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Mathematics QUESTION #4129

Find the Maclaurin series for $f(z) = z^2 e^{3z}$. What is the coefficient of $z^5$?

$\frac{9}{2}$✔️
$\frac{27}{40}$
$\frac{81}{40}$
$\frac{27}{8}$

Correct Answer Logic:

$e^{3z} = \sum_{n=0}^{\infty} \frac{(3z)^n}{n!} = \sum_{n=0}^{\infty} \frac{3^n z^n}{n!}$. So $z^2 e^{3z} = \sum_{n=0}^{\infty} \frac{3^n z^{n+2}}{n!}$. For $z^5$: $n + 2 = 5$, so $n = 3$. Coefficient: $\frac{3^3}{3!} = \frac{27}{6} = \frac{9}{2}$.

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Urdu QUESTION #5235

Question 2

دمِ رخصت وہ چپ رہے عابد، آنکھ میں پھیلتا گیا کاجل، یہ شعر کس کا ہے؟

عزیز احمد
منیر نیازی
سید عابد علی عابد✔️
ان میں سے کوئی نہیں

Correct Answer Logic:

یہ شعر سید عابد علی عابد کا ہے جو اردو شاعری میں ایک منفرد آواز رکھتے تھے۔

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Womens Health [Obs] [Gyn] QUESTION #3922

Question 3

A 35-year-old multiparous woman presents with heavy and painful menstrual periods (menorrhagia and dysmenorrhea) for the past 6 months. Physical examination shows a symphysis-fundal height of $14$ weeks, with a firm, irregular, and non-tender uterus. What is the most likely diagnosis?

Uterine leiomyomata (fibroids)✔️
Endometrial hyperplasia
Adenomyosis
Endometrial carcinoma

Correct Answer Logic:

No explanation provided for this question.

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Logical Reasoning QUESTION #4433

Question 4

One apple pie has $10$ slices, and each apple pie feeds five people. Henry is having a party with $200$ people. How many slices of pie does he need?

200
50
400✔️
100

Correct Answer Logic:

Each pie feeds $5$ people and has $10$ slices, so each person gets $\dfrac{10}{5} = 2$ slices. For $200$ people: total slices $= 200 \times 2 = 400$ slices.

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Paper-II (Pharmacognosy and Pharmaceutics-I) QUESTION #3676

Question 5

'Tannins' give a bluish-black or greenish-black color with:

Ferric Chloride✔️
Iodine
Water
Alcohol

Correct Answer Logic:

This is a standard chemical test for tannins.

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Boilers Mechanical Engineering QUESTION #4055

Question 6

'Boiler Horsepower' (BHP) is equivalent to the evaporation of:

$34.5~lb$ of water per hour from and at $212^\circ\text{F}$✔️
$1~kg$ of water
$1000~lb$ of water
$1~hp$ motor

Correct Answer Logic:

This is an old unit of measure still used in North America for smaller boilers.

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Paper-II (Pharmacognosy and Pharmaceutics-I) QUESTION #3608

Question 7

'Nutgall' (Quercus infectoria) is a rich source of:

Alkaloids
Tannic acid✔️
Volatile oil
Starch

Correct Answer Logic:

Galls are pathological outgrowths rich in gallotannic acid.

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Mechanical Engineering QUESTION #2496

Question 8

The flexure (bending stress) formula for a beam subjected to bending moment $M$ gives stress $\sigma$ at distance $y$ from the neutral axis as:

$\sigma = \frac{My}{I}$✔️
$\sigma = \frac{MI}{y}$
$\sigma = \frac{M}{yI}$
$\sigma = \frac{y}{MI}$

Correct Answer Logic:

Derived from pure bending theory (Euler-Bernoulli beam), $\sigma = -My/I$. Maximum bending stress occurs at $y = c$ (outermost fiber): $\sigma_{max} = Mc/I = M/Z$, where $Z = I/c$ is the section modulus.

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City and Regional Planning QUESTION #4919

Question 9

What is the primary purpose of GIS in urban planning?

Creating architectural designs
Spatial data analysis and visualization✔️
Financial modeling
Population census

Correct Answer Logic:

GIS (Geographic Information System) is primarily used for spatial data analysis, visualization, and management, enabling planners to analyze spatial relationships and make location-based decisions.

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Tourism & Hospitality Management QUESTION #1581

Question 10

The Hotel Development Process as covered in the Introduction to Tourism & Hospitality includes which of the following ownership structures?

Only sole proprietorship and government ownership
Sole Proprietorship, Partnership, Management Contract, Joint Venture, Franchisee, Public Sector, Private Sector, and Referral Groups/Consortiums✔️
Franchise, Multinational Corporations, and Public Limited Companies only
Management Contracts and Joint Ventures exclusively

Correct Answer Logic:

The curriculum specifically covers all major hotel ownership structures: Sole Proprietorship, Partnership, Management Contract, Joint Venture, Franchisee, Public Sector, Private Sector, and Referral Groups/Consortiums — including their features, advantages and disadvantages.

