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For a perfectly symmetric distribution, the third central moment $\mu_3 = 0$ (since positive and negative deviations cancel symmetrically). Therefore $\beta_1 = \dfrac{\mu_3^2}{\mu_2^3} = \dfrac{0}{\mu_2^3} = 0$. Note: $\beta_1 = 0$ indicates zero skewness.

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Statistics QUESTION #2013

Question 2365

The relative efficiency (RE) of a Completely Randomized Design (CRD) relative to an RCB design is used to indicate:

Whether the F-test is significant
How many times more observations CRD would need to achieve the same precision as RCB✔️
The ratio of treatment means in both designs
The difference in error degrees of freedom between designs

Correct Answer Logic:

Relative efficiency $RE = \dfrac{MS_E(\text{CRD})}{MS_E(\text{RCB})}$ estimates how many times more replications a CRD would need to attain the same precision as the RCB design. An $RE > 1$ indicates blocking was effective in reducing error variance, justifying the use of the RCB design.

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Paper-I (Anatomy/Physiology and Biochemistry/Microbiology) QUESTION #3081

Question 2366

The 'Axon' is a structure specifically found in which type of cell?

Osteocyte
Neuron✔️
Erythrocyte
Leukocyte

Correct Answer Logic:

The axon is the long threadlike part of a nerve cell along which impulses are conducted.

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HR and Management QUESTION #6466

Question 2367

The text's emphasis on 'most of these elements will affect you at some point in your career' suggests HRM knowledge is:

Only relevant for HR specialists
Universally applicable to all professionals✔️
Required only for senior executives
Optional for technical professionals

Correct Answer Logic:

HRM knowledge is universally applicable - whether you work in HRM or not, whether you work with organizations or have people working for you, you will be dealing with people and affected by HR practices. It's essential knowledge for all professionals.

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General Science and Ability QUESTION #253

Question 2368

The isotopes of any element contain equal number of:

Protons✔️
Neutrons
Both electrons and protons
None of these

Correct Answer Logic:

Isotopes are atoms of the same element with the same number of protons but different neutrons.+1

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Boilers Mechanical Engineering QUESTION #2491

Question 2369

A mechanism is defined in mechanism theory as:

Any collection of rigid bodies
A kinematic chain in which at least one link has been grounded (fixed to the frame)✔️
A chain with exactly one degree of freedom
A system with more links than kinematic pairs

Correct Answer Logic:

By Reuleaux's definition, a mechanism is a kinematic chain where at least one link is grounded (fixed) to the frame.

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Mathematics QUESTION #4129

Question 2370

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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Education QUESTION #6733

Question 2371

The concept of 'scaffolding' in instruction means:

Permanent support for all learners
Temporary support gradually removed as student competence increases✔️
Physical classroom structures
Rigid instructional sequences

Correct Answer Logic:

Scaffolding (Vygotsky) involves providing temporary support that's gradually withdrawn as learners develop independence. Like construction scaffolding, instructional scaffolds are temporary structures that enable learners to accomplish tasks beyond current independent capability, then are removed.

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Physics QUESTION #7839

Question 2372

Magnetic field inside a solenoid is:

Along its axis✔️
Circular around wires
Strongest at ends
Zero when current flows

Correct Answer Logic:

Inside ideal solenoid, field is uniform and parallel to axis.

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General Abilities QUESTION #7988

Question 2373

The equation $x + a = b$ has a solution in the set of natural numbers if:

a < b✔️
a > b
a = b
None of these

Correct Answer Logic:

$x + a = b \Rightarrow x = b - a$. For $x$ to be a natural number (positive integer), we need $b - a \geq 1$, i.e., $b > a$, or equivalently $a < b$.

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MCQs Section QUESTION #4850

Question 2374

Choose the word nearly similar in meaning to "CAJUN"

French-Canadian descendant✔️
American Indian
Native of the Everglades
Early inhabitant of the Bahama Islands

Correct Answer Logic:

Cajun refers to a member of a group of people in Louisiana descended from French-speaking Acadian immigrants who were expelled from Canada in the 18th century.

