An object is placed 10 cm in front of a lens. The image formed is real, inverted and of same size as the object. What is the focal length and nature of the lens?

The correct answer is A, 2 and 1. For a 4d orbital, n = 4 and l = 2, which gives l = 2 angular nodes and n − l − 1 = 1 radial node.

A node is a region where the probability of finding the electron is zero. Angular nodes are planes or cones through the nucleus, and their number equals the azimuthal quantum number l. Radial nodes are spherical shells, and their number is n − l − 1. The total number of nodes is always n − 1. For 4d: l = 2 for any d orbital, so 2 angular nodes; radial nodes = 4 − 2 − 1 = 1; total = 3, which equals n − 1. In the same way 3d has 2 angular and 0 radial nodes, and 2s has 0 angular and 1 radial node.

B is wrong: it reverses the two values.

C is wrong: 3 angular nodes belong to an f orbital (l = 3), not a d orbital.

D is wrong: 4 angular nodes would need l = 4, a g orbital, and the total of 4 exceeds n − 1 = 3.

Exam tip: angular nodes = l, radial nodes = n − l − 1, total nodes = n − 1.

The correct answer is A, Bacteria contain cytoplasm but viruses do not. A bacterium is a living cell filled with cytoplasm, while a virus is only genetic material inside a protein coat.

Bacteria are prokaryotic cells: they have a cell wall, a cell membrane, cytoplasm with ribosomes, and a circular DNA, but no nucleus bounded by a membrane and no membrane-bound organelles. Viruses are not cells at all. A virus particle (virion) is DNA or RNA wrapped in a protein capsid, sometimes with an outer envelope taken from the host. It has no cytoplasm, ribosomes or metabolism of its own, so it can multiply only inside a living host cell. This is why antibiotics act on bacteria but not on viruses.

B is wrong: bacteria, being prokaryotes, have no mitochondria.

C is wrong: viruses have no organelles, and bacteria have no mitochondria either.

D is wrong: bacteria do have a cell membrane, and viruses have no cell membrane, only a capsid and sometimes an envelope.

Exam tip: bacteria = prokaryotic cell, no mitochondria, killed by antibiotics; virus = nucleic acid + protein coat, not a cell.

The correct answer is C, Thiourea (accelerator). Accelerators speed up the vulcanisation of rubber; they are not a part of paint.

An oil paint is made of a pigment that gives colour and covering power, a vehicle or drying oil such as linseed oil that binds the film, a thinner that makes it easy to spread, a drier that speeds up hardening, fillers or extenders that add body, and an anti-skinning agent that stops a skin forming in the tin. Titanium dioxide is the most widely used white pigment, turpentine is the classic thinner, and polyhydroxy phenols are used as anti-skinning agents. Thiourea and similar compounds belong to rubber technology, where accelerators shorten the time sulphur takes to cross-link rubber.

A is wrong: turpentine oil is a standard thinner in paint.

B is wrong: polyhydroxy phenols are used in paint as anti-skinning agents.

D is wrong: titanium dioxide is the main white pigment in paints.

Exam tip: paint = pigment + vehicle (linseed oil) + thinner (turpentine) + drier + filler + anti-skinning agent.

The correct answer is C, Cell wall. Animal cells are bounded only by a flexible cell membrane; a rigid cell wall is found in plants, fungi and bacteria.

In plant cells the cell wall lies outside the cell membrane and is made mainly of cellulose; it gives shape, strength and protection against bursting when the cell takes in water. Fungi have walls of chitin and bacteria of peptidoglycan. Animal cells lack it, which lets them change shape, move and form tissues such as muscle. Other structures usually absent from animal cells are chloroplasts and a large central vacuole, while centrioles are typical of animal cells.

A is wrong: the cell membrane (plasma membrane) surrounds every living cell, animal or plant.

B is wrong: the endoplasmic reticulum, which makes proteins and lipids, is present in animal cells.

D is wrong: lysosomes, the digestive bags called suicide bags of the cell, are characteristic of animal cells.

Exam tip: plant cell = cell wall, chloroplast, large vacuole; animal cell = centrioles and lysosomes, no cell wall.

The correct answer is B, lowers the boiling point of the liquid. A liquid boils when its vapour pressure equals the pressure above it, so less outside pressure means boiling starts at a lower temperature.

As a liquid is heated, its vapour pressure rises. Boiling begins at the temperature where this vapour pressure matches the external pressure. At sea level, with about 101.3 kPa of pressure, water boils at 100 °C. High in the mountains the air pressure is lower, so water boils at around 70 to 90 °C, which is too cool to cook rice or pulses quickly. A pressure cooker does the opposite: it raises the pressure to about twice the normal value, so water boils near 120 °C and food cooks faster.

A is wrong: raising the pressure, not lowering it, raises the boiling point.

C is wrong: boiling point depends directly on the outside pressure.

D is wrong: with a lower boiling point the liquid reaches boiling sooner, not later.

Exam tip: low pressure, low boiling point (hills); high pressure, high boiling point (pressure cooker).