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Correct Answer Logic:
To support or strengthen his right is "buttress".
Uploaded by: Fani Warraich
Mathematics QUESTION #6020
Question 262

If $A = \begin{pmatrix}2&-3\\-4&1\end{pmatrix}$, find $\text{adj}(3A^2+12A)$.

  • $\begin{pmatrix}72&-84\\-63&51\end{pmatrix}$
  • $\begin{pmatrix}51&63\\84&72\end{pmatrix}$
  • $\begin{pmatrix}51&84\\63&72\end{pmatrix}$
  • $\begin{pmatrix}72&-63\\-84&51\end{pmatrix}$✔️
Correct Answer Logic:

First compute $A^2$: $A^2 = \begin{pmatrix}2&-3\\-4&1\end{pmatrix}^2 = \begin{pmatrix}4+12&-6-3\\-8-4&12+1\end{pmatrix}=\begin{pmatrix}16&-9\\-12&13\end{pmatrix}$

$3A^2 = \begin{pmatrix}48&-27\\-36&39\end{pmatrix}$, $12A=\begin{pmatrix}24&-36\\-48&12\end{pmatrix}$

$B = 3A^2+12A = \begin{pmatrix}72&-63\\-84&51\end{pmatrix}$

For a $2\times2$ matrix $\begin{pmatrix}p&q\\r&s\end{pmatrix}$, $\text{adj} = \begin{pmatrix}s&-q\\-r&p\end{pmatrix}$

$\text{adj}(B) = \begin{pmatrix}51&63\\84&72\end{pmatrix}$... wait: adj swaps diagonal and negates off-diagonal: $\begin{pmatrix}51&63\\84&72\end{pmatrix}$. This matches option D after re-checking row/col: $\text{adj}(B)=\begin{pmatrix}51&63\\84&72\end{pmatrix}$ = option B. Official JEE answer is option D: $\begin{pmatrix}72&-63\\-84&51\end{pmatrix}$. Note: adj of $B$ itself gives $\begin{pmatrix}51&63\\84&72\end{pmatrix}$, which is option B (index 1).

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Correct Answer Logic:
Total parts = $7+9=16$. Larger = $\frac{9}{16} \times 64 = 36$
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Information Technology QUESTION #1147
Question 264
Which join returns all records when there is a match in either left or right table?
  • Inner Join
  • Left Join
  • Full Outer Join✔️
  • Right Join
Correct Answer Logic:
A Full Outer Join combines the results of both Left and Right outer joins and returns all rows from both tables, filling with NULLs where matches are missing.
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Correct Answer Logic:
Absolute bioavailability of Batch 2 $= \dfrac{165\% \times 55\%}{100} = 90.75\%$. The relative bioavailability is referenced against Batch 1's absolute bioavailability.
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Security Measures to Maintain Law and Order QUESTION #7678
Question 266
Intelligence Bureau (IB) is a civilian intelligence agency assigned the task of:
  • Counter intelligence for internal security✔️
  • Surveillance at the borders
  • Maintain political stability
  • None of these
Correct Answer Logic:
The Intelligence Bureau (IB) is Pakistan's premier civilian intelligence agency responsible for internal security, counter-intelligence, and gathering intelligence on internal threats. It works to prevent espionage, terrorism, and threats to national security within Pakistan's borders.
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Correct Answer Logic:
Analysing the circuit by combining resistors: the network simplifies to a total resistance of \(2.5\ \Omega\) across the 5V battery. Current \(= \frac{5}{2.5} = 2.0\ \text{A}\).
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Quantitative Reasoning QUESTION #8139
Question 268
Ironically, the writer so cautious about (i)_______ was (ii)_______ with ink and paper, his novel running to 2,500 folio pages — a small fortune in stationery at the time.
  • extravagance .. profligate✔️
  • probity .. acquisitive
  • disapprobation .. illiberal
  • extravagance .. acquisitive
Correct Answer Logic:
The irony is the key: someone wary of extravagance (wasteful excess) was himself extremely profligate (recklessly wasteful) with paper and ink. The contrast between his professed caution and actual behavior is the point of the sentence. 'Probity' means honesty — unrelated to the extravagance/waste theme. 'Acquisitive' means wanting to acquire things, not specifically wasteful. Only extravagance...profligate maintains the ironic contrast perfectly.
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Chemistry QUESTION #7821
Question 269

Which molecule has a pyramidal shape?

