_{vm}=\frac{1}{\sqrt{2}}\sqrt{(\sigma_1-\sigma_2)^2+(\sigma_2-\sigma_3)^2+(\sigma_3-\sigma_1)^2}\geq S_y$.

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The Elections Act 2017 QUESTION #9419

Question 8849

Under Section 26(2), a person is entitled to enroll as a voter if they possess a National Identity Card issued by NADRA. The NIC must be possessed at any time till the:

Thirtieth day before polling day
Last day fixed for inviting claims, objections and applications for preparation, revision or correction of electoral rolls✔️
Day of announcement of the Election Programme
Date of publication of the preliminary electoral rolls

Correct Answer Logic:

Section 26(2)(c) requires possession of a NIC 'at any time till the last day fixed for inviting claims, objections and applications for preparation, revision or correction of electoral rolls'.

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Ability / HR / Governance / Special Education QUESTION #5651

Question 8850

The last date for submission of Supplementary Grant schedules to the Finance Division (Budget Wing) is 31st May. A Ministry submits its schedule on 1st June citing operational difficulties. Analytically what is the MOST LIKELY consequence?

The Finance Division will accept the schedule since the deadline is a guideline not a strict rule
The Finance Division will view the submission with disfavour; the Ministry should have anticipated the need well ahead of the financial year; the late submission may result in the supplementary grant not being processed✔️
The schedule is automatically rejected and the Ministry must wait for the next financial year
The Financial Adviser can grant an extension of up to 30 days on his own authority

Correct Answer Logic:

The Finance Division will look with disfavour upon any request for Supplementary Grants except in extraordinary circumstances. The system expects Ministries to anticipate requirements well ahead of the financial year. A submission after the 31st May deadline compounds this problem as the O.M. is explicit about this deadline. Late submissions risk not being entertained.

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The Elections Act 2017 QUESTION #9412

Question 8851

Under Section 14(1), the Commission must prepare a comprehensive Action Plan before a general election due on expiry of an Assembly's term. The minimum lead time for preparing this Action Plan is:

Six months before the general election
Three months before the general election
Four months before the general election✔️
Two months before the general election

Correct Answer Logic:

Section 14(1) states: 'The Commission shall, at least four months before the general election is due to be held on expiry of the term of an Assembly, prepare a comprehensive Action Plan'.

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Boilers Mechanical Engineering QUESTION #4033

Question 8852

The 'Saturation Temperature' of steam is:

The temperature at which it starts to freeze
The temperature at which water and steam coexist at a given pressure✔️
Always $200^\circ\text{C}$
The temperature of the chimney

Correct Answer Logic:

Adding more heat at this point turns more water into steam without raising the temperature.

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Business, Public administration and Policy QUESTION #10502

Question 8853

The process of assessing whether a particular policy has achieved its intended effects is called:

Policy legitimation
Policy formulation
Policy evaluation✔️
Policy implementation

Correct Answer Logic:

Policy evaluation is the systematic assessment of whether a policy has achieved its stated goals and at what cost, efficiency, and equity. It uses research methods (surveys, experiments, cost-benefit analysis) to judge policy effectiveness. Evaluation findings feed back into agenda setting, informing decisions to continue, modify, or terminate a policy.

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English QUESTION #8385

Question 8854

De Jure means:

by right
by law✔️
by the way
by itself

Correct Answer Logic:

De Jure means by law (legally).

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General Knowledge QUESTION #11471

Question 8855

In Microsoft Word, where can you toggle the visibility of Text Boundaries?

Customize from Tools menu
AutoText option from Insert menu
Options from Tools menu✔️
All of the above

Correct Answer Logic:

In MS Word (older versions), text boundaries are shown/hidden via Tools → Options → View tab → Text boundaries. In Word 2010+, it is under File → Options → Advanced → Show document content → Show text boundaries. Text boundaries show dotted lines around the text area defined by page margins.

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General Knowledge QUESTION #8986

Question 8856

Which vitamin cannot be stored in the human body?

Vitamin A
Vitamin C✔️
Vitamin D
Vitamin E

Correct Answer Logic:

Vitamin C is water-soluble and excreted.

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Statistics QUESTION #1981

Question 8857

In simple linear regression $\hat{X}_1 = a + b X_3$, the regression coefficient $b_{13}$ is given by:

$\dfrac{S_{11}}{S_{33}}$
$\dfrac{S_{13}}{S_{33}}$✔️
$\dfrac{S_{13}}{S_{11}}$
$\dfrac{S_{33}}{S_{13}}$

Correct Answer Logic:

The regression coefficient of $X_1$ on $X_3$ is $b_{13} = \dfrac{\sum(X_1 - \bar{X}_1)(X_3 - \bar{X}_3)}{\sum(X_3 - \bar{X}_3)^2} = \dfrac{S_{13}}{S_{33}}$, where $S_{13}$ is the corrected sum of cross-products and $S_{33}$ is the corrected sum of squares of $X_3$.

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Law QUESTION #9699

Question 8858

Under Article 121, when an accused claims a General Exception under the Pakistan Penal Code, the burden of proving the existence of circumstances bringing the case within that exception lies:

On the prosecution
On the Court to investigate
On the accused himself✔️
On the witnesses

Correct Answer Logic:

Article 121 places the burden of proving circumstances bringing the case within any General Exception of PPC on the accused, and the Court shall presume the absence of such circumstances.

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Maths QUESTION #4605

Question 8859

Simplify: $(x^3)(x^2)$

$x^5$✔️
$x^6$
$x^9$
$2x^5$

Correct Answer Logic:

When multiplying same base, add exponents: $x^3 \times x^2 = x^{3+2} = x^5$

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Chemistry QUESTION #7423

Question 8860

The correct order of atomic radii among Group 13 elements is:

B < Ga < Al < Tl < In
B < Al < Ga < In < Tl
B < Al < In < Ga < Tl
B < Ga < Al < In < Tl✔️

Correct Answer Logic:

Group 13 atomic radii — note the anomaly of Ga:

B (Period 2): smallest
Al (Period 3): larger than B
Ga (Period 4): slightly smaller than Al due to d-block contraction (3d¹⁰ electrons offer poor shielding)
In (Period 5): larger than Ga
Tl (Period 6): largest

Correct order: B < Ga < Al < In < Tl

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