Elements A, B and C occur as Dobereiner's triads. If the atomic mass of A is 40 and that of C is 137, what will be the atomic mass of B?

The correct answer is A, Glucose, Water and Oxygen. Green plants use sunlight trapped by chlorophyll to join carbon dioxide and water, and the balanced equation reads six molecules of carbon dioxide plus twelve of water giving one molecule of glucose, six of oxygen and six of water. Water therefore stands on both sides of the equation: twelve molecules are taken in as raw material and six are released again as a product. The oxygen that is given off comes from splitting water, not from carbon dioxide, a fact proved with heavy oxygen tracers. B is wrong because it drops the water formed during the reaction. C is wrong because starch is not made directly; glucose is the first stable product, and the plant later links glucose units together to store starch. D is wrong for the same reason, since it names starch in place of glucose. Exam tip: glucose first, starch only as storage, and the oxygen comes from water.

The correct answer is A, 250 cm. In an astronomical telescope set for normal adjustment, the magnifying power equals the focal length of the objective divided by the focal length of the eyepiece. Here the magnification is 100 and the eyepiece is 2.5 cm, so the objective must be 100 multiplied by 2.5, that is 250 cm. This is why astronomical telescopes are long instruments: a large objective focal length with a short eyepiece focal length gives high magnification, and in normal adjustment the tube length is roughly the sum of the two focal lengths. B is wrong because an objective of 40 cm would give a magnification of only 16. C is wrong because a focal length smaller than the eyepiece would shrink the image instead of enlarging it. D is wrong because 100 cm gives a magnification of 40. Exam tip: for a telescope magnification is objective divided by eyepiece, so the objective is the longer lens.

The correct answer is B, Surface tension and viscosity both decrease. Heating a liquid makes its molecules move faster and sit a little further apart, so the attraction between them weakens, and both properties depend on that attraction. Surface tension arises because molecules at the surface are pulled inward by their neighbours, and that inward pull fades as temperature rises until it reaches zero at the critical temperature. Viscosity in a liquid comes from molecules gripping each other as layers slide past, so the same weakening makes the liquid thinner and easier to pour, which is why warm oil flows far more freely than cold oil. A is wrong because surface tension falls rather than rises on heating. C is wrong because neither of the two rises. D is wrong because viscosity of a liquid falls, not rises. Exam tip: liquids thin out on heating, but a gas becomes more viscous when heated.

The correct answer is C, Germanium. Germanium is not used to build light emitting diodes because it is an indirect band gap semiconductor, so an electron falling back across the gap gives up most of its energy as heat in the crystal rather than as light. Its band gap is also very small, about 0.66 electron volt, which is far too little to produce visible light. Light emitting diodes are therefore made from direct band gap compounds, whose gap can be tuned to the colour wanted. A is wrong because gallium phosphide is used for green and yellow diodes. B is wrong because indium gallium nitride gives the blue and white diodes that made modern lighting possible and won the Nobel Prize in Physics in 2014. D is wrong because gallium arsenide is the standard material for red and infrared diodes, including the ones inside television remote controls. Exam tip: light emitting diodes need direct band gap materials such as gallium arsenide, gallium phosphide and indium gallium nitride; silicon and germanium are indirect and do not emit light.

The correct answer is C, At room temperature, surface tension of water is less than ethyl alcohol. This is the statement that is not correct, because water has a much higher surface tension than ethyl alcohol. At about twenty degrees Celsius water measures close to seventy two dynes per centimetre while ethyl alcohol is only about twenty two, since the hydrogen bonds between water molecules pull far more strongly than the weaker forces inside alcohol. That is also why alcohol spreads out thinly on a surface while water gathers into beads. A is a correct statement, because surface tension is expressed in dynes per centimetre in the older unit system and in newtons per metre in the SI system. B is correct, because the inward pull on the surface gives a small free drop the shape with the least area for its volume, which is a sphere. D is correct, because surface tension arises from the cohesive forces among the molecules of the liquid itself. Exam tip: water is about 72 dynes per centimetre and alcohol about 22; surface tension falls as temperature rises.