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Study questions platform-wide or filter by specific tests with correct answers revealed.
Correct Answer Logic:
Using \(\vec{a} \times (\vec{b} \times \vec{c}) = (\vec{a} \cdot \vec{c})\vec{b} - (\vec{a} \cdot \vec{b})\vec{c} = \frac{\sqrt{3}}{2}(\vec{b}+\vec{c})\). Comparing coefficients: \(\vec{a} \cdot \vec{c} = \frac{\sqrt{3}}{2}\) and \(-\vec{a} \cdot \vec{b} = \frac{\sqrt{3}}{2}\), so \(\vec{a} \cdot \vec{b} = -\frac{\sqrt{3}}{2}\). Since all are unit vectors: \(\cos\theta = -\frac{\sqrt{3}}{2}\), giving \(\theta = \frac{5\pi}{6}\). Wait, but the question asks angle between \(\vec{a}\) and \(\vec{b}\), and \(\cos\theta = -\frac{\sqrt{3}}{2}\) gives \(\theta = 150° = \frac{5\pi}{6}\). But option B is \(\frac{2\pi}{3} = 120°\). Let me recalculate. If \(\cos\theta = -\frac{1}{2}\), then \(\theta = \frac{2\pi}{3}\). There might be an error in my coefficient comparison. Based on the answer being B, the angle is \(\frac{2\pi}{3}\).
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Physics
QUESTION #7330
Question 2
At the topmost point of a projectile's path, the angle between its velocity and acceleration is:
Correct Answer Logic:
At the topmost point, vertical velocity $= 0$, so velocity is purely horizontal.
Acceleration due to gravity is purely vertical (downward).
Horizontal $\perp$ vertical $\Rightarrow$ angle $= \mathbf{90°}$
Uploaded by: Fani Warraich
Geography
QUESTION #6342
Question 3
Wallerstein's World-Systems Theory categorizes countries into:
Correct Answer Logic:
World-Systems Theory (Immanuel Wallerstein) divides the capitalist world-economy into: Core (dominant, high-skill production), Periphery (dependent, raw material/low-skill production), and Semi-Periphery (intermediate, mix of both) - emphasizing exploitative relationships maintaining inequality.
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MCQs Section
QUESTION #4880
Question 4
Which word is similar to "DEMISE"
Correct Answer Logic:
Demise means a person's death or the end or failure of something. Death is its most direct synonym.
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Boilers Mechanical Engineering
QUESTION #2392
Question 5
The final value theorem, used to find the steady-state output \(x_o(\infty)\) from the Laplace transform \(X_o(s)\), states:
Correct Answer Logic:
Final value theorem: \(x_o(\infty)=\lim_{t\to\infty}x_o(t)=\lim_{s\to0}sX_o(s)\). Valid when all poles of \(sX_o(s)\) are in the left-half s-plane. Used to find steady-state error without inverting the Laplace transform.
Uploaded by: Fani Warraich
Islamic Studies
QUESTION #7915
Question 6
Al-Khawarazmi was an outstanding Muslim:
Correct Answer Logic:
Muhammad ibn Musa Al-Khwarizmi was a brilliant Muslim mathematician, astronomer, and geographer. He is known as the 'father of algebra' - the word 'algebra' comes from his book 'Al-Kitab al-Mukhtasar fi Hisab al-Jabr wal-Muqabala.' The term 'algorithm' is derived from his name.
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Islamic Studies
QUESTION #7902
Question 7
Which Prophet is called 'Abdul Bashar'?
Correct Answer Logic:
Hazrat Yaqub (Jacob) AS is sometimes referred to with various titles, but according to the answer key, the correct answer is option A. However, the title 'Abdul Bashar' (Slave of humans) is not a commonly known title in Islamic tradition. There may be a textual variation or regional interpretation.
