RRB Technician Grade III 2024-25 30 December 2024 Shift 3 GK Questions – with answers & solutions

Correct Answer: Option 4 — Ovary
In a flower, the female reproductive part is the carpel (pistil), made of stigma, style and ovary. Pollination deposits pollen on the stigma, a pollen tube grows down through the style, and the male gamete fuses with the female gamete inside the ovule — this fusion is fertilisation and it produces the zygote.
After fertilisation, the flower is remodelled. The ovary grows rapidly and ripens to form the fruit, while the ovule turns into the seed and the zygote develops into the embryo. The parts no longer needed — petals, sepals, stamens, style and stigma — shrivel and fall off. The ripened ovary wall becomes the pericarp, which protects the seeds and aids their dispersal.
❌ Why the other options are incorrect
✗ Ovule — it lies inside the ovary and becomes the seed, not the fruit; the zygote divides inside it to form the embryo.
✗ Gynoecium — the collective name for all the carpels of a flower; it is the whole female whorl, not the specific part that ripens into a fruit.
✗ Pistil — the complete female unit (stigma + style + ovary); its stigma and style wither away, so only its basal ovary becomes the fruit.
📌 SSC & Railway Exam Facts
• Ovary → fruit; ovule → seed; zygote → embryo — a favourite one-line PYQ chain.
• Androecium = all stamens (male whorl); gynoecium = all carpels (female whorl).
• A fruit formed without fertilisation is parthenocarpic (seedless banana, grapes).
• Apple and pear are false fruits — they develop mainly from the thalamus, not the ovary.
• The study of fruits is Pomology; the study of flowers is Anthology.

Correct Answer: Option 3 — Proteins and sugars
Cartilage is a connective tissue in which the cells (chondrocytes) lie in small spaces called lacunae, widely spaced within a solid yet flexible matrix. As NCERT states, the matrix of cartilage is composed of proteins and sugars, which makes it firm enough to give shape and smooth enough to cushion joints.
Bone is the other hard connective tissue; its matrix is hard and rigid because it is rich in calcium and phosphorus compounds. Together, bone and cartilage form the skeletal system — bone provides the strong framework and anchors muscles, while cartilage smoothens bone surfaces at joints and shapes soft structures such as the nose, ear pinna, larynx and trachea.
❌ Why the other options are incorrect
✗ Phosphorus and sugars — phosphorus belongs to the bone matrix, not cartilage; cartilage has no mineral hardening of this kind.
✗ Calcium and sugars — calcium salts stiffen bone; a calcified matrix would remove the flexibility cartilage needs.
✗ Proteins and fats — fat is stored in adipose tissue (below the skin, between organs), which insulates the body; it is not the cartilage matrix.
📌 SSC & Railway Exam Facts
• Connective tissues — areolar, adipose, bone, cartilage, blood, tendon, ligament.
• Bone cells are osteocytes; cartilage cells are chondrocytes; both sit in lacunae.
• Blood is a fluid connective tissue whose matrix is plasma.
• Tendon joins muscle to bone; ligament joins bone to bone and is very elastic.
• An adult human has 206 bones; the ear pinna and nose tip are made of cartilage.

Correct Answer: Option 3 — Ovule
The ovule is the small structure inside the ovary that carries the female gamete (egg cell). When the pollen tube reaches it, the male gamete fuses with the egg and forms the zygote.
After fertilisation, the zygote divides several times inside the ovule to form the embryo, while the ovule itself develops a tough protective coat (the seed coat / testa) and loses water, gradually turning into the seed. The seed therefore has three parts — the embryo (future plant, with plumule and radicle), the cotyledon(s) storing food, and the seed coat. The surrounding ovary meanwhile ripens into the fruit.
❌ Why the other options are incorrect
✗ Gynoecium — the whole female whorl of the flower (all carpels together); it is not a single structure that becomes a seed.
✗ Ovary — it encloses the ovules and develops into the fruit, not the seed.
✗ Pistil — the full female unit (stigma + style + ovary); its stigma and style usually wither and fall off after fertilisation.
📌 SSC & Railway Exam Facts
• Ovule → seed; ovary → fruit; zygote → embryo.
• Seeds with two cotyledons are dicots (gram, pea); with one cotyledon are monocots (maize, wheat).
• In a germinating seed the plumule forms the shoot and the radicle forms the root.
• Endosperm is the food-storing tissue formed in double fertilisation; coconut water is liquid endosperm.
• Seed dispersal takes place by wind, water, animals and explosion of the fruit.

Correct Answer: Option 4 — Grass
An ecosystem is a self-contained unit in which living organisms interact with one another and with their physical surroundings. It has two components. Biotic components are all the living things — producers (green plants), consumers (herbivores, carnivores, omnivores, parasites) and decomposers (bacteria and fungi). Abiotic components are the non-living physical and chemical factors — soil, water, air, wind, rainfall, temperature, light, humidity and minerals.
Grass is a green plant. It makes its own food by photosynthesis, so it is a producer — the first trophic level of every grassland food chain (grass → deer → lion). Being alive, it is a biotic, not an abiotic, component.
❌ Why the other options are incorrect
✗ Rainfall — a climatic (abiotic) factor; it decides the water available and hence the type of vegetation in a region.
✗ Soil — the non-living medium that supplies minerals and anchorage; it is an edaphic abiotic factor.
✗ Wind — a physical abiotic factor; it helps in pollination and seed dispersal but is itself non-living.
📌 SSC & Railway Exam Facts
• The term ecosystem was coined by A. G. Tansley in 1935.
• Producers → herbivores (primary consumers) → carnivores form a food chain; interlinked chains form a food web.
• Only about 10% of energy passes to the next trophic level — the 10 per cent law of Lindeman.
• A forest, ocean or lake is a natural ecosystem; a garden, crop field or aquarium is artificial.
• Ocean is the largest ecosystem; the flow of energy in an ecosystem is unidirectional.

Correct Answer: Option 1 — It has a single chromosome.
A prokaryotic cell is a primitive cell that lacks a true nucleus. Its genetic material — a single, circular chromosome of naked DNA — lies free in the cytoplasm in a region called the nucleoid, which has no nuclear membrane around it. Bacteria and blue-green algae (cyanobacteria) are the standard examples.
Prokaryotic cells also lack membrane-bound organelles such as mitochondria, plastids, Golgi apparatus, endoplasmic reticulum and lysosomes; the only organelle present is the ribosome (70S). Respiration takes place on infoldings of the plasma membrane called mesosomes. In contrast, eukaryotic cells (plants, animals, fungi, protists) have a well-defined nucleus with a nuclear membrane and more than one chromosome.
❌ Why the other options are incorrect
✗ Membrane bound cell organelles are present. — false; membrane-bound organelles are a defining feature of eukaryotic cells only.
✗ Nuclear region is well defined and surrounded by nuclear membrane. — false; in prokaryotes the nuclear region is an undefined nucleoid with no nuclear membrane.
✗ It has more than one chromosome. — false; multiple chromosomes occur in eukaryotes; a prokaryote carries only one.
📌 SSC & Railway Exam Facts
• Prokaryote size is about 1–10 µm; eukaryote about 5–100 µm.
• Prokaryotic ribosome is 70S; eukaryotic (cytoplasmic) is 80S.
• Prokaryotes divide by binary fission, not by mitosis or meiosis.
• Extra small circular DNA in bacteria is the plasmid, widely used in genetic engineering.
• Human somatic cells have 46 chromosomes (23 pairs); E. coli has a single circular chromosome.

