Which one of the following cell organelles does NOT possess its own genetic material encoding proteins ?

The correct answer is A, The motion repeats after time T only once. This is the incorrect statement, because periodic motion repeats after every interval T, again and again.

The time period T of a pendulum is the time for one complete oscillation, that is, the smallest interval after which the bob returns to the same position moving in the same direction. Since the motion is periodic, it repeats after T, 2T, 3T and so on, without limit as long as no energy is lost. The formula T = 2π√(L/g) also assumes small swings; for large angles the period grows a little, so T stays constant only when the angular displacement is small.

B is correct: the period is by definition the least time after which motion repeats.

C is correct: if the motion repeats after T, it also repeats after any whole multiple nT.

D is correct: the period is independent of amplitude only for small angular displacements.

Exam tip: period = shortest repeat time; motion also repeats at every nT; isochronism holds only for small swings.

The correct answer is A, Mitochondria, nucleus, chloroplast. These are the three places in a eukaryotic cell where DNA is found.

The nucleus holds nearly all of a cell's DNA, packed with proteins into chromosomes. Mitochondria and chloroplasts each carry a small circular DNA of their own, together with 70S ribosomes, which lets them make some of their own proteins and divide independently. This supports the idea that both organelles descend from bacteria that once lived inside early cells. Every organelle in this group therefore contains DNA, which no other option can claim.

B is wrong: Golgi bodies package and send out proteins and have no DNA.

C is wrong: the plasma membrane is a lipid-protein layer with no DNA.

D is wrong: ribosomes are made of RNA and protein; they contain no DNA.

Exam tip: DNA in a eukaryotic cell: nucleus, mitochondria, chloroplasts; ribosomes contain RNA, not DNA.

The correct answer is A, 1 only. A chemical reaction produces only internal forces, which cannot change the motion of the centre of mass but can change internal kinetic energy.

By Newton's third law, internal forces come in equal and opposite pairs, so their sum is zero. The centre of mass of a system therefore accelerates only under an external force; with none acting, it keeps moving at the same velocity v whatever happens inside. Internal forces can, however, do work on the particles. A reaction that releases energy, such as an explosion, makes the fragments fly apart faster, raising their kinetic energy relative to the centre of mass. A shell that bursts in mid-air is the classic example: the pieces scatter, yet the centre of mass follows the original path.

Statement 2 is wrong: internal forces can and do change the kinetic energy of the parts relative to the centre of mass.

So B and C, which accept Statement 2, are wrong, and D is wrong because Statement 1 is correct.

Exam tip: internal forces never change total momentum or centre-of-mass velocity, but they can change kinetic energy.

The correct answer is A, Density of water at 4°C is 1000 kg/m³. Water is densest at 4 °C, where one cubic metre has a mass of almost exactly 1000 kg.

Most liquids grow steadily denser as they cool, but water behaves oddly below 4 °C: it expands again as it cools towards 0 °C. This is called the anomalous expansion of water, and it makes 4 °C the point of maximum density, about 1000 kg/m³ or 1 g/cm³. Because of it, in winter the densest water at 4 °C sinks to the bottom of lakes while ice forms on top, so fish survive beneath the frozen surface.

B is wrong: at 0 °C liquid water is slightly less dense, about 999.8 kg/m³, because it has expanded below 4 °C.

C is wrong: 100 kg/m³ is a tenth of water's real density, far too low.

D is wrong: 10 kg/m³ is only a hundredth of the true value of about 1000 kg/m³ at 4 °C.

Exam tip: water is densest at 4 °C (1000 kg/m³ = 1 g/cm³); ice is lighter, about 917 kg/m³, so it floats.

The correct answer is B, liquid to vapour without a change of temperature. Latent heat is absorbed during a change of state while the temperature stays fixed.

When water boils at 100 °C, adding more heat does not raise its temperature; the energy goes into breaking the attractions between molecules so that liquid turns into vapour. The heat needed per kilogram for this change at the boiling point is the specific latent heat of vaporisation. For water it is about 2.26 × 10⁶ J/kg, which is why steam at 100 °C causes worse burns than boiling water at the same temperature: it releases this extra heat on condensing.

A is wrong: latent heat is defined at constant temperature; any temperature change involves specific heat instead.

C is wrong: vapour turning into liquid gives out heat (condensation); heat is not "needed" for it.

D is wrong: it combines the wrong direction with a temperature change.

Exam tip: latent heat = change of state at constant temperature; water: fusion 3.34 × 10⁵ J/kg, vaporisation 2.26 × 10⁶ J/kg.