12 October 2026 Current Affairs: Headlines, GK & MCQs

The correct answer is D, Lactase. Lactase breaks down lactose, the sugar in milk, so a person who still makes enough of it can digest milk at any age.

Lactase is made by the cells lining the small intestine. It splits lactose into two simple sugars, glucose and galactose, which the body can then absorb. Babies produce plenty of it because milk is their only food, but in most people its production falls after weaning. When lactose is not digested, bacteria in the large intestine ferment it, causing gas, bloating and loose motions. This condition is called lactose intolerance.

A is wrong: cellulase breaks down cellulose, the fibre of plant cell walls, and humans do not make it at all.

B is wrong: amylase, found in saliva and pancreatic juice, digests starch, not milk sugar.

C is wrong: pectase acts on pectin in plant tissue and has no role in human digestion of milk.

Exam tip: lactase digests lactose, maltase digests maltose, sucrase digests sucrose, and amylase digests starch.

The correct answer is C, 1, 4, 3, 2. The events fall in 1972, 1974, 1985 and 2001 in that order, which is also UPSC's official key.

The Simla Agreement was signed on 2 July 1972 by Indira Gandhi and Zulfikar Ali Bhutto after the 1971 war; it turned the ceasefire line in Kashmir into the Line of Control. India's first nuclear test, code-named Smiling Buddha, was held at Pokhran on 18 May 1974. The SAARC Charter was signed at the first summit in Dhaka on 8 December 1985. The Agra Summit between Atal Bihari Vajpayee and Pervez Musharraf took place in July 2001 and ended without a joint declaration.

A is wrong: it puts the 1985 SAARC Charter before the 1974 test.

B is wrong: it starts with the 1974 test, but the Simla Agreement came two years earlier.

D is wrong: it begins with the test and also places the 2001 Agra Summit before the 1985 SAARC Charter.

Exam tip: Simla 1972, Pokhran-I 1974, SAARC Dhaka 1985, Lahore bus 1999, Agra 2001.

The correct answer is C, Both 1 and 2. S-waves are transverse waves: they shake the ground at right angles to their direction of travel, and that sideways motion forms crests and troughs.

An earthquake sends out two kinds of body waves. P-waves (primary) are the fastest and work like sound waves, pushing and pulling the material in the same direction as the wave moves; they pass through solids, liquids and gases. S-waves (secondary) arrive later and vibrate the material perpendicular to the wave direction in the vertical plane, which is why they create troughs and crests. S-waves travel only through solids, and their absence beyond the shadow zone told scientists that the outer core is liquid.

A is wrong: statement 2 is also correct, since the perpendicular vibration is what defines an S-wave.

B is wrong: statement 1 is correct too, as the crests and troughs follow from that vibration.

D is wrong: both statements describe S-waves accurately.

Exam tip: P-waves are longitudinal and go through all states of matter; S-waves are transverse and go through solids only.

The correct answer is C, Magnesium. Plants need magnesium in fairly large amounts, so it is a macronutrient, not a micronutrient.

Plant nutrients are grouped by how much of them a plant needs. Macronutrients are needed in large quantities: carbon, hydrogen, oxygen, nitrogen, phosphorus, potassium, calcium, magnesium and sulphur. Micronutrients, or trace elements, are needed in very small amounts: iron, manganese, copper, zinc, boron, molybdenum, chlorine and nickel. Magnesium sits at the centre of every chlorophyll molecule and activates many enzymes, which is why a plant needs so much of it; its shortage yellows the older leaves between the veins.

A is wrong: iron is a micronutrient, needed in small amounts for making chlorophyll and for enzymes of respiration.

B is wrong: manganese is a micronutrient that helps split water during photosynthesis.

D is wrong: chlorine is a micronutrient that also takes part in the water-splitting step of photosynthesis.

Exam tip: N, P, K plus Ca, Mg, S are macronutrients; Fe, Mn, Cu, Zn, B, Mo, Cl and Ni are micronutrients.

The correct answer is A, Raja Man Singh of Gwalior. Man Kautuhal was compiled under the patronage of Raja Man Singh Tomar, who ruled Gwalior from 1486 to 1516.

Man Singh Tomar was a great patron of music, and his court is closely linked with the growth of the Dhrupad style of Hindustani singing. Man Kautuhal, a treatise on music and ragas, was prepared by scholars of his court and is named after him. In the reign of Aurangzeb, Faqirullah translated it into Persian as Rag Darpan, which is how much of its content survives. Man Singh also built the Man Mandir palace inside Gwalior Fort.

B is wrong: Tansen, Akbar's court singer, trained in the Gwalior tradition but lived after Man Singh and did not commission this work.

C is wrong: Meera Bai was a Bhakti poet-saint of Rajasthan, known for her devotional songs to Krishna, not for a music treatise.

D is wrong: Amir Khusrau lived in the Delhi Sultanate period, about two centuries earlier.

Exam tip: Man Kautuhal = Raja Man Singh Tomar of Gwalior; its Persian version Rag Darpan = Faqirullah.

The correct answer is D, increase to four times of its original value. Gravitational force varies inversely as the square of the distance, so halving the distance makes the force 2 × 2 = 4 times larger.

Newton's law of universal gravitation says F = G m₁m₂ / r², where m₁ and m₂ are the two masses, r is the distance between their centres and G is the universal gravitational constant. The masses of the Earth and the Moon do not change here, so only r matters. Replacing r with r/2 puts (r/2)² = r²/4 in the denominator, and dividing by a quarter multiplies the force by four. Likewise, doubling the distance would cut the force to one quarter.

A is wrong: halving the force would need the distance to grow, not shrink, and by a factor of √2.

B is wrong: a doubling would hold only if force varied inversely with distance, not with its square.

C is wrong: the force depends on distance, so it cannot stay the same when the distance changes.

