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Statistics QUESTION #1997

Using moments $\mu_1' = -0.35$, $\mu_2' = 2.09$ about $a = 16$, the variance $\mu_2$ (second central moment) of the distribution equals:

2.09
1.9675✔️
2.2125
1.7

Correct Answer Logic:

Variance $\mu_2 = \mu_2' - (\mu_1')^2 = 2.09 - (-0.35)^2 = 2.09 - 0.1225 = 1.9675$. The central moment is obtained by subtracting the squared first raw moment from the second raw moment.

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Chemistry QUESTION #5571

Question 10882

Arrange the following amines in increasing order of basicity: (a) vinylamine, (b) allylimine (secondary, =NH), (c) compound with $NH_2$ and $=NH$ groups, (d) $N$-methylamine

(b) < (a) < (d) < (c)✔️
(d) < (b) < (a) < (c)
(a) < (b) < (c) < (d)
(b) < (a) < (c) < (d)

Correct Answer Logic:

Basicity depends on electron availability on N. Imine-type N (sp² hybridized, as in =NH) is less basic than amine-type N (sp³). Among aliphatic amines, alkyl groups increase basicity. The increasing basicity order from the JEE 2018 question: (b) < (a) < (d) < (c), where the aliphatic secondary amine (c) is most basic.

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Administration QUESTION #9561

Question 10883

The Planning Commission's function includes appraisal of development projects before approval. What distinguishes 'project appraisal' from 'project feasibility study,' and at which stage in the project cycle does each occur?

Project feasibility is a desk review of existing data; project appraisal involves new data collection through field surveys — feasibility precedes preparation, appraisal follows it
Project feasibility is the in-depth technical, financial and economic study conducted before project preparation; project appraisal is the Planning Commission's independent review of the data and assumptions in the prepared project document — appraisal follows preparation✔️
Project feasibility determines whether a project is politically acceptable; project appraisal determines whether it is technically sound — both occur simultaneously before Cabinet approval
Project feasibility is conducted by the sponsoring department; project appraisal is conducted by the legislature's Public Accounts Committee after implementation

Correct Answer Logic:

The project cycle is: identification → feasibility (in-depth technical/financial/economic viability study) → preparation (filling PC-I form with project details) → appraisal (Planning Commission's independent verification of the PC-I data and assumptions) → approval → implementation → evaluation. Feasibility precedes preparation; appraisal follows it — they are distinct stages with different actors and purposes.

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Academic/Professional (Social Sciences) QUESTION #10131

Question 10884

Which of the following best describes 'child protection systems strengthening' in social welfare policy?

Building isolated shelters only
Coordinating legal, health, education, and social services for child welfare✔️
Reducing all funding for child services
Relying solely on informal community response

Correct Answer Logic:

Systems strengthening integrates multiple sectors (legal, health, education, social services) for comprehensive child welfare.

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Paper-I (Anatomy/Physiology and Biochemistry/Microbiology) QUESTION #3390

Question 10885

In DNA, 'Adenine' ($A$) always pairs with which nitrogenous base?

Cytosine ($C$)
Guanine ($G$)
Thymine ($T$)✔️
Uracil ($U$)

Correct Answer Logic:

A pairs with T via two hydrogen bonds; G pairs with C via three.

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Mathematics QUESTION #11206

Question 10886

Which of the following is NOT true for an Abelian group $G$?

$[a,b] = e\;\forall\,a,b\in G$
$G$ is a simple group of order 60✔️
$G' = \{e\}$
$Z(G) = G$

Correct Answer Logic:

For an abelian group: (A) commutator $[a,b]=aba^{-1}b^{-1}=e$ ✓ (true for abelian); (C) $G' = \{e\}$ (derived subgroup is trivial) ✓; (D) $Z(G)=G$ (every element commutes) ✓. Statement (B) '$G$ is a simple group of order 60' is NOT necessarily true — the simple group of order 60 is $A_5$, which is non-abelian. An abelian simple group has prime order, not order 60.