Correct Answer: Option 4 — Enzymes
Enzymes are protein molecules made by living cells that speed up biochemical reactions without being used up or changed themselves — exactly what a catalyst does. Because they are produced by living organisms, they are called biological catalysts or biocatalysts.
Each enzyme is highly specific: it acts on one substrate only, which is explained by the lock-and-key model. Enzymes also work only within a narrow range of temperature and pH — pepsin needs an acidic medium in the stomach, while trypsin needs an alkaline medium in the small intestine. In digestion, amylase breaks starch into sugar, pepsin and trypsin break protein into amino acids, and lipase breaks fat into fatty acids and glycerol.
❌ Why the other options are incorrect
✗ Mucus — a slimy secretion that protects and lubricates the stomach lining against HCl; it has no catalytic action.
✗ Hydrochloric acid — it makes the stomach acidic, kills germs and activates pepsinogen into pepsin, but it is an acid, not an enzyme.
✗ Digestive juices — these are mixtures (saliva, gastric juice, pancreatic juice, bile); the catalysts are the enzymes contained in them, not the juices themselves.
📌 SSC & Railway Exam Facts
• Almost all enzymes are proteins; ribozymes are the RNA exception.
• Enzymes are denatured (destroyed) by high temperature, which is why fever affects digestion.
• Ptyalin (salivary amylase) acts at pH ≈ 6.8 in the mouth; pepsin at pH ≈ 2.
• Bile contains no enzyme; it only emulsifies fat and provides an alkaline medium.
• The term enzyme was coined by Wilhelm Kühne; the first enzyme crystallised was urease (J. B. Sumner).

Correct Answer: Option 1 — Mitochondria
Mitochondria are the powerhouses of the cell. They release the energy needed for all life activities in the form of ATP (Adenosine Tri Phosphate) — the energy currency of the cell. During aerobic respiration inside the mitochondria, glucose is oxidised and the energy released is used to join ADP + inorganic phosphate → ATP.
Whenever the cell needs energy, the terminal phosphate bond of ATP is broken by water, releasing about 30.5 kJ/mol. This fixed packet of energy then drives the endothermic (energy-absorbing) reactions of the cell, such as the making of new proteins and the contraction of muscles. A mitochondrion has a double membrane, the inner one deeply folded into cristae to increase surface area, and it possesses its own DNA and ribosomes.
❌ Why the other options are incorrect
✗ Ribosome — the site of protein synthesis; it consumes ATP but does not produce it and is not a membrane-bound organelle.
✗ Chloroplast — the organelle of photosynthesis in plant cells; it traps light energy, and is absent in animal cells.
✗ Lysosome — the suicidal bag of the cell containing digestive enzymes that break down worn-out organelles and foreign material.
📌 SSC & Railway Exam Facts
• ATP is called the energy currency of the cell; the term mitochondria was given by Carl Benda.
• Inner folds of the mitochondrion are cristae; the fluid inside is the matrix.
• Aerobic respiration yields 38 ATP per glucose molecule; anaerobic yields only 2 ATP.
• Mitochondria and chloroplast are semi-autonomous — they have their own DNA and ribosomes.
• Organelle tags — Golgi apparatus: packaging and dispatch; ER: transport; lysosome: suicidal bag; ribosome: protein factory.

Correct Answer: Option 4 — Spirogyra
Spirogyra is a filamentous green alga found in ponds, easily recognised by its spiral (ribbon-like) chloroplast. It reproduces asexually by fragmentation: when the filament matures, it simply breaks into two or more fragments, and each fragment grows into a new Spirogyra filament.
Fragmentation is possible only because the body of Spirogyra is simple and unspecialised — every cell of the filament is similar and capable of growth. In organisms with specialised tissues and organs, breaking the body apart would be fatal, so this method is limited to simple multicellular forms. As it involves one parent and no gametes, the offspring are genetically identical clones.
❌ Why the other options are incorrect
✗ Plasmodium — the malarial parasite; it reproduces by multiple fission, where one cell divides at once into many daughter cells.
✗ Amoeba — a unicellular protozoan that reproduces by binary fission in any plane; it also forms pseudopodia for movement and feeding.
✗ Hydra — reproduces by budding, where an outgrowth forms due to repeated cell division at one specific site and later detaches.
📌 SSC & Railway Exam Facts
• Spirogyra is called pond silk or water silk and has a spiral chloroplast.
• Binary fission — Amoeba, Leishmania, Paramecium; multiple fission — Plasmodium.
• Planaria shows regeneration; cut pieces regrow into complete animals.
• Yeast and Hydra reproduce by budding; Rhizopus by spore formation.
• Malaria is caused by Plasmodium, carried by the female Anopheles mosquito.

Correct Answer: Option 3 — Short and branched
The neuron (nerve cell) is the structural and functional unit of the nervous system and the longest cell in the human body. It has three parts — the cell body (cyton), the dendrites, and the axon.
Dendrites are the short, highly branched extensions that arise from the cell body. Their branching gives a very large surface area to receive stimuli (information) from other neurons or from receptor cells, and they carry the impulse towards the cell body. The axon, in contrast, is a single long, unbranched fibre that carries the impulse away from the cell body to the next cell. Impulse flow is therefore dendrite → cell body → axon → synapse.
❌ Why the other options are incorrect
✗ Short and unbranched — being unbranched would give too little surface to collect signals; dendrites are always richly branched.
✗ Long and unbranched — this describes the axon, which is long and typically unbranched along its length.
✗ Long and branched — dendrites are short, not long; length is the distinguishing feature of the axon.
📌 SSC & Railway Exam Facts
• The gap between two neurons is the synapse; a nerve-muscle junction is the neuromuscular junction.
• The impulse crosses the synapse through chemicals called neurotransmitters (e.g. acetylcholine).
• Nerve impulse is an electrochemical signal; nervous tissue makes the brain, spinal cord and nerves.
• The myelin sheath on the axon speeds up the impulse and gives insulation.
• Reflex arc path — receptor → sensory neuron → spinal cord → motor neuron → effector (muscle).

Correct Answer: Option 2 — Muscle tissues are made up of cuboidal cells.
Muscle tissue is made of long, elongated, cylindrical or spindle-shaped cells called muscle fibres, not cuboidal cells. Cuboidal cells belong to cuboidal epithelium, which lines the kidney tubules and salivary ducts. So Option 2 is the incorrect statement.
Muscle cells contain the special contractile proteins actin and myosin, whose sliding causes contraction and relaxation — this is what produces all body movement. Muscles are of three kinds: striated (voluntary/skeletal) muscles of the limbs, which show alternate light and dark bands; smooth (unstriated, involuntary) muscles of the alimentary canal and blood vessels; and cardiac muscle of the heart, which is striated but involuntary.
❌ Why the other options are incorrect
✗ Special contractile proteins are present in muscles. — true; actin and myosin bring about contraction.
✗ Microscopes reveal alternate light and dark bands in voluntary muscles. — true; that is why skeletal muscle is called striated or striped muscle.
✗ The limbs have voluntary muscles. — true; limb muscles move under our conscious will, hence voluntary.
📌 SSC & Railway Exam Facts
• Muscle cells are also called muscle fibres, and are the longest cells in many animals.
• Cardiac muscle is striated, uninucleate, branched and involuntary; it never tires.
• Smooth muscle cells are spindle-shaped with a single nucleus and no striations.
• Muscle fatigue is caused by accumulation of lactic acid during anaerobic respiration.
• The four animal tissues are epithelial, connective, muscular and nervous.

