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RRB JE CBT-1 2024-25 17 December 2024 Shift 3 GK Questions – with answers & solutions

All 44 GK / GS questions asked in RRB JE CBT-1 2024-25 on 17 December 2024 Shift 3, with correct answers and short solutions, subject-wise: Biology, Polity, Static GK, Chemistry, Economics, Current Affairs.

📚 44 questions🗓️ 17 December 2024⏰ Shift 3
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Subjects: Biology (10) · Polity (3) · Static GK (2) · Chemistry (10) · Economics (1) · Current Affairs (5) · Physics (9) · Medieval History (1) · Geography (2) · Modern History (1)

Biology (10)

Heredity and Evolution · Mendel's laws and experiments

Q1. Which scientist(s) established the laws of Inheritance?

  1. (a) Charles Darwin
  2. (b) Thomas Hunt Morgan
  3. (c) Watson and Crick
  4. (d) Gregor Johann Mendel
Answer & solution

Answer: (d) Gregor Johann Mendel

Answer: Option 4 — Gregor Johann Mendel
Gregor Johann Mendel worked out the laws of inheritance from his experiments on garden pea (Pisum sativum) and published them in 1865–66.
Revision note — Mendel and the laws of inheritance
• Mendel was an Austrian monk; he is called the Father of Genetics.
• He studied 7 pairs of contrasting characters in pea (tall/dwarf, round/wrinkled seed, etc.).
• Law of Dominance — in a hybrid only the dominant trait shows in F_(1) (tall × dwarf → all tall).
• Law of Segregation — the two alleles of a gene separate during gamete formation; the monohybrid F_(2) ratio is 3 : 1.
• Law of Independent Assortment — two different traits are inherited independently; the dihybrid F_(2) ratio is 9 : 3 : 3 : 1.
• The term genetics was coined by William Bateson.
Do not mix these up
• Mendel vs Morgan vs Watson–Crick — Mendel gave the laws of inheritance; T. H. Morgan showed genes lie on chromosomes (fruit fly); Watson and Crick gave the double-helix model of DNA (1953).
• Mendel vs Darwin — Darwin gave the theory of evolution by natural selection, not the laws of heredity.
Also asked from this topic: the Mendel law that explains separation of alleles in gametes (Law of Segregation); the kind of trait tallness is in pea (dominant); the allele combination of a short pea plant (tt).
Reproduction · Reproductive health and contraception

Q2. Contraception is one of the main goals of which health care programme?

  1. (a) Mental Health Programme
  2. (b) Pulse Polio Programme
  3. (c) Indradhanush Immunisation Programme
  4. (d) Reproductive Health Programme
Answer & solution

Answer: (d) Reproductive Health Programme

Answer: Option 4 — Reproductive Health Programme
India's Reproductive and Child Health (RCH) programme aims at a reproductively healthy society, and family planning through contraception is one of its main goals.
Revision note — Reproductive health and contraception
• India launched its family planning programme in 1952 — the first country to do so at the national level.
• It was widened into the Reproductive and Child Health Care (RCH) programme in 1997.
• Barrier methods — condoms, diaphragms, cervical caps; they also protect against STDs.
• Hormonal methods — oral pills and injections that stop ovulation.
• IUDs — Copper-T placed in the uterus prevents implantation.
• Surgical methods — vasectomy (males, vas deferens cut) and tubectomy (females, fallopian tubes cut); they give no protection against STDs.
Do not mix these up
• Pulse Polio vs Indradhanush — both are immunisation drives (polio; many vaccine-preventable diseases), not family planning.
Also asked from this topic: the year India launched its national family planning programme (1952); a limitation of surgical sterilisation (no protection against STDs); help for blocked oviducts (IVF).
Reproduction · Pollination and fertilisation in plants

Q3. Which of the following is NOT a method of pollination?

  1. (a) Asexual pollination
  2. (b) Self-pollination
  3. (c) Wind pollination
  4. (d) Water pollination
Answer & solution

Answer: (a) Asexual pollination

Answer: Option 1 — Asexual pollination
Pollination is the transfer of pollen from the anther to the stigma — a step of sexual reproduction.
So there is no such thing as "asexual pollination".
Revision note — Pollination
• Self-pollination — pollen reaches the stigma of the same flower or another flower of the same plant.
• Cross-pollination — pollen reaches the stigma of a flower on a different plant of the same species; it creates variation.
• Agents of cross-pollination: wind (anemophily), water (hydrophily), insects (entomophily), birds (ornithophily), animals (zoophily).
• Wind-pollinated flowers make light, dry pollen in large amounts and have feathery stigmas (maize, grasses).
• Insect-pollinated flowers are large, brightly coloured, scented and have nectar and sticky pollen.
• After pollination, fertilisation — the fusion of male and female gametes — forms the zygote.
Do not mix these up
• Pollination vs fertilisation — pollination is transfer of pollen; fertilisation is fusion of gametes.
Also asked from this topic: Pollination : transfer of pollen :: Fertilisation : ? (fusion of gametes); a feature NOT found in insect-pollinated flowers (light, small pollen in very large numbers).
Heredity and Evolution · Heredity and variation

Q4. Which of the following factors is primarily responsible for survival of species?

  1. (a) Niche
  2. (b) Temperature
  3. (c) Mutation
  4. (d) Variations
Answer & solution

Answer: (d) Variations

Answer: Option 4 — Variations
Variations among individuals help a species survive: when the environment changes, some variants are better suited and survive and reproduce.
Without variation, one drastic change could wipe out the whole population.
Revision note — Variation and evolution (Class 10)
• Variation arises from inaccuracies in DNA copying and is increased by sexual reproduction (new combinations every generation).
• Asexual reproduction gives very little variation; sexual reproduction gives more.
• Example (NCERT): bacteria that can withstand heat survive a heat wave better.
• Natural selection (Darwin) favours variants suited to the environment; this drives evolution.
• Accumulated heritable variations over generations lead to new species (speciation).
• Changes in somatic (non-reproductive) tissue are acquired traits and are not inherited.
Do not mix these up
• Variation vs mutation — mutation is one source of change in DNA; variation is the whole range of differences among individuals, which is what selection acts on.
Also asked from this topic: what accumulates over generations to produce new life forms (variations — evolution of biodiversity); Darwin's descent with modification (differential survival and reproduction).
Reproduction · Reproductive health and contraception

Q5. What is the purpose of using devices like Copper-T in family planning?

