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Mathematics QUESTION #964

Let $\alpha, \beta, \gamma$ and $\delta$ be the coefficients of $x^7, x^5, x^3$ and $x$ respectively in the expansion of $\left(x + \sqrt{x^3-1}\right)^5 + \left(x - \sqrt{x^3-1}\right)^5,\ x > 1$. If $u$ and $v$ satisfy the equations $\alpha u + \beta v = 18$ and $\gamma u + \delta v = 20$, then $u + v$ equals:

5✔️
3
4
8

Correct Answer Logic:

Expanding using binomial theorem, the sum eliminates odd-powered terms of $\sqrt{x^3-1}$. Collecting coefficients: $\alpha=2, \beta=10, \gamma=10, \delta=2$. Solving $2u+10v=18$ and $10u+2v=20$ gives $u=\frac{8}{6}, v=\frac{14}{6}$... yielding $u+v=5$.

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Mechanical Engineering QUESTION #2553

Question 502

The second moment of area of a rectangle $b \times h$ about its centroidal axis parallel to $b$ is:

$\dfrac{bh^3}{3}$
$\dfrac{b^3h}{12}$
$\dfrac{bh^3}{12}$✔️
$\dfrac{bh^2}{6}$

Correct Answer Logic:

The centroidal second moment about the horizontal centroidal axis of a rectangle is $\bar{I}_x=\frac{bh^3}{12}$. The value $\frac{bh^3}{3}$ is about the base (bottom edge), obtained by the parallel-axis theorem.

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Islamic Studies QUESTION #210

Question 503

Which financial institution was established by Caliph Umar (رضي الله عنه)?

Bayt al-Mal✔️
Islamic Bank
Zakat Fund
All of these

Correct Answer Logic:

The Bayt al-Mal was the state treasury for collecting and distributing revenues.

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Security Measures to Maintain Law and Order QUESTION #929

Question 504

How does a 'Security Audit' differ from a routine inspection?

It is shorter
It is a systematic, independent review✔️
It is conducted by the media
It involves no paperwork

Correct Answer Logic:

Audits are deep, structured evaluations used to ensure that security programs meet national and international standards.

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Paper-I (Anatomy/Physiology and Biochemistry/Microbiology) QUESTION #3416

Question 505

Which property of water allows it to absorb a lot of heat with minimal temperature change?

High Surface Tension
High Specific Heat Capacity✔️
Low Density
Freezing point

Correct Answer Logic:

This helps in maintaining body temperature (thermoregulation).

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Physics QUESTION #4414

Question 506

The wave that has the highest frequency and penetrating power is:

X-rays
Ultraviolet rays
Gamma rays✔️
Microwaves

Correct Answer Logic:

Gamma rays ($\gamma$-rays) have the highest frequency ($> 10^{19}\ Hz$) and shortest wavelength in the electromagnetic spectrum. Their high energy ($E = hf$) gives them the greatest penetrating power.

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Reading and Writing (Module-1) QUESTION #5393

Question 507

Research conducted by planetary scientist Katarina Miljkovic suggests that the Moon's surface may not accurately _______ early impact events. When the Moon was still forming, its surface was softer, and asteroid or meteoroid impacts would have left less of an impression; thus, evidence of early impacts may no longer be present. Which choice completes the text with the most logical and precise word or phrase?

reflect✔️
receive
evaluate
mimic

Correct Answer Logic:

'Reflect' means show or make apparent. The context indicates the Moon's surface may not accurately show signs of early impacts due to its softer condition when forming.

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Education QUESTION #1482

Question 508

Which educational philosophy emphasizes teaching ideas that are everlasting and seeks enduring realities through great literature, art, philosophy, and religion?

Pragmatism
Perennialism✔️
Realism
Existentialism

Correct Answer Logic:

Perennialism focuses on teaching ideas that are everlasting and seeks enduring realities which are constant, found through great literature, art, philosophy, and religion. Key proponents include Robert Hutchins and Mortimer Adler.

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Architecture QUESTION #2342

Question 509

In the ACI Direct Design Method for flat slabs, the total factored static moment $M_o$ for a panel with factored load $w_u$ per unit area, transverse span $l_2$, and clear span $l_n$ is:

$M_o = \dfrac{w_u l_2 l_n^2}{12}$
$M_o = \dfrac{w_u l_1 l_n^2}{8}$
$M_o = \dfrac{w_u l_2 l_n^2}{8}$✔️
$M_o = \dfrac{w_u l_2^2 l_n}{8}$

Correct Answer Logic:

Per ACI 318, $M_o = \dfrac{w_u l_2 l_n^2}{8}$ where $l_2$ is the panel width transverse to the analysis direction and $l_n$ is the clear span. $M_o$ is then split between positive and negative moments (typically 65% negative, 35% positive for interior spans) and further distributed between column and middle strips.

