Study questions platform-wide or filter by specific tests with correct answers revealed.
Maximum power transfer theorem: load resistance should equal:
For maximum power, R_L = R_source (Thévenin resistance).
Let $X$ be the set of all integers $n$ satisfying $2 \leq |n| \leq 5$. Compare:
Quantity A: The absolute value of the greatest integer in $X$
Quantity B: The absolute value of the least integer in $X$
The set $X$ consists of all integers $n$ with $2 \leq |n| \leq 5$.
These are: $-5, -4, -3, -2, 2, 3, 4, 5$.
The greatest integer in $X$ is $5$, and $|5| = 5$.
The least integer in $X$ is $-5$, and $|-5| = 5$.
Both absolute values equal $5$, so the two quantities are equal.
A business owner purchased a delivery vehicle and made these payments:
| Item | Amount ($) |
|---|---|
| Delivery vehicle purchase price | 28,000 |
| Fitting shelves inside the vehicle | 3,000 |
| Painting business logo on the vehicle | 2,000 |
What was the total capital expenditure?
Option C ($31,000) is correct.
Capital expenditure includes costs that bring a non-current asset into use or improve its capacity:
- Vehicle purchase price: $28,000
- Fitting shelves (improves functionality): $3,000
Total CapEx = $31,000
Painting the logo ($2,000) is revenue expenditure — a marketing cost that does not add to the asset's useful life.
Given that $r > s > 0$, compare the two quantities below.
Column A: $\dfrac{rs}{r}$
Column B: $\dfrac{rs}{s}$
Simplify each expression:
- Column A: $\dfrac{rs}{r} = s$
- Column B: $\dfrac{rs}{s} = r$
Since we are given $r > s > 0$, it follows that $r > s$.
Therefore Column B ($r$) is greater than Column A ($s$).
Rhesus (Rh) Isoimmunization Prevention is critical in Rh-negative pregnant women:
Sensitizing events requiring Anti-D administration:
- Amniocentesis, CVS, cordocentesis
- Antepartum hemorrhage (APH)
- External cephalic version (ECV)
- Abdominal trauma
- Miscarriage/termination
- Ectopic pregnancy
- Delivery (within 72 hours)
Routine prophylaxis: Anti-D 300 mcg IM at 28 weeks (and some protocols: 28 + 34 weeks).
Dose:
- First trimester sensitizing event: \(250\,\text{IU}\) (50 mcg)
- After 20 weeks / delivery: \(500\,\text{IU}\) (100 mcg) or \(300\,\text{mcg}\) (1500 IU)
The Kleihauer-Betke test estimates fetal-maternal hemorrhage volume to calculate additional Anti-D dose needed:
\[\text{Additional dose} = \frac{\% \text{fetal cells} \times \text{maternal blood volume}}{30} \times 300\,\mu\text{g}\]
Without prophylaxis, risk of sensitization after delivery = 16%. With Anti-D = reduced to <0.1%.
Draft statement of financial position: Ordinary share capital $900,000; Share premium $80,000; General reserve $96,000; Retained earnings (opening) $230,000; Profit for year $145,000. What is the maximum dividend the company can declare?
Option C ($471,000) is correct.
Dividends can only be paid from distributable (revenue) reserves:
- Retained earnings: $230,000
- Profit for year: $145,000
- General reserve: $96,000
Total = $471,000
Share premium ($80,000) is a capital reserve — not distributable.
Using only principal values of inverse functions, describe the set $A=\left\{x\geq0:\tan^{-1}(2x)+\tan^{-1}(3x)=\dfrac{\pi}{4}\right\}$.
Apply the addition formula: $\tan^{-1}(2x)+\tan^{-1}(3x)=\tan^{-1}\!\left(\dfrac{5x}{1-6x^2}\right)$ when $6x^2<1$.
Setting equal to $\pi/4$: $\dfrac{5x}{1-6x^2}=1 \Rightarrow 5x=1-6x^2 \Rightarrow 6x^2+5x-1=0$
$x=\dfrac{-5\pm\sqrt{25+24}}{12}=\dfrac{-5\pm7}{12}$
$x=\dfrac{2}{12}=\dfrac{1}{6}$ or $x=\dfrac{-12}{12}=-1$.
Since $x\geq0$, only $x=\dfrac{1}{6}$ is valid. Check: $6\cdot(1/6)^2=1/6<1$ ✓. So $A=\{1/6\}$ — a singleton.
Sign in to join the conversation and share your thoughts.
Log In to Comment