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Electrical Engineering QUESTION #2167

The z-transform of $x[n] = a^n u[n]$ is $X(z) = \frac{z}{z-a}$ with ROC $|z|>|a|$. For $a = 0.8$, the final value $\lim_{n \to \infty} x[n]$ is:

$0$✔️
$1$
$0.8$
Diverges to infinity

Correct Answer Logic:

Since $|a| = 0.8 < 1$, $\lim_{n\to\infty}(0.8)^n = 0$. Confirmed by the Final Value Theorem: $\lim_{z\to1}(z-1)X(z) = \lim_{z\to1}\frac{z(z-1)}{z-0.8} = 0$.

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Mathematics QUESTION #1307

Question 2842

The D'Alembert solution of the wave equation $u_{xx}=\dfrac{1}{c^2}u_{tt}$ with $u(x,0)=f(x)$ and $u_t(x,0)=g(x)$ is:

$u(x,t)=\dfrac{f(x+ct)+f(x-ct)}{2}+\dfrac{1}{2c}\int_{x-ct}^{x+ct}g(s)\,ds$✔️
$u(x,t)=f(x+ct)+f(x-ct)$
$u(x,t)=\dfrac{f(x+ct)-f(x-ct)}{2}+\dfrac{1}{c}\int_0^x g(s)\,ds$
$u(x,t)=f(x)g(t)$

Correct Answer Logic:

D'Alembert's formula gives the general solution of the 1D wave equation: $u(x,t)=\dfrac{f(x+ct)+f(x-ct)}{2}+\dfrac{1}{2c}\int_{x-ct}^{x+ct}g(s)\,ds$. It represents two travelling waves moving in opposite directions.

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Biology QUESTION #4198

Question 2843

How many ATPs are produced during oxidative phase of glycolysis?

2
4✔️
34
36

Correct Answer Logic:

During glycolysis, 4 ATP are produced in the oxidative (payoff) phase.

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Basic Mathematics QUESTION #2852

Question 2844

Find the area of a triangle with base 24 cm and height 10 cm.

110 cm²
120 cm²✔️
130 cm²
240 cm²

Correct Answer Logic:

Area of triangle $= \dfrac{1}{2} \times \text{base} \times \text{height} = \dfrac{1}{2} \times 24 \times 10 = 120 \text{ cm}^2$.

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Computer Science QUESTION #1129

Question 2845

Which technique works by selecting the local optimal choice at each step?

Dynamic Programming
Divide and Conquer
Greedy Algorithm✔️
None of these

Correct Answer Logic:

A Greedy Algorithm makes the choice that looks best at the current moment with the hope that these local optimal choices will lead to a global optimum.

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Tourism & Hospitality Management QUESTION #1652

Question 2846

According to the HRM course, 'Pay for Performance (PFP)' systems in hospitality organizations involve which of the following plan types covered in the curriculum?

Only annual salary increments based on years of service
Individual PFP plans (merit pay and incentive systems), Group Incentive Plans, and Managerial and Executive Incentive Pay — with determinants of effective PFP and legal implications✔️
Guaranteed hourly wage increases tied to inflation rates
Commission-only compensation for all hotel departments

Correct Answer Logic:

Module 8 of the HRM course covers Pay for Performance comprehensively: determinants of effective PFP, main problems with PFP, legal implications, individual PFP plans (merit pay and incentive systems), group incentive plans, and managerial/executive incentive pay — covering the full spectrum of performance-linked compensation applicable in hospitality organizations.

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Chemistry QUESTION #73

Question 2847 (Select all that apply)

Which of the following best explains why phenol reacts with aqueous NaOH, but alcohols do not?

Phenol is weakly acidic due to resonance stabilization of phenoxide ion.✔️
Phenol form hydrogen bonding that facilitates ionization.
Alcohols contain a strong O-H bond that cannot be broken by weak bases.
Phenol has a lower boiling point than alcohol.

Correct Answer Logic:

Phenol is about a million times more acidic than alcohol because the resonance stabilization of the phenoxide ion lowers the energy of the product, favoring the reaction with NaOH.

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Professional QUESTION #1829

Question 2848

According to Section 8(4), civil servants who are selected for promotion to a higher post in one batch shall, on promotion, retain their inter se seniority as in which post?

The post to which they are being promoted
The higher post effective from the date of notification
The lower post from which they were promoted✔️
The post determined by the Selection Board

Correct Answer Logic:

Section 8(4) provides that seniority in a post to which a civil servant is promoted takes effect from the date of regular appointment to that post. However, the proviso adds that civil servants selected for promotion in one batch shall retain their inter se seniority as in the lower post — meaning relative order among them is preserved from before promotion.