Exam tip: inverse-square law: distance ½ gives force ×4; distance ×3 gives force ⅑.

The correct answer is A, lactic acid. During a hard sprint the muscles run short of oxygen and switch to anaerobic respiration, which leaves lactic acid behind.

In every cell, glucose is first broken down into pyruvic acid by glycolysis. When oxygen is plentiful, pyruvic acid is fully oxidised to carbon dioxide and water in the mitochondria, releasing a lot of energy. During intense exercise the blood cannot bring oxygen fast enough, so muscle cells turn pyruvic acid into lactic acid to keep producing a little energy quickly. The build-up of lactic acid is linked with the cramps and burning pain felt after a sprint; rest and deep breathing let the body clear it.

B is wrong: carbon dioxide is a product of aerobic respiration and is removed through the lungs, so it does not collect in the muscles.

C is wrong: pyruvic acid is only an intermediate; in oxygen shortage it is converted to lactic acid rather than piling up.

D is wrong: ethanol is made by anaerobic respiration in yeast, not in human muscle.

Exam tip: no oxygen in muscle gives lactic acid; no oxygen in yeast gives ethanol and CO2.

The correct answer is B, Singareni Collieries Company Limited. Incorporated in 1920 and later taken over by the government, SCCL is India's oldest government-owned coal mining company.

Coal was found in the Godavari valley near Yellandu in the 1870s, and the Hyderabad (Deccan) Company began mining there in 1886. In 1920 it became The Singareni Collieries Company Limited, a public limited company, and the Hyderabad State government bought a majority of its shares in 1945. Today the Government of Telangana holds 51% and the Government of India 49%. It mines in the Godavari valley coalfields of Telangana.

A is wrong: Neyveli Lignite Corporation was set up in 1956 to mine lignite in Tamil Nadu.

C is wrong: Coal India Limited was formed in 1975, after the coal mines were nationalised in 1971–73.

D is wrong: Mahanadi Coalfields Limited is a subsidiary of Coal India created in 1992 for the Odisha coalfields.

Exam tip: SCCL 1920 (Telangana, oldest); NLC 1956; Coal India 1975; MCL 1992.

The correct answer is A, Silver < Nichrome < Glass. Silver is the best conductor, nichrome is an alloy with high resistivity, and glass is an insulator with enormous resistivity.

Resistivity is a property of the material itself, measured in ohm-metre. At room temperature silver has about 1.6 × 10⁻⁸ Ω m, the lowest of all metals, which is why it conducts electricity better than copper. Nichrome, an alloy of nickel and chromium, has about 1.1 × 10⁻⁶ Ω m, roughly a hundred times more than silver, so it is used for the heating coils of irons, toasters and heaters. Glass has a resistivity of about 10¹⁰ to 10¹⁴ Ω m, so it hardly conducts at all.

B is wrong: it reverses the order and puts the insulator first.

C is wrong: glass resists current far more than nichrome, so it cannot come in the middle.

D is wrong: nichrome has much higher resistivity than silver, not lower.

Exam tip: conductors (silver, copper) < alloys (nichrome, manganin) < insulators (glass, rubber).

The correct answer is A, Larger while standing than while lying. The body's weight stays the same, but standing puts it on the small area of the feet, so the pressure is greater.

Pressure is force per unit area: P = F / A. A person's weight is the force, and it does not change with posture. When standing, the weight rests on the soles of the two feet, a small area, so the pressure on the sand is large and the feet sink in. When lying down, the same weight spreads over the whole back, a much larger area, so the pressure falls and the body hardly sinks. This is why camels have broad feet for sand, and why skis and wide tracks are used on snow.

B is wrong: it reverses the effect; a smaller contact area gives a larger pressure.

C is wrong: the force is the same, but the area changes, so the pressure cannot stay the same.

D is wrong: the time of day has no effect on pressure; only force and area matter.

Exam tip: same force, smaller area means more pressure: sharp knives, nails and narrow heels.

The correct answer is C. Nominal GDP values each year's output at that year's own (current) prices, not at constant prices, so this statement is not correct.

GDP is the money value of all final goods and services produced within a country in a year. Nominal GDP uses current prices, so it can rise simply because prices have gone up. Real GDP removes this effect by valuing the output of every year at the prices of one base year, which shows the true change in production. The ratio of nominal to real GDP, multiplied by 100, gives the GDP deflator, a broad measure of inflation.

A is correct: valuing different years at common, or base-year, prices is exactly how real GDP is worked out.

B is correct: potential GDP is the output the economy could produce with full employment of labour and capital.

D is correct: real GDP divided by population gives real GDP per capita, a common measure of living standards.

Exam tip: nominal GDP = current prices; real GDP = constant (base-year) prices; deflator = nominal ÷ real × 100.

The correct answer is B, magnesium carbonate and hydrochloric acid. A carbonate reacts with an acid at room temperature to give carbon dioxide, and only carbon dioxide turns limewater milky.

The reaction is MgCO₃ + 2HCl → MgCl₂ + H₂O + CO₂. The fizzing comes from carbon dioxide escaping. When this gas is passed through limewater, a solution of calcium hydroxide, it forms insoluble calcium carbonate, which makes the water look milky: Ca(OH)₂ + CO₂ → CaCO₃ + H₂O. If more carbon dioxide is passed for a long time, the milkiness disappears as soluble calcium hydrogen carbonate forms. Every carbonate and hydrogen carbonate behaves this way with acids.

A is wrong: zinc and hydrochloric acid give hydrogen gas, which burns with a pop but does not affect limewater.

C is wrong: methane and oxygen do not react at room temperature; they need a flame to burn.

D is wrong: copper is below hydrogen in the reactivity series and does not react with dilute hydrochloric acid at all.

Exam tip: metal + acid gives hydrogen (pop test); carbonate + acid gives CO2 (limewater test).