Correct Answer: Option 4 — large central vacuole
In a mature plant cell a single large central vacuole may occupy 50–90 % of the cell volume. It is bounded by a membrane called the tonoplast and is filled with cell sap — a solution of water, sugars, amino acids, mineral salts, pigments and waste products.
The vacuole performs two key jobs stated in the question. By taking in water it presses the cytoplasm outward against the cell wall, creating turgor pressure, which keeps the cell turgid and gives rigidity and support to non-woody stems and leaves. It also acts as the cell's storehouse and dustbin, holding useful substances and isolating toxic wastes that the plant cannot excrete. Animal cells, by contrast, have only small, temporary vacuoles.
❌ Why the other options are incorrect
✗ small ribosome — the site of protein synthesis; it is a tiny non-membranous granule and stores nothing.
✗ leucoplasts — colourless plastids that store starch, oils and proteins; they are storage granules, not the turgidity-maintaining organelle.
✗ chromoplasts — coloured plastids (other than green) that give flowers and fruits their red, orange and yellow colours to attract pollinators.
📌 SSC & Railway Exam Facts
• The vacuole membrane is the tonoplast; the fluid inside is cell sap.
• Amoeba has a food vacuole and a contractile vacuole for osmoregulation.
• Loss of turgor causes wilting; regaining water restores firmness.
• Plastids — chloroplast (green, photosynthesis), chromoplast (coloured), leucoplast (colourless, storage).
• Features unique to plant cells — cell wall, plastids and a large central vacuole.

Correct Answer: Option 3 — Amoeba
Amoeba is a unicellular, freshwater protozoan that has no fixed shape. Its outer boundary is only a flexible plasma membrane — there is no rigid cell wall — so the cell can push out finger-like projections of cytoplasm called pseudopodia ("false feet") in any direction. As the pseudopodia are formed and withdrawn, the shape of Amoeba keeps changing continuously.
The pseudopodia serve two purposes: locomotion (amoeboid movement) and ingestion of food, which they surround and enclose in a food vacuole — a process called phagocytosis. In our own body, white blood cells (WBCs) move and engulf germs in the same amoeboid way.
❌ Why the other options are incorrect
✗ Yeast — a unicellular fungus with a rigid cell wall; it keeps a definite oval shape and reproduces by budding.
✗ Paramoecium — a unicellular protozoan with a definite slipper-like shape maintained by a firm pellicle; it swims using cilia.
✗ Bacteria — they have a tough cell wall and hold fixed shapes — cocci (round), bacilli (rod), spirilla (spiral), vibrio (comma).
📌 SSC & Railway Exam Facts
• Amoeba shows holozoic nutrition and reproduces by binary fission in any plane.
• Its contractile vacuole removes excess water — it performs osmoregulation.
• Amoebic dysentery (amoebiasis) is caused by Entamoeba histolytica.
• Cell shape is maintained by the cell wall in plants, fungi and bacteria; animal cells have none.
• The cell was discovered by Robert Hooke (1665); Leeuwenhoek first saw free-living cells.

Correct Answer: Option 4 — chemotropism
Chemotropism is the directional growth movement of a plant part in response to a chemical stimulus. The standard NCERT example is exactly the one in this question: the growth of the pollen tube towards the ovule.
After pollination, the pollen grain lands on the stigma and germinates. Chemical substances (sugars and calcium compounds) secreted by the stigma, style and ovule guide the growing pollen tube downwards through the style so that it reaches the ovule inside the ovary and delivers the male gametes for fertilisation. As with all tropic movements, the direction of the growth is decided by the direction of the stimulus — here, the chemical gradient.
❌ Why the other options are incorrect
✗ hydrotropism — growth in response to water; roots bending towards moisture in the soil, not the pollen tube's guidance.
✗ phototropism — growth in response to light; shoots bend towards light (positive) and roots away (negative).
✗ geotropism — growth in response to gravity; roots grow downwards (positive) and shoots upwards (negative), as already stated in the question itself.
📌 SSC & Railway Exam Facts
• Tropic movements — photo-, geo-, hydro-, chemo- and thigmotropism (touch, as in tendrils).
• Tropic movements are slow and growth-dependent, controlled by auxin.
• Nastic movements are non-directional — e.g. Mimosa pudica folding on touch.
• The pollen tube was first observed by Giovanni Battista Amici.
• Fertilisation in flowering plants is double fertilisation, discovered by S. G. Nawaschin.

Correct Answer: Option 2 — Urethra
The urethra is the tube that runs through the penis and opens to the outside. In the male, the vas deferens (carrying sperms from the testes) joins the tube coming from the urinary bladder, so the urethra serves as the common passage for both semen and urine. This is a key difference from the female, where the urinary and reproductive openings are separate.
The two fluids never pass together: a sphincter mechanism at the base of the bladder closes the urinary route during ejaculation, so semen (sperms + secretions of the seminal vesicles and prostate gland) passes out alone.
❌ Why the other options are incorrect
✗ Urinary bladder — a muscular sac that only stores urine received from the kidneys through the ureters; sperms never enter it.
✗ Vas deferens — the duct that carries sperms only, from the epididymis to the ejaculatory duct; it carries no urine.
✗ Scrotum — the skin pouch outside the abdomen that holds the testes at a temperature 2–3 °C lower than the body, needed for sperm formation.
📌 SSC & Railway Exam Facts
• Male reproductive parts — testes, scrotum, epididymis, vas deferens, seminal vesicles, prostate gland, urethra and penis.
• Semen = sperms + secretions of seminal vesicles and prostate gland.
• Testosterone from the testes causes male secondary sexual characters (voice change, facial hair).
• Excretory path — kidney → ureter → urinary bladder → urethra.
• In females, urethra and vagina have separate openings; fertilisation occurs in the fallopian tube.

Correct Answer: Option 4 — Na₂SO₄(aq) + BaCl₂(aq) → BaSO₄(s) + 2NaCl(aq)
In a double displacement reaction, two compounds exchange their ions (radicals) with each other to form two new compounds. Its general pattern is AB + CD → AD + CB. The tell-tale sign is that both reactants are compounds — no free element takes part.
In option 4, sodium sulphate and barium chloride simply swap partners: Ba²⁺ joins SO₄²⁻ to give barium sulphate, and Na⁺ joins Cl⁻ to give sodium chloride. Because BaSO₄ is insoluble, it separates out as a white precipitate, shown by the (s) — so this is also a precipitation reaction.
The other three equations each begin with a free metal (Zn, Fe or Pb) attacking a salt solution, which makes them displacement, not double displacement, reactions.
⚗️ The Reaction
Na₂SO₄(aq) + BaCl₂(aq) → BaSO₄(s) + 2NaCl(aq)
• Both compounds exchange their ions — Ba²⁺ pairs with SO₄²⁻, Na⁺ pairs with Cl⁻.
• The coefficient 2 before NaCl balances the 2 Na and 2 Cl atoms.
• BaSO₄ is a white insoluble precipitate; it is also used as the "barium meal" in X-ray imaging of the stomach.
❌ Why the other options are incorrect
✗ Zn(s) + CuSO₄(aq) → ZnSO₄(aq) + Cu(s) — a displacement reaction; the free metal zinc, being more reactive than copper, pushes Cu out of its salt. Only one exchange takes place.
✗ Fe(s) + CuSO₄(aq) → FeSO₄(aq) + Cu(s) — again displacement; iron displaces copper, and the blue solution turns light green as brown copper deposits on the iron.
✗ Pb(s) + CuCl₂(aq) → PbCl₂(aq) + Cu(s) — displacement too; lead is above copper in the reactivity series, so it replaces copper. A free element is involved, so it cannot be double displacement.
📌 SSC & Railway Exam Facts
• Double displacement: AB + CD → AD + CB; displacement: A + BC → AC + B.
• A double displacement giving an insoluble solid is a precipitation reaction.
• AgNO₃ + NaCl → AgCl↓ (white) + NaNO₃ is the classic PYQ precipitation example.
• Neutralisation (acid + base → salt + water) is also a double displacement reaction.
• Reactivity series: K > Na > Ca > Mg > Al > Zn > Fe > Pb > H > Cu > Hg > Ag > Au.

