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Boilers Mechanical Engineering QUESTION #2429

Question 2061

The Fourier number (Fo) in transient conduction is defined as $Fo = \alpha t / L_c^2$. It physically represents:

Dimensionless time of thermal diffusion: $\frac{\alpha t}{L_c^2}$✔️
Ratio of convective to conductive heat transfer
Ratio of buoyancy to viscous forces
Ratio of momentum diffusivity to thermal diffusivity

Correct Answer Logic:

The Fourier number $Fo=\alpha t/L_c^2$ is dimensionless time measuring how far thermal diffusion has penetrated into the body relative to its characteristic dimension $L_c$.

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Math (Module-1) QUESTION #5465

Question 2062

Right triangles $PQR$ and $STU$ are similar, with $P$ corresponding to $S$. If the measure of angle $Q$ is $18^\circ$, what is the measure of angle $S$?

$18^\circ$
$72^\circ$✔️
$82^\circ$
$162^\circ$

Correct Answer Logic:

In right triangle $PQR$, $\angle P + \angle Q = 90^\circ \implies \angle P = 90^\circ - 18^\circ = 72^\circ$. Since $P$ corresponds to $S$, $\angle S = 72^\circ$.

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General Science and Ability QUESTION #185

Question 2063

‘Blue dwarfs’ and ‘Red giants’ respectively refer to:

Moons of Jupiter
Young star and Old star✔️
Old star and Young star
None of these

Correct Answer Logic:

Blue dwarfs are typically young/hot stars; Red giants are stars in late evolution.

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Accounting & Finance QUESTION #9622

Question 2064

In a Creditors Control Account, which of the following items would appear on the DEBIT side?

Credit purchases for the period
Opening balance of creditors
Purchase returns to suppliers✔️
Closing balance of creditors

Correct Answer Logic:

The Creditors Control Account credit side records: opening balance and credit purchases (amounts owed to suppliers). The debit side records: purchase returns, payments made to suppliers, discounts received, and the closing balance (carried forward). Purchase returns reduce what is owed to creditors, hence they appear on the debit side.

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Mathematics QUESTION #6961

Question 2065

If $\cos^{-1}\!\left(\dfrac{2}{3x}\right)+\cos^{-1}\!\left(\dfrac{3}{4x}\right)=\dfrac{\pi}{2}$ for $x>\dfrac{3}{4}$, find $x$.

$\dfrac{\sqrt{145}}{12}$✔️
$\dfrac{\sqrt{145}}{10}$
$\dfrac{\sqrt{146}}{12}$
$\dfrac{\sqrt{145}}{11}$

Correct Answer Logic:

$\cos^{-1}A+\cos^{-1}B=\pi/2 \Rightarrow \cos^{-1}A=\pi/2-\cos^{-1}B=\sin^{-1}B$, i.e., $A=\sin(\cos^{-1}B)=\sqrt{1-B^2}$.

$\dfrac{2}{3x}=\sqrt{1-\dfrac{9}{16x^2}}$

Square: $\dfrac{4}{9x^2}=1-\dfrac{9}{16x^2}$

Multiply by $144x^2$: $64=144x^2-81 \Rightarrow 144x^2=145 \Rightarrow x=\dfrac{\sqrt{145}}{12}$

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General Knowledge QUESTION #8719

Question 2066

Who was the world's first female Prime Minister of a country?

Margaret Thatcher (England)
Srimavo Bandaranaike (Sri Lanka)✔️
Golda Meir (Israel)
Indira Gandhi (India)

Correct Answer Logic:

Sirimavo Bandaranaike became PM of Sri Lanka in 1960.

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Mathematics QUESTION #4148

Question 2067

Using variation of parameters for $y'' + y = \sec(x)$, what is the Wronskian $W$ of $y_1 = \cos(x)$ and $y_2 = \sin(x)$?

$0$
$1$
$-1$✔️
$\sec^2(x)$

Correct Answer Logic:

$W = \begin{vmatrix} \cos(x) & \sin(x) \ -\sin(x) & \cos(x) \end{vmatrix} = \cos^2(x) + \sin^2(x) = 1$.

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Chemistry QUESTION #1078

Question 2068

Statement I: Ferromagnetism is considered as an extreme form of paramagnetism. Statement II: The number of unpaired electrons in Cr$^{2+}$ ion ($Z=24$) is the same as that of Nd$^{3+}$ ion ($Z=60$).

Statement I is true but Statement II is false✔️
Statement I is false but Statement II is true
Both Statement I and Statement II are true
Both Statement I and Statement II are false

Correct Answer Logic:

Statement I is true — ferromagnetism arises from cooperative alignment of magnetic dipoles in domains, and is indeed an extreme form of paramagnetism. Statement II: Cr$^{2+}$ ([Ar]3d$^4$) has 4 unpaired electrons. Nd$^{3+}$ ([Xe]4f$^3$) has 3 unpaired electrons. They are NOT the same. Statement II is false.

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Islamic Studies QUESTION #231

Question 2069

Hudaybiyyah peace document was written from the Muslims' side by:

Abu Bakar Siddiq
Zaid bin Thabit
Ali bin Abi Talib✔️
None of these

Correct Answer Logic:

Hazrat Ali (RA) served as the scribe for the Treaty of Hudaybiyyah.