The correct answer is C, Magnesium. A magnesium atom sits at the centre of every chlorophyll molecule, so a plant cannot make chlorophyll without it.

Chlorophyll is built around a ring-shaped structure called a porphyrin, with a single magnesium ion held at its centre. This is the pigment that absorbs red and blue light and gives leaves their green colour. When magnesium is short, older leaves turn yellow between the veins, a condition called chlorosis. A similar ring with iron at the centre forms haem, the part of haemoglobin that carries oxygen in our blood, a pairing examiners like to test.

A is wrong: calcium builds cell walls (as calcium pectate) and helps cell division, but it is not part of chlorophyll.

B is wrong: iron is needed for the enzymes that help make chlorophyll, yet it is not in the chlorophyll molecule; magnesium is.

D is wrong: potassium controls the opening and closing of stomata and activates enzymes, but has no place in chlorophyll.

Exam tip: chlorophyll has magnesium at its centre; haemoglobin has iron; vitamin B12 has cobalt.

The correct answer is C, New Guinea. With an area of about 7.86 lakh sq km, New Guinea is the world's second-largest island, after Greenland.

New Guinea lies just north of Australia and is shared by two countries: its western half belongs to Indonesia and its eastern half is the mainland of Papua New Guinea. It is mountainous and covered with dense rainforest. Australia is not counted here because it is treated as a continent. After Greenland and New Guinea, the next largest islands are Borneo, Madagascar, Baffin Island and Sumatra, in that order.

A is wrong: Borneo, shared by Indonesia, Malaysia and Brunei, is the third largest, at about 7.43 lakh sq km.

B is wrong: Madagascar, off the south-east coast of Africa, is fourth, at about 5.87 lakh sq km.

D is wrong: Sumatra, in Indonesia, is sixth, at about 4.73 lakh sq km.

Exam tip: largest islands in order: Greenland, New Guinea, Borneo, Madagascar, Baffin, Sumatra.

The correct answer is A, a nitrogenous base, deoxyribose sugar and phosphate group. Each nucleotide of DNA is made of these three parts, and many nucleotides joined together form the polynucleotide chain.

In a DNA strand, the sugar of one nucleotide is linked to the phosphate of the next by a phosphodiester bond, making a sugar-phosphate backbone. The nitrogenous bases stick out from this backbone: adenine, guanine, cytosine and thymine. Two such chains run in opposite directions and are held together by hydrogen bonds between the bases, A with T and G with C, giving the double helix described by Watson and Crick in 1953. The sugar is deoxyribose, which has one oxygen atom fewer than ribose.

B is wrong: ribose sugar is found in RNA, not DNA.

C is wrong: a DNA chain has only one kind of sugar, deoxyribose, and it must contain bases.

D is wrong: without a sugar the bases and phosphates cannot be linked into a chain.

Exam tip: DNA = deoxyribose + A, G, C, T; RNA = ribose + A, G, C, U.

The correct answer is C, Methane. Buried organic waste rots without air in a landfill, and bacteria that work without oxygen release methane.

Food scraps, paper and garden waste make up a large share of city garbage. Once they are covered in a landfill, oxygen is soon used up and anaerobic bacteria take over, producing landfill gas that is roughly half methane and half carbon dioxide. Methane is a powerful greenhouse gas, many times stronger than carbon dioxide over a short period, and it can catch fire, which is why landfill sites such as Ghazipur in Delhi often see fires. Modern landfills capture this gas and burn it to generate electricity.

A is wrong: nitrogen is the main gas of the air and is not a major product of rotting waste.

B is wrong: hydrogen forms only briefly as an intermediate and is quickly used up by other bacteria.

D is wrong: oxygen is consumed, not released, as waste decomposes.

Exam tip: rotting without air in landfills, paddy fields and cattle digestion gives methane, the main part of biogas.

The correct answer is A, Cell wall. Bacteria have a cell wall and human cells do not, so a drug that attacks the cell wall harms only the bacteria.

The bacterial cell wall is made of peptidoglycan, a mesh of sugars and short peptides that gives the cell its shape and stops it bursting. Penicillin blocks the enzymes that build the cross-links of this mesh. A growing bacterium then makes a weak wall, takes in water and bursts. Human cells have only a plasma membrane and no peptidoglycan, so they are left alone. Alexander Fleming discovered penicillin in 1928 from the mould Penicillium notatum.

B is wrong: human cells also have a plasma membrane, so attacking it would harm our cells too.

C is wrong: some antibiotics, such as tetracycline, act on bacterial ribosomes, but penicillin does not.

D is wrong: penicillin does not act on the bacterial chromosome or DNA.

Exam tip: penicillin, discovered by Fleming in 1928, works by blocking the bacterial cell wall.

The correct answer is A, A candidate who wins may not get the majority of votes. Under First Past the Post, the candidate with the most votes wins, even if that is far less than half of all votes cast. This is also UPSC's official key.

India uses this system, also called the simple plurality system, for elections to the Lok Sabha and the state Legislative Assemblies. The country is divided into constituencies, each electing one member, and voters choose a candidate rather than a party. In a contest of many candidates, someone with 35% of the votes can win if no rival does better. As a result, a party's share of seats can be much larger or smaller than its share of votes.

B is wrong: First Past the Post uses single-member constituencies, so each one elects only one representative.

C is wrong: voting for a party list is a feature of proportional representation, not of First Past the Post.

D is wrong: seats in proportion to votes is exactly what proportional representation aims at.

Exam tip: India uses FPTP for Lok Sabha and Assemblies, and proportional representation by single transferable vote for Rajya Sabha and the President.

The correct answer is D, Olivine. Olivine is a silicate of magnesium and iron that forms greenish crystals and is common in basalt.

