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Mathematics QUESTION #6954

Question 1

Evaluate: $\displaystyle\lim_{x\to0}\dfrac{x\cot(4x)}{\sin^2 x\cdot\cot^2(2x)}$

2
4
1✔️

Correct Answer Logic:

Rewrite using $\cot\theta = \cos\theta/\sin\theta$:

$\dfrac{x\cdot\cos4x/\sin4x}{\sin^2x\cdot\cos^22x/\sin^22x}$

As $x\to0$: $\sin4x\approx4x$, $\sin2x\approx2x$, $\sin x\approx x$, all cosines $\to1$:

$\approx\dfrac{x\cdot\frac{1}{4x}}{x^2\cdot\frac{1}{4x^2}} = \dfrac{\frac{1}{4}}{\frac{1}{4}} = \mathbf{1}$

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Civil / Architecture QUESTION #2353

Question 2

In LRFD design of steel tension members per AISC, the design strength for the fracture limit state (net section rupture) with $\phi_t = 0.75$ is:

$\phi_t P_n = 0.90 F_y A_g$
$\phi_t P_n = 0.75 F_u A_e$✔️
$\phi_t P_n = 0.85 F_y A_g$
$\phi_t P_n = 0.75 F_y A_e$

Correct Answer Logic:

For tension member fracture limit state: $\phi_t P_n = 0.75 F_u A_e$ where $F_u$ is the tensile strength, $A_e$ is the effective net area ($A_e = U \cdot A_n$, with $U$ being the shear lag factor), and $\phi_t = 0.75$. For yielding on the gross section: $\phi_t P_n = 0.90 F_y A_g$. The governing limit state is the lesser value.

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Urdu QUESTION #5115

Question 3

چہارشنبہ ہفتے کا کون سا دن ہے؟

اتوار
پیر
منگل
بدھ✔️

Correct Answer Logic:

چہارشنبہ فارسی میں چوتھے دن یعنی بدھ کے لیے استعمال ہوتا ہے۔

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Agronomy QUESTION #2092

Question 4

Drought escape as a mechanism of crop adaptation to water deficit differs from drought tolerance in that:

Drought escape requires genetic modification while tolerance is a natural trait
Drought escape is a phenological strategy — completing the life cycle (particularly the sensitive reproductive stage) before or during periods when water deficit occurs — without requiring the plant to physiologically withstand low tissue water potentials✔️
Drought escape results in higher yield than drought tolerance under all conditions
Drought escape involves waxy leaf surfaces to reduce transpiration

Correct Answer Logic:

Drought adaptation mechanisms: Escape (phenological — early maturity, photoperiod sensitivity completes grain fill before drought); Avoidance (reducing water loss: deep roots, stomatal closure, leaf rolling, reduced leaf area); Tolerance (maintaining function at low tissue water potential: osmotic adjustment, desiccation tolerance). Escape is a timing strategy, not a physiological response to stress.

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Quantitative Reasoning QUESTION #8030

Question 5

The theory of cosmic evolution holds that the universe, having originated in a state of simplicity and _______, has since transformed _______ into great variety.

homogeneity .. differentiated✔️
equilibrium .. modulated
contrast .. metamorphosed
proportion .. accelerated

Correct Answer Logic:

The sentence describes a universe moving from unity/sameness to diversity. Homogeneity...differentiated is the best fit: the universe began as uniform (homogeneous) and then became differentiated (divided into varied forms). 'Equilibrium...modulated' doesn't capture the idea of increasing variety as strongly.

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General Knowledge QUESTION #2617

Question 6

The BIOS (Basic Input Output Services) performs which of the following functions when a computer is first switched on?

It connects the computer to the internet automatically
It converts electrical power from the wall outlet into computer-usable power
It helps initialize the hardware in the computer and gets the operating system up and running✔️
It stores all user documents and settings permanently

Correct Answer Logic:

BIOS (Basic Input Output Services) is software stored on a ROM chip that helps initialize the hardware in our computer and gets our operating system up and running. It is the first software that runs when you press the power button.

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Paper-I (Anatomy/Physiology and Biochemistry/Microbiology) QUESTION #3337

Question 7

'Incubation' period is the time between:

Infection and the appearance of signs/symptoms✔️
Starting and finishing a meal
Being born and growing up
Taking an antibiotic and feeling better

Correct Answer Logic:

During this time, the microbe is multiplying but hasn't reached levels to cause symptoms.

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English QUESTION #2692

Question 8

Correct the sentence: 'She is more taller than her sister.'

She is more tall.
She is taller than her sister.✔️
She is most tall.
She is as tall.

Correct Answer Logic:

Double comparatives (more + -er) are incorrect; 'taller' is sufficient.

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Mathematics QUESTION #4129

Question 9

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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Islamic Studies QUESTION #7910

Question 10

The second battle fought between Muslims of Medina and Quraish of Makkah was:

Badr
Uhud✔️
Khandak
Khyber

Correct Answer Logic:

The second battle was the Battle of Uhud fought in 3 AH (625 CE). It occurred after the Battle of Badr and before the Battle of Khandak. Although Muslims initially gained the upper hand, the battle ended inconclusively after some archers disobeyed orders and left their positions.

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Pharmacology and Toxicology QUESTION #3860

Question 11

Which pharmacological effect would be expected following systemic administration of atropine?

Constriction of the pupil
Increased gastric motility
Micturition
Increased heart rate✔️

Correct Answer Logic:

Atropine is a competitive muscarinic antagonist. By blocking parasympathetic (vagal) tone at the sinoatrial node, it removes the brake on heart rate, causing tachycardia (increased heart rate).

