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Mathematics QUESTION #6967

Evaluate $\sin^{-1}\!\left(\dfrac{12}{13}\right)-\sin^{-1}\!\left(\dfrac{3}{5}\right)$.

$\pi-\sin^{-1}\!\left(\dfrac{63}{65}\right)$
$\dfrac{\pi}{2}-\sin^{-1}\!\left(\dfrac{56}{65}\right)$✔️
$\dfrac{\pi}{2}-\cos^{-1}\!\left(\dfrac{9}{65}\right)$
$\pi-\cos^{-1}\!\left(\dfrac{33}{65}\right)$

Correct Answer Logic:

Let $A=\sin^{-1}(12/13)$: $\sin A=12/13,\ \cos A=5/13$.

Let $B=\sin^{-1}(3/5)$: $\sin B=3/5,\ \cos B=4/5$.

$\sin(A-B)=\sin A\cos B-\cos A\sin B=\dfrac{12}{13}\cdot\dfrac{4}{5}-\dfrac{5}{13}\cdot\dfrac{3}{5}=\dfrac{48}{65}-\dfrac{15}{65}=\dfrac{33}{65}$... Hmm, but let me check $\cos(A-B)$: $=\cos A\cos B+\sin A\sin B=\dfrac{5}{13}\cdot\dfrac{4}{5}+\dfrac{12}{13}\cdot\dfrac{3}{5}=\dfrac{20+36}{65}=\dfrac{56}{65}$.

So $A-B=\cos^{-1}(56/65)=\pi/2-\sin^{-1}(56/65)$. Answer: $\dfrac{\pi}{2}-\sin^{-1}\!\left(\dfrac{56}{65}\right)$.

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Mathematics QUESTION #1278

Question 2

If a homomorphism $\varphi: G\to H$ is injective, then:

Every element of H has a preimage in G
$\ker\varphi$ is trivial (contains only identity)✔️
G and H have the same order
$\varphi$ must also be surjective

Correct Answer Logic:

An injective (one-to-one) homomorphism has trivial kernel: if $\varphi(g)=e_H$ then $\varphi(g)=\varphi(e_G)$, and by injectivity $g=e_G$. So $\ker\varphi=\{e_G\}$. This is both a necessary and sufficient condition for injectivity of a group homomorphism.

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General Knowledge QUESTION #8776

Question 3

The term 'Hung Parliament' describes a situation in which:

Prime Minister avoids Parliament sessions
Prime Minister refuses to step down after no-confidence
No single party has a majority in the house✔️
The ruling party lost majority in the upper house

Correct Answer Logic:

Hung Parliament means no party has an absolute majority.

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MCQs Section QUESTION #4890

Question 4

Which word is opposite to "CONSCIENTIOUS"

Uncorrupt
Honourable
Principled
Profligate✔️

Correct Answer Logic:

Conscientious means wishing to do one's work thoroughly and carefully. Its antonym is Profligate, meaning recklessly wasteful and utterly lacking in moral principles.

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Civil / Architecture QUESTION #2372

Question 5

In prestressed concrete design, the concept of the 'load balancing method' (T.Y. Lin's method) involves selecting the tendon profile such that the transverse component of prestress forces:

Maximizes the bending moment at midspan to increase the section capacity
Exactly balances a chosen portion of the applied gravity loads, resulting in a uniformly stressed (axially loaded) cross-section under the balanced load✔️
Eliminates all tensile stresses in the section at every load level
Positions the pressure line (C-line) at the kern point of the section

Correct Answer Logic:

In the load balancing method (T.Y. Lin, 1963), the tendon is profiled (typically parabolic for UDL) so its vertical component exactly counteracts a chosen portion of the gravity load (usually dead load or total service load). Under the balanced load $w_b = \dfrac{8 P e}{L^2}$, the beam is in pure axial compression with uniform stress $f = P/A$. Remaining loads (unbalanced) are analyzed by conventional elastic methods.

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Islamic Studies QUESTION #8254

Question 6

Which was the first revealed divine book?

Torait✔️
Zabur
Anjeel
Holy Quran

Correct Answer Logic:

The Torah (Tawrat) revealed to Prophet Musa (Moses) AS is considered the first of the major revealed books, though scrolls (Suhuf) were given to earlier prophets like Ibrahim (AS). The four major revealed books in chronological order are: (1) Torah to Musa (AS), (2) Zaboor to Daud (AS), (3) Injeel (Gospel) to Isa (AS), and (4) Quran to Muhammad (PBUH). Muslims believe in all divine revelations but consider the Quran as the final and preserved scripture.

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Pakistan Affairs QUESTION #9056

Question 7

The Chief Election Commissioner of Pakistan is appointed for a term of:

Five years✔️
As determined by the President
Same term as the assemblies
Three years

Correct Answer Logic:

The CEC serves a 5-year term.

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General Science and Ability QUESTION #195

Question 8

The amount of data transmitted for a given amount of time is called:

Noise
Bandwidth✔️
Frequency
None of these

Correct Answer Logic:

Bandwidth is the capacity of a wired or wireless network communications link.

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Tourism & Hospitality Management QUESTION #1599

Question 9

The Cultural Tourism course distinguishes between 'tangible' and 'intangible' cultural heritage. Which of the following correctly pairs each type with an example from the Pakistan context?

