The primary theme of the Holy Quran is the guidance of mankind. The Quran addresses human beings, their relationship with Allah, their purpose in life, moral and ethical conduct, and the path to success in this world and the Hereafter. While it contains laws, stories, and descriptions of events, all these serve the central purpose of guiding humanity toward righteousness and submission to Allah.

For a girl to have hemophilia ($X^h X^h$), she must receive $X^h$ from both parents. The mother must be a carrier ($X^H X^h$) and the father must be hemophiliac ($X^h Y$).

From \(\vec{a} \times \vec{c} + \vec{b} = \vec{0}\), we get \(\vec{a} \times \vec{c} = -\vec{b}\). Taking dot product with \(\vec{a}\): \(\vec{a} \cdot (\vec{a} \times \vec{c}) = -\vec{a} \cdot \vec{b}\). Since \(\vec{a} \cdot (\vec{a} \times \vec{c}) = 0\), we have \(\vec{a} \cdot \vec{b} = 0\), which checks: \((1)(-1)+(-1)(1)+(0)(1) = 0\). Nope: \(\vec{a} = \hat{i}-\hat{j}\) (only 2D) and \(\vec{b} = \hat{i}+\hat{j}+\hat{k}\), so \(\vec{a} \cdot \vec{b} = 1-1 = 0\). Good. Taking magnitude: \(|\vec{a} \times \vec{c}| = |\vec{b}| = \sqrt{3}\). Also \(|\vec{a} \times \vec{c}|^2 = |\vec{a}|^2|\vec{c}|^2 - (\vec{a} \cdot \vec{c})^2\), so \(3 = 2|\vec{c}|^2 - 16\), giving \(|\vec{c}|^2 = \frac{19}{2}\).

Bacteria like *Streptomyces* and *Pseudomonas* are used for $B_{12}$ synthesis.

Androgyny reflects a blend of positive masculine and feminine traits in one individual.

Average = $\frac{10+20+30+40}{4} = \frac{100}{4} = 25$

Prudence directly applies: expenditure must not be prima facie more than the occasion demands and every government servant must exercise the same vigilance over public funds as a person of ordinary prudence would over their own money. Lavish hospitality directly contradicts this standard even if within budget.

Corticosteroids exert their anti-asthmatic effect by broadly suppressing the airway inflammatory response, reducing oedema, mucus production, and inflammatory cell infiltration, thereby improving airflow.

The clot provides a protective barrier for the bacteria.

Microorganisms are generally defined as being less than $1\text{ mm}$ in diameter and often require a microscope to see.

Simplifying: \(2|\sqrt{x}-3| + x - 6\sqrt{x} + 6 = 0\). Let \(t = \sqrt{x}\), so \(2|t-3| + t^2 - 6t + 6 = 0\). For \(t \geq 3\): \(2(t-3) + t^2 - 6t + 6 = 0\), giving \(t^2 - 4t = 0\), so \(t=0\) or \(t=4\). Only \(t=4\) satisfies \(t \geq 3\). For \(t < 3\): \(2(3-t) + t^2 - 6t + 6 = 0\), giving \(t^2 - 8t + 12 = 0\), so \(t=2\) or \(t=6\). Only \(t=2\) satisfies \(t<3\). Thus \(t \in \{2,4\}\), giving \(x \in \{4, 16\}\). S contains 2 elements.

\(\dfrac{1}{3}\% \text{ of } x = 9\)
\(\dfrac{x}{300} = 9\)
\(x = 2700\)

Bengaluru (Bangalore) is known as the 'Garden City of India' due to its numerous parks and gardens, including Lalbagh and Cubbon Park.

The Integrated Management of Childhood Illness (IMCI) is a strategy developed by WHO and UNICEF to address the major causes of death among children under 5 years of age. IMCI focuses on:

• Pneumonia
• Diarrhea
• Malaria
• Measles
• Malnutrition

IMCI has three components:

1. Improving health worker skills
2. Strengthening health systems
3. Improving family and community practices

In Pakistan, IMCI is implemented through primary health care facilities and is a key area for community health nursing practice and supervision.

Literary warrant is the principle that a subject heading or classification number should only be established when there is actual published literature on the topic to justify it. It grounds controlled vocabulary in existing documented knowledge.

Ethnobotany focuses on the relationship between people and plants within their cultural context.

The Quick Ratio formula is:

$\text{Quick Ratio} = \dfrac{\text{Current Assets} - \text{Inventory} - \text{Prepaid Expenses}}{\text{Current Liabilities}}$

$2.0 = \dfrac{5{,}000 - 2{,}000 - 0}{\text{CL}} = \dfrac{3{,}000}{\text{CL}}$

$\text{CL} = \dfrac{3{,}000}{2.0} = \mathbf{Rs.\ 1{,}500}$

The quick ratio excludes inventory and prepaid expenses from current assets since these are less liquid. Dividing quick assets by the ratio gives current liabilities.

Sum $= 5$. One part $= 40/5 = 8$. Girls $= 2 \times 8 = 16$.

This is a $1^\infty$ indeterminate form. Take logarithm:

$\ln p = \lim_{x\to0^+}\dfrac{\ln(1+\tan^2\sqrt{x})}{2x}$

Let $t=\sqrt{x}$, so $x=t^2$, $x\to0^+$ means $t\to0^+$:

$= \lim_{t\to0^+}\dfrac{\ln(1+\tan^2 t)}{2t^2} = \lim_{t\to0^+}\dfrac{\tan^2 t}{2t^2} = \dfrac{1}{2}$

(using $\ln(1+u)\approx u$ for small $u$ and $\lim_{t\to0}\frac{\tan t}{t}=1$)

Fringe width = ?D/d = (500?10???10)/(1?10??) = 5?10?? m = 5 mm