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Pharmacology and Toxicology QUESTION #3862

Question 510

Which of the following statements regarding methadone is INCORRECT?

Can be given parenterally
Is an opioid antagonist✔️
Has a long elimination half-life
Has significant analgesic activity

Correct Answer Logic:

Methadone is a full opioid agonist, not an antagonist. It has high oral bioavailability, can be given parenterally, has a long half-life ($24$–$36$ hours), and is an effective analgesic.

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General Science and Ability QUESTION #252

Question 511

The minimum amount of vitamin stored in the human body is of:

Vitamin D
Vitamin C✔️
Vitamin E
Vitamin A

Correct Answer Logic:

Water-soluble vitamins like Vitamin C are not stored in large amounts compared to fat-soluble ones.+2

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General Knowledge QUESTION #4471

Question 512

_____ is the author of “Essay on Population (1798)”.

Thomas Malthus✔️
Ester Boserup
Garret Hardin
None of these

Correct Answer Logic:

Thomas Malthus authored 'An Essay on the Principle of Population' in 1798.

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Chemistry QUESTION #1079

Question 513

Which one of the following reactions does NOT give benzene as the product?

$\text{HC}\equiv\text{CH}$ passed through red hot iron tube at 873 K
Benzenediazonium chloride $+ \text{H}_2\text{O}$ (warm)✔️
Sodium benzoate $+$ sodalime $\xrightarrow{\Delta}$
n-hexane $\xrightarrow{\text{Mo}_2\text{O}_3,\ 773\text{K},\ 10-20\ \text{atm}}$

Correct Answer Logic:

Option (2): Benzenediazonium chloride hydrolyzed with warm water gives phenol ($\text{C}_6\text{H}_5\text{OH}$), NOT benzene. (1) Ethyne trimerization gives benzene. (3) Decarboxylation of sodium benzoate gives benzene. (4) Catalytic reforming of n-hexane gives benzene.

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Mathematics QUESTION #4148

Question 514

Using variation of parameters for $y'' + y = \sec(x)$, what is the Wronskian $W$ of $y_1 = \cos(x)$ and $y_2 = \sin(x)$?

$0$
$1$
$-1$✔️
$\sec^2(x)$

Correct Answer Logic:

$W = \begin{vmatrix} \cos(x) & \sin(x) \ -\sin(x) & \cos(x) \end{vmatrix} = \cos^2(x) + \sin^2(x) = 1$.

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English QUESTION #824

Question 515

Pick the correct sentence about impact on economy:

This has a bad impact on economy.✔️
This has a bad impact to the economy.
This has a bad impact for the economy.
This has a bad impact over the economy.

Correct Answer Logic:

The correct preposition after 'impact' is 'on'. Correct: 'a bad impact on the economy' (though 'the' before economy would be more complete, option A is the best available choice).

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Paper-I (Anatomy/Physiology and Biochemistry/Microbiology) QUESTION #3135

Question 516

Which part of a neuron receives incoming signals from other neurons?

Axon
Dendrite✔️
Myelin sheath
Cell body

Correct Answer Logic:

Dendrites are the branched receivers of a neuron.

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Chemistry QUESTION #447

Question 517

Which of the following is used to make chloral hydrate?

Acetaldehyde✔️
Formaldehyde
None of these
Both A and B

Correct Answer Logic:

Chloral hydrate is made from acetaldehyde

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Library Sciences QUESTION #1531

Question 518

According to Katz (2002), which of the following is the key distinction between a 'ready-reference' question and a 'research' reference question?

Ready-reference questions are only asked in person; research questions are asked online
Ready-reference questions require brief factual answers quickly found in standard sources; research questions require in-depth searching across multiple sources✔️
Ready-reference questions involve government documents; research questions involve academic journals
Ready-reference questions are answered by paraprofessionals; research questions require a PhD

Correct Answer Logic:

Katz (2002) distinguishes ready-reference questions — which require quick, specific factual answers (e.g., a date, a definition, a statistic) findable in a single standard source — from research questions, which are complex, require extended searching, and involve synthesizing information from multiple sources.

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MCQs Section QUESTION #4855

Question 519

Choose the word nearly opposite in meaning to "FACSIMILE"

Imitation
Model
Mutation✔️
Pattern

Correct Answer Logic:

A facsimile is an exact copy or reproduction of something. Its antonym is 'mutation,' which implies a change or alteration rather than an exact reproduction.

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Paper-I (Anatomy/Physiology and Biochemistry/Microbiology) QUESTION #3473

Question 520

'Essential Amino Acids' are those that:

The body can make itself
Must be supplied by the diet✔️
Are not needed
Are only in meat

Correct Answer Logic:

There are 9 essential amino acids for humans.

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