Tangible: Folk music and dance; Intangible: Mohenjo-daro ruins
Tangible: Archaeological sites and architecture; Intangible: Folklores, performing arts, and traditional sports✔️
Tangible: National museums; Intangible: Government tourism policy
Tangible: Fairs and festivals; Intangible: Ancient coins and artifacts

Correct Answer Logic:

The Cultural Tourism course explicitly distinguishes tangible heritage (archaeological sites, museums, architecture, arts & crafts) from intangible heritage (folklores, performing arts, music, drama, dance, traditional sports, food & gastronomy). This distinction is critical to heritage management and UNESCO frameworks.

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Nursing QUESTION #9147

Question 10

A woman at 24 weeks gestation is diagnosed with preterm premature rupture of membranes (PPROM). Which combination of interventions is MOST evidence-based?

Immediate induction of labor to prevent infection
Hospitalization + antibiotics (erythromycin) + antenatal corticosteroids + nifedipine tocolysis✔️
Oral antibiotics at home with weekly follow-up
Cerclage placement and progesterone supplementation only

Correct Answer Logic:

PPROM = Rupture of membranes before 37 weeks gestation without labor.

Evidence-based management bundle (ACOG/RCOG):

Intervention	Rationale	Drug/Dose
Hospitalization	Monitor for chorioamnionitis, cord prolapse	—
Antibiotics	Prolong latency period, reduce chorioamnionitis	Erythromycin 250 mg QID × 10 days (avoid amoxicillin-clavulanate — associated with NEC)
Antenatal corticosteroids	Fetal lung maturity (if 24–34 weeks)	Betamethasone 12 mg IM × 2 doses, 24 hr apart
MgSO₄ neuroprotection	If <32 weeks, reduces cerebral palsy	$4\,\text{g}$ IV loading dose
GBS prophylaxis	If GBS status unknown	Penicillin G IV

Tocolysis: Short-term tocolysis (48 hr) to allow steroids to act, but not for prolonged tocolysis as it may mask infection signs. Nifedipine or indomethacin used.

Chorioamnionitis signs (mandate delivery regardless of GA): fever, uterine tenderness, fetal tachycardia, maternal tachycardia, foul-smelling liquor, elevated CRP/WBC.

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General Knowledge QUESTION #8828

Question 11

The constellation 'Southern Cross' (Crux) consists of how many main stars?

Seven Stars
Four Stars✔️
Five Stars
None of these

Correct Answer Logic:

The Southern Cross has four main stars.

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Home Economics QUESTION #6271

Question 12

Which term describes the 'head-to-toe' pattern of physical development in infants?

Hierarchical
Proximodistal
Differentiation
Cephalocaudal✔️

Correct Answer Logic:

Cephalocaudal development means growth and motor control proceed from the head downward to the feet.

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Accounting & Finance QUESTION #6140

Question 13

Which item results in a credit entry in the statement of profit or loss?

A reduction in the allowance for irrecoverable debts✔️
An increase in the allowance for irrecoverable debts
The creation of an allowance for irrecoverable debts
The writing off of a trade receivable as irrecoverable

Correct Answer Logic:

Option A is correct.

When the allowance is reduced, the previously charged expense is released: Debit allowance account; Credit statement of profit or loss — effectively increasing profit.

Options B, C, D all result in debit entries (expenses) that reduce profit.

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Statistics QUESTION #1963

Question 14

The statistical measure that describes the extent to which numerical data tends to scatter or deviate around a central average is known as:

Dispersion✔️
Regression
Correlation
Kurtosis

Correct Answer Logic:

Dispersion refers to the spread or scatter of data values around an average. Common measures include range, variance $\sigma^2$, and standard deviation $\sigma$.

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Pakistan Affairs QUESTION #597

Question 15

Comrade', Newspaper was published by:

Abdul Majid Salik
Maulana Zafar Ali Khan
Maulana Mohammad Ali Jauhar✔️
None of These

Correct Answer Logic:

Maulana Mohammad Ali Jauhar launched the English weekly Comrade in 1911.

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Physical Education QUESTION #6809

Question 16

The 'Philanthropinum' schools established in Germany were unique because they:

Banned physical activity to focus on theology
Integrated systematic physical exercises into the daily school schedule✔️
Used physical punishment as the primary teaching tool
Were only open to professional soldiers

Correct Answer Logic:

Based on Enlightenment ideals, these schools were among the first to make PE a formal and scientific part of the modern school curriculum.

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General Abilities QUESTION #4518

Question 17

What is $\sqrt{169}$?

$11$
$13$✔️
$17$
$84.5$

Correct Answer Logic:

$13^2 = 169$, therefore $\sqrt{169} = 13$

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The Constitution of Pakistan QUESTION #9355

Question 18

Under Article 239(5), as substituted by the 27th Amendment 2025, courts now have what jurisdiction over constitutional amendments?

Plenary power to review on all grounds
Can review only if fundamental rights are violated
No court shall have jurisdiction to call in question any amendment to the Constitution on any ground whatsoever✔️
Can review if the amendment violates the basic structure doctrine

Correct Answer Logic:

Article 239(5) as substituted by the 27th Amendment 2025 completely ousts all judicial jurisdiction: 'no court shall have jurisdiction to call in question any amendment to the Constitution on any ground whatsoever.' Article 239(6) further declares there is 'no limitation whatever' on Parliament's amending power.

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