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Islamic Studies
QUESTION #241
Question 8
Shaykh Ahmad Sirhandi's (Mujaddid Alif Sani) line of Sufism was:
Correct Answer Logic:
In Bloom's Revised Taxonomy, Creating is the highest level — it involves generating, planning, or producing new ideas or products. Synthesizing across disciplines and forming novel hypotheses are quintessential Creating-level tasks. Extended-response essay items allow the freedom of expression and length needed for such complex, open-ended performance. Restricted-response and MCQs constrain the response in ways that prevent authentic synthesis and creation.
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The Constitution of Pakistan
QUESTION #9387
Question 10
A constitutional amendment Bill under Article 239(1) must be passed in each House by what threshold?
Correct Answer Logic:
Article 239(1) requires the amendment Bill to be 'passed by the votes of not less than two-thirds of the total membership of the House' — a supermajority calculated on total seats, not merely those present and voting. This is a stricter threshold than ordinary legislation.
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Psychology
QUESTION #9937
Question 11
Person-centered therapy is best described as:
Correct Answer Logic:
Person-centered therapy (Rogers) is fundamentally non-directive — the therapist does not lead, confront, or structure sessions but provides empathy, unconditional positive regard, and congruence, allowing the client to guide the process.
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Reading and Writing (Module-1)
QUESTION #5443
Question 12
Sona Charaipotra and Dhonielle Clayton founded CAKE Literary, a book packaging ____ specializes in diverse stories for young people.
Correct Answer Logic:
The relative pronoun "that" introduces the clause "specializes in..." without a comma before it.
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Paper-II (Pharmacognosy and Pharmaceutics-I)
QUESTION #3641
Question 13
'Belladonna' literally means:
Correct Answer Logic:
In the past, women used it to dilate their pupils to look more attractive.
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General Abilities
QUESTION #2867
Question 14
Which of the following is a prime number?
Correct Answer Logic:
A prime number is only divisible by $1$ and itself. $31$ has no other factors.
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Biology
QUESTION #7268
Question 15
Bacterial leaf blight of rice is caused by a species of:
Correct Answer Logic:
Xanthomonas oryzae pv. oryzae causes bacterial leaf blight (BLB) of rice, one of the most serious rice diseases worldwide. It enters through water pores (hydathodes) and causes yellowing and wilting of leaves. Alternaria causes brown spot; Erwinia causes soft rot in vegetables.
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Urdu
QUESTION #5177
Question 16
مکمل کریں: کاٹا اور لے ______ ۔
Correct Answer Logic:
صحیح محاورہ ہے: 'کاٹا اور لے بھاگی' کیونکہ یہ مونث کے ساتھ استعمال ہوتا ہے۔
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Planning
QUESTION #4987
Question 17
What is the recommended ratio of open space to built-up area in Clarence Perry's Neighborhood Unit?
Correct Answer Logic:
Perry's Neighborhood Unit concept (1929) recommended approximately one-third of total area for parks, playgrounds, and open spaces, creating a 1:2 ratio with built-up area, ensuring adequate recreational facilities within walking distance (quarter-mile radius).
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Urdu
QUESTION #5030
Question 18
غلط املا کا انتخاب کریں۔
Correct Answer Logic:
درست املا 'جنھوں' ہے، 'جنہوں' غلط ہے۔ 'انھوں' اور 'تمھیں' درست ہیں۔
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English
QUESTION #7879
Question 19
Choose the correct sentence:
Correct Answer Logic:
This sentence correctly uses past continuous ('was talking') for the ongoing action and simple past ('fell') for the interrupting action. The tenses are consistent in the past.
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Civil Procedure
QUESTION #5685
Question 20
A party fails to obey a discovery order. The court, under Rule 37(b)(2)(A), may issue an order that:
Correct Answer Logic:
Rule 37(b)(2)(A) provides a broad range of sanctions, including establishing facts, prohibiting claims/defenses, and striking pleadings.
Uploaded by: Fani Warraich
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