Arterioles are known as the 'resistance vessels' because they can significantly constrict or dilate.

Multiples of 4 in $\{1,\ldots,20\}$: $\{4,8,12,16,20\}$ — 5 elements. Their images must be multiples of 3 in $\{1,\ldots,20\}$: $\{3,6,9,12,15,18\}$ — 6 elements.

Assign the 5 multiples-of-4 to 5 of the 6 multiples-of-3 (injectively, since $f$ is onto): $6 \times 5 \times 4 \times 3 \times 2 = 6!/(6-5)! = 720$... but we need surjection on all 20 elements.

The remaining 15 domain elements map to the remaining 15 codomain elements (after fixing the 5 images above): $(15)!$ ways. But 1 multiple-of-3 is unused by the multiples-of-4, so it must be covered by remaining 15 elements.

Total $= 6! \times (15)! = (15)! \times 6!$

Bohr effect: increased CO₂ decreases O₂ binding

An Assur dyad is the simplest system group (zero-DOF group): 2 links (\(n=2\)) and 3 full (5th-class) kinematic pairs (\(c_5=3\)), satisfying \(3n-2c_5=3(2)-2(3)=0\).

Pakistan was ranked 142nd out of 146 countries in the 2023 report.

For two lines to be coplanar, the scalar triple product of their direction ratios and the vector joining points on the lines must be zero. The direction ratios are \((1, 1, -k)\) and \((k, 2, 1)\). A point on the first line is \((2, 3, 4)\) and on the second is \((1, 4, 5)\). The vector joining them is \((-1, 1, 1)\). Setting up the determinant: \(\begin{vmatrix} -1 & 1 & 1 \\ 1 & 1 & -k \\ k & 2 & 1 \end{vmatrix} = 0\). Expanding: \(-1(1+2k) - 1(1+k^2) + 1(2-k) = 0\), which simplifies to \(k^2 + 3k = 0\), giving \(k = 0\) or \(k = -3\). Thus, k has exactly two values.

Slope angle \(\theta = \tan^{-1}\left(\dfrac{\text{rise}}{\text{run}}\right) = \tan^{-1}\left(\dfrac{18}{28}\right) = \tan^{-1}(0.643) \approx 33°\

In architectural design, comfortable stair angles range from 25° to 40°. The ideal is around 30°–35°.

This is why building codes specify maximum riser heights (typically 190 mm) and minimum tread depths (typically 250 mm) — to keep the angle in a safe, comfortable range.

For two Carnot engines in series where the work output is equal ($W_A = W_B$):

$Q_1 - Q_2 = Q_2 - Q_3$

Since $Q \propto T$ for a Carnot cycle, we can write:
$T_1 - T_2 = T_2 - T_3$

Rearranging for $T_2$:
$2T_2 = T_1 + T_3 \implies T_2 = \frac{600 + 400}{2} = 500 \text{ K}$.

Wilson first agreed to negotiate but then refused to compromise—this reveals something contradictory about his position. Rigidity...betrayed is correct: his actual rigidity (inflexibility) was betrayed (revealed/exposed) by refusing to compromise after initially seeming open to negotiation.

Bravely is an adverb (describes how an action is done).

• At C2: Priority order is $-OH > -COOH > -C(H)(Cl)CH_3 > -H$. The sequence is counter-clockwise, but since $H$ is on the horizontal line, it is 2S.
• At C3: Priority order is $-Cl > -CH(OH)COOH > -CH_3 > -H$. The sequence is clockwise, but with $H$ on the horizontal line, it is 3R.

Mean = 6 (from \(\sum x_i = 54\)). Variance = \(\frac{\sum x_i^2}{9} - 36 = \frac{360}{9} - 36 = 4\). SD = 2.

Alkaptonuria (defective homogentisate oxidase) and albinism (defective tyrosinase) are both inherited as autosomal recessive traits. They are expressed only when an individual is homozygous for the defective allele (aa). Carriers (Aa) are phenotypically normal. Sir Archibald Garrod (1902) first described alkaptonuria as an 'inborn error of metabolism' — the first known example of autosomal recessive inheritance and the biochemical basis of genetic disease. Both involve defects in the tyrosine metabolic pathway.

The Aligarh Movement (1870s onward) was fundamentally an educational movement. Sir Syed Ahmad Khan sought to encourage Muslims of the subcontinent to pursue modern, Western-style education alongside Islamic learning. The Muhammadan Anglo-Oriental College at Aligarh (later Aligarh Muslim University) was its flagship institution.

Correct Answer: A — Education.

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 \(|\vec{u}|^2 = 16 + 64 + 256 = 336\).

At maximum height vertical velocity = 0. Using v = u - gt: 0 = u - (9.8)(3); u = 29.4 m/s.

Section 2(d) defines pay to include technical pay, special pay, personal pay, and any other emoluments declared by the prescribed authority to be pay. Daily allowance is a separate entitlement and is not included within the statutory definition of 'pay' under the Act.

The dorsal columns ascend ipsilaterally and decussate only in the medulla (internal arcuate fibers), whereas the spinothalamic tract decussates almost immediately at the segmental level of entry. This difference explains the classic dissociated sensory pattern in Brown-Séquard syndrome.

The Suez Canal connects the Mediterranean and Red Seas.

Telepathy is the supposed ability to read minds.