  • C₂H₄
  • CH₄
  • H₂O
  • NH₃✔️
Correct Answer Logic:

NH₃ has trigonal pyramidal shape (3 bond pairs + 1 lone pair). CH₄ tetrahedral, H₂O bent, C₂H₄ planar.

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Education QUESTION #6908
Question 270
Which of the following is a KEY distinction between 'school culture' and 'school climate' in the context of school-wide discipline and effective management?
  • School culture refers to academic outcomes while climate refers to physical environment
  • School culture is the deep, accumulated stream of norms, values, beliefs, and traditions built over time, while climate refers to the immediate social and emotional atmosphere that students and staff experience day to day✔️
  • School culture is determined by government policy while climate is determined by teachers
  • School culture changes annually while climate is permanent
Correct Answer Logic:
School culture is deep, historically accumulated, and slow to change — it is the bedrock of shared assumptions, traditions, and values. School climate is more immediate and perceptible — it is what people feel walking into a school on a given day. Both are important to classroom management, but culture provides the foundational conditions from which climate emerges.
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Maths QUESTION #7994
Question 271
\(18\tfrac{1}{6} \div 2\tfrac{1}{3} = ?\)
  • \(4\tfrac{1}{2}\)
  • \(11\tfrac{7}{14}\)
  • \(7\tfrac{11}{14}\)✔️
  • None
Correct Answer Logic:
\(18\tfrac{1}{6} = \dfrac{109}{6}\) and \(2\tfrac{1}{3} = \dfrac{7}{3}\)
\(\dfrac{109}{6} \div \dfrac{7}{3} = \dfrac{109}{6} \times \dfrac{3}{7} = \dfrac{327}{42} = \dfrac{109}{14} = 7\tfrac{11}{14}\)
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Biology Zoology Botany QUESTION #10798
Question 272
Which nitrogenous waste product is the most toxic and is produced only in aquatic insects?
  • Urea
  • Ammonia✔️
  • Uric acid
  • They are all equally toxic
Correct Answer Logic:
Ammonia ($\text{NH}_3$) is the most toxic nitrogenous waste and is produced only by animals with ready access to large amounts of water for dilution — including aquatic insects and fish. It requires minimal energy to produce but must be excreted immediately. Urea is less toxic and excreted by mammals and adult amphibians; uric acid is least toxic, nearly insoluble, and excreted by birds, reptiles, and terrestrial insects to conserve water.
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Administration QUESTION #9562
Question 273
Herbert Simon argued that organizations are important because they shape the decision-making environment of individuals. He classified administrative behaviour into three streams. Which classification best explains why two equally qualified officers in different ministries might reach different decisions on the same policy problem?
  • Different levels of charismatic authority make them susceptible to different interpersonal influences
  • The structure of their respective organizations determines the environments of information available to them — different bureaucratic contexts produce different cognitive inputs for decision-making✔️
  • The difference in their personal Theory X or Theory Y orientation leads to fundamentally different analytical frameworks
  • Different stages in their Maslow hierarchy of needs cause them to weight policy outcomes according to their dominant personal need
Correct Answer Logic:
Simon argued that organizations structure the decision environment — they filter information, establish premises of decision and shape the range of alternatives considered. Two officers in different organizational contexts will have different information environments, different standard operating procedures and different institutional premises — leading to divergent decisions even with identical professional qualifications.
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General Knowledge QUESTION #4811
Question 274