Correct Answer: Option 1 — CH₂
A homologous series is a family of organic compounds that have the same general formula and the same functional group, in which each member differs from the next by one −CH₂− unit. The compounds given — CH₄ (methane), C₂H₆ (ethane) and C₃H₈ (propane) — are the first three alkanes, general formula CₙH₂ₙ₊₂.
Counting the atoms proves it: going from CH₄ to C₂H₆ adds 1 carbon and 2 hydrogens, and from C₂H₆ to C₃H₈ again adds 1 carbon and 2 hydrogens. That added unit is exactly CH₂.
Each step also raises the molecular mass by 14 u (C = 12, H₂ = 2). Because the members differ only in chain length, they show similar chemical properties but a gradual change in physical properties — melting point, boiling point and density rise steadily as the chain grows.
❌ Why the other options are incorrect
✗ CH — adding only CH would give C₂H₅ from CH₄, which is not a stable molecule; the hydrogen count would not fit CₙH₂ₙ₊₂.
✗ CH₃ — this is the methyl group, an alkyl substituent, not the difference between two successive members; adding CH₃ to CH₄ would give C₂H₇, which does not exist.
✗ CH₄ — methane itself is the first member of the series; the difference between CH₄ and C₂H₆ is only CH₂, not a whole CH₄.
📌 SSC & Railway Exam Facts
• Successive members of a homologous series differ by −CH₂−, i.e. by 14 u in molecular mass.
• Alkane = CₙH₂ₙ₊₂ (saturated), alkene = CₙH₂ₙ, alkyne = CₙH₂ₙ₋₂ (both unsaturated).
• First four alkanes: methane CH₄, ethane C₂H₆, propane C₃H₈, butane C₄H₁₀.
• Methane (CH₄) is the main constituent of CNG and biogas; it is also called marsh gas.
• Members of a homologous series have similar chemical but graded physical properties.

Correct Answer: Option 4 — Unique ability to form bonds with other atoms of carbon.
Catenation is the property of an element to link its own atoms together to form long chains, branched chains and closed rings. Carbon shows catenation to a far greater extent than any other element, and this single property is the reason organic chemistry exists as a separate branch with millions of carbon compounds.
Carbon can catenate so well because its C–C bond is exceptionally strong and stable (carbon is small, so the shared electrons are held tightly by the nucleus). Carbon also has a valency of 4 (tetravalency), so after joining other carbon atoms it still has spare bonds for hydrogen, oxygen, nitrogen, sulphur or halogens.
The bonds formed can be single (C–C), double (C=C) or triple (C≡C), which allows chains, branches and rings such as benzene.
❌ Why the other options are incorrect
✗ Bonds with other atoms of nitrogen — nitrogen does catenate, but only very weakly; in any case catenation is defined as bonding with atoms of the same element, and here that element is carbon.
✗ Bonds with other atoms of oxygen — oxygen's catenation is extremely limited (only H₂O₂-type peroxide links); this is not the definition of catenation for carbon.
✗ Bonds with other atoms of hydrogen — hydrogen is monovalent and can form only one bond, so it cannot form chains at all; C–H bonding is not catenation.
📌 SSC & Railway Exam Facts
• Catenation = self-linking of atoms of the same element; shown best by carbon, then silicon and sulphur.
• Carbon is tetravalent (valency 4) — configuration 2, 4 — and forms covalent bonds.
• Carbon's two special properties — catenation and tetravalency — give rise to millions of compounds.
• Allotropes of carbon: diamond (hardest natural substance), graphite (conducts electricity), fullerene (C₆₀, buckminsterfullerene).
• Graphite is soft and slippery; diamond has no free electron, so it does not conduct electricity.

Correct Answer: Option 3 — Water is the solvent.
A solution is a homogeneous mixture of two or more substances. It has two parts: the solvent, which is the component present in the larger amount and which dissolves the other, and the solute, which is present in the smaller amount and gets dissolved.
When sugar is stirred into water, the water is far greater in quantity and does the dissolving, so water is the solvent and sugar is the solute. The solution is homogeneous — the sugar particles (smaller than 1 nm) spread uniformly, the mixture stays transparent, shows no Tyndall effect, and cannot be separated by filtration.
Water dissolves so many substances that it is called the universal solvent. A solution in which water is the solvent is called an aqueous solution, marked (aq).
❌ Why the other options are incorrect
✗ Water is the solute — reversed; the solute is the dissolved substance present in the smaller amount, which here is sugar, not water.
✗ Both water and sugar are solvents — a solution can have only one solvent; the remaining components are solutes.
✗ Sugar is the solvent — sugar is the substance that gets dissolved and is present in the smaller quantity, so it is the solute.
📌 SSC & Railway Exam Facts
• Solution = solute + solvent; the solvent is the component present in the larger amount.
• Water is the universal solvent; its solutions are called aqueous solutions, (aq).
• Particle size: true solution < 1 nm, colloid 1–1000 nm, suspension > 1000 nm.
• A true solution is homogeneous, transparent, stable and shows no Tyndall effect.
• Concentration = (mass of solute / mass of solution) × 100 gives the mass percentage.

Correct Answer: Option 2 — combination reaction
In a combination (synthesis) reaction, two or more reactants join together to form a single product. Its general form is A + B → AB.
Here calcium oxide (CaO, quick lime) and water combine to give just one product, calcium hydroxide, Ca(OH)₂ (slaked lime) — two reactants, one product — so it is a textbook combination reaction.
The word "+ Heat" on the product side shows that heat is released, so the reaction is also exothermic. The process is called the slaking of lime; so much heat comes out that the water hisses and boils. A suspension of slaked lime in water is lime water, which turns milky with CO₂ — the standard test for carbon dioxide.
⚗️ The Reaction
CaO(s) + H₂O(l) → Ca(OH)₂(aq) + Heat
• Two reactants → one product, so it is a combination reaction.
• Heat is written on the product side, so it is exothermic.
• Ca(OH)₂ + CO₂ → CaCO₃↓ + H₂O — this is why lime water turns milky.
❌ Why the other options are incorrect
✗ Wurtz reaction — an organic reaction in which two alkyl halides react with sodium in dry ether to give a higher alkane; it has nothing to do with lime and water.
✗ Wurtz fittig reaction — also organic, joining an aryl halide and an alkyl halide with sodium; again an organic coupling reaction, not an inorganic combination.
✗ decomposition reaction — there a single compound breaks up into two or more products, e.g. CaCO₃ → (heat) CaO + CO₂; here two reactants join, which is the exact opposite.
📌 SSC & Railway Exam Facts
• Combination: A + B → AB; decomposition: AB → A + B.
• CaO = quick lime, Ca(OH)₂ = slaked lime, CaCO₃ = limestone; Ca(OH)₂ solution = lime water.
• Lime water turns milky with CO₂ because insoluble CaCO₃ is formed.
• Exothermic: respiration, burning of fuels, slaking of lime; endothermic: photosynthesis, decomposition of CaCO₃.
• Decomposition by heat = thermal, by light = photolytic (2AgCl → 2Ag + Cl₂), by electricity = electrolytic.

Correct Answer: Option 1 — Joseph Proust
The Law of Constant Proportions, also called the Law of Definite Proportions, was given by the French chemist Joseph Louis Proust in 1799. It states that a pure chemical compound always contains the same elements combined in the same fixed proportion by mass, no matter where the sample comes from or how it is prepared.
For example, water (H₂O) always has hydrogen and oxygen in the mass ratio 1 : 8 — whether it is taken from a river, from rain or made in the laboratory. Likewise ammonia (NH₃) always has N : H = 14 : 3, and carbon dioxide (CO₂) always has C : O = 3 : 8.
This law, together with the Law of Conservation of Mass (Lavoisier), formed the experimental base on which John Dalton built his atomic theory in 1808.
❌ Why the other options are incorrect
✗ Ernest Rutherford — performed the α-particle scattering (gold foil) experiment and discovered the nucleus; he is called the Father of Nuclear Physics.
✗ JJ Thomson — discovered the electron (1897) and gave the plum-pudding (watermelon) model of the atom; he did not state any law of proportions.
✗ E Goldstein — discovered anode rays (canal rays), which led to the discovery of the proton; again unconnected with the law of constant proportions.
📌 SSC & Railway Exam Facts
• Law of Constant (Definite) Proportions — Joseph Proust; Law of Conservation of Mass — Antoine Lavoisier.
• In water, H : O = 1 : 8 by mass; in CO₂, C : O = 3 : 8; in NH₃, N : H = 14 : 3.
• Dalton's atomic theory (1808) explained both of these laws.
• Electron — J. J. Thomson, proton — E. Goldstein/Rutherford, neutron — James Chadwick (1932).
• Law of Multiple Proportions — John Dalton; Avogadro's law — Amedeo Avogadro.

