Live practice

For a concave lens, \(f=-15\) cm and virtual image \(v=-10\) cm.

The image is virtual, erect and diminished between lens and focus.

Nervous signals are electrochemical, travel along particular neurons, act in milliseconds and are usually brief and precisely targeted. Hormones are chemical, travel in blood, act only on receptor-bearing targets, start more slowly and often last longer or affect many tissues. Nervous control suits rapid actions; endocrine control suits growth, metabolism and long-term regulation. The systems interact.

In aerobic respiration, pyruvate enters mitochondria and is completely oxidised through the Krebs cycle and electron transport chain.

Hydrogenation is addition of hydrogen across carbon-carbon double or triple bonds in the presence of a catalyst such as nickel:

Industrially, vegetable oils are hydrogenated to produce semi-solid fats such as vanaspati ghee or margarine.

Barrier coating: paint, oil or grease prevents oxygen and water from reaching iron. Galvanising: a zinc coat blocks the environment and also corrodes preferentially if the coating is scratched. Alloying iron to make stainless steel is another method.

Fix two clean iron nails through a cork and connect them in series with a battery, switch and bulb. Place the cork over a beaker so that the nail ends dip into the test liquid.

With dilute HCl, the bulb glows because HCl forms mobile ions in water. Rinse the apparatus and repeat with glucose solution and then alcohol solution. The bulb does not glow because these molecular substances do not ionise to produce \(\ce{H+}\) ions.

Thus acidic behaviour depends on formation of hydronium ions in water, not merely on hydrogen atoms being present in the formula.

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.

Simplify the expression before substitution and preserve one-sided information.

Substitution into the original expression verifies the stated domain and final value.

Translate every condition into an equation and retain exact values throughout the conic calculation.

The last line satisfies the original conditions and supplies every requested part.