As $x\to1^+$: let $h=x-1>0$, so $h\to0^+$. Then $|1-x|=h$, $[1-x]=[-h]=-1$.

$\sin\!\left(\dfrac{\pi}{2}[-h]\right)=\sin\!\left(\dfrac{\pi}{2}\cdot(-1)\right)=\sin(-\pi/2)=-1$

Numerator: $(1-|x|+\sin h)\cdot(-1)$. As $x\to1^+$: $|x|=x=1+h$, so $1-|x|=-h$.

Numerator $= (-h+\sin h)(-1) = h-\sin h$

Denominator: $h\cdot(-1)=-h$

Limit $= \dfrac{h-\sin h}{-h} = -(1-\dfrac{\sin h}{h})\to-(1-1)=\mathbf{0}$

Resistance of the bulb: $R_b = \frac{V^2}{P} = \frac{(120)^2}{60} = 240\,\Omega$

Before heater is switched on: Current $= \frac{120}{240+6} = \frac{120}{246}\,\text{A}$. Voltage across bulb $= \frac{120 \times 240}{246} \approx 116.9\,\text{V}$.

Resistance of heater: $R_h = \frac{(120)^2}{240} = 60\,\Omega$. Parallel combination: $R_p = \frac{240 \times 60}{300} = 48\,\Omega$.

After heater is switched on: Voltage across combination $= \frac{120 \times 48}{48+6} = \frac{5760}{54} \approx 106.67\,\text{V}$.

Decrease $= 116.9 - 106.67 \approx 10.04\,\text{V}$. Answer: D.

Let Julio's salary be $J$ and Maria's old salary be $M_{old}$.

Given: $M_{old} = 1.24J$

Maria's new salary: $M_{new} = M_{old} - 0.24M_{old} = 0.76M_{old} = 0.76(1.24J) = 0.9424J$

Comparing:

• Column A: $J = 1.0J$
• Column B: $0.9424J$

Since $1.0 > 0.9424$, Column A (Julio's salary) is greater than Column B (Maria's new salary).

Therefore, Column A is greater.

Option D (24.85%) is correct.

ROCE = Profit from operations ÷ Capital Employed × 100

Capital Employed = Shareholders' equity + Non-current liabilities = $423,000 + $80,000 = $503,000

(Current liabilities are excluded from capital employed.)

ROCE = $125,000 ÷ $503,000 × 100 = 24.85%