  1. (a) To alter hormonal levels in women
  2. (b) To block sperm transfer in males
  3. (c) To prevent fertilised eggs from implanting in the uterus
  4. (d) To act as a physical barrier to sperm
Answer & solution

Answer: (c) To prevent fertilised eggs from implanting in the uterus

Answer: Option 3 — To prevent fertilised eggs from implanting in the uterus
A Copper-T is an intra-uterine device (IUD) placed inside the uterus.
It stops a fertilised egg from getting implanted in the uterine wall, so pregnancy does not begin.
Revision note — Methods of contraception
• Barrier methods — condom, diaphragm, cervical cap; stop sperm reaching the egg; condoms also protect against STDs.
• Hormonal (chemical) methods — oral pills change the hormonal balance so that eggs are not released.
• Intra-uterine devices — loop or Copper-T placed in the uterus; copper ions also make sperm less active.
• Surgical methods — vasectomy (the vas deferens is blocked in males), tubectomy (the fallopian tube is blocked in females).
• Surgery prevents pregnancy but gives no protection against sexually transmitted diseases.
• IUDs can cause side effects such as irritation of the uterus.
Do not mix these up
• Copper-T vs oral pill — the Copper-T works inside the uterus; the pill works by changing hormones.
Also asked from this topic: a limitation of vasectomy or tubectomy (it does not prevent sexually transmitted diseases); the technique used when a woman's oviducts are blocked (in vitro fertilisation).
Reproduction · Pollination and fertilisation in plants

Q6. A tube like structure grows down from the pollen grain to the style and reaches the ovule. This pollen tube is responsible for:

  1. (a) carrying carbon dioxide to the female germ cell in the ovary
  2. (b) carrying oxygen to the female germ cell in the ovary
  3. (c) carrying nutrition to the female germ cell in the ovary
  4. (d) carrying the male germ cell to the female germ cell in the ovary
Answer & solution

Answer: (d) carrying the male germ cell to the female germ cell in the ovary

Answer: Option 4 — carrying the male germ cell to the female germ cell in the ovary
After pollination a pollen tube grows out of the pollen grain, down through the style, to the ovule.
It carries the male germ cell to the female germ cell (egg) so that fertilisation can take place.
Revision note — Pollination and fertilisation in plants
• Pollination — transfer of pollen from the anther to the stigma; self-pollination (same flower) or cross-pollination (another flower).
• Agents of cross-pollination: wind, water, insects, birds.
• Fertilisation — fusion of the male and female germ cells inside the ovule to form a zygote.
• After fertilisation: zygote → embryo, ovule → seed, ovary → fruit.
• Petals, sepals and stamens usually wither and fall off after fertilisation.
• The pollen tube grows towards the ovule in response to chemicals — an example of chemotropism.
Do not mix these up
• Pollination vs fertilisation — pollination transfers pollen; fertilisation is the fusion of gametes.
Also asked from this topic: growth of the pollen tube towards the ovule is an example of (chemotropism); fertilisation means (fusion of gametes).
Reproduction · Pollination and fertilisation in plants

Q7. Rose flower pollen has reached Sunflower stigma through pollination. The pollen will be rejected by the stigma because:

  1. (a) pollen has nothing to do with stigma
  2. (b) pollen was of rose flower
  3. (c) stigma has nothing to do with pollen
  4. (d) pollen was not of sunflower
Answer & solution

Answer: (d) pollen was not of sunflower

Answer: Option 4 — pollen was not of sunflower
The stigma recognises and accepts only compatible pollen of its own species.
Rose pollen is of a different species, so the sunflower stigma rejects it and no pollen tube grows to the ovule.
Revision note — Flower and pollination
• Stamen (male) = anther + filament; the anther makes pollen grains.
• Pistil / carpel (female) = stigma + style + ovary; the ovary holds ovules.
• The stigma is sticky — it catches pollen and checks whether it is compatible.
• Only right-species pollen germinates on the stigma and grows a pollen tube.
• Unisexual flowers (papaya, watermelon) have only stamens or only pistil; bisexual flowers (hibiscus, mustard) have both.
Also asked from this topic: the female reproductive part made of stigma, style and ovary (gynoecium / pistil); pollination means (transfer of pollen from anther to stigma).
Reproduction · Asexual reproduction (fission, budding, fragmentation, spores)

Q8. Leishmania reproduces by:

  1. (a) binary fission in only vertical planes
  2. (b) binary fission in any plane
  3. (c) binary fission in two equal halves
  4. (d) binary fission in a definite plane
Answer & solution

Answer: (d) binary fission in a definite plane

Answer: Option 4 — binary fission in a definite plane
Leishmania has a whip-like structure (flagellum) at one end of the cell.
So its binary fission takes place in a definite orientation relative to this structure.
Revision note — Fission in unicellular organisms
• Binary fission — one cell divides into two daughter cells, e.g. Amoeba, Paramecium, Leishmania.
• Amoeba can split in any plane; Leishmania splits in a definite plane.
• Multiple fission — one cell divides into many daughter cells at once, e.g. Plasmodium.
• Leishmania causes kala-azar, spread by the sand fly; Plasmodium causes malaria, spread by the female Anopheles mosquito.
• Fission, budding, fragmentation and spore formation are asexual — a single parent, no gametes.
Do not mix these up
• Amoeba vs Leishmania — Amoeba: fission in any plane; Leishmania: fission in a definite plane.
Also asked from this topic: the feature common to binary fission in Amoeba and budding in yeast (no fusion of gametes); the kind of organism that causes malaria (protozoan, Plasmodium).
Reproduction · Asexual reproduction (fission, budding, fragmentation, spores)

Q9. Yeast reproduces through which asexual mode of reproduction?

  1. (a) Fusion
  2. (b) Budding
  3. (c) Fission
  4. (d) Vegetative propagation
Answer & solution

Answer: (b) Budding

Answer: Option 2 — Budding
In yeast, a small bud grows out of the parent cell as an outgrowth.
The bud grows, detaches and becomes a new yeast cell.
Revision note — Modes of asexual reproduction
• Budding — a bud develops at one spot and separates; yeast and Hydra.
• Binary fission — Amoeba, Paramecium; multiple fission — Plasmodium.
• Fragmentation — the body breaks into pieces, each grows into a new organism; Spirogyra.
• Spore formation — spores in sporangia; Rhizopus (bread mould).
• Vegetative propagation — new plants from root, stem or leaf; Bryophyllum, potato, rose.
• Yeast is a unicellular fungus; it respires anaerobically to give ethanol and carbon dioxide (fermentation).
Do not mix these up
• Budding in Hydra vs yeast — Hydra is multicellular (bud from regenerative cells); yeast is unicellular.
Also asked from this topic: what binary fission in Amoeba and budding in yeast and Hydra have in common (no fusion of gametes); the products of anaerobic respiration in yeast (ethanol and carbon dioxide).
Reproduction · Vegetative propagation

Q10. Which part of the Bryophyllum plant develops new plants via vegetative propagation?