Correct Answer: Option 1 — Zn(s) + CuSO₄(aq) → ZnSO₄(aq) + Cu(s)
In a displacement reaction, a more reactive element pushes out (displaces) a less reactive element from its compound. Its general form is A + BC → AC + B, and the giveaway is that one reactant is a free element and one is a compound.
In option 1, zinc is above copper in the reactivity series, so zinc displaces copper from copper sulphate. The blue colour of the CuSO₄ solution fades as it changes into colourless zinc sulphate, and reddish-brown copper is deposited on the zinc strip — the classic laboratory demonstration.
⚗️ The Reaction
Zn(s) + CuSO₄(aq) → ZnSO₄(aq) + Cu(s)
• Zn is more reactive than Cu, so it takes the place of Cu in the sulphate.
• Zn is oxidised (Zn → Zn²⁺ + 2e⁻) and Cu²⁺ is reduced (Cu²⁺ + 2e⁻ → Cu) — a redox reaction as well.
• The blue solution turns colourless and brown copper settles out.
❌ Why the other options are incorrect
✗ 2AgCl(s) → 2Ag(s) + Cl₂(g) — a decomposition reaction; a single compound breaks into two substances in sunlight (photolytic decomposition), which is why silver chloride is used in photography and turns grey on standing in light.
✗ CaO(s) + H₂O(l) → Ca(OH)₂(aq) — a combination reaction; two reactants unite to give a single product, slaked lime, with heat released.
✗ C(s) + O₂(g) → CO₂(g) — also a combination reaction (and a combustion); carbon and oxygen join to form one product, with no element being displaced from a compound.
📌 SSC & Railway Exam Facts
• Displacement: A + BC → AC + B; a more reactive element displaces a less reactive one.
• Reactivity series: K > Na > Ca > Mg > Al > Zn > Fe > Pb > H > Cu > Hg > Ag > Au.
• Fe + CuSO₄ → FeSO₄ + Cu — blue solution turns light green; a favourite PYQ.
• Cu + ZnSO₄ → no reaction, because copper is less reactive than zinc.
• 2AgBr → (sunlight) 2Ag + Br₂ and 2AgCl → (sunlight) 2Ag + Cl₂ are photolytic decompositions.

Correct Answer: Option 1 — Helium
Atomicity is the number of atoms present in one molecule of an element. Helium is a noble gas of group 18, and its atom already has a completely filled outermost shell — the electronic configuration of helium is simply 2, a complete duplet.
Because its outer shell is already full, helium has no tendency to gain, lose or share electrons. It therefore does not bond even with its own kind and exists as single, separate atoms. Such elements are called monatomic, and their atomicity is 1. All noble gases — He, Ne, Ar, Kr, Xe and Rn — are monatomic, which is why they are also called inert or noble gases.
By contrast, nitrogen, oxygen and hydrogen all have incomplete outer shells, so two of their atoms share electrons and exist as diatomic molecules with atomicity 2.
❌ Why the other options are incorrect
✗ Nitrogen — configuration 2, 5; two atoms share three pairs of electrons to form N₂ with a very strong triple bond; atomicity 2.
✗ Oxygen — configuration 2, 6; two atoms share two pairs to form O₂ with a double bond; atomicity 2. Its allotrope ozone, O₃, is triatomic.
✗ Hydrogen — configuration 1; two atoms share one pair to complete their duplets, forming H₂; atomicity 2.
📌 SSC & Railway Exam Facts
• Monatomic (atomicity 1): all noble gases — He, Ne, Ar, Kr, Xe, Rn.
• Diatomic (atomicity 2): H₂, N₂, O₂, F₂, Cl₂, Br₂, I₂.
• Triatomic: O₃ (ozone); tetra-atomic: P₄; poly-atomic: S₈.
• Helium is the second most abundant element in the universe and is used in weather balloons because it is light and non-inflammable.
• Noble gases occupy group 18; helium has 2 electrons, the rest have 8 electrons in the outermost shell.

Correct Answer: Option 1 — Bronze
An alloy is a homogeneous mixture of two or more metals, or of a metal with a non-metal. Alloys are made because they are harder, stronger and more corrosion-resistant than the pure metals they come from.
Bronze is the alloy of copper (Cu) and tin (Sn), roughly 90 % copper and 10 % tin. It is much harder than pure copper, does not corrode easily, and has been used since the Bronze Age for statues, medals, bells and coins.
The classic exam pairing to remember is: brass = copper + zinc, while bronze = copper + tin. Mixing these two up is the commonest mistake in this question.
❌ Why the other options are incorrect
✗ Solder — an alloy of lead (Pb) and tin (Sn); it has a very low melting point, which is why it is used for welding electrical wires. It contains no copper.
✗ Brass — an alloy of copper (Cu) and zinc (Zn), not copper and tin; it is yellow, malleable and used for utensils and musical instruments.
✗ Gold — gold (Au) is a pure element, not an alloy at all. Jewellery gold is an alloy of gold with copper or silver, but gold itself is an element.
📌 SSC & Railway Exam Facts
• Bronze = Cu + Sn; Brass = Cu + Zn; Solder = Pb + Sn; German silver = Cu + Zn + Ni.
• Stainless steel = Fe + Cr + Ni; Steel = Fe + C; Duralumin = Al + Cu + Mg + Mn.
• Amalgam is an alloy in which one metal is mercury (Hg).
• 24 carat gold is pure gold; 22 carat gold contains about 91.6 % gold with copper or silver.
• Alloying changes the properties of a metal — iron rusts, but stainless steel does not.

Correct Answer: Option 2 — 14
The atomic number (Z) of an element is the number of protons in its nucleus, and the mass number (A) is the total number of protons and neutrons (nucleons). So the number of neutrons is found by subtracting:
Number of neutrons = A − Z
For aluminium (Al), the atomic number is 13 and the mass number is 27, written as ²⁷₁₃Al.
⚗️ The Calculation
Number of neutrons = A − Z = 27 − 13 = 14
• Protons = 13, electrons = 13 (a neutral atom), neutrons = 14.
• Electronic configuration of Al = 2, 8, 3, so its valency is 3 and it forms Al³⁺.
• Neutrons are neutral; they were discovered by James Chadwick in 1932.
Aluminium is the most abundant metal in the Earth's crust. It is extracted from its ore bauxite (Al₂O₃·2H₂O) by the Hall–Héroult electrolytic process.
❌ Why the other options are incorrect
✗ 15 — would need a mass number of 28; it comes from mis-remembering aluminium's mass number as 28 instead of 27.
✗ 27 — this is the mass number of aluminium, i.e. protons + neutrons, not the neutrons alone.
✗ 13 — this is the atomic number, i.e. the number of protons (and electrons), not neutrons.
📌 SSC & Railway Exam Facts
• Neutrons = mass number − atomic number (A − Z).
• Aluminium: Z = 13, A = 27, neutrons = 14, configuration 2, 8, 3, valency 3.
• Isotopes — same atomic number, different mass number (¹H, ²H, ³H; ³⁵Cl, ³⁷Cl).
• Isobars — same mass number, different atomic number (⁴⁰Ca and ⁴⁰Ar).
• Hydrogen (¹H) is the only atom with no neutron; Al is the most abundant metal in the Earth's crust.