Olivine takes its name from its olive-green colour. It crystallises early from hot magma that is low in silica, which is why it turns up in basalt, gabbro and peridotite and makes up much of the Earth's upper mantle. Its main elements are magnesium, iron and silica. A clear, gem-quality olivine is sold as the jewel peridot. Feldspar and quartz, by contrast, are the commonest minerals of the crust and are richer in silica.

A is wrong: amphibolite is a metamorphic rock made mostly of amphibole minerals, not a single mineral.

B is wrong: feldspar is made of silicon and oxygen with sodium, potassium, calcium and aluminium, and is light cream to salmon pink.

C is wrong: pyroxene contains calcium and aluminium along with magnesium, iron and silica, and is usually green or black.

Exam tip: olivine = green, Mg-Fe silicate, basalt, gem peridot; feldspar = half of the crust.

The correct answer is B, Water and dissolved minerals. Xylem carries water along with the minerals dissolved in it from the roots up to the stem and leaves.

Plants have two kinds of conducting tissue. Xylem is made of tracheids, vessels, xylem parenchyma and xylem fibres; most of its conducting cells are dead and form long tubes. Water absorbed by the roots carries nitrates, phosphates and other minerals, and this solution rises mainly because transpiration from the leaves pulls the water column upward. Phloem is the other tissue, and it carries food made in the leaves to the rest of the plant. Xylem moves materials only upward; phloem can move them both ways.

A is wrong: xylem does carry water, but the minerals dissolved in it travel too, so "water" alone is incomplete.

C is wrong: gases enter and leave mainly through stomata and lenticels by diffusion, not through xylem.

D is wrong: food, mainly sucrose, is carried by phloem, not xylem.

Exam tip: xylem = water and minerals, upward; phloem = food, both directions (translocation).

The correct answer is B, 1 and 2 only. The Sugamya Bharat Abhiyan is a campaign to make places, transport and information accessible; it is run by the Department of Empowerment of Persons with Disabilities and has no pension component.

Also called the Accessible India Campaign, it was launched on 3 December 2015, the International Day of Persons with Disabilities. It works on three fronts: the built environment (making government buildings, airports and stations barrier-free with ramps, lifts and accessible toilets), the transport system, and information and communication technology (accessible websites, sign language on TV). Its goal is equal opportunity and an inclusive society in which persons with disabilities can live independently.

A is wrong: statement 3 is incorrect, because disability pensions come under other schemes, not this campaign.

C is wrong: it wrongly includes statement 3 and leaves out statement 1, which is correct.

D is wrong: statement 2 is also correct, as building an inclusive society is the campaign's aim.

Exam tip: Sugamya Bharat Abhiyan, 3 Dec 2015, DEPwD; three pillars: buildings, transport, ICT.

The correct answer is A, greater than the speed of sound. A body moving faster than sound outruns its own sound waves, which pile up into a shock wave heard on the ground as a sonic boom.

In air at room temperature, sound travels at about 343 m/s. A supersonic jet or a bullet moving faster than this leaves its sound waves behind, and they bunch together into a cone-shaped shock wave trailing the object. When the edge of this cone sweeps over a listener, the sudden change in air pressure is heard as a loud bang, strong enough to rattle or even crack window glass. Speeds are often given as a Mach number, the ratio of the object's speed to the speed of sound, so supersonic means Mach 1 or more.

B is wrong: no material object can travel faster than light.

C is wrong: below the speed of sound the waves spread ahead of the source, so no shock wave forms.

D is wrong: at exactly the speed of sound the waves bunch up at the nose, but the boom heard on the ground comes from supersonic flight.

Exam tip: Mach 1 = speed of sound; above Mach 1 is supersonic and above Mach 5 hypersonic.

The correct answer is C, Blue. A leaf from a sunny day is full of starch made by photosynthesis, and iodine turns starch blue-black.

This is the standard school test for starch in a leaf. Boiling the leaf in water kills its cells and softens it so that the solutions can enter. Boiling it in alcohol, usually over a water bath because alcohol catches fire easily, dissolves the chlorophyll, leaving the leaf pale or nearly colourless. When iodine solution is then added, the starch stored in the leaf reacts with it and the leaf turns blue-black. A leaf kept in the dark for two days before the test shows no blue colour, proving that light is needed for photosynthesis.

A is wrong: the leaf is colourless only before iodine is added; the starch then turns it blue.

B is wrong: the green chlorophyll has already been removed by the boiling alcohol.

D is wrong: a starch-free leaf would show the brown colour of iodine, not white, and this leaf has starch.

Exam tip: iodine test: starch gives blue-black; alcohol removes chlorophyll before the test.

The correct answer is B, Desert, Tropical thorny, Moist deciduous, Mangrove. The route runs from the dry west to the wet east coast, so the vegetation changes as rainfall rises.

Bikaner lies in the Thar Desert of western Rajasthan, where rainfall is below about 25 cm and only desert plants such as khejri and cactus grow. Moving east through eastern Rajasthan and the drier parts of central India, rainfall of roughly 25 to 70 cm supports tropical thorn forests of acacia, babool and ber. Further east, in Chhattisgarh, Jharkhand and Odisha, rainfall of about 100 to 200 cm supports moist deciduous forests of sal and teak. Konark is on the Odisha coast near the Mahanadi delta, where tidal creeks support mangroves.

A is wrong: it puts thorny vegetation before the desert, but Bikaner itself is in the desert.

C is wrong: it starts with moist deciduous forest and ends with desert, the reverse of the journey.

D is wrong: mangroves grow only at the coast, so they must come last, after the inland deciduous forests.

Exam tip: more rain, richer forest: desert < thorn < dry deciduous < moist deciduous < evergreen; mangroves on tidal coasts.

The correct answer is C, increases heavily. In a short circuit the live and neutral wires touch, the resistance of the path falls almost to zero, and the current shoots up.

