D-Fructose satisfies all conditions: (A) Found in honey — ✓. (B) Keto sugar (ketohexose) — ✓. (C) Exists in \(\alpha\) and \(\beta\)-anomeric forms (in cyclic pyranose/furanose forms) — ✓. (D) Laevorotatory (rotates plane of polarized light to left, hence the 'D' prefix refers to configuration, not optical rotation) — ✓. D-Glucose is dextrorotatory.

Prime factorization: \(12 = 2^2 \times 3\), \(18 = 2 \times 3^2\), \(24 = 2^3 \times 3\). LCM = \(2^3 \times 3^2 = 8 \times 9 = 72\).

3

Cooling removes heat — typically using water — to bring the fuel temperature below its ignition point. This is the most common firefighting method.

Using sum-to-product formulas: \((\cos x + \cos 4x) + (\cos 2x + \cos 3x) = 0\). This gives \(2\cos\frac{5x}{2}\cos\frac{3x}{2} + 2\cos\frac{5x}{2}\cos\frac{x}{2} = 0\), which factors as \(2\cos\frac{5x}{2}(\cos\frac{3x}{2} + \cos\frac{x}{2}) = 0\). Either \(\cos\frac{5x}{2} = 0\) or \(\cos\frac{3x}{2} + \cos\frac{x}{2} = 0\). For the first: \(\frac{5x}{2} = \frac{\pi}{2}, \frac{3\pi}{2}, \frac{5\pi}{2}, \frac{7\pi}{2}, \frac{9\pi}{2}\), giving \(x = \frac{\pi}{5}, \frac{3\pi}{5}, \pi, \frac{7\pi}{5}, \frac{9\pi}{5}\) (5 solutions). For the second: \(2\cos x \cos\frac{x}{2} = 0\), giving \(\cos x = 0\) or \(\cos\frac{x}{2} = 0\). From \(\cos x = 0\): \(x = \frac{\pi}{2}, \frac{3\pi}{2}\) (2 more solutions not in first set). From \(\cos\frac{x}{2} = 0\): \(x = \pi\) (already counted). Total = 5 + 2 = 7 solutions.

Stress is defined as $\frac{\text{Force}}{\text{Area}}$ [cite: 457].

• Force (Weight) $W \propto \text{Volume} \times \text{density} \propto L^3$
• Area $A \propto L^2$
• $\text{Stress} \propto \frac{L^3}{L^2} \propto L$
• Since $L$ increases by $9$, the stress increases by a factor of $9$[cite: 457].

Under normal conditions, $100\%$ of glucose is reabsorbed in the PCT.

Stored kinetic energy $= H\times S_{rated} = 5\times100 = 500\,\text{MJ}$. Swing equation inertia: $M = \frac{GH}{\pi f_s} = \frac{100\times5}{\pi\times50} = \frac{500}{157.08} \approx 3.18\,\text{MJ·s/rad}$.

The film history of the subcontinent and Pakistan involves several important firsts that students commonly confuse:

• First silent film from Lahore (Punjab): The Daughter of Today (1924), produced by Premier Film Company, directed by Mian Abdur Rasheed Kardar (A.R. Kardar)
• First Punjabi (talkie) film from Lahore: Heer Ranjha (1932), released one year after Alam Ara (1931) — meaning Lahore was almost as fast as Bombay in adopting sound cinema
• First Pakistani film after independence: Teri Yaad (Urdu), released at Perbhat (Sanober) Cinema, Lahore on 7 August 1948 (Eid-ul-Fitr Day). It was a commercial failure but historic as the inaugural film of the new Pakistani industry.

Note: Jugnu (1947) was the last major pre-partition Pakistani film. Khazanchi (1941) was famous for Master Ghulam Haidar's introduction of Punjabi folk music and Baby Noor Jehan as playback singer.

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

Ominous means threatening or foreshadowing evil; opposite is promising.

'Over' is used to indicate movement at a higher level than something else.

The set [1, -1] does not have closure property under addition because 1 + 1 = 2, which is not in the set.

اردو ڈرامے کا آغاز آغا حشر کاشمیری سے ہوتا ہے جنہیں اردو ڈرامے کا شیکسپیئر بھی کہا جاتا ہے۔

The two angles giving the same range are $\theta$ and $(90°-\theta)$.

$t_1 = \dfrac{2u\sin\theta}{g}$, $\quad t_2 = \dfrac{2u\cos\theta}{g}$

$t_1 t_2 = \dfrac{4u^2\sin\theta\cos\theta}{g^2} = \dfrac{2u^2\sin2\theta}{g^2} = \dfrac{2R}{g}$

Therefore $t_1 t_2 \propto \mathbf{R}$

Humidity = water vapour (liquid) dissolved in air (gas) → Liquid in gas (II). Alloys = solid metals dissolved in solid → Solid in solid (I)... wait alloys can be solid in liquid or solid in solid. Mercury amalgams = solid/liquid metal dissolved in mercury (liquid) → Liquid in solid (IV)... Smoke = solid particles in gas → Solid in gas (III). Matching: A-II, B-I, C-IV, D-III.

PIA's first international flight was in 1954 (to London).

Skeletal muscle is voluntary (conscious control) and multinucleated.

Obligate (or agrestal) weeds are ecologically specialized to agricultural habitats — they germinate with crop seeds, mimic crop morphology (Vavilovian mimicry), and cannot compete in undisturbed natural vegetation. Examples include Phalaris minor in wheat and Echinochloa crus-galli in rice. Their persistence is entirely dependent on continued soil disturbance through tillage.

Article 63A(3) requires the Presiding Officer to refer within two days (deemed referred if not done). The Chief Election Commissioner then places it before the Election Commission which must decide within 30 days. An appeal against the Election Commission's decision lies to the Federal Constitutional Court, which decides within 90 days.