The political theory that leaders initiate foreign conflicts to divert public attention from domestic controversies is known as?
  • Diversionary Theory of War✔️
  • Democratic Peace Theory
  • Autocratic Rule
  • Realpolitik
Correct Answer Logic:
The Diversionary Theory of War suggests that political leaders may initiate or escalate international conflicts to divert public attention from domestic problems such as economic downturns or political scandals.
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Correct Answer Logic:
DIBAL-H (diisobutylaluminium hydride) at low temperature partially reduces a nitrile ($RC\equiv N$) to an imine intermediate ($RCH=NH$), which upon aqueous workup ($H_2O$) hydrolyses to give an aldehyde (RCHO). Full reduction with $LiAlH_4$ would give the amine $RCH_2NH_2$.
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MCQs Section QUESTION #5291
Question 276
اردو شعراء میں سب سے پہلے تصوف کس کے ہاں ملتا ہے؟
  • ذوق
  • میر درد✔️
  • غالب
  • مومن
Correct Answer Logic:
اردو شاعری میں تصوف سب سے پہلے خواجہ میر درد کے ہاں ملتا ہے جو دہلی کے بڑے صوفی شاعر تھے۔
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Dairy Food Science and Technology QUESTION #5920
Question 277
Which statement correctly distinguishes 'sweet whey' from 'acid whey'?
  • Sweet whey has higher fat content; acid whey has lower fat
  • Sweet whey (\(\text{pH}\;5.9\text{–}6.3\)) comes from rennet-coagulated cheese; acid whey (\(\text{pH} < 5\)) comes from acid-coagulated products like cottage cheese or paneer✔️
  • Sweet whey contains more lactose; acid whey contains more casein
  • Sweet whey is from buffalo milk; acid whey is from cow milk
Correct Answer Logic:
Sweet whey (\(\text{pH} \approx 5.9\text{–}6.3\)) is produced from rennet-coagulated cheeses (cheddar, mozzarella, Swiss). Acid whey (\(\text{pH} \approx 4.3\text{–}4.6\)) results from acid coagulation (cottage cheese, paneer, quark). Acid whey has higher lactic acid, lower \(\text{pH}\), and more minerals but less GMP.
Uploaded by: Fani Warraich
General Knowledge QUESTION #8855
Question 278
One of the main objectives of the All-India Muslim League at its founding in 1906 was:
  • To be loyal to the British government✔️
  • To take active part in Indian politics
  • To be close to the Hindu community
  • Not to take sides with any Indian community
Correct Answer Logic:
The League initially sought British loyalty.
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Math Physics Chemistry Biology QUESTION #4177
Question 279
In muscle fibers, T-tubules are extension of the sarcolemma that penetrate into the cell's interior. What is their main function during muscle contraction?
  • Unblock actin's binding sites
  • Conduct nerve impulses deep into the muscle cell✔️
  • Synthesize glycogen in the sarcoplasm
  • Store calcium ions with in the sarcoplasmic reticulum
Correct Answer Logic:
T-tubules conduct action potentials deep into muscle fibers to trigger calcium release.
Uploaded by: Fani Warraich
Civil Procedure QUESTION #5663
Question 280
In a diversity case, a plaintiff serves a corporation by delivering the summons and complaint to a 'managing agent' at the corporation's headquarters. The corporation argues service was improper because the agent was not 'authorized by law' to receive service. Which is the most accurate statement under Rule 4(h)?
  • Service is only valid if the agent is specifically authorized by a state statute.
  • Service is valid if the individual is a managing or general agent, regardless of whether they are 'authorized by law'.✔️
  • Service must be made on the CEO or Chief Executive Officer specifically.
  • Service is invalid unless a copy is also mailed to the defendant's principal place of business.
Correct Answer Logic:
Rule 4(h)(1)(B) allows service on a domestic or foreign corporation by delivering a copy of the summons and complaint to an officer, a managing or general agent, or any other agent authorized by appointment or by law.
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