By Ohm's law, current I = V / R. Normally the appliances in a circuit provide resistance and keep the current within safe limits. When damaged insulation lets the live wire touch the neutral wire directly, the current bypasses the appliances and the resistance becomes very small, so for the same supply voltage the current becomes very large. This heats the wires sharply (heat ∝ I²Rt) and can start a fire. A fuse or a miniature circuit breaker (MCB) breaks the circuit when this happens.

A is wrong: lower resistance means more current, not less.

B is wrong: the resistance changes sharply, so the current cannot stay the same.

D is wrong: the current does not fluctuate; it rises to a very high value until a fuse or breaker cuts it.

Exam tip: short circuit means resistance near zero and huge current; overloading means too many appliances on one socket.

The correct answer is C, 2 only. Graphite has free electrons that can move through it, so it conducts electricity; diamond and fullerene do not conduct well.

In graphite, each carbon atom is bonded to only three others, forming flat sheets of hexagons. The fourth electron of every atom is free to move along the sheets, which lets graphite carry current; that is why it is used for electrodes in dry cells and electric arcs. In diamond, every carbon atom is bonded to four others in a rigid three-dimensional network, leaving no free electrons, so diamond is an insulator even though it conducts heat very well. Fullerene, such as the football-shaped C60, has its electrons held within the molecule and is a poor conductor.

A is wrong: diamond is an electrical insulator.

B is wrong: it includes diamond, which does not conduct electricity.

D is wrong: neither diamond nor fullerene is a good conductor, and it leaves out graphite.

Exam tip: graphite is the only common non-metal that conducts electricity; diamond is the hardest natural substance.

The correct answer is A, Structural unemployment. When the jobs on offer need skills, or are in places, that do not match the workers available, people stay jobless even though vacancies exist.

Structural unemployment comes from long-term changes in the economy: new technology, the decline of old industries, or a shift of demand from one region to another. A handloom weaver who loses work to power looms, or a worker in one state while the jobs are in another, cannot simply take the vacancies that exist. It usually lasts longer than other kinds and is reduced by skill training, education and help with moving to where the work is. India's Skill India programme targets this kind of unemployment.

B is wrong: disguised unemployment means more people working on a job than needed, as on small family farms, where removing some does not cut output.

C is wrong: "altered unemployment" is not a recognised type of unemployment.

D is wrong: cyclical unemployment rises and falls with the business cycle, during a recession or slowdown.

Exam tip: skill or place mismatch = structural; recession = cyclical; extra hands on a farm = disguised; between jobs = frictional.

The correct answer is C, Cu + PbCl2 → CuCl2 + Pb. Copper is less reactive than lead, so it cannot push lead out of its compound.

In a displacement reaction, a more reactive metal takes the place of a less reactive metal in its salt solution. The reactivity series, from more to less reactive, runs: potassium, sodium, calcium, magnesium, aluminium, zinc, iron, lead, hydrogen, copper, mercury, silver, gold. Magnesium, zinc and iron are all above copper, so each of them displaces copper from copper sulphate; the blue solution fades and reddish-brown copper is deposited. Copper, however, lies below lead, so it has no power to displace lead from lead chloride.

A is wrong: iron is more reactive than copper, so this reaction takes place, the classic iron nail in copper sulphate experiment.

B is wrong: zinc is above copper in the series and readily displaces it.

D is wrong: magnesium is far more reactive than copper and displaces it easily.

Exam tip: a metal displaces only those below it in the reactivity series: K, Na, Ca, Mg, Al, Zn, Fe, Pb, H, Cu, Hg, Ag, Au.

The correct answer is B, Canada. The New Development Bank was founded by the five BRICS countries, and Canada is not one of them.

The founding members are Brazil, Russia, India, China and South Africa. They agreed to set up the bank at the BRICS summit in Fortaleza, Brazil, in July 2014, and it began work in 2015 with its headquarters in Shanghai, China. Its first president was K. V. Kamath of India. The bank lends money for infrastructure and sustainable development projects in member and other developing countries. It was earlier called the BRICS Development Bank, and it has since admitted some new members, but the founders remain the five BRICS nations.

A is wrong: Brazil is a founding member and hosted the 2014 Fortaleza summit where the bank was agreed.

C is wrong: Russia is one of the five founding BRICS members.

D is wrong: India is a founding member and gave the bank its first president.

Exam tip: NDB: Fortaleza 2014, headquarters Shanghai, first president K. V. Kamath; AIIB headquarters Beijing.

The correct answer is C, R only. On a level curve, friction alone supplies the centripetal force, so a cyclist slips when the needed force exceeds the maximum friction.

The condition for no slipping is mv²/r ≤ μmg, which gives v² ≤ μgr. Here μgr = 0.1 × 10 × 10 = 10, so the safe speed limit is √10, about 3.16 m/s. The mass cancels out, which is why identical cycles do not matter. Any rider faster than about 3.16 m/s needs more inward force than friction can give and skids outward.

A is wrong: P at 2 m/s needs v² = 4, well within the limit of 10, so P does not slip.

B is wrong: Q at 3 m/s needs v² = 9, still below 10, so Q also stays safe.

D is wrong: only R, with v² = 25, crosses the limit; P and Q are below it.

Exam tip: on a flat curve the maximum safe speed is v = √(μgr), and it does not depend on mass.

The correct answer is A, T will be slightly greater than T₀. The formula T₀ = 2π√(L/g) holds only for small swings; at large amplitudes the period grows.

The small-angle formula assumes sin θ ≈ θ. For larger angles the restoring force mg sin θ is less than mgθ, so the bob is pulled back a little more weakly and takes longer to complete each swing. A good approximation is T ≈ T₀(1 + θ²/16), with θ in radians. At 60° (about 1.05 rad) this gives a period roughly 7% longer than T₀, so the swing is noticeably but only slightly slower.

B is wrong: the weaker restoring force can only lengthen the period, never shorten it.

C is wrong: T equals T₀ exactly only in the limit of very small amplitude, not at 60°.