Correct Answer: Option 3 — A mixture of iron nails in water
A homogeneous mixture has a uniform composition throughout; its components cannot be told apart and there is no visible boundary between them — a true solution such as salt in water is the standard example. A heterogeneous mixture, in contrast, has a non-uniform composition and its parts can be seen separately.
Iron nails dropped into water do not dissolve at all. The nails simply lie at the bottom and remain clearly visible, forming two distinct phases — solid iron and liquid water. The mixture is therefore heterogeneous, and it can be separated by simply picking out the nails or using a magnet. Since the question asks which is NOT homogeneous, this is the answer.
The other three all dissolve completely, giving true solutions whose particles are smaller than 1 nm, which are transparent, stable and show no Tyndall effect.
❌ Why the other options are incorrect
✗ A mixture of copper sulphate in water — CuSO₄ dissolves fully to give a clear blue solution; uniform throughout, hence homogeneous.
✗ A mixture of salt in water — the classic true solution; salt dissolves completely and is recovered by evaporation, not by filtration.
✗ A mixture of sugar in water — sugar dissolves fully and spreads uniformly, so it is also a homogeneous true solution.
📌 SSC & Railway Exam Facts
• Homogeneous: true solutions, alloys (brass, bronze), air; heterogeneous: suspensions, colloids, iron filings in sand.
• Particle size: true solution < 1 nm, colloid 1–1000 nm, suspension > 1000 nm.
• Iron filings are separated from a mixture using a magnet.
• A colloid looks homogeneous but is actually heterogeneous — e.g. milk.
• Tyndall effect is shown by colloids and suspensions, never by a true solution.

Correct Answer: Option 4 — 4
A chemical equation is balanced when the number of atoms of each element is the same on both sides, as required by the Law of Conservation of Mass — matter can neither be created nor destroyed in a chemical reaction.
⚗️ The Calculation
3Fe + xH₂O → Fe₃O₄ + 4H₂
• Iron (Fe): 3 on the left, 3 in Fe₃O₄ on the right — already balanced.
• Oxygen (O): left side has x O atoms; right side has 4 O atoms in Fe₃O₄ ⇒ x = 4.
• Hydrogen (H): left side has 2x = 2 × 4 = 8 H atoms; right side has 4 × 2 = 8 H atoms in 4H₂ — it checks out.
• The balanced equation is 3Fe + 4H₂O → Fe₃O₄ + 4H₂.
This is the well-known reaction of iron with steam. Heated iron reacts with steam (not with cold water) to form iron(II, III) oxide, Fe₃O₄ (magnetic oxide of iron) and to liberate hydrogen gas. Note that only coefficients may be changed while balancing — a subscript inside a formula must never be altered.
❌ Why the other options are incorrect
✗ 1 — gives only 1 O and 2 H on the left against 4 O and 8 H on the right; the equation stays badly unbalanced.
✗ 5 — puts 5 O on the left but Fe₃O₄ needs only 4 O, leaving one oxygen atom unaccounted for.
✗ 3 — gives 3 O and 6 H on the left, short of the 4 O and 8 H required on the right.
📌 SSC & Railway Exam Facts
• Balancing is based on the Law of Conservation of Mass (Antoine Lavoisier).
• 3Fe + 4H₂O → Fe₃O₄ + 4H₂ — iron reacts with steam, not with cold water.
• Fe₃O₄ is the magnetic oxide of iron; its mineral form is magnetite.
• While balancing, change only the coefficients, never the subscripts in a formula.
• 2Mg + O₂ → 2MgO, 2H₂ + O₂ → 2H₂O and N₂ + 3H₂ ⇌ 2NH₃ are standard balanced equations.

Correct Answer: Option 3 — A solution is basic with a high hydroxide ion concentration.
The pH scale runs from 0 to 14 and measures the concentration of hydrogen ions, H⁺ (H₃O⁺), in a solution:
pH < 7 → acidic (more H⁺ than OH⁻), pH = 7 → neutral (H⁺ = OH⁻), pH > 7 → basic (more OH⁻ than H⁺).
A solution of pH = 10 lies above 7, so it is basic (alkaline). As the pH rises above 7, the H⁺ concentration falls and the OH⁻ concentration rises — the two always move in opposite directions. Hence a pH-10 solution has a high hydroxide ion (OH⁻) concentration and a low hydrogen ion concentration.
Such a solution turns red litmus blue, gives a pink colour with phenolphthalein, tastes bitter and feels soapy. Common examples near pH 10 are milk of magnesia and a solution of washing soda.
❌ Why the other options are incorrect
✗ Basic with a high hydrogen ion concentration — the conclusion "basic" is right but the reason is wrong; a high H⁺ concentration means a low pH, i.e. an acid.
✗ Acidic with a high hydrogen ion concentration — this would be true only for pH < 7; a pH of 10 is on the basic side of neutral.
✗ Acidic with a high hydroxide ion concentration — self-contradictory; a high OH⁻ concentration makes a solution basic, never acidic.
📌 SSC & Railway Exam Facts
• pH = 0–7 acidic, 7 neutral, 7–14 basic; pH + pOH = 14.
• Lower pH → higher H⁺; higher pH → higher OH⁻; the two are inversely related.
• Indicators: litmus (red/blue), methyl orange (red in acid, yellow in base), phenolphthalein (colourless in acid, pink in base).
• Gastric juice pH ≈ 1.2, lemon ≈ 2.2, pure water = 7, milk of magnesia ≈ 10, NaOH ≈ 14.
• pH paper / universal indicator gives the approximate pH; onion and vanilla are olfactory indicators.

Correct Answer: Option 2 — 1000 J/s
Power is the rate of doing work, so P = W/t. Its SI unit is therefore the joule per second, which is given the special name watt (W):
1 W = 1 J/s
The prefix kilo means one thousand, so
1 kW = 1000 W = 1000 J/s
A 1 kW electric heater therefore converts 1000 joules of electrical energy into heat every second. Keep the difference clear: kilowatt (kW) measures power, a rate, while the kilowatt-hour (kWh) measures energy — the energy used by a 1 kW appliance in one hour, equal to 3.6 × 10⁶ J. The kWh is the "unit" printed on an electricity bill.
❌ Why the other options are incorrect
✗ 1 J/s — this is just 1 watt, one-thousandth of a kilowatt; the prefix kilo has been ignored.
✗ 100 J/s — this is 100 W, roughly the rating of an old filament bulb; the factor is ten times too small.
✗ 10 J/s — this is only 10 W, a hundred times smaller than a kilowatt.
📌 SSC & Railway Exam Facts
• Power P = W/t = Energy/Time; SI unit watt (W) = J s⁻¹.
• 1 kW = 1000 W; 1 MW = 10⁶ W; 1 GW = 10⁹ W; 1 horsepower (hp) = 746 W.
• 1 kWh = 1000 W × 3600 s = 3.6 × 10⁶ J — the commercial unit of electrical energy.
• Electrical power: P = VI = I²R = V²/R.
• Power is a scalar quantity; the watt is named after James Watt.

Correct Answer: Option 4 — P = VI
When a charge Q is driven through a potential difference V, the work done by the source is W = VQ. Power is the rate of doing that work, so
P = W/t = V × (Q/t) = V × I
because I = Q/t. Hence the electric power supplied to (or consumed by) any circuit element is
P = V I
measured in watts when V is in volts and I in amperes. Using Ohm's law V = IR, the same expression can be rewritten as P = I²R and P = V²/R. That is why a 220 V, 100 W bulb draws a current of I = P/V = 100/220 ≈ 0.45 A.
❌ Why the other options are incorrect
✗ P = V/I — by Ohm's law V/I is simply the resistance R, measured in ohms, not power.
✗ P = V²I — squaring the voltage *and* multiplying by current gives far too large a quantity; the correct squared forms are I²R and V²/R, each involving resistance.
✗ P = V²/I — dividing by current instead of multiplying is dimensionally wrong; at a fixed voltage, more current must mean more power drawn, not less.
📌 SSC & Railway Exam Facts
• P = VI = I²R = V²/R; SI unit watt (W); 1 W = 1 J/s.
• Ohm's law: V = IR, valid at constant temperature.
• Joule's law of heating: H = I²Rt.
• A bulb marked 220 V, 60 W has resistance R = V²/P = 220²/60 ≈ 807 Ω.
• Electrical energy consumed = P × t; billed in kWh, where 1 kWh = 3.6 × 10⁶ J.