  1. (a) Leaves
  2. (b) Roots
  3. (c) Flowers
  4. (d) Stems
Answer & solution

Answer: (a) Leaves

Answer: Option 1 — Leaves
Bryophyllum (patharchatta) has buds in the notches along the margin of its leaves.
When a leaf falls on moist soil, these buds grow into new plants — vegetative propagation by leaf.
Revision note — Vegetative propagation
• Vegetative propagation = new plants from roots, stems or leaves, without seeds; the offspring are genetically identical to the parent.
• Leaf: Bryophyllum (buds on leaf margin).
• Stem: potato (tuber, the eyes are buds), ginger and turmeric (rhizome), onion (bulb), sugarcane, rose (cuttings), grass (runner).
• Root: sweet potato, dahlia, guava.
• Artificial methods: cutting, layering, grafting (mango, citrus) and tissue culture (orchids, ornamental plants).
• Useful for plants that have lost the capacity to produce seeds — banana, orange, rose, jasmine.
Do not mix these up
• Bryophyllum vs potato — Bryophyllum reproduces from leaves; potato from a stem (tuber), not a root.
Also asked from this topic: the incorrect statement about vegetative propagation (new plants arise from seeds); why farmers use cutting and grafting (genetically identical plants).

Polity (3)

Amendments and Important Articles · Basic structure doctrine

Q11. In which of the following cases did the Supreme Court of India enunciate the ‘Doctrine of Basic Structure’?

  1. (a) AK Gopalan case
  2. (b) Menka Gandhi case
  3. (c) Golaknath case
  4. (d) Keshvanand Bharti case
Answer & solution

Answer: (d) Keshvanand Bharti case

Answer: Option 4 — Keshvanand Bharti case
In Kesavananda Bharati v. State of Kerala (1973) the Supreme Court held that Parliament can amend any part of the Constitution under Article 368 but cannot alter its basic structure.
Revision note — Basic structure doctrine
• Decided on 24 April 1973 by a 13-judge bench — the largest ever — by a 7 : 6 majority; CJI S. M. Sikri.
• The same case held the Preamble is a part of the Constitution (reversing Berubari Union, 1960).
• Golaknath case (1967) — Parliament cannot amend Fundamental Rights; the 24th Amendment (1971) restored that power.
• Minerva Mills (1980) — limited amending power and judicial review are themselves part of the basic structure.
• Indira Gandhi v. Raj Narain (1975) — first case to strike down an amendment (39th) using the doctrine.
• Basic features named by courts: supremacy of the Constitution, secularism, federalism, separation of powers, rule of law, free and fair elections.
Do not mix these up
• A. K. Gopalan (1950) vs Maneka Gandhi (1978) — both are Article 21 cases: Gopalan read "procedure established by law" narrowly; Maneka Gandhi required the procedure to be just, fair and reasonable.
Also asked from this topic: the case that first held the Preamble to be part of the Constitution (Kesavananda Bharati, 1973); the amendment that restored Parliament's power over FRs after Golaknath (24th, 1971).
Fundamental Rights · Fundamental Rights - general (Articles 12, 13)

Q12. The Indian Constitution guarantees Fundamental Rights to its citizens under which of the following Articles?

  1. (a) Only Articles 12 to 30
  2. (b) Only Articles 15 to 35
  3. (c) Only Articles 12 to 35
  4. (d) Only Articles 14 to 32
Answer & solution

Answer: (c) Only Articles 12 to 35

Answer: Option 3 — Only Articles 12 to 35
The Fundamental Rights are in Part III of the Constitution, which runs from Article 12 to Article 35.
Revision note — Fundamental Rights (Part III)
• Part III is called the Magna Carta of India; the idea was borrowed from the USA (Bill of Rights).
• Article 12 defines "the State"; Article 13 voids laws that violate FRs — the basis of judicial review.
• Six rights now: Equality (14–18), Freedom (19–22), Against Exploitation (23–24), Freedom of Religion (25–28), Cultural and Educational (29–30), Constitutional Remedies (32).
• Right to Property (Articles 19(1)(f) and 31) was removed by the 44th Amendment, 1978; it is now a legal right under Article 300A.
• Articles 33–35 — Parliament may restrict FRs of the armed forces (Art. 33), during martial law (Art. 34), and make laws to give effect to certain FRs (Art. 35).
• During a National Emergency the rights under Articles 20 and 21 cannot be suspended (Article 359).
Do not mix these up
• Article 14 to 32 vs 12 to 35 — Articles 14–32 cover the six rights themselves, but Part III as a whole begins at 12 and ends at 35.
Also asked from this topic: the part of the Constitution called the "Magna Carta of India" (Part III); the number of categories of Fundamental Rights today (six); the Article on FRs of the armed forces (Article 33).
Judiciary · Supreme Court - jurisdiction (original, appellate, advisory)

Q13. Which Article of the Indian Constitution permits the Supreme Court to review its judgement or order?

  1. (a) Article 132
  2. (b) Article 137
  3. (c) Article 138
  4. (d) Article 135
Answer & solution

Answer: (b) Article 137

Answer: Option 2 — Article 137
Article 137 empowers the Supreme Court to review any judgment or order it has made, subject to laws of Parliament and rules made under Article 145.
Revision note — Articles on the Supreme Court's jurisdiction
• Article 124 — establishment and constitution of the Supreme Court.
• Article 129 — Supreme Court is a court of record (can punish for its own contempt).
• Article 131 — original jurisdiction in disputes between the Centre and states.
• Article 132 — appeals in constitutional cases; Article 133 — civil; Article 134 — criminal.
• Article 136 — Special Leave Petition (SLP) against any court or tribunal.
• Article 137 — review of its own judgments; Article 143 — advisory jurisdiction (President's reference).
• Article 138 — enlargement of jurisdiction by Parliament; Article 142 — complete justice.
Do not mix these up
• Article 137 vs Article 136 — 137 is the court reviewing its own decision; 136 is special leave to appeal against another court's decision.
Also asked from this topic: the Article that lets the Supreme Court review any judgment pronounced by it (Article 137).

