Two resistors, each of 20 ohms, are connected in parallel and this combination is connected across a 40 V supply voltage. Find the resistance in the circuit.

The correct answer is B, 15 moles. The number of moles is the given mass divided by the molar mass, so 60 grams of helium divided by 4 grams per mole gives 15 moles. Helium has an atomic mass of 4, and because it is a noble gas its molecules are single atoms, so its molar mass is 4 grams and not 8. Each of those 15 moles holds 6.022 into 10 to the power 23 atoms, and at standard temperature and pressure the sample would fill about 336 litres, since one mole of any gas takes 22.4 litres. A is wrong because 12 moles uses 5 grams per mole and borrows the 12 of carbon. C is wrong because 10 moles would need a molar mass of 6, which helium does not have. D is wrong because 25 moles would need a molar mass of 2.4, the mass of no element. Exam tip: moles equal mass in grams divided by molar mass, so 4 grams of helium is exactly one mole.

The correct answer is D, 1 mole of Carbon will contain the same number of atoms as present in 1 mole of Helium. A mole is a count, not a weight: one mole of any element holds 6.022 into 10 to the power 23 atoms, the Avogadro number, whatever the element is. So one mole of carbon and one mole of helium each hold that many atoms. What differs is the mass, because the gram atomic mass is the mass of one mole: one mole of carbon weighs 12 grams while one mole of helium weighs 4 grams, so the carbon sample is three times heavier even though the atom count is equal. A and B are wrong because they turn the three-times ratio of masses into a ratio of atoms. C is wrong for the same reason, only in the reverse direction. Exam tip: a mole is always 6.022 into 10 to the power 23 particles; the atomic mass changes the weight, never the number.

The correct answer is D, Oil in water. Oil does not dissolve in water; it stays as a separate layer or as floating droplets, so the mixture is heterogeneous and the boundary between the two liquids can be seen. A homogeneous mixture has the same composition throughout and its parts cannot be told apart even under a microscope, which is what happens when a solid dissolves in water to give a true solution. Oil and water part because water is a polar liquid while oil is non-polar, and like dissolves like; shaking them with a soap gives an emulsion, which is still not homogeneous. A is wrong because copper sulphate dissolves to give a clear blue solution of one phase. B is wrong because sugar in water is the classic true solution. C is wrong because common salt dissolves completely into sodium and chloride ions. Exam tip: a true solution is homogeneous, while a suspension and an emulsion such as oil in water or milk are heterogeneous.

The correct answer is A, 0.36 A. Reduce the parallel pair first: 20 into 30 divided by 50 gives 12 ohms. Adding the 8 ohm resistor in series makes the circuit resistance 20 ohms, so the battery drives 12 volts divided by 20 ohms, that is 0.6 ampere, through the whole circuit. That current passes through the 12 ohm combination and drops 0.6 into 12, which is 7.2 volts across it. Both parallel branches share this same 7.2 volts, so the 20 ohm branch carries 7.2 divided by 20, which is 0.36 ampere. B is wrong because 0.12 ampere matches no branch of this circuit. C is wrong because 0.24 ampere is the current in the 30 ohm branch, and the two branch currents add up to 0.6. D is wrong because 0.60 ampere is the total current from the battery, not the share of the 20 ohm resistor. Exam tip: in parallel the voltage is common and the current splits in the inverse ratio of the resistances.

The correct answer is C, effort arm length is always less than load arm length. In a class 3 lever the effort is applied between the fulcrum and the load, so the effort always sits nearer the fulcrum and its arm is the shorter of the two. Because mechanical advantage is the effort arm divided by the load arm, a class 3 lever has a mechanical advantage below one: it needs more force than the load, but it gains speed and a longer sweep at the far end. Forceps, sugar tongs, a stapler, a fishing rod and the human forearm lifting a weight are the standard examples. A is wrong because that freedom belongs to a class 1 lever, where the fulcrum may sit anywhere between effort and load. B is wrong because the two arms are equal only in the special class 1 case of a balance. D is wrong because a longer effort arm is the mark of a class 2 lever, such as a nutcracker. Exam tip: class 1 fulcrum in the middle, class 2 load in the middle, class 3 effort in the middle.