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The Elections Act 2017 QUESTION #9439

Question 2070

Under Section 84(3), if a voter fails to prove identity through biometric or new technology adopted under sub-section (2), what is the consequence?

The voter is referred to the Returning Officer for a decision
The voter is refused a ballot paper
Such failure shall not disentitle the voter to cast his vote if otherwise entitled✔️
The voter must cast a tendered ballot paper

Correct Answer Logic:

Section 84(3) states: 'Failure of a voter to prove his identity through the new technology shall not disentitle him to cast his vote if he is otherwise entitled so to do under this section.'

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MCQs Section QUESTION #4838

Question 2071

Pick the word nearly similar in meaning to "TORPOR"

Fever
Lethargy✔️
Taciturn
Torrid

Correct Answer Logic:

Torpor means a state of physical or mental inactivity; sluggishness or dormancy. Lethargy, meaning lack of energy and enthusiasm, is its closest synonym.

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Islamic Studies QUESTION #341

Question 2072

Imam Muslim Bin Hijaj Qusheri (author of Sahih Muslim) died in:

260 AH
261 AH✔️
262 AH
263 AH

Correct Answer Logic:

He passed away in 261 AH in Nishapur.

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Statistics QUESTION #1992

Question 2073

For a symmetric distribution, Bowley's coefficient of skewness is 0 and Pearson's coefficient $\beta_1 = \dfrac{\mu_3^2}{\mu_2^3}$ equals:

$1$
$0$✔️
$-1$
$3$

Correct Answer Logic:

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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Boilers Mechanical Engineering QUESTION #4037

Question 2074

'Air Preheater' is located:

In the water tank
In the flue gas path after the economizer✔️
Inside the furnace
In the office

Correct Answer Logic:

It heats incoming combustion air, further improving efficiency.

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General Knowledge QUESTION #4780

Question 2075

The headquarters of Greenpeace International is located in which city?

Vancouver
Amsterdam✔️
London
Paris

Correct Answer Logic:

Greenpeace International's headquarters is located in Amsterdam, Netherlands, though the organization was originally founded in Vancouver, Canada in 1971.

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Pakistan Affairs QUESTION #619

Question 2076

Who started the Nationalisation of Banks in Pakistan?

General Ayub Khan
Nawaz Sharif
Z.A. Bhutto✔️
None of these

Correct Answer Logic:

Zulfikar Ali Bhutto nationalized major industries and banks in 1974 .

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Mathematics QUESTION #7475

Question 2077

Let $\vec{u}$ be a vector coplanar with the vectors $\vec{a} = 2\hat{i} + 3\hat{j} - \hat{k}$ and $\vec{b} = \hat{j} + \hat{k}$. If $\vec{u}$ is perpendicular to $\vec{a}$ and $\vec{u} \cdot \vec{b} = 24$, then $|\vec{u}|^2$ is equal to:

256
84
336✔️
315

Correct Answer Logic:

Since $\vec{u}$ is coplanar with $\vec{a}$ and $\vec{b}$, we can write $\vec{u} = x\vec{a} + y\vec{b} = x(2\hat{i}+3\hat{j}-\hat{k}) + y(\hat{j}+\hat{k}) = 2x\hat{i} + (3x+y)\hat{j} + (-x+y)\hat{k}$. Condition $\vec{u} \perp \vec{a}$: $\vec{u} \cdot \vec{a} = 2x(2) + (3x+y)(3) + (-x+y)(-1) = 0$, giving $4x + 9x + 3y + x - y = 0$, so $14x + 2y = 0$, thus $y = -7x$. Condition $\vec{u} \cdot \vec{b} = 24$: $(3x+y)(1) + (-x+y)(1) = 24$, giving $3x+y-x+y = 24$, so $2x+2y = 24$, thus $x+y = 12$. From $y=-7x$: $x-7x = 12$, so $-6x=12$ and $x=-2$, giving $y=14$. Thus $\vec{u} = -4\hat{i} + 8\hat{j} + 16\hat{k}$, and $|\vec{u}|^2 = 16 + 64 + 256 = 336$.

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English QUESTION #2749

Question 2078

Choose the correct ARTICLE: 'He is ___ engineer.'

a
an✔️
the
no article

Correct Answer Logic:

'An' is used before words beginning with a vowel sound. 'Engineer' begins with the vowel sound /ɛ/. So 'an engineer' is grammatically correct.

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General Knowledge QUESTION #8844

Question 2079

The point where the White Nile and Blue Nile join (confluence) is located in which country?

Egypt
Sudan✔️
Palestine
Jordan

Correct Answer Logic:

The two Niles meet at Khartoum, Sudan.

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The Elections Act 2017 QUESTION #9432

Question 2080

Under Section 61(1) [as amended 2023], the nomination deposit for election to the National Assembly is Rs. 30,000 and for Provincial Assembly is Rs. 20,000. What does Section 61(3) [as amended 2023] now provide regarding refundability of this deposit?

It is refunded if the candidate secures more than one-eighth of total votes polled
It is refunded only if the candidate wins the election
The sum deposited shall be non-refundable✔️
It is refunded upon submission of election expense return

Correct Answer Logic:

Section 61(3), as substituted by the Elections (Second Amendment) Act 2023, now states: 'The sum deposited shall be non-refundable' — eliminating the earlier refund provisions.

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