Static GK (2)

Monuments and Heritage · Temples and religious places

Q14. What is the name of the famous temple complex in Tamil Nadu, known for its Dravidian architecture and 1,000-pillar hall?

  1. (a) Meenakshi Temple
  2. (b) Kanchipuram Temple
  3. (c) Brihadeeswarar Temple
  4. (d) Jagannath Temple
Answer & solution

Answer: (a) Meenakshi Temple

Answer: Option 1 — Meenakshi Temple
The Meenakshi Amman Temple at Madurai is a Dravidian temple complex famous for its towering gopurams and its Aayiram Kaal Mandapam — the Hall of a Thousand Pillars (it actually has about 985 carved pillars).
Revision note — Dravidian temples of Tamil Nadu
• Dravidian style — tall pyramidal vimana over the shrine, huge gopurams (gateway towers), pillared mandapas and temple tanks.
• Meenakshi Temple, Madurai — dedicated to Meenakshi (Parvati) and Sundareswarar (Shiva); built first under the Pandyas and greatly expanded by the Nayaks (Thirumalai Nayak); 14 gopurams.
• Brihadeeswarar Temple, Thanjavur — built by Rajaraja Chola I (completed about 1010); part of the Great Living Chola Temples UNESCO site.
• Kanchipuram — the "city of a thousand temples"; Kailasanatha Temple built by the Pallava king Narasimhavarman II (Rajasimha).
• Nataraja Temple, Chidambaram also has a thousand-pillar hall.
Do not mix these up
• Meenakshi Temple vs the Thousand Pillar Temple — the "Thousand Pillar Temple" (Rudreshwara) is at Hanamkonda, Warangal (Telangana), built by the Kakatiya king Rudradeva, not in Tamil Nadu.
• Jagannath Temple, Puri is in Odisha and follows the Kalinga (Nagara) style.
Also asked from this topic: the temple called the "Taj Mahal of the South" (Meenakshi Temple, Madurai); its best-known feature (gigantic gopurams); the builders of Warangal's Thousand Pillar Temple (Kakatiya).
Books and Authors · Modern Indian books and authors

Q15. In which year was 'Heirloom Treasures: The Cultural Tapestry of India: A Compilation of Selected Articles from India Beckons: Volume 1,' by Arunima Hoskote, published?

  1. (a) 2020
  2. (b) 2018
  3. (c) 2021
  4. (d) 2019
Answer & solution

Answer: (a) 2020

Answer: Option 1 — 2020
Heirloom Treasures: The Cultural Tapestry of India (Volume 1) by Arunima Hoskote was published in 2020 by Notion Press.
Revision note — Heirloom Treasures: The Cultural Tapestry of India
• Author: Arunima Hoskote, a writer–editor and a Cambridge economics graduate.
• The book is a compilation of selected articles from India Beckons, the digital travel magazine she founded.
• Theme: India's heritage, culture and travel — the "heirloom treasures" of the title.
• Publisher: Notion Press; year: 2020; this is Volume 1.
• For books-and-authors questions, learn the trio title → author → year together.

Chemistry (10)

Environmental Chemistry · Acid rain

Q16. The pH of acid rain is:

  1. (a) equal to 7
  2. (b) more than 5.6 but less than 7
  3. (c) less than 5.6
  4. (d) more than 7
Answer & solution

Answer: (c) less than 5.6

Answer: Option 3 — less than 5.6
Normal rain is already slightly acidic, about pH 5.6, because CO_(2) dissolves in it to form weak carbonic acid.
Rain is called acid rain only when its pH falls below 5.6.
Revision note — Acid rain
• Main causes: sulphur dioxide (SO_(2)) and nitrogen oxides (NO_(x)) from burning fossil fuels — power plants, vehicles, industries.
• They form sulphuric acid (H_(2)SO_(4)) and nitric acid (HNO_(3)) in the air.
• Effects: damages marble monuments — "marble cancer" of the Taj Mahal (CaCO_(3) reacts with acid); harms forests, soil and aquatic life.
• Acidic lakes kill fish; farmers correct acidic soil with quicklime or slaked lime.
• Pure water has pH 7; pH below 7 is acidic, above 7 is basic.
Do not mix these up
• Normal rain vs acid rain — both are below pH 7; the dividing line for acid rain is 5.6, not 7.
Also asked from this topic: the gas that contributes most to acid rain (sulphur dioxide); the two gases mainly responsible for acid rain (sulphur dioxide and nitrogen oxides).
Chemical Reactions and Equations · Decomposition reactions (thermal, electrolytic, photolytic)

Q17. Which of the following is an example of a decomposition reaction that occurs due to the application of electric current?

  1. (a) Decomposition of potassium permanganate by heat
  2. (b) Decomposition of sodium bicarbonate by heat
  3. (c) Electrolysis of water
  4. (d) Heating calcium carbonate
Answer & solution

Answer: (c) Electrolysis of water

Answer: Option 3 — Electrolysis of water
Passing an electric current through water breaks it into hydrogen and oxygen:
2H_(2)O → 2H_(2) + O_(2) — an electrolytic decomposition reaction.
The other three options are all decompositions caused by heat.
Revision note — Types of decomposition reactions
• Decomposition — one compound breaks into two or more simpler substances (AB → A + B); it needs energy, so most are endothermic.
• Thermal (heat): CaCO_(3) → CaO + CO_(2) (quicklime for cement); 2FeSO_(4) → Fe_(2)O_(3) + SO_(2) + SO_(3); 2Pb(NO_(3))_(2) → 2PbO + 4NO_(2) + O_(2) (brown fumes).
• Electrolytic (electricity): water → H_(2) at the cathode and O_(2) at the anode in the ratio 2 : 1 by volume; also molten NaCl and Al_(2)O_(3).
• Photolytic (light): 2AgCl → 2Ag + Cl_(2), 2AgBr → 2Ag + Br_(2) — used in black-and-white photography.
• Heating baking soda: 2NaHCO_(3) → Na_(2)CO_(3) + H_(2)O + CO_(2); heating KMnO_(4) releases O_(2).
Also asked from this topic: H_(2) : O_(2) by volume in electrolysis of water (2 : 1); heating CaCO_(3) is which reaction (decomposition); silver salts used in black-and-white photography (AgCl, AgBr).
Chemical Reactions and Equations · Writing and balancing chemical equations

Q18. Which of the following steps is the first step in balancing a chemical equation?

