Which instrument is used to test the purity of milk?

The correct answer is B, newton. One newton is the force that gives a mass of one kilogram an acceleration of one metre per second squared, which follows directly from the equation force equals mass times acceleration. Its dimensional formula is therefore M L T⁻².

Option A, the joule, is the unit of work and energy: one joule is the work done when a force of one newton moves its point of application through one metre. Option C, the watt, is the unit of power, that is the rate of doing work, and equals one joule per second. Option D, the pascal, is the unit of pressure and equals one newton per square metre. All four are derived units named after scientists, and papers often list them together to see whether you can match each with its quantity.

The correct answer is C, seven. The SI system, adopted in 1960 by the General Conference on Weights and Measures, rests on seven base units: the metre, the kilogram, the second, the ampere, the kelvin, the mole and the candela. Every other unit in science is derived from these by multiplication and division.

Options A and B fall short of the list and usually come from forgetting the mole or the candela, which are the two least familiar. Option D, nine, comes from adding the radian and the steradian, the units of plane angle and solid angle; these were long treated as a separate class called supplementary units and are not counted among the base units. A safe way to remember the seven is by their quantities: length, mass, time, current, temperature, amount of substance and luminous intensity.

The correct answer is C, newton. The newton is a derived unit: it is built from the kilogram, the metre and the second, since force equals mass times acceleration, and it can be written as one kilogram metre per second squared. Derived units are always expressible in terms of the base units.

Option A, the kelvin, is the base unit of thermodynamic temperature. Option B, the mole, is the base unit for the amount of substance and contains as many entities as there are atoms in a fixed quantity of carbon-12 under the older definition. Option D, the candela, is the base unit of luminous intensity and is the one most often forgotten in the list. In this style of question the odd one out is almost always a unit named after a scientist, such as the newton, joule, watt, pascal or hertz.

The correct answer is A, luminous intensity, that is the brightness of a source of light in a given direction. The candela takes its name from the candle, which was once used as a rough standard of light, and it is one of the seven base units of the SI system.

Option B, electric current, is measured in ampere, named after the French scientist Andre-Marie Ampere. Option C, amount of substance, is measured in mole, which is the chemist's counting unit for atoms and molecules. Option D, pressure, is measured in pascal, a derived unit equal to one newton per square metre. Two related units are worth knowing alongside the candela: the lumen for luminous flux and the lux for illuminance, that is the light falling on a surface.

The correct answer is B, distance. A light year is the distance that light, moving at about three lakh kilometres per second, covers in one year, which works out to roughly 9.46 trillion kilometres. It is used for the enormous distances between stars, where kilometres would run to unmanageable numbers.

Option A is the trap built into the name; the word year refers to the time taken by the light, not to the quantity measured. Option C, speed, has its own units such as metres per second. Option D, brightness, is measured by other quantities altogether, such as magnitude in astronomy. Two more distance units belong with this one: the astronomical unit, the mean distance between the Earth and the Sun, and the parsec, which equals about 3.26 light years.