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Mathematics QUESTION #6028

Let $S=\left\{t\in\mathbb{R}: f(x)=|x-\pi|\cdot(e^{|x|}-1)\sin|x|\right.$ is not differentiable at $t\}$. Find $S$.

$\{\pi\}$
$\{0,\pi\}$
$\emptyset$ (empty set)✔️
$\{0\}$

Correct Answer Logic:

Check $x=0$: $f(x)=|x-\pi|(e^{|x|}-1)\sin|x|$. Near $x=0$, both $(e^{|x|}-1)$ and $\sin|x|$ have factors of $|x|$, so $f(x)\approx |x-\pi|\cdot|x|^2$ near 0, which is differentiable at 0.

Check $x=\pi$: near $\pi$, $(e^{|x|}-1)\sin|x|$ is smooth and non-zero ($e^\pi\sin\pi=0$!). Since $\sin\pi=0$, the product $(e^{|x|}-1)\sin|x|$ vanishes at $\pi$, making $f(x)=0$ near $\pi$ — wait, $\sin\pi=0$, so $f(\pi)=0$. Checking differentiability more carefully shows $f$ is differentiable at $\pi$ too.

Therefore $S=\boldsymbol{\emptyset}$.

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Math Physics Chemistry Biology QUESTION #738

Question 4242

At what temperature the velocity of sound is doubled than as that of at 10°C:

859°C✔️
560°C
760°C
500°C

Correct Answer Logic:

v ∝ √T. For v to double: T2 = 4T1. T1 = 10+273 = 283K; T2 = 4x283 = 1132K = 859°C.

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English QUESTION #8358

Question 4243

ARID means:

Fertile
barren✔️
Quaint
talkative

Correct Answer Logic:

Arid means very dry; barren means infertile — but barren is closer? Actually arid = dry, barren = unable to produce. Key says B barren.

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Mathematics QUESTION #1255

Question 4244

If $\varphi: \mathbb{Z}_6 \to \mathbb{Z}_6$ is a one-to-one (injective) homomorphism, then $\ker(\varphi)$ is:

{$\bar{0}, \bar{2}, \bar{4}$}
{$\bar{0}, \bar{3}$}
{$\bar{0}$}✔️
All of $\mathbb{Z}_6$

Correct Answer Logic:

A one-to-one (injective) homomorphism has trivial kernel. Since $\ker(\varphi) = \{x : \varphi(x) = 0\}$ and $\varphi$ is injective, only $\varphi(0)=0$, so $\ker(\varphi) = \{\bar{0}\}$.

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Physics QUESTION #7305

Question 4245

A car travels from X to Y with uniform speed $v_u$ and returns with uniform speed $v_d$. The average speed for the entire round trip is:

$\dfrac{v_u + v_d}{2}$
$\sqrt{v_u v_d}$
$\dfrac{2v_u v_d}{v_u + v_d}$✔️
$\dfrac{v_u v_d}{v_u + v_d}$

Correct Answer Logic:

Let distance X to Y $= d$. Total distance $= 2d$.

Total time $= \dfrac{d}{v_u} + \dfrac{d}{v_d} = d\cdot\dfrac{v_u + v_d}{v_u v_d}$

Average speed $= \dfrac{2d}{d\cdot\dfrac{v_u+v_d}{v_u v_d}} = \mathbf{\dfrac{2v_u v_d}{v_u + v_d}}$ (harmonic mean)

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General Abilities QUESTION #4591

Question 4246

Simplify: $7y - 2y + 4y$

$3y$
$9y$✔️
$14y$
$5y$

Correct Answer Logic:

Combine like terms: $7y - 2y + 4y = (7-2+4)y = 9y$

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MCQs Section QUESTION #4878

Question 4247

Which word is similar to "ACRIMONIOUS"

Bitter✔️
Provocative
Cheap
Volatile

Correct Answer Logic:

Acrimonious means having or showing strong bitterness or ill feeling in speech or manner. Bitter is its closest synonym.

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Physics QUESTION #1165

Question 4248

At constant pressure and volume, the exact relation between $C_p$ and $C_v$ is:

C_p > C_v
$C_p / C_v > 1$
$C_p - C_v = R$
All of these✔️

Correct Answer Logic:

All three relations are simultaneously true for an ideal gas: (A) $C_p > C_v$ because at constant pressure extra heat is needed to do work against expansion. (B) $C_p/C_v = \gamma > 1$. (C) The Mayer relation: $C_p - C_v = R$ (per mole). So all of these are correct.

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Paper-I (Anatomy/Physiology and Biochemistry/Microbiology) QUESTION #3446

Question 4249

Which mineral is required for the 'Activation of ATP' in many enzymatic reactions?

Calcium
Magnesium✔️
Sodium
Chloride

Correct Answer Logic:

Many kinases require $Mg^{2+}$ as a cofactor.

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Physical Education QUESTION #6806

Question 4250

Which historical period is most associated with the suppression of physical culture due to the belief that 'the body is a hindrance to the soul'?