D is wrong: the mass of the bob cancels out in the equation of motion, at any amplitude.

Exam tip: simple pendulum period is independent of mass always, and independent of amplitude only for small swings.

The correct answer is D, -2.0 D. Power is the reciprocal of focal length in metres, and a concave lens has a negative focal length.

The power of a lens is P = 1/f, with f in metres, and its unit is the dioptre (D). By the sign convention, a concave (diverging) lens has a negative focal length, so here f = -0.5 m. Then P = 1/(-0.5) = -2.0 D. A convex lens of the same focal length would have a power of +2.0 D. Opticians write spectacle prescriptions in dioptres, and a minus sign means a diverging lens for short sight (myopia).

A is wrong: +0.5 D simply copies the focal length and also uses the wrong sign.

B is wrong: -0.5 D has the right sign but forgets to take the reciprocal.

C is wrong: +2.0 D is the correct size but the sign of a convex lens.

Exam tip: P = 1/f (metres); convex is plus, concave is minus; 1 D means a focal length of 1 m.

The correct answer is C, Chemical and electrical. The second industrial revolution, from about 1850 to 1914, was driven by steel, chemicals, electricity and oil.

The first industrial revolution began in Britain around 1760 and rested on cotton textiles, coal, iron and the steam engine. The second wave, led by Germany and the United States as well as Britain, brought new science-based industries. Chemical firms made synthetic dyes, fertilisers and explosives, while electrical industries grew from the dynamo, the electric light bulb and power stations. Cheap steel from the Bessemer process and the internal combustion engine belong to this phase too.

A is wrong: coal and iron were the backbone of the first industrial revolution.

B is wrong: mechanised cotton spinning and weaving (spinning jenny, water frame, power loom) started the first revolution.

D is wrong: James Watt's improved steam engine also belongs to the first revolution, in the late 18th century.

Exam tip: first revolution = cotton, coal, iron, steam; second revolution = steel, chemicals, electricity, oil.

The correct answer is B, dust particles in the air scatter light into our eyes. A beam seen from the side is visible only because tiny particles send some of its light sideways.

Light travelling in a straight line cannot enter our eyes unless something redirects it towards us. Fine dust, smoke and water droplets in the air scatter light in all directions, so part of each sunbeam reaches an observer standing to one side. This is the Tyndall effect, the same reason a torch beam shows up in fog or sunlight looks like shafts in a dusty room or a forest. In perfectly clean air the beam would be invisible from the side.

A is wrong: reflection needs a smooth surface and sends light in one fixed direction; tiny particles scatter it everywhere.

C is wrong: refraction is bending at a boundary between two media and does not light up a beam's path.

D is wrong: scattering can partly polarise light, but polarisation is not what makes the particles visible.

Exam tip: sunbeams in a dusty room and a headlight beam in fog are both examples of the Tyndall effect.

The correct answer is B, Prayaga Prashasti of Samudragupta. Harishena was the court poet and minister of the Gupta ruler Samudragupta and wrote this praise-poem in his honour.

The Prayaga Prashasti, also called the Allahabad Pillar Inscription, is in elegant Sanskrit and is engraved on the same pillar that carries an edict of Ashoka. It lists Samudragupta's campaigns in north India, his southern expedition against the kings of the Deccan, and the frontier rulers who paid him tribute. Because of these conquests, historian V. A. Smith called him the "Napoleon of India". The inscription is the main source for his reign.

A is wrong: the Nashik inscription was issued by Gautami Balashri, mother of the Satavahana king Gautamiputra Satakarni.

C is wrong: the Deopara Prashasti praises the Sena king Vijayasena of Bengal and was composed by the poet Umapatidhara.

D is wrong: the Hathigumpha inscription near Bhubaneswar records the deeds of Kharavela, the Jain king of Kalinga.

Exam tip: Harishena = Samudragupta; Ravikirti = Aihole inscription of Pulakeshin II.

The correct answer is D, 5 kg. Using Q = mcΔT, the mass works out to 20,000 ÷ (400 × 10) = 5 kg.

The heat needed to warm a body is Q = mcΔT, where m is the mass, c the specific heat capacity and ΔT the rise in temperature. Here Q = 20 kJ = 20,000 J, c = 400 J/(kg °C) and ΔT = 25 - 15 = 10 °C. So m = Q/(cΔT) = 20,000/4,000 = 5 kg. A value of 400 J/(kg °C) is close to that of copper, which is why metals heat up quickly compared with water, whose specific heat is about 4,200 J/(kg °C).

A is wrong: 0.1 kg would absorb only 400 J for a 10 °C rise.

B is wrong: 1 kg would need just 4,000 J, a fifth of the heat given.

C is wrong: 10 kg would need 40,000 J, twice the heat supplied.

Exam tip: convert kJ to J before using Q = mcΔT, and remember water's specific heat is about 4.2 kJ/(kg °C).

The correct answer is A, Earth. Among the four rocky inner planets, Earth is the largest, with a diameter of about 12,742 km.

The inner or terrestrial planets are Mercury, Venus, Earth and Mars, all made of rock and metal. Earth is the biggest and also the densest planet in the solar system. Venus comes a close second at about 12,104 km and is often called Earth's twin for its similar size. Mars is roughly half Earth's width and Mercury is the smallest planet of all. The giant outer planets, led by Jupiter, are far larger, but none of them is in the options.

B is wrong: Venus, at about 12,104 km across, is slightly smaller than Earth.

C is wrong: Mars measures about 6,779 km, roughly half of Earth's diameter.

D is wrong: Mercury, about 4,880 km across, is the smallest planet in the solar system.

Exam tip: inner planets by size: Earth > Venus > Mars > Mercury; overall largest is Jupiter.

The correct answer is D, 1 only. A light year is a unit of distance, not of time or brightness.