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Mathematics QUESTION #4158

Question 2375

For the Laplace equation $u_{xx} + u_{yy} = 0$ on $0 < x < a$, $0 < y < b$ with $u(0,y) = u(a,y) = u(x,0) = 0$ and $u(x,b) = f(x)$, what is the general form of solution using separation of variables?

$u(x,y) = \sum_{n=1}^{\infty} B_n \sin(\frac{n\pi x}{a})\sinh(\frac{n\pi y}{a})$✔️
$u(x,y) = \sum_{n=1}^{\infty} B_n \cos(\frac{n\pi x}{a})\cosh(\frac{n\pi y}{a})$
$u(x,y) = \sum_{n=1}^{\infty} B_n \sin(\frac{n\pi x}{a})\cos(\frac{n\pi y}{b})$
$u(x,y) = \sum_{n=1}^{\infty} B_n e^{\frac{n\pi x}{a}}\sin(\frac{n\pi y}{b})$

Correct Answer Logic:

Boundary conditions $u(0,y) = u(a,y) = 0$ suggest $X(x) = \sin(\frac{n\pi x}{a})$. Condition $u(x,0) = 0$ gives $Y(0) = 0$, so $Y(y) = \sinh(\frac{n\pi y}{a})$.

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Logical Reasoning QUESTION #3954

Question 2376

The committee's decision was _____; even those who initially disagreed eventually gave their _____.

unanimous...assent✔️
divided...permission
final...refusal
ambiguous...support

Correct Answer Logic:

No explanation provided for this question.

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General Ability and Fire Fighting QUESTION #5633

Question 2377

Which agent is recommended for a fire involving magnesium shavings in a machine shop?

Water
Wet Chemical
CO2
Specialized Dry Powder✔️

Correct Answer Logic:

Magnesium is a combustible metal (Class D fire). Water reacts violently with burning magnesium. Only specialized dry powder agents designed for Class D fires should be used.

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Civil Engineering QUESTION #2134

Question 2378

In irrigation engineering, the duty of water ($\Delta$) and delta ($D$) are related to base period ($B$) in days by the equation:

D = B × $\Delta$
D = $\dfrac{8.64 \times B}{\Delta}$✔️
D = $\dfrac{\Delta}{8.64 \times B}$
D = $\dfrac{B}{8.64 \times \Delta}$

Correct Answer Logic:

Duty ($\Delta$) = area (hectares) irrigated by 1 cumec (1 m³/s) of water flowing continuously for base period $B$ (days). Delta ($D$) = total depth of water (meters) required by the crop in base period. Relationship: $D = \dfrac{8.64 \times B}{\Delta}$, derived from: 1 cumec flowing for $B$ days delivers $8.64B \times 10^4$ liters over $\Delta$ hectares. This fundamental relationship governs canal design and water distribution in irrigation systems.

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Civil Engineering QUESTION #2130

Question 2379

The Biochemical Oxygen Demand (BOD) test measures:

The total dissolved oxygen concentration in a water sample
The amount of dissolved oxygen consumed by biological organisms in oxidizing organic matter in a water sample at 20°C over 5 days (BOD₅) — used as an indirect measure of organic pollution load in wastewater✔️
The chemical oxygen demand using potassium dichromate oxidation
The concentration of pathogenic bacteria in sewage effluent

Correct Answer Logic:

BOD₅ (standard 5-day, 20°C test) measures DO consumed by aerobic microorganisms decomposing carbonaceous organic matter in a diluted, incubated sample. It is the most widely used parameter for characterizing wastewater strength and assessing treatment plant performance. BOD₅ captures ~60–70% of ultimate BOD. Typical BOD₅ values: raw domestic sewage 200–300 mg/L; treated effluent <20 mg/L (secondary); <10 mg/L (tertiary).

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Boilers Mechanical Engineering QUESTION #2498

Question 2380

In Mohr's circle for plane stress, the principal stresses $\sigma_1$ and $\sigma_2$ occur at points where:

The circle has maximum radius
The circle intersects the $\sigma$-axis (shear stress $\tau = 0$)✔️
The shear stress is maximum
The normal stress equals the average stress

Correct Answer Logic:

Principal stresses are defined as the normal stresses acting on planes where shear stress is zero. On Mohr's circle, these correspond to the two points where the circle intersects the horizontal $\sigma$-axis (i.e., $\tau = 0$).

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