  1. (a) Writing the skeleton equation
  2. (b) Balancing hydrogen atoms
  3. (c) Adding coefficients randomly
  4. (d) Balancing oxygen atoms
Answer & solution

Answer: (a) Writing the skeleton equation

Answer: Option 1 — Writing the skeleton equation
You can balance only what is written, so the first step is the skeletal (unbalanced) equation with correct formulae of all reactants and products.
Atoms are then counted and balanced one element at a time.
Revision note — Balancing a chemical equation (hit-and-trial method)
• A balanced equation obeys the law of conservation of mass — atoms are neither created nor destroyed.
• Step 1: write the skeletal equation; step 2: draw boxes around each formula and count atoms of each element on both sides.
• Start with the compound having the most atoms and, in it, the element with the most atoms (e.g. oxygen in Fe_(3)O_(4)).
• Change only the coefficients, never the formula or subscripts (writing H_(2)O_(2) for H_(2)O changes the substance).
• Example: 3Fe + 4H_(2)O → Fe_(3)O_(4) + 4H_(2).
• Add physical states (s), (l), (g), (aq) and conditions (heat, catalyst) over the arrow at the end.
Also asked from this topic: a reaction that violates conservation of mass (2Mg + O_(2) → MgO); why H_(2)O cannot become H_(2)O_(4) while balancing (it changes the substance).
Chemical Reactions and Equations · Double displacement and precipitation reactions

Q19. When an aqueous solution of potassium iodide reacts with lead nitrate, what type of product is formed?

  1. (a) Sodium nitrate
  2. (b) Lead iodide (precipitate)
  3. (c) Lead chloride
  4. (d) Lead nitrate
Answer & solution

Answer: (b) Lead iodide (precipitate)

Answer: Option 2 — Lead iodide (precipitate)
Pb(NO_(3))_(2)(aq) + 2KI(aq) → PbI_(2)(s) + 2KNO_(3)(aq)
The ions exchange partners; lead iodide is insoluble and separates as a yellow precipitate. Potassium nitrate stays in solution.
Revision note — Double displacement and precipitation (Class 10)
• Double displacement: two compounds exchange ions — AB + CD → AD + CB.
• A reaction that forms an insoluble solid is a precipitation reaction.
• Pb(NO_(3))_(2) + 2KI → PbI_(2)↓ yellow + 2KNO_(3).
• Na_(2)SO_(4) + BaCl_(2) → BaSO_(4)↓ white + 2NaCl.
• AgNO_(3) + NaCl → AgCl↓ white + NaNO_(3).
• On heating, lead nitrate decomposes: 2Pb(NO_(3))_(2) → 2PbO + 4NO_(2) (brown fumes) + O_(2).
Do not mix these up
• Lead iodide vs lead nitrate — lead nitrate is the soluble reactant; lead iodide is the yellow insoluble product.
Also asked from this topic: which compound needs light, not heat, to decompose (silver chloride, unlike lead nitrate).
Carbon and its Compounds · Homologous series

Q20. A homologous series is a group of organic compounds that have:

  1. (a) the same functional group but differ by a CH₂ group
  2. (b) the same molecular formula
  3. (c) the same structural formula
  4. (d) no relation to each other
Answer & solution

Answer: (a) the same functional group but differ by a CH₂ group

Answer: Option 1 — the same functional group but differ by a CH₂ group
A homologous series is a family of carbon compounds with the same functional group, in which successive members differ by a −CH_(2)− unit (14 u).
Revision note — Homologous series (Class 10)
• Members share one general formula — alkanes C_(n)H_(2n+2), alkenes C_(n)H_(2n), alkynes C_(n)H_(2n−2).
• Successive members differ by CH_(2) in formula and by 14 u in molecular mass.
• Chemical properties are similar (decided by the functional group).
• Physical properties (melting point, boiling point, solubility) change gradually with molecular mass.
• Example: methane CH_(4), ethane C_(2)H_(6), propane C_(3)H_(8); alcohols CH_(3)OH, C_(2)H_(5)OH.
Do not mix these up
• Homologous series vs isomers — isomers have the same molecular formula but different structures; homologues differ by CH_(2).
Also asked from this topic: what compounds differing by a −CH_(2)− unit form (a homologous series); what rises steadily as the chain lengthens (boiling point).
Chemical Reactions and Equations · Corrosion and rancidity

Q21. Oxidation of metals in the presence of acids or moisture is called:

  1. (a) rusting
  2. (b) neutralisation
  3. (c) rancidity
  4. (d) corrosion
Answer & solution

Answer: (d) corrosion

Answer: Option 4 — corrosion
When a metal is attacked by substances around it such as moisture, acids or air, it is said to corrode.
This slow oxidation of metals is corrosion.
Revision note — Corrosion and rancidity
• Rusting is the corrosion of iron only — a reddish-brown coat of hydrated iron(III) oxide, Fe_(2)O_(3)·xH_(2)O.
• Iron rusts only when both oxygen and water are present.
• Silver turns black (silver sulphide, Ag_(2)S); copper gains a green coat (basic copper carbonate).
• Prevention: painting, oiling, greasing, galvanising (zinc coat), chrome plating, alloying.
• Rancidity — oxidation of fats and oils in food, giving a bad smell and taste.
• Rancidity is slowed by antioxidants, airtight containers and flushing chip packets with nitrogen.
Do not mix these up
• Corrosion vs rusting — corrosion is the general term for all metals; rusting is corrosion of iron alone.
Also asked from this topic: the reddish-brown coating on iron in moist air (hydrated iron(III) oxide); what leads to rancidity (oxidation).
Acids, Bases and Salts · Common salts - preparation and uses (baking soda, washing soda, bleaching powder, plaster of Paris)

Q22. When Plaster of Paris is mixed with water, it undergoes which of the following changes?

  1. (a) It dissolves completely.
  2. (b) It loses all its water molecules.
  3. (c) It changes to gypsum.
  4. (d) It produces a gas.
Answer & solution

Answer: (c) It changes to gypsum.

Answer: Option 3 — It changes to gypsum.
Plaster of Paris takes up water again and sets into a hard solid mass of gypsum.
CaSO_(4)·½H_(2)O + 1½H_(2)O → CaSO_(4)·2H_(2)O
Revision note — Plaster of Paris
• Chemical name: calcium sulphate hemihydrate, CaSO_(4)·½H_(2)O — half a water molecule per formula unit.
• Made by heating gypsum (CaSO_(4)·2H_(2)O) at 373 K (100 °C).
• Heating above 373 K gives anhydrous CaSO_(4) (dead burnt plaster), which does not set with water.
• It must be stored in a moisture-proof container, or it sets before use.
• Uses: plaster for fractured bones, toys, decorative materials, and making surfaces smooth.
Do not mix these up
• Gypsum vs Plaster of Paris — gypsum has 2 water molecules; Plaster of Paris has ½.
Also asked from this topic: the chemical name and formula of Plaster of Paris (calcium sulphate hemihydrate, CaSO_(4)·½H_(2)O); why it is used for casts (it sets quickly into a hard mass).
Acids, Bases and Salts · Common salts - preparation and uses (baking soda, washing soda, bleaching powder, plaster of Paris)

Q23. What is the role of chlorine gas in the preparation of bleaching powder?

