Rationalise the denominator by multiplying by $\dfrac{\sqrt{2}+\sqrt{1+\cos x}}{\sqrt{2}+\sqrt{1+\cos x}}$:

Denominator becomes $2-(1+\cos x)=1-\cos x$.

$\lim_{x\to0}\dfrac{\sin^2x(\sqrt{2}+\sqrt{1+\cos x})}{1-\cos x}$

Use $\dfrac{\sin^2x}{1-\cos x}=\dfrac{1-\cos^2x}{1-\cos x}=1+\cos x$:

$=\lim_{x\to0}(1+\cos x)(\sqrt{2}+\sqrt{1+\cos x})=(1+1)(\sqrt{2}+\sqrt{2})=2\cdot2\sqrt{2}=\mathbf{4\sqrt{2}}$

Wait: $2\times2\sqrt{2}=4\sqrt{2}$... but option A is 4. Let me recheck: $(2)(\sqrt{2}+\sqrt{2})=2\cdot2\sqrt{2}=4\sqrt{2}$. Answer: $4\sqrt{2}$ is not listed as option A (which is 4). The correct answer is $\mathbf{4\sqrt{2}}$ (index 1).

The Crude Birth Rate (CBR) is calculated as:

\\text{CBR} = \\frac{\\text{Number of live births in a year}}{\\text{Mid-year total population}} \\times 1000

It is expressed per 1,000 population. Pakistan's CBR is approximately 26–28 per 1,000 population.

Comparison with other fertility measures:

• General Fertility Rate (GFR) uses women aged 15–49 as denominator
• Total Fertility Rate (TFR) is the average number of children a woman would have in her lifetime
• Option 3 is the formula for Crude Death Rate (CDR)

$(0.0001)^2 = (10^{-4})^2 = 10^{-8}$

$0.01 = 10^{-2}$

$\dfrac{0.01}{(0.0001)^2} = \dfrac{10^{-2}}{10^{-8}} = 10^{-2-(-8)} = 10^6$

So $0.01$ is $10^6$ times as great as $(0.0001)^2$.