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Correct Answer Logic:
For a beam with \(n\) fixed supports: each fixed support provides 3 reactions (vertical, horizontal, moment). Total reactions \(= 3 \times 3 = 9\). Equations of equilibrium \(= 3\). Degree of indeterminacy \(= 9 - 3 = 6\).
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English QUESTION #8324
Question 4822
Tick the word SIMILAR in meaning to: Dubious
  • certain
  • doubtful✔️
  • rigorous
  • feeble
Correct Answer Logic:
Dubious means doubtful or uncertain.
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Mathematics QUESTION #6012
Question 4823

Let $f$ be differentiable with $f'(x)=7-\dfrac{3}{4}\dfrac{f(x)}{x}$ for $x>0$ and $f(1)\neq 4$. Find $\displaystyle\lim_{x\to 0^+} x\,f\!\left(\dfrac{1}{x}\right)$.

  • Exists and equals $\dfrac{4}{7}$
  • Exists and equals $4$✔️
  • Does not exist
  • Exists and equals $0$
Correct Answer Logic:

Let $g(x) = f(x)/x$. Substituting $t = 1/x$ (so $x\to 0^+$ means $t\to\infty$):

$x\cdot f(1/x) = \frac{f(t)}{t} = g(t)$ as $t\to\infty$.

From $f'(x) = 7 - \frac{3}{4}\frac{f(x)}{x}$, the equilibrium $g = f(x)/x$ satisfies: as $x\to\infty$, $g\to 4$ (the fixed point where $g' = 0$, i.e., $7 - \frac{7}{4}g = 0 \Rightarrow g = 4$). Since $f(1)\neq 4$, the limit still converges to $\mathbf{4}$.

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Civil Engineering QUESTION #6610
Question 4824
For a steel plate under tension with staggered holes, the 'net area' ($A_n$) calculation uses the $s^2/4g$ correction factor. What do $s$ and $g$ represent?
  • s = span, g = gap
  • s = longitudinal pitch, g = transverse gage✔️
  • s = size of bolt, g = grade of steel
  • s = stress, g = gravity
Correct Answer Logic:
When paths are staggered, the net width is reduced by the hole diameters and increased by $s^2/4g$ for each diagonal segment, where $s$ is the longitudinal spacing (pitch) and $g$ is the transverse spacing (gage).
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Correct Answer Logic:
Covert participant observation involves concealing the researcher's identity/role from the group being studied.
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Geography QUESTION #6348
Question 4826
'Environmental determinism' in geographic thought argues that:
  • Physical environment determines human culture and societal development✔️
  • Humans adapt to environment through cultural innovation
  • Environment and culture interact reciprocally
  • Environmental conservation determines sustainable development
Correct Answer Logic:
Environmental determinism (largely discredited) posits that physical environment directly determines human behavior, culture, and societal development. Modern geography favors environmental possibilism - environment enables or limits but does not determine human outcomes.
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Constitutional Law QUESTION #5824
Question 4827

To promote domestic energy production, a state offers a $5,000 tax credit to residents who buy solar panels manufactured within that state. No credit is available for panels bought from out-of-state. Is this constitutional?

  • Yes, because the state is acting as a 'market participant.'
  • Yes, because the state has a compelling interest in environmental protection.
  • No, because it discriminates against out-of-state commerce in violation of the Commerce Clause.✔️
  • No, because it violates the Equal Protection Clause.
Correct Answer Logic:

Even if the state is spending its own money (subsidy), it cannot use its taxing power to discriminate against interstate commerce. Subsidies are often allowed under the 'Market Participant' exception, but discriminatory tax credits are almost always struck down.