One light year is the distance light travels through a vacuum in one Julian year. Light moves at about 3 × 10⁸ m/s, so a light year is about 9.46 × 10¹⁵ m, or nearly 9.5 trillion km. Astronomers use it for distances between stars and galaxies; the nearest star after the Sun, Proxima Centauri, is about 4.2 light years away. The word "year" in the name misleads many students into thinking it measures time.

Statement 2 is wrong: the year is used only to define the distance; the unit itself measures length.

Statement 3 is wrong: intensity of light is measured in units such as the candela and lux, not the light year.

So A, B and C, which include statement 2 or 3, are all wrong.

Exam tip: light year, parsec (about 3.26 light years) and astronomical unit are all units of distance.

The correct answer is C, Polynesia. New Zealand forms the south-western corner of the Polynesian Triangle in the Pacific Ocean.

The Pacific islands are grouped into three regions. Polynesia ("many islands") is a vast triangle with Hawaii in the north, Easter Island in the east and New Zealand in the south-west; it also includes Samoa, Tonga and Tahiti. The Maori, New Zealand's first people, are Polynesians who reached the islands by canoe around the 13th century, and their language is close to Hawaiian and Tahitian.

A is wrong: Micronesia ("small islands") lies north of the equator and includes Guam, the Marshall Islands and Kiribati.

B is wrong: Melanesia covers Papua New Guinea, Fiji, the Solomon Islands, Vanuatu and New Caledonia, north-west of New Zealand.

D is wrong: the Hawaiian chain is a single archipelago at the northern tip of Polynesia, far from New Zealand.

Exam tip: Polynesian Triangle corners = Hawaii, Easter Island, New Zealand; Fiji is Melanesia; Guam is Micronesia.

The correct answer is A, The ring has higher kinetic energy. Rotational kinetic energy is ½Iω², and the ring has the larger moment of inertia.

For a thin ring about the axis through its centre and perpendicular to its plane, all the mass sits at distance R, so I = MR². For a uniform disc, much of the mass lies closer to the axis, so I = ½MR². At the same angular velocity ω, the ring has KE = ½MR²ω² while the disc has only ¼MR²ω². The ring therefore carries twice the rotational kinetic energy of the disc. The farther mass lies from the axis, the harder a body is to spin and the more energy it stores.

B is wrong: the disc has the smaller moment of inertia, so it has less energy at the same ω.

C is wrong: equal mass and radius do not mean equal moment of inertia; mass distribution matters.

D is wrong: a spinning body has rotational kinetic energy even when its centre of mass is at rest.

Exam tip: ring I = MR², disc I = ½MR², solid sphere I = ⅖MR²; rotational KE = ½Iω².

The correct answer is D, Plasma Membrane. The plasma membrane is made of lipids and proteins and contains no DNA or RNA.

The plasma membrane is the outer boundary of the cell. It is a phospholipid bilayer with proteins and some carbohydrates set in it, described by the fluid mosaic model, and it controls what enters and leaves the cell. It is selectively permeable but carries no genetic material and makes no proteins of its own. Nucleic acids are found in the nucleus, ribosomes, mitochondria and chloroplasts.

A is wrong: the nucleolus, inside the nucleus, makes ribosomal RNA and is rich in RNA and DNA.

B is wrong: chloroplasts have their own circular DNA and ribosomes, a sign of their origin from bacteria.

C is wrong: ribosomes are built of ribosomal RNA (rRNA) and proteins, so they clearly contain nucleic acid.

Exam tip: organelles with nucleic acid: nucleus, nucleolus, ribosome, mitochondria, chloroplast; the plasma membrane has none.

The correct answer is B, both statements are true but Statement II does not explain Statement I. The Act provided dyarchy at the Centre and autonomy in the provinces, two separate reforms.

The Government of India Act, 1935 abolished dyarchy in the provinces, which the 1919 Act had begun, and replaced it with provincial autonomy: provinces got responsible governments with ministers answerable to elected legislatures. At the same time it moved dyarchy to the Centre, dividing federal subjects into reserved subjects (defence, foreign affairs) under the Governor-General and transferred subjects under ministers. The central part depended on the All-India Federation, which never came into being. Provincial autonomy was a reform for the provinces; it is not the reason dyarchy was set up at the Centre.

A is wrong: the two reforms stand side by side; one does not cause or explain the other.

C is wrong: provincial autonomy was granted and took effect in 1937, so Statement II is true.

D is wrong: the Act did provide for dyarchy at the Centre, so Statement I is true.

Exam tip: 1919 Act = dyarchy in provinces; 1935 Act = provincial autonomy plus dyarchy at the Centre.

The correct answer is A: any energy transfer that does not involve a temperature difference in some way is not heat. Heat, by definition, is energy that flows because of a temperature difference.

Thermodynamics recognises two ways in which a system can exchange energy with its surroundings: heat and work. Heat is the energy that flows from a hotter body to a colder one purely because their temperatures differ, by conduction, convection or radiation. Work is energy transferred by a force acting through a distance, such as a piston compressing a gas, and needs no temperature difference. So if a transfer has nothing to do with a temperature difference, it must be work or some other form, not heat.

B is wrong: work can transfer energy between bodies at the same temperature.

C is wrong: most objects expand on heating, so their length and volume change.

D is wrong: even when temperatures differ, energy can also pass as work at the same time.

Exam tip: heat = energy in transit due to temperature difference; work = energy transfer by force; first law: ΔU = Q - W.

The correct answer is C, 9 percent. The Approach Paper to the Twelfth Five Year Plan, released in 2011, aimed at average GDP growth of 9% a year for 2012–17.

The Twelfth Plan carried the theme "Faster, Sustainable and More Inclusive Growth". The Planning Commission's Approach Paper, approved by the National Development Council in October 2011, set the 9% target, up from the 8.2% achieved in the Eleventh Plan. Because the economy slowed sharply in 2012, the final Plan document approved in December 2012 cut the target to 8%. The Twelfth Plan was the last Five Year Plan, as the Planning Commission was replaced by NITI Aayog on 1 January 2015.

