Live practice

Test each possible divisor within \(A\):

\(R=\{(1,1),(1,2),(1,3),(1,4),(1,6),(2,2),(2,4),(2,6),(3,3),(3,6),(4,4),(6,6)\}\).

Every member divides itself, so every member appears both as a first and a second coordinate.

The object \(\{3,4\}\) is one element of \(A\); the individual numbers 3 and 4 are not elements. Also, every set contains \(\varnothing\) as a subset, but \(\varnothing\) need not be an element.

Therefore (ii), (iii), (iv), (vi) and (x) are correct. Statements (i), (v), (vii), (viii), (ix) and (xi) are incorrect.

No. Biodegradable waste causes fewer long-term persistence problems, but a large amount still overloads natural decomposition. Rotting waste can produce foul odour and methane, support flies and pathogens, and contaminate water. Rapid microbial decomposition in a water body reduces dissolved oxygen and can kill aquatic organisms. Proper segregation, composting, treatment and reduction are therefore necessary even for biodegradable waste.

Live and neutral become connected through very low resistance. Since \(I=\frac{V}{R}\), current rises suddenly to a very large value until protection disconnects it.

\[\begin{aligned}\frac{1}{R} &= \frac{1}{100}+\frac{1}{50}+\frac{1}{500}\\&= 0.032\end{aligned}\], so \(R=31.25\) Ω.

A planet is close enough to appear as an extended disc composed of many point sources. Atmospheric fluctuations brighten or shift different points differently, and these effects average out at the eye. Its total brightness and apparent position remain comparatively steady.

A lens must transmit light. Water, glass and transparent plastic can refract light; opaque clay cannot serve as an optical lens.

The anther is the pollen-producing part of a stamen. Its pollen sacs contain pollen grains carrying male gametes.

Cytokinin is a plant hormone that promotes cell division. Insulin, thyroxine and oestrogen are animal hormones.

Mammals and birds maintain a constant body temperature and have high energy demands. A four-chambered heart prevents mixing, so tissues receive blood with a high oxygen concentration at systemic pressure while lungs are protected at lower pressure. Efficient aerobic respiration supplies the ATP needed for active life and thermoregulation.