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Agronomy QUESTION #2094

Question 2849

The concept of 'phenotypic plasticity' in crop adaptation to variable environments refers to:

The ability of a plant's DNA sequence to mutate in response to environmental stress
The capacity of a single genotype to express a range of phenotypes (morphological, physiological, or behavioral) in response to different environmental conditions — without genetic change — allowing crops to partially buffer yield across variable environments✔️
The selection of different varieties (genotypes) for each target environment
The use of plastic mulch films to modify the crop microenvironment

Correct Answer Logic:

Phenotypic plasticity describes genotype × environment (G×E) interaction at the individual plant level: one genotype producing different trait expressions (leaf area, tiller number, root architecture, phenology) across environments. Crops with high plasticity can partially self-regulate resource capture. Breeders must distinguish genetic adaptation (G) from plasticity (GEI) when evaluating varieties across diverse environments.

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Physics QUESTION #398

Question 2850

The acceleration is proportional to the displacement and is directed towards mean position in __________ motion.

Gravity
Simple harmonic✔️
Uniform
Projectile

Correct Answer Logic:

This defines simple harmonic motion

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Physics QUESTION #4413

Question 2851

The energy of a Simple Harmonic oscillation depends upon the:

Frequency
Time period
Wavelength
Amplitude✔️

Correct Answer Logic:

Total energy of a simple harmonic oscillator: $E = \dfrac{1}{2}k A^2 = \dfrac{1}{2}m\omega^2 A^2$. The energy is directly proportional to the square of the amplitude $A$. It does not depend on frequency or time period independently.

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Biology QUESTION #577

Question 2852

Which of the following damages wooden ships?

Sepia
Limax
Teredo✔️
Ostrea

Correct Answer Logic:

Teredo (shipworm) damages wooden ships

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Urdu QUESTION #5207

Question 2853

آودِ ہندی اور اردوئے معلی کس کی تصنیف ہے؟

ڈپٹی نذیر احمد
مرزا غالب✔️
مولوی عبدالحق
ان میں سے کوئی نہیں

Correct Answer Logic:

آودِ ہندی اور اردوئے معلی مرزا غالب کی خطوط پر مبنی تصانیف ہیں۔

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Tourism & Hospitality Management QUESTION #1647

Question 2854

The Religious/Sacred Tourism course identifies which classification system for sacred places in Pakistan that covers multiple religious traditions?

A classification based solely on the age and architectural style of religious buildings
A classification covering sacred places of Muslims, Christians, Buddhists, Hindus, Jains, Parsis, Sikhs, and Kalashas — including mosques, tombs, stupas, monasteries, temples, churches, and gurdwaras✔️
A classification based exclusively on UNESCO heritage status
A government-issued ranking of pilgrimage sites by annual visitor numbers

Correct Answer Logic:

Module 4 of the Religious/Sacred Tourism course provides a comprehensive multi-faith classification of religious and sacred places in Pakistan, specifically covering: Muslims, Christians, Buddhists, Hindus, Jains, Parsis, Sikhs, and Kalashas — and their respective heritage types including mosques, tombs, stupas, monasteries, temples, dharmasalas, sacred caves, churches, and gurdwaras.

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Paper-I (Anatomy/Physiology and Biochemistry/Microbiology) QUESTION #3162

Question 2855

Which condition results from a deficiency of 'Vitamin D' in children?

Scurvy
Rickets✔️
Beriberi
Pellagra

Correct Answer Logic:

Rickets causes softening and weakening of bones.

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General Knowledge QUESTION #2594

Question 2856

A group of 8 bits is known as:

A Kilobyte
A Nibble
A Byte✔️
A Megabit

Correct Answer Logic:

A byte is a group of 8 bits. It is the fundamental unit of digital data storage. All larger units — kilobytes, megabytes, gigabytes — are multiples of bytes. A single character like the letter 'A' typically requires 1 byte to store.

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General Science and Ability QUESTION #257

Question 2857

A pencil dipped in water appears bent due to:

Reflection
Diffraction
Refraction✔️
None of these

Correct Answer Logic:

Refraction is the change in direction of a wave passing from one medium to another.

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Physics QUESTION #387

Question 2858

Two cylinders of equal mass are made from same material. The one with the larger diameter accelerates __________ the other under the action of same torque.

Faster than✔️
Slower than
Equal to
None of these

Correct Answer Logic:

Smaller moment of inertia leads to faster acceleration

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Geography QUESTION #1247

Question 2859

The process involved in Himalayan orogeny is:

Volcanism
Plate convergence✔️
Plate divergence
None of these

Correct Answer Logic:

The Himalayan mountain range was formed by the convergence (collision) of the Indian Plate and the Eurasian Plate, which began approximately 50 million years ago. As the Indian subcontinent moved northward and collided with Eurasia, the intervening Tethys Sea sediments were folded and uplifted to form the Himalayas. This is a classic example of continent-continent collision.

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General Knowledge QUESTION #169

Question 2860

Which article of Pakistan's constitution talks about a clean environment?

Article 8A
Article 9A
Article 7A
None of these✔️

Correct Answer Logic:

While the right to a clean environment is read into Article 9 (Right to Life), there is no specific Article 9A/8A/7A.

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