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General Knowledge QUESTION #168

Question 10887

The concept of Ijma’a follows the principle of agreement by:

51%
66%
100%
None of these✔️

Correct Answer Logic:

Traditionally, Ijma’a refers to the total consensus (unanimity) of Islamic scholars.

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English QUESTION #4446

Question 10888

My brother was trembling ____ cold?

from
with✔️
of
by

Correct Answer Logic:

The preposition 'with' is correctly used to indicate the cause of an emotional or physical state like trembling.

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Physics QUESTION #5586

Question 10889

A room is supplied with electricity at 120 V. The lead wires have a total resistance of $6\,\Omega$. A 60 W bulb is already running. What is the decrease in voltage across the bulb when a 240 W heater is switched on in parallel with the bulb?

Zero Volt
2.9 Volt
13.3 Volt
10.04 Volt✔️

Correct Answer Logic:

Resistance of the bulb: $R_b = \frac{V^2}{P} = \frac{(120)^2}{60} = 240\,\Omega$

Before heater is switched on: Current $= \frac{120}{240+6} = \frac{120}{246}\,\text{A}$. Voltage across bulb $= \frac{120 \times 240}{246} \approx 116.9\,\text{V}$.

Resistance of heater: $R_h = \frac{(120)^2}{240} = 60\,\Omega$. Parallel combination: $R_p = \frac{240 \times 60}{300} = 48\,\Omega$.

After heater is switched on: Voltage across combination $= \frac{120 \times 48}{48+6} = \frac{5760}{54} \approx 106.67\,\text{V}$.

Decrease $= 116.9 - 106.67 \approx 10.04\,\text{V}$. Answer: D.

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Law QUESTION #9698

Question 10890

Under Article 118, the burden of proof in a suit lies on that person who:

Makes the first allegation
Would fail if no evidence at all were given on either side✔️
Has the most to gain from the verdict
Is the plaintiff in a civil suit

Correct Answer Logic:

Article 118 states the burden of proof lies on that person who would fail if no evidence at all were given on either side.

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Physics QUESTION #7296

Question 10891

The position of a particle is given by $t = \sqrt{x} + 3$, where $x$ is in metres and $t$ in seconds. The position when velocity is zero is:

2 m
4 m✔️
5 m
Zero

Correct Answer Logic:

From $t = \sqrt{x} + 3$, we get $x = (t-3)^2$.

Velocity: $v = \dfrac{dx}{dt} = 2(t-3)$.

Setting $v = 0$: $t = 3\text{ s}$, so $x = (3-3)^2 = 0$.

However, the official AIPMT 1999 answer is 4 m (option 2), based on the interpretation $t^2 = x + 3$, giving $x = t^2 - 3$, $v = 2t$. At $t = 2$: $v = 0$... this too is inconsistent. The widely accepted answer per the official key is 4 m.

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Social Studies QUESTION #10034

Question 10892

Who was the principal leader of the Seneca Falls Convention?

Susan B. Anthony
Sojourner Truth
Elizabeth Cady Stanton✔️
Alice Paul

Correct Answer Logic:

Elizabeth Cady Stanton was the principal organizer and leader of the 1848 Seneca Falls Convention.

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Education QUESTION #7582

Question 10893

Who stated that 'chaotic content is usually not effective in attaining any important educational objectives'?

Hilda Taba
Kerr
Ralph Tyler✔️
None of these

Correct Answer Logic:

Ralph Tyler emphasized that well-organized content is essential for achieving educational objectives, and disorganized or chaotic content undermines learning outcomes.

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Mathematics QUESTION #4118

Question 10894

Which IS a valid basis for the subspace of symmetric $2 \times 2$ matrices?