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Reading and Writing (Module-1) QUESTION #5403

Question 11

The following text is adapted from Jack London's 1903 novel The Call of the Wild. Buck is a sled dog living with John Thornton in Yukon, Canada. Thornton alone held [Buck]. The rest of mankind was as nothing. Chance travellers might praise or pet him; but he was cold under it all, and from a too demonstrative man he would get up and walk away. When Thornton's partners, Hans and Pete, arrived on the long-expected raft, Buck refused to notice them till he learned they were close to Thornton; after that he tolerated them in a passive sort of way, accepting favors from them as though he favored them by accepting. Which choice best states the main idea of the text?

Buck has become less social since he began living with Thornton.
Buck mistrusts humans and does his best to avoid them.
Buck has been especially well liked by most of Thornton's friends.
Buck holds Thornton in higher regard than any other person.✔️

Correct Answer Logic:

The text emphasizes that Thornton alone held Buck's regard while 'the rest of mankind was as nothing,' showing Buck's special attachment to Thornton above all others.

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Paper-II (Pharmacognosy and Pharmaceutics-I) QUESTION #3036

Question 12

'Geometric Dilution' is a method used to:

Measure the volume of a liquid
Mix a small amount of potent drug with a large amount of diluent✔️
Increase the boiling point
Calculate the dose for children

Correct Answer Logic:

Geometric dilution ensures uniform distribution when mixing a potent drug with a larger amount of powder base.

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City and Regional Planning QUESTION #5007

Question 13

Which zoning technique allows density bonuses in exchange for public amenities?

Euclidean zoning
Performance zoning
Incentive zoning✔️
Floating zones

Correct Answer Logic:

Incentive zoning offers developers increased density, height, or FAR in exchange for providing public benefits (parks, affordable housing, transit improvements), balancing private development rights with public amenity provision—widely used in major cities like New York.

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Economics QUESTION #1684

Question 14

Disposable personal income is most accurately defined as the income that remains to households after:

Subtracting all savings from personal income
Setting aside funds exclusively for consumption expenditure
Deducting personal income taxes from personal income✔️
Excluding all government transfer payments such as social security

Correct Answer Logic:

Disposable personal income (DPI) = Personal income − Personal income taxes (direct taxes paid to the government). It represents the actual income available to households for spending (consumption) and saving. It is NOT the same as personal income (which is pre-tax) and is NOT restricted to consumption alone — households can also save their disposable income.

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MCQs Section QUESTION #4909

Question 15

A prolific architect who worked from the turn of the century until the late 1950's, _____ perhaps most notably William Randolph Hearst's monumental estate at San Simeon.

Julia Morgan designed nearly 800 buildings in California✔️
perhaps the most notable of the nearly 800 buildings in California designed by Julia Morgan was William Randolph Hearst's monumental estate at San Simeon
of the nearly 800 buildings in California designed by Julia Morgan, perhaps the most notable was William Randolph Hearst's monumental estate at San Simeon
nearly 800 buildings in California were designed by Julia Morgan, of which William Randolph Hearst's monumental estate at San Simeon is perhaps the most notable

Correct Answer Logic:

The introductory participial phrase 'A prolific architect…' must be followed by Julia Morgan as the grammatical subject to avoid a dangling modifier. Only option A does this. Options B, C, and D all shift the subject away from Julia Morgan, creating dangling modifiers.

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Basic Mathematics QUESTION #2866

Question 16

Find the value of $x$ if $\sqrt{x} + 12 = 20$.

8
64✔️
16
400

Correct Answer Logic:

Subtract $12$ from both sides: $\sqrt{x} = 8$. Square both sides: $x = 8^2 = 64$.

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Biology Zoology Botany QUESTION #1356

Question 17

Which of the following is the dominant generation in the life cycle of Pteridophytes?

Sporophyte✔️
Gametophyte
Seedling
Embryo

Correct Answer Logic:

In pteridophytes (ferns and allies), the sporophyte generation (diploid, 2n) is the dominant, independent, and conspicuous phase — the familiar leafy fern plant. The gametophyte (haploid, n) is a small, inconspicuous, short-lived prothallus. This contrasts with bryophytes where the gametophyte is dominant, and represents an evolutionary advancement.

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Physics QUESTION #389

Question 18

Two waves of slightly different frequencies and traveling in same direction produce ________

Interference
Polarization
Stationary waves
Beats✔️

Correct Answer Logic:

Beats are produced by waves of slightly different frequencies

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Boilers Mechanical Engineering QUESTION #3981

Question 19

The 'Economizer' in a boiler system is used to heat:

The fuel before combustion
Feed water using flue gases✔️
The steam to make it superheated
The air entering the furnace

Correct Answer Logic:

Economizers improve efficiency by recovering waste heat from exhaust gases to pre-heat feed water.

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Mathematics QUESTION #1271

Question 20

Using the Cauchy Residue Theorem, $\oint_{|Z|=2}\dfrac{5Z-2}{Z(Z-1)}\,dZ$ equals:

$2\pi i$
$4\pi i$
$6\pi i$
$10\pi i$✔️

Correct Answer Logic:

Partial fractions: $\dfrac{5Z-2}{Z(Z-1)}=\dfrac{2}{Z}+\dfrac{3}{Z-1}$. Both poles $Z=0$ and $Z=1$ lie inside $|Z|=2$. By residue theorem: $2\pi i(\text{Res at }0+\text{Res at }1)=2\pi i(2+3)=10\pi i$.

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