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English QUESTION #2651

Question 12

Change the sentence to active voice: 'The window was broken by the boy.'

The boy breaks the window.
The boy had broken the window.
The boy broke the window.✔️
The boy is breaking the window.

Correct Answer Logic:

The passive 'was broken' indicates Simple Past, so the active verb must be 'broke'.

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Accounting Finance and Punjab Sales Tax on Services QUESTION #2582

Question 13

Under section 5(2) of the Act, a notification issued by the Government amending the Second Schedule (adding, modifying or deleting any entry regarding taxable services or rates) shall be effective from what date?

Three months before the date of notification
The date of approval by the Provincial Assembly
Such date as may be specified in the notification, but not prior to the date on which the notification is PUBLISHED in the Official Gazette✔️
The first day of the next financial year

Correct Answer Logic:

Section 5(2) provides a strict rule: the notification shall be effective from such date as may be specified therein, but SUCH DATE SHALL NOT BE PRIOR TO THE DATE ON WHICH THE NOTIFICATION IS PUBLISHED in the official Gazette — preventing retrospective taxation through subordinate legislation.

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Tourism & Hospitality Management QUESTION #1641

Question 14

The Restaurant Management course covers 'revenue control and operational control' as management functions. Which of the following correctly identifies the four measures used to appraise restaurant operational performance?

Profit margin, tax liability, depreciation, and asset value
Appraising revenue, appraising cost, appraising profits, and appraising the whole operation through profit measures✔️
Customer satisfaction scores, staff turnover rates, hygiene inspection results, and supplier ratings
Menu engineering, portion control, waste management, and staff scheduling

Correct Answer Logic:

Module 4 of the Restaurant Management course (Procedures) specifically identifies the operational control framework as comprising four appraisal components: appraising revenue (sales analysis), appraising cost (cost of sales and labour), appraising profits (profit margin measures), and appraising the whole operation — forming the complete financial control cycle for restaurant management.

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Statistics QUESTION #1982

Question 15

The partial correlation coefficient $r_{12.3}$ between $X_1$ and $X_2$ after eliminating the linear effect of $X_3$ is computed as the simple correlation between:

$X_1$ and $X_2$ directly
The residuals $X_{1.3}$ and $X_{2.3}$ from their respective regressions on $X_3$✔️
The standardized values of $X_1$ and $X_2$
The ranked values of $X_1$ and $X_2$

Correct Answer Logic:

The partial correlation $r_{12.3}$ is defined as the Pearson correlation between the residuals $X_{1.3} = X_1 - \hat{X}_{1|X_3}$ and $X_{2.3} = X_2 - \hat{X}_{2|X_3}$. This removes the linear influence of $X_3$ from both $X_1$ and $X_2$ before computing their correlation.

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Mathematics QUESTION #6977

Question 16

A test paper has 5 questions, each with three answer choices of which only one is correct. What is the probability that a student scoring purely by guessing gets 4 or more questions right?

$\dfrac{17}{3^5}$
$\dfrac{13}{3^5}$
$\dfrac{11}{3^5}$✔️
$\dfrac{10}{3^5}$

Correct Answer Logic:

This is a binomial distribution with $n=5$, $p=\dfrac{1}{3}$ (correct), $q=\dfrac{2}{3}$ (wrong).

$P(X \geq 4) = P(X=4) + P(X=5)$

$P(X=4) = \binom{5}{4}\left(\dfrac{1}{3}\right)^4\left(\dfrac{2}{3}\right)^1 = 5 \cdot \dfrac{1}{81} \cdot \dfrac{2}{3} = \dfrac{10}{243}$

$P(X=5) = \binom{5}{5}\left(\dfrac{1}{3}\right)^5 = \dfrac{1}{243}$

$P(X \geq 4) = \dfrac{10}{243} + \dfrac{1}{243} = \dfrac{11}{243} = \dfrac{11}{3^5}$

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CISA QUESTION #6828

Question 17

An IS auditor finds that database administrators regularly use shared administrative accounts rather than individual accounts. What is the MOST significant control deficiency?

Inefficient password management
Lack of individual accountability and inability to attribute actions to specific individuals✔️
Violation of policy
Increased security costs

Correct Answer Logic:

Shared accounts eliminate individual accountability—a fundamental security and auditing principle. When multiple people use the same credentials, it becomes impossible to determine who performed specific actions, preventing investigation of incidents, fraud detection, and establishing non-repudiation.

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Geography QUESTION #1244

Question 18

The colour of a star is an indication of its:

Size
Distance away
Surface temperature✔️
None of these

Correct Answer Logic:

The colour of a star directly indicates its surface temperature. Cool stars (around 3,000 K) appear red; medium-temperature stars like the Sun (~5,500 K) appear yellow-white; hot stars (30,000+ K) appear blue-white. This is described by Wien's Displacement Law. A star's colour does not directly indicate its size or distance.

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General Knowledge QUESTION #2601

Question 19

The RGB model is used in computing to:

Define the speed of data processing in a computer
Represent colors on digital displays using combinations of red, green, and blue✔️
Encode text characters into binary values
Measure the storage capacity of a hard drive

Correct Answer Logic:

RGB (Red, Green, Blue) is the basic model of representing colors on digital displays. By combining different intensities of these three primary light colors (each from 0–255), virtually any color visible to the human eye can be produced on screen.

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Physics QUESTION #394

Question 20

The cobalt is absorbed by

Bones
Skin
Liver✔️
Thyroid gland

Correct Answer Logic:

Radioactive cobalt accumulates in liver

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