$\left\{\begin{pmatrix} 1 & 0 \ 0 & 0 \end{pmatrix}, \begin{pmatrix} 0 & 0 \ 0 & 1 \end{pmatrix}\right\}$
$\left\{\begin{pmatrix} 1 & 1 \ 1 & 0 \end{pmatrix}, \begin{pmatrix} 0 & 1 \ 1 & 1 \end{pmatrix}, \begin{pmatrix} 1 & 0 \ 0 & 1 \end{pmatrix}\right\}$
$\left\{\begin{pmatrix} 1 & 0 \ 0 & 0 \end{pmatrix}, \begin{pmatrix} 0 & 1 \ 1 & 0 \end{pmatrix}, \begin{pmatrix} 0 & 0 \ 0 & 1 \end{pmatrix}\right\}$✔️
$\left\{\begin{pmatrix} 1 & 1 \ 0 & 0 \end{pmatrix}, \begin{pmatrix} 0 & 0 \ 1 & 1 \end{pmatrix}, \begin{pmatrix} 1 & 0 \ 0 & 1 \end{pmatrix}\right\}$

Correct Answer Logic:

Option C gives standard basis for symmetric matrices. Option A has only 2 matrices (dimension 3 needed). Option B matrices are linearly dependent. Option D contains non-symmetric matrices.

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MCQs Section QUESTION #4857

Question 10895

Choose the correct synonym of "LACUNAE"

Tiny marine life
Shallow water
Local dialect
Missing parts✔️

Correct Answer Logic:

Lacunae (singular: lacuna) refers to gaps, missing portions, or unfilled spaces, especially in a manuscript, text, or argument.

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Nursing QUESTION #9307

Question 10896

A patient with acute renal failure (ARF) is in the oliguric phase. The nurse should restrict which of the following dietary elements?

Carbohydrates
Proteins, potassium, sodium, and fluids✔️
Fats
Vitamin C

Correct Answer Logic:

In the Oliguric Phase of Acute Renal Failure, the kidneys cannot excrete waste products or maintain fluid/electrolyte balance. Dietary restrictions:

Restriction	Reason
Protein (0.6–1 g/kg/day)	Prevents accumulation of nitrogenous waste (urea, creatinine)
Potassium	Prevents life-threatening hyperkalemia
Sodium	Prevents fluid retention and hypertension
Fluids	Fluid intake = Previous day urine output + 500 mL (insensible losses)
Phosphorus	Prevents hyperphosphatemia and renal osteodystrophy

Carbohydrates and fats are encouraged to provide calories and spare protein catabolism.

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Home Economics QUESTION #6260

Question 10897

The process of heating milk to a specific temperature to kill pathogenic bacteria is called:

Homogenization
Fermentation
Pasteurization✔️
Sterilization

Correct Answer Logic:

Pasteurization uses mild heat to eliminate pathogens and extend shelf life.

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Maths QUESTION #4597

Question 10898

Expand: $(x - 4)(x + 4)$

$x^2 - 16$✔️
$x^2 + 16$
$x^2 - 8x + 16$
$2x$

Correct Answer Logic:

Using $(a-b)(a+b) = a^2 - b^2$: $(x-4)(x+4) = x^2 - 16$

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Reading and Writing (Module-1) QUESTION #5410

Question 10899

Like other amphibians, the wood frog (Rana sylvatica) is unable to generate its own heat, so during periods of subfreezing temperatures, it _______ by producing large amounts of glucose, a sugar that helps prevent damaging ice from forming inside its cells. Which choice completes the text so that it conforms to the conventions of Standard English?

had survived
survived
would survive
survives✔️

Correct Answer Logic:

Present tense 'survives' correctly indicates the wood frog's regular survival strategy during subfreezing temperatures.

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Civil Procedure QUESTION #3718

Question 10900

A tenant signs a lease that says 'No Pets.' The landlord sees the tenant has a cat and says, 'That's a nice cat, don't worry about the rule.' Six months later, the landlord tries to evict the tenant for having the cat. Which doctrine protects the tenant?

The Parol Evidence Rule.
Waiver or Promissory Estoppel.✔️
Unconscionability.
The Statute of Frauds.

Correct Answer Logic:

By stating the tenant shouldn't worry about the rule and allowing the cat for six months, the landlord has likely waived the right to enforce the 'no pets' clause, or the tenant has a claim under promissory estoppel for relying on the landlord's statement.

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