If $\tan^{-1}x, \tan^{-1}y, \tan^{-1}z$ are in A.P., then $2\tan^{-1}y=\tan^{-1}x+\tan^{-1}z$.

Also $x,y,z$ in A.P. means $2y=x+z$.

From $2\tan^{-1}y=\tan^{-1}x+\tan^{-1}z$: using the addition formula, $\tan(2\tan^{-1}y)=\tan(\tan^{-1}x+\tan^{-1}z)$, i.e., $\dfrac{2y}{1-y^2}=\dfrac{x+z}{1-xz}$.

Substituting $x+z=2y$: $\dfrac{2y}{1-y^2}=\dfrac{2y}{1-xz}$. So $1-y^2=1-xz$, giving $y^2=xz$.

Combined with $x+z=2y$ (A.P.) and $y^2=xz$ (G.P.) $\Rightarrow x=y=z$.

This is a binomial experiment: $n=10$, $p=P(\text{green})=\dfrac{15}{25}=\dfrac{3}{5}$, $q=\dfrac{2}{5}$.

$\text{Variance} = npq = 10 \times \dfrac{3}{5} \times \dfrac{2}{5} = 10 \times \dfrac{6}{25} = \dfrac{60}{25} = \dfrac{12}{5}$

Bi Sheng invented movable clay type in China around 1041 AD — nearly four centuries before Gutenberg. However, the Chinese writing system contains thousands of characters (Mandarin has over 50,000, with several thousand in common use), compared to the 26-letter Latin alphabet used in European languages. Setting up movable type for Chinese therefore required an enormous number of individual pieces, making it cumbersome and time-consuming — often slower than traditional block printing for short or medium runs. By contrast, a European printer needed only a small set of metal type for the entire alphabet, making Gutenberg's press extraordinarily efficient for European languages. This alphabetic advantage is a key reason the printing press became a revolutionary mass communication tool in Europe but remained a marginal improvement in China. Interestingly, Gutenberg also used durable oil-based ink and rag paper introduced to Europe via Muslim trade routes, further improving output quality.

This sentence has a contrast structure: spacecraft currently face little risk, but the future will be less _____. Whatever fills the blank must describe the current relatively safe state that will diminish in the future.

• Crowded — the future would logically become more crowded, not less. “Less crowded” contradicts the premise.
• Invulnerable — possible in isolation, but not a natural descriptor of an orbital environment as a whole.
• Protected — implies external protective mechanisms, which is not the argument’s focus.
• Benign — means safe and harmless. The current environment is benign (low risk), and the future will be less benign (more dangerous). This fits perfectly.

Correct Answer: D — Benign. The logic requires a word describing the current “safe” state that will erode as more satellites are launched.

The BCG (Bacillus Calmette-Guérin) vaccine protects against tuberculosis (TB), particularly severe forms in children:

• Miliary tuberculosis
• Tuberculous meningitis

In Pakistan's EPI schedule, BCG is given at birth or as early as possible as a single intradermal dose of 0.05 ml (in infants) into the left upper arm. A tuberculin skin test (Mantoux) that is positive before vaccination is a contraindication. Pakistan has one of the highest TB burdens globally, making BCG vaccination critical in community health nursing practice.