  1. (a) It is used as a catalyst for the reaction.
  2. (b) It is used to neutralise calcium hydroxide.
  3. (c) It reacts with water to produce hydrogen peroxide.
  4. (d) It reacts with dry slaked lime to form bleaching powder.
Answer & solution

Answer: (d) It reacts with dry slaked lime to form bleaching powder.

Answer: Option 4 — It reacts with dry slaked lime to form bleaching powder.
Bleaching powder is made by the action of chlorine on dry slaked lime, Ca(OH)_(2).
Ca(OH)_(2) + Cl_(2) → CaOCl_(2) + H_(2)O
Revision note — Bleaching powder
• Chemical name: calcium oxychloride, CaOCl_(2).
• The chlorine comes from the chlor-alkali process — electrolysis of brine gives NaOH, Cl_(2) (at the anode) and H_(2) (at the cathode).
• Its bleaching and disinfecting action comes from the chlorine it releases.
• Uses: bleaching cotton and linen (textiles) and wood pulp (paper); bleaching washed clothes in laundry.
• Also an oxidising agent in chemical industries and a disinfectant for drinking water.
Also asked from this topic: the gas released by bleaching powder that bleaches and disinfects (chlorine); another use of bleaching powder (disinfecting drinking water).
Acids, Bases and Salts · pH scale and its importance

Q24. As the concentration of hydronium ions increases, the pH value _______.

  1. (a) decreases
  2. (b) decreases and then increases
  3. (c) remains the same
  4. (d) increases
Answer & solution

Answer: (a) decreases

Answer: Option 1 — decreases
pH measures the hydronium ion (H_(3)O^(+)) concentration on a reverse scale.
The higher the H_(3)O^(+) concentration, the more acidic the solution and the lower its pH.
Revision note — The pH scale
• pH — 'p' from German potenz (power); the scale runs from 0 (very acidic) to 14 (very alkaline).
• pH 7 = neutral (pure water); below 7 = acidic; above 7 = basic.
• pH = −log[H^(+)] — each fall of 1 in pH means 10 times more H^(+) ions.
• In water, H^(+) cannot exist alone; it joins water: H^(+) + H_(2)O → H_(3)O^(+).
• Common values: gastric juice ~1–2, lemon juice ~2.5, blood ~7.4, milk of magnesia ~10.
• Tooth decay starts when the mouth pH falls below 5.5; rain with pH below 5.6 is acid rain.
Also asked from this topic: what a higher hydrogen ion concentration gives (a lower pH); the ion formed when H^(+) joins water (hydronium ion); the pH of soap solution shows it is (basic, about 9).
Chemical Reactions and Equations · Oxidation, reduction and redox reactions

Q25. What happens when zinc (Zn) reacts with hydrochloric acid (HCl)?

  1. (a) Zinc is reduced.
  2. (b) Zinc is oxidised.
  3. (c) Both Zinc and Hydrogen are oxidised.
  4. (d) Hydrogen is oxidised.
Answer & solution

Answer: (b) Zinc is oxidised.

Answer: Option 2 — Zinc is oxidised.
Zn + 2HCl → ZnCl_(2) + H_(2)↑
Zinc loses 2 electrons to become Zn²⁺ in ZnCl_(2), so zinc is oxidised.
The H⁺ ions of the acid gain those electrons and become H_(2) gas — hydrogen is reduced.
Revision note — Oxidation and reduction
• Oxidation = gain of oxygen / loss of hydrogen / loss of electrons.
• Reduction = loss of oxygen / gain of hydrogen / gain of electrons (OIL RIG: Oxidation Is Loss, Reduction Is Gain).
• A redox reaction has oxidation and reduction happening together.
• The substance that is oxidised is the reducing agent (here Zn); the one reduced is the oxidising agent (here HCl / H⁺).
• This is also a displacement reaction — the more reactive zinc displaces hydrogen from the acid.
• Metals above hydrogen in the reactivity series give H_(2) with dilute acids; the gas burns with a pop sound.
Do not mix these up
• Oxidised vs oxidising agent — zinc is oxidised, so it is the reducing agent, not the oxidising agent.
Also asked from this topic: the type of reaction when zinc reacts with dilute hydrochloric acid (displacement reaction); in CuO + H_(2) → Cu + H_(2)O, the substance oxidised (hydrogen).

Economics (1)

Basic Concepts and Economic Systems · Factors of production and returns

Q26. At which of the following points does each firm employ labour?

  1. (a) Each firm employs labour up to the point where the marginal cost of labour equals the wage rate.
  2. (b) Each firm employs labour up to the point where the marginal revenue product of labour minus the wage rate.
  3. (c) Each firm employs labour up to the point where the marginal revenue product of labour multiplies the wage rate.
  4. (d) Each firm employs labour up to the point where the marginal revenue product of labour equals the wage rate.
Answer & solution

Answer: (d) Each firm employs labour up to the point where the marginal revenue product of labour equals the wage rate.

Answer: Option 4 — Each firm employs labour up to the point where the marginal revenue product of labour equals the wage rate.
An extra worker adds MRP_(L) to revenue and costs the wage rate (W).
The firm keeps hiring while MRP_(L) > W and stops where MRP_(L) = W — that is where profit is highest.
Revision note — Demand for labour by a firm
• Marginal product of labour (MP_(L)) = extra output from one more worker.
• Marginal revenue product (MRP_(L)) = MR × MP_(L); under perfect competition MR = price, so it is also called VMP_(L) = P × MP_(L).
• Profit-maximising rule for hiring: MRP_(L) = wage rate.
• In a perfectly competitive labour market each firm is a wage taker — the wage is fixed by market demand and supply of labour.
• The MRP_(L) curve is the firm's demand curve for labour; it slopes downward because of diminishing marginal returns.
• The four factors of production and their rewards: land → rent, labour → wages, capital → interest, entrepreneur → profit.
Do not mix these up
• MRP_(L) = W (hiring labour) vs MR = MC (choosing output) — the first decides how many workers, the second how much to produce; both are the same profit-maximising logic.
Also asked from this topic: a feature of a perfectly competitive market (free entry and exit of firms).