The Ancient Greek Period
The Middle Ages✔️
The Enlightenment
The Renaissance

Correct Answer Logic:

During the Middle Ages, asceticism often led to the neglect of the body in favor of spiritual discipline.

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The Elections Act 2017 QUESTION #9443

Question 4251

Section 90(5) also provides what happens if the prescribed mark is equally divided between two spaces — meaning exactly half falls in each candidate's space. The result is:

The vote is counted for the candidate whose name appears first alphabetically
The ballot paper shall be deemed invalid✔️
The Presiding Officer has discretion to assign it to either candidate
The vote is counted for the candidate with fewer votes at that point

Correct Answer Logic:

Section 90(5) further provides: 'where the prescribed mark is divided equally between two such spaces, the ballot paper shall be deemed invalid.'

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English QUESTION #8525

Question 4252

The synonym of 'Banish' is:

Recall
Expel✔️
Digest
Exonerate

Correct Answer Logic:

Banish means to expel or send away.

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General Abilities QUESTION #2877

Question 4253

Average of $12, 15, 18, 21, 24$ is:

15
18✔️
21
20

Correct Answer Logic:

Since the numbers are in an arithmetic progression, the average is the middle term: $18$.

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Physics QUESTION #1190

Question 4254

As per quantum physics, the observables 'E' and _________ cannot be simultaneously measured with hundred percent accuracy.

p_x
t✔️
x
None of these

Correct Answer Logic:

The energy-time uncertainty relation is $\Delta E \cdot \Delta t \geq \frac{\hbar}{2}$. Energy $E$ and time $t$ are complementary observables that cannot both be known precisely simultaneously. This is analogous to the position-momentum uncertainty: $\Delta x \cdot \Delta p_x \geq \frac{\hbar}{2}$. So 'E' is paired with 't' in the uncertainty principle.

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Ability / HR / Governance / Special Education QUESTION #1890

Question 4255

What happens to the pay and service status of a government servant placed on leave under Rule 5(1)(i) who is ultimately NOT dismissed removed reduced or compulsorily retired?

The leave is treated as extraordinary leave without pay
The leave is treated as duty on full pay✔️
The leave period is counted toward pension only
The leave is regularized as earned leave

Correct Answer Logic:

Rule 8-A explicitly provides that if such a government servant is not punished he shall rejoin duty and the leave period shall be treated as duty on full pay.

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Nursing QUESTION #9208

Question 4256

Which theoretical framework by Nola Pender focuses on helping individuals achieve higher levels of wellbeing rather than merely avoiding disease?

Self-Care Deficit Theory
Health Promotion Model✔️
Adaptation Model
Theory of Reasoned Action

Correct Answer Logic:

Correct Answer: B — Health Promotion Model

Pender's Health Promotion Model (HPM, 1982; revised 1996) is grounded in social cognitive theory and emphasizes positive health behaviors rather than disease avoidance.

Key components of the HPM:

Individual Characteristics and Experiences: Prior behavior, personal factors (biological, psychological, sociocultural)
Behavior-Specific Cognitions and Affect: Perceived benefits, perceived barriers, perceived self-efficacy, activity-related affect, interpersonal and situational influences
Behavioral Outcome: Commitment to a plan of action → Health-promoting behavior

The HPM is widely used by Charge and Head Nurses in patient education, community health programs, and chronic disease management to motivate patients toward healthier lifestyles.

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General Knowledge QUESTION #2633

Question 4257

A FACTORY RESET on a device results in:

Installing new software updates and the latest operating system version
Resetting the device to the settings it came with from the factory, erasing all user data✔️
Increasing the device's processing speed by clearing temporary files only
Connecting the device to a new network and user account

Correct Answer Logic:

A factory reset resets a device to the settings it came with from the factory. This erases all user data, installed applications, settings, and personal files, returning the device to its original out-of-the-box state. It is commonly used to troubleshoot serious issues or prepare a device for a new user.

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Paper-I (Anatomy/Physiology and Biochemistry/Microbiology) QUESTION #3505

Question 4258

'Agar' is a mucilaginous substance obtained from:

Land plants
Seaweeds (Red Algae)✔️
Animal bones
Fungi

Correct Answer Logic:

Agar is derived from Gelidium and Gracilaria species.

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Boilers Mechanical Engineering QUESTION #2501

Question 4259

Poisson's ratio $\nu$ is defined as the ratio of:

$\text{Axial strain}/\text{Lateral strain}$
$\text{Lateral strain}/\text{Axial strain}$ (magnitude)✔️
$\text{Shear strain}/\text{Normal strain}$
$\text{Normal stress}/\text{Lateral stress}$

Correct Answer Logic:

Poisson's ratio: $\nu = -\varepsilon_{lateral}/\varepsilon_{axial}$ (the negative sign makes $\nu$ positive). For most metals, $\nu \approx 0.25\text{–}0.35$.

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General Knowledge QUESTION #8792

Question 4260

Which line divides the Turkish and Greek Cypriot communities?

Yellow Line
Green Line✔️
Curzon Line
Maginot Line

Correct Answer Logic:

The Green Line divides Cyprus.

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