Correct Answer: Option 4 — N m²/kg²
Start from Newton's universal law of gravitation:
F = G M m / r²
Making G the subject,
G = F r² / (M m)
Now substitute the units: force F is in newtons (N), the distance squared r² is in m², and the product of the two masses Mm is in kg². Therefore
Unit of G = N m² / kg² = N m² kg⁻²
Its numerical value is G = 6.67 × 10⁻¹¹ N m² kg⁻², and it is the same everywhere in the universe — independent of the masses, of the medium between them and of the location, which is exactly why it is called the *universal* constant.
❌ Why the other options are incorrect
✗ N m²/kgs⁻¹ — this brings in a second (time) unit, which never appears in G; the derivation gives only force, length and mass.
✗ N m²/kg⁻¹ — dividing by kg⁻¹ is the same as multiplying by kg, so this has mass in the wrong place and only to the first power.
✗ N kgm² — here mass is multiplied instead of divided; mass must sit in the denominator, squared.
📌 SSC & Railway Exam Facts
• G = 6.67 × 10⁻¹¹ N m² kg⁻²; it is a scalar and a universal constant.
• F = GMm/r² — gravitational force obeys the inverse-square law and is always attractive.
• g = GM/R²; on Earth g ≈ 9.8 m s⁻², unit m s⁻² — never confuse G with g.
• G was measured experimentally by Henry Cavendish (1798) with a torsion balance.
• Gravitation is the weakest of the four fundamental forces but has infinite range.

Correct Answer: Option 4 — Increasing the displacement.
The work done by a constant force is
W = F × s (more generally W = F s cos θ)
Work is therefore directly proportional to both the force and the displacement produced in the direction of the force. Increasing either of them increases the work.
So if the displacement is made larger while the force stays the same, the work done rises in the same proportion. Pushing a box with a force of 10 N through 2 m does 20 J of work; pushing it through 5 m with the same force does 50 J. Notice that mass does not appear in the formula at all — the work done by a given force over a given displacement is the same whatever the body's mass.
❌ Why the other options are incorrect
✗ Reducing the displacement. — this decreases the work, since W ∝ s; if s becomes zero, the work done is zero.
✗ Reducing the mass. — mass is not part of W = Fs; changing it may change the acceleration, but not the work done by a stated force over a stated displacement.
✗ Reducing the force. — this also decreases the work, because W ∝ F.
📌 SSC & Railway Exam Facts
• W = F s cos θ; work is maximum at θ = 0° and zero at θ = 90°.
• SI unit of work is the joule (J); 1 J = 1 N m = 1 kg m² s⁻²; CGS unit erg, 1 J = 10⁷ erg.
• Work is a scalar quantity; it can be positive, negative or zero.
• Work done against gravity in lifting a body: W = mgh.
• Work–energy theorem: net work done = change in kinetic energy.

Correct Answer: Option 4 — At C, centre of curvature
For a concave mirror, when the object is placed exactly at the centre of curvature C, the reflected rays meet again at C itself. The image formed is real, inverted and exactly the same size as the object — magnification m = −1.
This follows from the mirror formula. With u = −R = −2f:
1/v + 1/u = 1/f gives 1/v = 1/f − 1/(−2f)… solving gives v = −2f, so the image is also at a distance 2f = R from the pole, and m = −v/u = −1.
This is the only position for a concave mirror that produces an image of the same size as the object, which is why it is used in the laboratory to find the radius of curvature of a concave mirror.
❌ Why the other options are incorrect
✗ Between focus F and pole P — the image is then virtual, erect and enlarged, formed behind the mirror (the shaving-mirror position).
✗ At focus F — the reflected rays become parallel, so the image is formed at infinity and is highly enlarged (used in searchlights and headlights).
✗ Between focus F and centre of curvature C — the image is real, inverted and enlarged, formed beyond C, not equal in size.
📌 SSC & Railway Exam Facts
• Concave mirror, object at C → image at C, real, inverted, same size (m = −1).
• Object at infinity → image at F, highly diminished; object beyond C → image between F and C, diminished.
• Object between P and F → image behind the mirror, virtual, erect, enlarged — the only erect image a concave mirror gives.
• Mirror formula 1/v + 1/u = 1/f; magnification m = −v/u = h'/h; R = 2f.
• A convex mirror always gives a virtual, erect, diminished image, whatever the object position.

Correct Answer: Option 2 — in front of, behind
The centre of curvature (C) is the centre of the imaginary sphere of which the mirror forms a part. Where it lies depends on which face of that sphere is silvered.
A concave mirror is silvered on its bulging outer surface and reflects from the hollow inner surface, so the centre of the sphere lies on the same side as the reflecting surface — that is, in front of the mirror. For a concave mirror C is therefore a real point that light can actually reach.
A convex mirror reflects from the bulging outer surface, so the centre of the sphere falls on the far side — behind the mirror. For a convex mirror both C and the principal focus F are virtual points behind the surface. In each case the distance PC is the radius of curvature R, with R = 2f.
❌ Why the other options are incorrect
✗ in front of, in front of — correct for the concave mirror but wrong for the convex one, whose C is virtual and behind it.
✗ behind, behind — true only if both mirrors were convex; a concave mirror's C is a real point in front of it.
✗ behind, in front of — this reverses the two mirrors completely.
📌 SSC & Railway Exam Facts
• R = 2f, so f = R/2; a mirror of R = 30 cm has f = 15 cm.
• In the New Cartesian sign convention, a concave mirror has f negative and a convex mirror f positive.
• A concave mirror is converging; a convex mirror is diverging.
• Convex mirrors are used as rear-view mirrors because they give an erect, diminished image with a wide field of view.
• Mirror formula: 1/v + 1/u = 1/f; magnification m = −v/u = h'/h.

Correct Answer: Option 2 — least scattered by fog or smoke
When light passes through fog, smoke or dust, its rays are scattered sideways by the tiny suspended particles. According to Rayleigh's law of scattering, the amount of scattering varies inversely as the fourth power of the wavelength:
Scattering ∝ 1/λ⁴
Red light has the longest wavelength in the visible spectrum (about 620–750 nm), so it is scattered the least of all colours. A red beam therefore travels the greatest distance through fog or smoke without being spread out, and remains visible from far away.
That is exactly why danger signals, traffic stop lights, brake lights and railway signals are red — the driver can see them from a safe stopping distance even in poor visibility. Violet and blue, having the shortest wavelengths, would scatter away long before reaching the observer.
❌ Why the other options are incorrect
✗ not scattered at all by fog or smoke — too strong a statement; red is scattered, only much less than the other colours. No colour escapes scattering completely.
✗ highest scattered by fog or smoke — this is true of violet and blue, not red; a strongly scattered colour would fade quickly and make a poor signal.
✗ highest reflected by fog or smoke — the effect involved here is scattering, not reflection, and a strongly reflected light would be thrown back rather than reaching the observer.
📌 SSC & Railway Exam Facts
• Rayleigh scattering ∝ 1/λ⁴ — shorter wavelength means more scattering.
• Order of wavelength: VIBGYOR, violet shortest (≈400 nm), red longest (≈700 nm).
• The sky looks blue because blue is scattered most; the Sun looks red at sunrise and sunset because the long path lets only red through.
• Danger/stop signals are red; red also has the least deviation in a prism.
• The Tyndall effect is the scattering of light by colloidal particles.