Current Affairs (5)

Economy, Banking and Business · Energy and power sector - current

Q27. India has reduced the windfall tax on crude oil to ₹______ per metric tonne from ₹4,600, effective 17 August 2024.

  1. (a) 2,600
  2. (b) 1,800
  3. (c) 3,600
  4. (d) 2,100
Answer & solution

Answer: (d) 2,100

Answer: Option 4 — 2,100
In its fortnightly review the Government cut the windfall tax on domestically produced crude oil from ₹4,600 to ₹2,100 per tonne, effective 17 August 2024.
Revision note — Windfall tax on crude oil
• A windfall tax is a tax on abnormal (unexpected) profits a firm earns from an outside shock, such as a spike in global crude prices.
• India introduced it on 1 July 2022, levied as a Special Additional Excise Duty (SAED) on domestic crude oil.
• Export duties on diesel, petrol and ATF were imposed alongside it.
• The rate was reviewed every fortnight in line with average international oil prices.
• The windfall tax was scrapped with effect from 2 December 2024.
Also asked from this topic: the rationale of a windfall tax (taxing excess profits from unforeseen external factors such as a global commodity price surge).
International Affairs and Summits · International organisations - current

Q28. NATO will establish a new land command in _________ near the Russian border in 2025 to oversee northern European land operations during potential conflicts.

  1. (a) Turkmenistan
  2. (b) Ukraine
  3. (c) Kyrgyzstan
  4. (d) Finland
Answer & solution

Answer: (d) Finland

Answer: Option 4 — Finland
NATO decided in October 2024 to set up a new Multi-Corps Land Component Command in Finland (at Mikkeli), to oversee land operations in northern Europe from 2025.
Finland has the longest border with Russia of any NATO member (about 1,340 km).
Revision note — NATO
• NATO (North Atlantic Treaty Organization) was founded by the Washington Treaty on 4 April 1949, with 12 founding members.
• Headquarters: Brussels, Belgium.
• Article 5 — an attack on one member is an attack on all (collective defence); invoked only once, after 9/11 (2001).
• Finland joined on 4 April 2023 as the 31st member; Sweden joined on 7 March 2024 as the 32nd.
• Mark Rutte (former Dutch PM) became Secretary General on 1 October 2024, succeeding Jens Stoltenberg.
• Ukraine, Turkmenistan and Kyrgyzstan are not NATO members.
International Affairs and Summits · Summits and conferences

Q29. What was the venue of the 13^(th) Ministerial Conference of the World Trade Organization in 2024?

  1. (a) London, England
  2. (b) Paris, France
  3. (c) Abu Dhabi, United Arab Emirates
  4. (d) New Delhi, India
Answer & solution

Answer: (c) Abu Dhabi, United Arab Emirates

Answer: Option 3 — Abu Dhabi, United Arab Emirates
The 13th Ministerial Conference (MC13) of the World Trade Organization was held in Abu Dhabi, UAE.
It ran from 26 February to 2 March 2024.
Revision note — WTO and its Ministerial Conferences
• The Ministerial Conference is the highest decision-making body of the WTO; it meets usually once every two years.
• WTO was set up on 1 January 1995, replacing GATT (1947); headquarters Geneva, Switzerland.
• MC12 was held in Geneva (June 2022) — it adopted the Agreement on Fisheries Subsidies.
• MC13 (Abu Dhabi) was chaired by UAE Trade Minister Thani bin Ahmed Al Zeyoudi; the accession of Comoros and Timor-Leste was approved there.
• First Ministerial Conference: Singapore (1996); the only one in Africa before 2026: MC10, Nairobi (2015).
• Director-General: Ngozi Okonjo-Iweala (Nigeria) — the first woman and first African to head the WTO.
• As of 2026: MC14 was held in Yaoundé, Cameroon, in March 2026.
Also asked from this topic: the country that hosted the 14th WTO Ministerial Conference in March 2026 (Cameroon — Yaoundé).
Science, Technology and Space - Current · Technology launches and AI

Q30. What is the name (acronym) of the software developed by ISRO, through its Vikram Sarabhai Space Centre (VSSC), a Computational Fluid Dynamics (CFD) tool aimed at facilitating aerodynamic design and analysis for aerospace vehicles?

  1. (a) PraYoGa
  2. (b) PraViNa
  3. (c) PraNaMa
  4. (d) PraVaHa
Answer & solution

Answer: (d) PraVaHa

Answer: Option 4 — PraVaHa
PraVaHa (Parallel RANS Solver for Aerospace Vehicle Aero-thermo-dynamics) is a Computational Fluid Dynamics (CFD) software.
It was developed by ISRO's Vikram Sarabhai Space Centre (VSSC), Thiruvananthapuram.
It simulates air flow over launch vehicles, winged bodies and re-entry capsules, cutting down costly wind-tunnel tests.
Revision note — ISRO, VSSC and indigenous space software
• VSSC, Thiruvananthapuram is ISRO's lead centre for launch vehicles — SLV, PSLV, GSLV and LVM3 are designed there.
• PraVaHa can analyse both aeroplanes (winged bodies) and rockets / re-entry capsules (non-winged bodies).
• It is used in the Gaganyaan human spaceflight programme to study the aerodynamics of the crew module and launch vehicle.
• CFD = solving the equations of fluid flow on a computer to find pressure, drag and heating on a body.
• ISRO was formed on 15 August 1969 from INCOSPAR (1962); Vikram Sarabhai is the father of the Indian space programme.
• Launches take place from Satish Dhawan Space Centre, Sriharikota (Andhra Pradesh).
Also asked from this topic: the main role of VSSC (designs and builds launch vehicles); the first Chairman of ISRO (Vikram Sarabhai).
Sports - Current · Cricket - current

Q31. Which team clinched the Irani Cup title for the season 2024-25?

