Live practice

1. \(A\cup B=\{1,2,3,4,5,6\}\).
2. \(A\cup C=\{1,2,3,4,5,6,7,8\}\).
3. \(B\cup C=\{3,4,5,6,7,8\}\).
4. \(B\cup D=\{3,4,5,6,7,8,9,10\}\).
5. \(A\cup B\cup C=\{1,2,3,4,5,6,7,8\}\).
6. \(A\cup B\cup D=\{1,2,3,4,5,6,7,8,9,10\}\).
7. \(B\cup C\cup D=\{3,4,5,6,7,8,9,10\}\).

Each piece has \(\frac{R}{5}\). Five equal pieces in parallel give \[\begin{aligned}R' &= (\frac{R}{5})/5\\&= \frac{R}{25}\end{aligned}\]. Thus \(\frac{R}{R}'=25\).

Here \(u=-25\) cm, \(f=+10\) cm.

The positive v and negative height show a real, inverted, diminished image between F and 2F.

Both occur without conscious choice. An involuntary action is a routine internal activity controlled mainly by autonomic centres or hormones, such as heartbeat or peristalsis. A reflex is a rapid, stereotyped response triggered by a specific stimulus and conducted through a reflex arc, such as withdrawing from heat.

Photosynthesis requires carbon dioxide, water, chlorophyll and light. Therefore all listed requirements are necessary.

Soap is a salt of a strong base and weak carboxylic acid. Its solution is mildly alkaline. Therefore red litmus turns blue, while blue litmus remains blue.

Sulphur burns to form sulphur dioxide:

Dry litmus shows no change because water is needed to form an acidic solution. Moist blue litmus turns red because sulphur dioxide dissolves in water to form sulphurous acid:

(a) Zinc + sulphuric acid → zinc sulphate + hydrogen

(b) Magnesium + hydrochloric acid → magnesium chloride + hydrogen

(c) Aluminium + sulphuric acid → aluminium sulphate + hydrogen

(d) Iron + hydrochloric acid → iron(II) chloride + hydrogen

Define the sample space and count each favourable outcome once.

The final value lies in [0,1]; complement pairs also sum to one, providing an independent check.

Form the required totals explicitly and divide by the full number of observations.

The variance is nonnegative and the reported standard deviation is its positive square root.