A is wrong: 7% was below even the growth recorded in the Eleventh Plan and was never the target.

B is wrong: 8% was the revised target of the final Plan document, not of the Approach Paper.

D is wrong: 10% was considered as a high-growth scenario but not adopted as the target.

Exam tip: Twelfth Plan: Approach Paper 9%, final document 8%; last plan before NITI Aayog.

The correct answer is C, Transformer. A transformer raises or lowers an AC voltage using electromagnetic induction between two coils.

A transformer has a primary and a secondary coil wound on a common soft-iron core. The changing current in the primary sets up a changing magnetic flux, which induces a voltage in the secondary. The ratio of voltages equals the ratio of turns: a step-up transformer has more turns in the secondary, and a step-down transformer has fewer. Power stations step voltage up for long-distance transmission to cut line losses, and substations step it down for homes. It works only with AC, because a steady DC gives no changing flux.

A is wrong: a generator converts mechanical energy into electrical energy.

B is wrong: a motor converts electrical energy into mechanical energy.

D is wrong: a vibrator is a switching device that interrupts current; it does not transform AC voltages in this way.

Exam tip: Vs/Vp = Ns/Np; transformers work on mutual induction and only with AC.

The correct answer is C, 2 m/s. All the potential energy at the top turns into kinetic energy at the mean position, so v = √(2gh) = √(2 × 10 × 0.20) = 2 m/s.

When the bob is released from rest at height h, it has potential energy mgh and no kinetic energy. Ignoring air resistance, mechanical energy is conserved, and at the lowest point (the mean position) all of it is kinetic: ½mv² = mgh. The mass cancels, giving v = √(2gh). With h = 0.20 m and g = 10 m/s², v² = 4, so v = 2 m/s. This is the bob's greatest speed in the swing.

A is wrong: the bob is momentarily at rest at the extreme positions, not at the mean position, where it is fastest.

B is wrong: 1 m/s would need a drop of only 0.05 m.

D is wrong: √10 m/s (about 3.16 m/s) would need a drop of 0.5 m.

Exam tip: for any free fall or frictionless swing from rest, v = √(2gh), independent of mass and path.

The correct answer is C, Both I and II. Two equal forces give a resultant of the same size only when they are 120° apart, and the resultant then makes 60° with each.

For two forces of magnitude F at angle θ, the resultant is R² = F² + F² + 2F² cos θ. Setting R = F gives 1 = 2 + 2 cos θ, so cos θ = -½ and θ = 120°, which is 2π/3. Because the two forces are equal, the resultant bisects the angle between them, so it makes 60°, or π/3, with each force. The three vectors form an equilateral triangle when drawn head to tail, which is an easy way to picture it.

A is wrong: Statement II is also correct, since the forces must be 2π/3 apart.

B is wrong: Statement I is also correct, since the resultant bisects the 120° angle.

D is wrong: both statements follow directly from the parallelogram law.

Exam tip: equal forces at 120° give a resultant equal to each; at 90° it is F√2; at 60° it is F√3.

The correct answer is B, Fleming's left-hand rule. It gives the direction of the force on a current-carrying conductor placed in a magnetic field.

Stretch the thumb, forefinger and middle finger of the left hand so that they are mutually perpendicular. If the forefinger points along the magnetic field and the middle finger along the current, the thumb shows the direction of the force, and so of the motion. This is the principle of the electric motor, which is why the left-hand rule is often called the motor rule. The force is largest when the conductor is perpendicular to the field.

A is wrong: the right-hand thumb rule (Maxwell's rule) gives the direction of the magnetic field around a current-carrying wire.

C is wrong: Fleming's right-hand rule gives the direction of induced current in a generator.

D is wrong: Hund's rule is from chemistry and tells how electrons fill orbitals of equal energy.

Exam tip: Left hand = motor (force); Right hand = generator (induced current); thumb = motion, fore = field, middle = current.

The correct answer is D, Steatite. Most Harappan seals were carved from steatite, a soft soapstone that hardens when fired.

Steatite is easy to cut, so craftsmen could carve fine animal figures and signs of the Harappan script on it. After carving, the seals were usually coated and heated, which turned the surface hard and white. Thousands of such square seals have been found at Mohenjo-daro, Harappa and Lothal; the best known shows a seated figure surrounded by animals, often called the Pashupati seal, and many carry a unicorn-like bull. The seals were probably used to mark goods in trade.

A is wrong: sandstone was used for some sculptures, such as the Harappa torso, not for seals.

B is wrong: lapis lazuli, brought from Badakhshan in Afghanistan, was used for beads and ornaments.

C is wrong: jasper was another bead stone, not the standard seal material.

Exam tip: Harappan seals = steatite; Dancing Girl = bronze; Priest-King = steatite.

The correct answer is C, Mitochondria and plastids. Both carry their own DNA and ribosomes and can make some of their own proteins.

Mitochondria, the powerhouses of the cell, and plastids such as chloroplasts each contain a small circular DNA molecule and 70S ribosomes, much like bacteria. This is the basis of the endosymbiotic theory: they are thought to have begun as free-living bacteria that were taken into an early cell and stayed on. Because they have their own genes, they are called semi-autonomous organelles and divide on their own inside the cell. Mitochondrial DNA passes almost entirely from the mother.

A is wrong: plastids have DNA, but the endoplasmic reticulum, a network of membranes, has none.

B is wrong: mitochondria have DNA, but the endoplasmic reticulum does not.

D is wrong: lysosomes and the Golgi apparatus are membrane sacs with enzymes and no genetic material.

Exam tip: semi-autonomous organelles = mitochondria and chloroplasts (own DNA, 70S ribosomes).