Correct Answer: Option 2 — I = I₁ + I₂ + I₃
In a parallel combination all three resistors are connected between the same two points, so each of them has the same potential difference V across it. The main current arriving at the junction divides among the three branches and joins up again afterwards.
By the conservation of charge (Kirchhoff's junction rule), the current entering a junction equals the total current leaving it:
I = I₁ + I₂ + I₃
Since I = V/R(eq) and I₁ = V/R₁, I₂ = V/R₂, I₃ = V/R₃, dividing throughout by V gives the standard result
1/R(eq) = 1/R₁ + 1/R₂ + 1/R₃
The equivalent resistance of a parallel group is therefore always smaller than the smallest individual resistance.
❌ Why the other options are incorrect
✗ R(eq) = R₁ + R₂R₃/(R₂ + R₃) — this is for a mixed circuit, where R₂ and R₃ are in parallel and that pair is in series with R₁; it does not describe three resistors all in parallel.
✗ 1/I = 1/I₁ + 1/I₂ + 1/I₃ — the reciprocal rule applies to the resistances in parallel, never to the currents; currents simply add.
✗ R(eq) = R₃ + R₂R₁/(R₂ + R₁) — again a series–parallel mixed combination (R₁ ∥ R₂, in series with R₃), not a pure parallel group.
📌 SSC & Railway Exam Facts
• Parallel: 1/R(eq) = 1/R₁ + 1/R₂ + 1/R₃; voltage same, currents add.
• Series: R(eq) = R₁ + R₂ + R₃; current same, voltages add.
• Two resistors in parallel: R(eq) = R₁R₂/(R₁ + R₂); n equal resistances R in parallel give R/n.
• Household appliances are wired in parallel so each gets the full 220 V and can be switched independently.
• Ohm's law: V = IR; I = Q/t; SI unit of resistance is the ohm (Ω).

Correct Answer: Option 4 — same
You must separate two different quantities here — resistance and resistivity.
Resistance does depend on the shape of the wire:
R = ρ l / A
So doubling the area A would halve the resistance.
But resistivity ρ is a characteristic property of the material itself. It is defined as the resistance of a conductor of that material of unit length and unit cross-sectional area, and it depends only on the nature of the material and its temperature — not on the length, the area, or the shape of the specimen. A thick copper bus-bar and a thin copper wire have very different resistances but exactly the same resistivity.
Therefore doubling the cross-sectional area leaves the resistivity unchanged.
❌ Why the other options are incorrect
✗ doubled — nothing about ρ increases with area; this confuses resistivity with a geometry-dependent quantity.
✗ one fourth — there is no inverse-square dependence on area anywhere in R = ρl/A, let alone in ρ.
✗ halved — this is what happens to the resistance, not to the resistivity; it is the classic trap in this question.
📌 SSC & Railway Exam Facts
• R = ρl/A; resistivity ρ = RA/l; SI unit of ρ is the ohm metre (Ω m).
• ρ depends only on the material and temperature; R depends additionally on length and area.
• Resistivity of metals increases with temperature; that of semiconductors decreases.
• Silver has the lowest resistivity, followed by copper; nichrome has a high resistivity and is used in heating elements.
• Conductivity σ = 1/ρ, unit Ω⁻¹ m⁻¹ (S m⁻¹).

Correct Answer: Option 4 — Yellow
When white light passes through a glass prism it splits into its seven colours — this is dispersion. The splitting happens because the refractive index of glass is different for different colours: it is largest for violet and smallest for red, since
μ increases as the wavelength λ decreases
A larger refractive index means a larger bending, so the angle of deviation follows the order
Violet > Indigo > Blue > Green > Yellow > Orange > Red
Among the four colours offered — Blue, Green, Violet and Yellow — yellow has the longest wavelength (about 570–590 nm). It therefore has the smallest refractive index in glass and is bent through the minimum angle.
❌ Why the other options are incorrect
✗ Blue — wavelength about 450–495 nm, much shorter than yellow, so blue bends considerably more.
✗ Green — wavelength about 495–570 nm, still shorter than yellow; green deviates more than yellow but less than blue.
✗ Violet — the shortest wavelength (≈400 nm) of all, so it has the largest refractive index and suffers the maximum deviation — the exact opposite of what is asked.
📌 SSC & Railway Exam Facts
• Dispersion order VIBGYOR: violet deviates most, red least.
• Refractive index μ = c/v = sin i / sin r (Snell's law); μ is higher for shorter wavelengths.
• Red has the longest wavelength and the highest speed inside glass; violet the shortest wavelength and the lowest speed.
• Newton first demonstrated dispersion with a prism and recombined the colours with a second, inverted prism.
• A rainbow is formed by refraction, total internal reflection and dispersion of sunlight in water droplets.

Correct Answer: Option 4 — Stretching a rubber band
Potential energy is the energy a body possesses because of its position or its configuration (shape). When you stretch a rubber band, the work you do against the elastic restoring force changes the shape of the band and is stored inside it as elastic potential energy.
Nothing is lost: release the band and that stored energy is at once converted into the kinetic energy of the flying band. The same idea explains a stretched bow, a compressed spring (PE = ½kx²) and a wound-up watch spring.
For this to count as *stored* energy, the change must be recoverable — the system must be able to give the energy back. That is exactly what an elastic body does, and what a burning or a sliding body does not.
❌ Why the other options are incorrect
✗ Moving a pencil across a table — the work done here goes into kinetic energy and is then lost as heat by friction; nothing is stored.
✗ Lighting a matchstick — this releases stored chemical energy as heat and light; it is the opposite of storing energy.
✗ Pushing a vehicle on the plane road — the road is level, so there is no gain in height and no change of shape; the work done is spent against friction and in giving the vehicle kinetic energy.
📌 SSC & Railway Exam Facts
• Gravitational PE = mgh; Elastic PE of a spring = ½kx²; both in joules.
• KE = ½mv²; Mechanical energy = KE + PE.
• Energy is a scalar; it can be transformed but never created or destroyed.
• Examples of stored PE: stretched bow, compressed spring, water in a dam, charged capacitor, food and fuel (chemical PE).
• Work–energy theorem: net work done = change in kinetic energy.

Correct Answer: Option 1 — Speed of light in vacuum > speed of light in transparent medium
The absolute refractive index of a medium is defined as
μ = c/v
where c is the speed of light in vacuum (3 × 10⁸ m/s) and v is its speed in the medium.
A fraction is greater than 1 only when the numerator is larger than the denominator. So μ > 1 exactly when c > v — that is, when light travels slower inside the medium than in vacuum. Light always slows down on entering any material medium, because it is repeatedly absorbed and re-emitted by the atoms, so every transparent medium has μ greater than 1.
For example, for water v = 2.25 × 10⁸ m/s, giving μ = 3/2.25 = 1.33; for ordinary glass μ ≈ 1.5, and for diamond μ = 2.42, the largest among common substances.
❌ Why the other options are incorrect
✗ Speed of light in vacuum = speed of light in transparent medium — then μ = c/v = 1 exactly, which is the case for vacuum itself, not for a transparent medium.
✗ Wavelength of light gets change as it moves from denser to rarer medium — the wavelength does change on refraction, but that is a consequence of the change of speed (frequency stays constant), not the defining cause of μ > 1.
✗ Speed of light in vacuum < speed of light in transparent medium — this would give μ < 1, meaning light travels faster than c in matter, which is impossible.
📌 SSC & Railway Exam Facts
• μ = c/v = sin i / sin r (Snell's law); μ has no unit — it is a pure ratio.
• c = 3 × 10⁸ m/s in vacuum, the maximum possible speed in nature.
• μ (water) = 1.33, μ (glass) ≈ 1.5, μ (diamond) = 2.42 — highest among common media.
• On refraction the frequency stays the same; the speed and wavelength change.
• Higher μ means optically denser; light bends towards the normal entering a denser medium and away entering a rarer one.