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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: \(\frac{\alpha t}{L_c^2}\)โœ”๏ธ
  • 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 \(L_c\).
Uploaded by: Fani Warraich
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 $S$, $\angle S = 72^\circ$.
Uploaded by: Fani Warraich
General Science and Ability QUESTION #185
Question 2063
โ€˜Blue dwarfsโ€™ and โ€˜Red giantsโ€™ respectively refer to:
  • Moons of Jupiter
  • Young star and Old starโœ”๏ธ
  • 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.
Uploaded by: Fani Warraich
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 suppliersโœ”๏ธ
  • 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.
Uploaded by: Fani Warraich
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 $x$.

  • $\dfrac{\sqrt{145}}{12}$โœ”๏ธ
  • $\dfrac{\sqrt{145}}{10}$
  • $\dfrac{\sqrt{146}}{12}$
  • $\dfrac{\sqrt{145}}{11}$
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 $144x^2$: $64=144x^2-81 \Rightarrow 144x^2=145 \Rightarrow x=\dfrac{\sqrt{145}}{12}$

Uploaded by: Fani Warraich
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)โœ”๏ธ
  • Golda Meir (Israel)
  • Indira Gandhi (India)
Correct Answer Logic:
Sirimavo Bandaranaike became PM of Sri Lanka in 1960.
Uploaded by: Fani Warraich
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 falseโœ”๏ธ
  • 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 โ€” 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.
Uploaded by: Fani Warraich
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 Talibโœ”๏ธ
  • 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 entitledโœ”๏ธ
  • 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.'
Uploaded by: Fani Warraich
MCQs Section QUESTION #4838
Question 2071
Pick the word nearly similar in meaning to "TORPOR"
  • Fever
  • Lethargyโœ”๏ธ
  • 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 AHโœ”๏ธ
  • 262 AH
  • 263 AH
Correct Answer Logic:
He passed away in 261 AH in Nishapur.
Uploaded by: Fani Warraich
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 economizerโœ”๏ธ
  • Inside the furnace
  • In the office
Correct Answer Logic:
It heats incoming combustion air, further improving efficiency.
Uploaded by: Fani Warraich
General Knowledge QUESTION #4780
Question 2075
The headquarters of Greenpeace International is located in which city?
  • Vancouver
  • Amsterdamโœ”๏ธ
  • 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.
Uploaded by: Fani Warraich
Pakistan Affairs QUESTION #619
Question 2076
Who started the Nationalisation of Banks in Pakistan?
  • General Ayub Khan
  • Nawaz Sharif
  • Z.A. Bhuttoโœ”๏ธ
  • None of these
Correct Answer Logic:
Zulfikar Ali Bhutto nationalized major industries and banks in 1974 .
Uploaded by: Fani Warraich
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
  • anโœ”๏ธ
  • the
  • no article
Correct Answer Logic:
'An' is used before words beginning with a vowel sound. 'Engineer' begins with the vowel sound /ษ›/. So 'an engineer' is grammatically correct.
Uploaded by: Fani Warraich
General Knowledge QUESTION #8844
Question 2079
The point where the White Nile and Blue Nile join (confluence) is located in which country?
  • Egypt
  • Sudanโœ”๏ธ
  • Palestine
  • Jordan
Correct Answer Logic:
The two Niles meet at Khartoum, Sudan.
Uploaded by: Fani Warraich
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-refundableโœ”๏ธ
  • 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' โ€” eliminating the earlier refund provisions.
Uploaded by: Fani Warraich