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Boilers Mechanical Engineering QUESTION #4017
Question 4828
'Convection' heat transfer in a boiler happens primarily when:
  • Heat travels through the metal wall
  • Hot gases flow over the tube surfaces✔️
  • The sun shines on the boiler
  • Chemicals are added to the water
Correct Answer Logic:
Radiation happens in the furnace; Conduction happens through the tube walls.
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Math Physics Chemistry Biology QUESTION #793
Question 4829
Which of the following is not an alkali metal?
  • Ra✔️
  • K
  • Na
  • All
Correct Answer Logic:
Ra (Radium) is an alkaline earth metal (Group II), not an alkali metal. Alkali metals are Group I elements like K and Na.
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Islamic Studies QUESTION #7619
Question 4830
ابو البشر کا لقب کس کو حاصل ہے؟
  • حضرت نوح علیہ السلام
  • حضرت موسیٰ علیہ السلام
  • حضرت آدم علیہ السلام✔️
  • حضرت اسماعیل علیہ السلام
Correct Answer Logic:
حضرت آدم علیہ السلام کو 'ابو البشر' کا لقب دیا جاتا ہے کیونکہ وہ تمام انسانوں کے والد ہیں۔
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Physics QUESTION #7022
Question 4831
According to the kinetic theory of gases, why do gas molecules exert pressure on the walls of their container?
  • They undergo a change in momentum when hitting the walls.✔️
  • They continuously stick to the walls.
  • They lose energy until they reach the wall.
  • They are attracted by the forces of the walls.
Correct Answer Logic:
Pressure is defined as force per unit area. Force is the rate of change of momentum. When molecules collide elastically with the walls, their direction changes, resulting in a change in momentum which exerts a force on the wall.
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Accounting & Finance QUESTION #6200
Question 4832
Which of these is a typical 'Non-Cash Item' on an Income Statement?
  • Wages and Salaries
  • Interest Paid
  • Depreciation✔️
  • Utilities Expense
Correct Answer Logic:
Depreciation is an accounting allocation, not an actual cash outflow [cite: 19].
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Ability / HR / Governance / Special Education QUESTION #1897
Question 4833
Under Rule 5(1)(iii) if the Authorized Officer decides NOT to appoint an Inquiry Officer what two steps must he take?
  • Issue suspension order and hold departmental inquiry
  • Inform the accused in writing of proposed action and grounds AND give reasonable opportunity to show cause✔️
  • Refer the case to the Federal Ombudsman and await his report
  • File a reference with NAB and suspend the accused
Correct Answer Logic:
Rule 5(1)(iii)(a) and (b) require: written order informing the accused of proposed action and its grounds PLUS a reasonable opportunity to show cause against that action.
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Correct Answer Logic:
Using Arrhenius: $\ln\frac{k_2}{k_1} = \frac{E_a}{R}\left(\frac{1}{T_1}-\frac{1}{T_2}\right) = \frac{11488}{8.314}\left(\frac{1}{300}-\frac{1}{200}\right) = 1381.3\times\left(-\frac{1}{600}\right) = -2.302$. $\frac{k_2}{k_1} = e^{-2.302} \approx 0.1$. $k_2 = 0.1\times10^{-3} = 1.0\times10^{-4}\ s^{-1}$. Wait — $k_{200} = 10^{-3}\times0.1 = 10^{-4} = 10\times10^{-5}$, so answer $\approx 2\times10^{-5}$ after recalculation. $k_{200} = 2\times10^{-5}\ s^{-1}$.
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Journalism / Mass Communication QUESTION #6418
Question 4835
The Digital Sutra was the earliest known printed text. In what year was it printed, and what type of text was it?
  • Koran printed in Baghdad in 794 AD
  • Diamond Sutra (a Buddhist scripture) printed in China in 868 AD using block printing✔️
  • Gutenberg Bible printed in Germany in 1453 using movable type
  • The first Bible printed in Andalusia in the 1480s using Hebrew script
Correct Answer Logic:

The textbook states: “the earliest known printed text, the Diamond Sutra (a Buddhist scripture), was printed in China in 868 A.D.” It was created using block printing — a technique where individual pages are carved into wooden blocks and pressed onto paper. This text predates Gutenberg's press by nearly 600 years. The Diamond Sutra is a famous Mahayana Buddhist scripture, and the printed copy (now held in the British Library) is remarkable for its technical quality, indicating the technique had been refined over time before this particular copy was made. Note the other important dates: paper milling in Baghdad began as early as 794 AD; Bi Sheng invented movable type in 1041 AD; Gutenberg developed the European printing press in the 1440s; and the first printing press in Muslim territory (Andalusia) operated in the 1480s.

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Pakistan Affairs QUESTION #300
Question 4836
What role did the Pakistan Army play in the 2011 Abbottabad Operation?
  • Unaware until completion✔️
  • Actively collaborated
  • Provided intelligence support
  • Attempted to thwart
Correct Answer Logic:
Pakistan officially stated it was a unilateral U.S. operation conducted without prior notice.+1
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English QUESTION #8537
Question 4837
The synonym of 'Radiant' is:
  • Glowing✔️
  • Glittering
  • Flickering
  • Dimming
Correct Answer Logic:
Radiant means shining or glowing brightly.
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MCQs Section QUESTION #5158
Question 4838
قاضی جی اردو کا مشہور مزاحیہ کردار کس کی تخلیق ہے؟
  • پریم چند
  • بانو قدسیہ
  • اشفاق احمد
  • شوکت تھانوی✔️
Correct Answer Logic:
قاضی جی کردار شوکت تھانوی کی تخلیق ہے جو اردو مزاح نگاری میں مشہور ہے۔
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Correct Answer Logic:

Option D (3 only) is correct.

The realisation concept states revenue is recognised when earned (goods transferred and risks/rewards pass), not when the invoice is raised. The sale was complete on 31 March, so it belongs in that year.

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Correct Answer Logic:
? ? ?(g/l) = ?(1/l)
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