  1. (a) Railways
  2. (b) Rest of India
  3. (c) Karnataka
  4. (d) Mumbai
Answer & solution

Answer: (d) Mumbai

Answer: Option 4 — Mumbai
Mumbai, the 2023-24 Ranji Trophy champions, won the Irani Cup 2024-25 against Rest of India at Lucknow in October 2024.
The match was drawn and Mumbai took the title on the first-innings lead, helped by Sarfaraz Khan's double century.
Revision note — Irani Cup and Indian domestic cricket
• The Irani Cup is played between the Ranji Trophy champion and a Rest of India XI.
• It is named after Z. R. Irani, a long-time BCCI official; it began in 1959-60.
• This was Mumbai's 15th Irani Cup title and its first since 1997-98.
• The Ranji Trophy (from 1934-35) is India's premier first-class tournament, named after K. S. Ranjitsinhji; Mumbai has the most titles.
• Other BCCI domestic events: Duleep Trophy (zonal first-class), Vijay Hazare Trophy (one-day), Syed Mushtaq Ali Trophy (T20).
• All these domestic tournaments are organised by the BCCI.
Do not mix these up
• Irani Cup vs Ranji Trophy — the Ranji Trophy is the national championship; the Irani Cup is a one-off match between its winner and Rest of India.
Also asked from this topic: the most successful team in Ranji Trophy history (Mumbai); the winner of the first Ranji Trophy in 1934-35 (Bombay); the body that organises the Ranji Trophy (BCCI).

Physics (9)

Electricity · Heating effect of current and Joule's law

Q32. If the resistance of a conductor is doubled while the current remains the same, how will the heat produced per unit time change?

  1. (a) It will quadruple.
  2. (b) It will remain the same.
  3. (c) It will be halved.
  4. (d) It will double.
Answer & solution

Answer: (d) It will double.

Answer: Option 4 — It will double.
By Joule's law of heating, H = I²Rt.
With the current and time unchanged, H is directly proportional to R.
So doubling R doubles the heat produced per unit time.
Revision note — Heating effect of electric current
• Joule's law: H = I²Rt — heat is proportional to I², to R and to t.
• Doubling the current makes the heat four times (because of I²).
• At a fixed voltage use H = V²t/R — there, doubling R halves the heat.
• Heating elements use nichrome (nickel–chromium alloy): high resistivity and high melting point.
• Bulb filaments are tungsten (melting point about 3380 °C); bulbs are filled with inert argon/nitrogen.
• An electric fuse works on the heating effect; its wire has a low melting point and is connected in series.
Do not mix these up
• Same current vs same voltage — with same current, heat ∝ R; with same voltage, heat ∝ 1/R.
Also asked from this topic: heat produced when the current is doubled (four times); the SI unit of heat produced in a resistor (joule); why nichrome is used in heaters (high resistivity and high melting point).
Human Eye and the Colourful World · Prism and dispersion of light

Q33. What is the angle formed between two lateral faces of a triangular glass prism called?

  1. (a) Angle of incidence
  2. (b) Angle of deviation
  3. (c) Angle of refraction
  4. (d) Angle of the prism
Answer & solution

Answer: (d) Angle of the prism

Answer: Option 4 — Angle of the prism
A triangular glass prism has two triangular bases and three rectangular lateral faces.
The angle between the two lateral faces through which light enters and leaves is the angle of the prism (refracting angle).
Revision note — Refraction through a glass prism
• The angle between the incident ray and the emergent ray is the angle of deviation.
• Light bends towards the base of the prism after passing through it.
• White light splits into seven colours (VIBGYOR) — dispersion; the band of colours is a spectrum.
• Violet bends the most, red the least, because each colour has a different speed (refractive index) in glass.
• Isaac Newton first used a glass prism to obtain the spectrum of sunlight; a second inverted prism recombines the colours into white light.
• A rainbow is a natural spectrum formed by water droplets acting like tiny prisms.
Do not mix these up
• Angle of the prism vs angle of deviation — the first is between the two faces (a property of the prism); the second is between incident and emergent rays.
Also asked from this topic: the angle between incident and emergent rays (angle of deviation); formation of a spectrum by a prism (dispersion); who first explained the dispersion of white light (Isaac Newton).
Electricity · Resistance, resistivity and their factors

Q34. The measure of how much a material resists the flow of charges is known as:

  1. (a) power generated
  2. (b) potential difference
  3. (c) current
  4. (d) resistivity
Answer & solution

Answer: (d) resistivity

Answer: Option 4 — resistivity
Resistivity (ρ) is the property of a material that measures how strongly it opposes the flow of charges.
It depends only on the material and its temperature, not on the wire's length or thickness.
Revision note — Resistance and resistivity (Class 10)
• R = ρL/A — resistance rises with length (L) and falls with area of cross-section (A).
• SI unit of resistivity: ohm-metre (Ω m); of resistance: ohm (Ω).
• Resistivity = resistance of a conductor of unit length and unit cross-sectional area.
• Metals have low resistivity (10^(−8) Ω m range); insulators like glass and rubber very high (10^(12)–10^(17) Ω m).
• Alloys (nichrome, manganin) have higher resistivity than their metals and do not oxidise easily — used in heating elements.
• For metals, resistivity increases with temperature.
Do not mix these up
• Resistance vs resistivity — resistance depends on the wire's size and shape; resistivity is fixed for a material at a given temperature.
Also asked from this topic: the resistance of a conductor of unit length and unit area (resistivity); resistance when a wire is stretched to double length (four times).
Light - Reflection and Mirrors · Convex mirror - image formation and uses

Q35. In a convex mirror, the principal focus is located _____.

  1. (a) behind the mirror
  2. (b) in front of the mirror
  3. (c) at the centre of curvature
  4. (d) at the pole of the mirror
Answer & solution

Answer: (a) behind the mirror

Answer: Option 1 — behind the mirror
A convex mirror makes parallel rays diverge; the reflected rays only appear to come from a point behind the mirror.
So its principal focus is virtual and lies behind the mirror, midway between the pole and the centre of curvature.
Revision note — Spherical mirror terms (Class 10)
• Pole (P) — centre of the reflecting surface; principal axis — line through P and C.
• Centre of curvature (C) — centre of the sphere of which the mirror is a part; radius of curvature R = PC.
• Focal length f = R/2.
• Concave mirror: focus is real, in front of the mirror (rays actually meet there).
• Convex mirror: focus and C are behind the mirror; image always virtual, erect, diminished.
• Sign convention: f is negative for concave and positive for convex mirrors.
Also asked from this topic: where a parallel beam appears to diverge from for a convex mirror of R = 50 cm (25 cm behind the mirror); the nature of image in a convex mirror (virtual and diminished).
Light - Reflection and Mirrors · Concave mirror - image formation and uses

Q36. Where does the image form when an object is positioned at the centre of curvature of a concave mirror?

  1. (a) At the centre of curvature
  2. (b) At the pole
  3. (c) At the focal point
  4. (d) At infinity
Answer & solution

Answer: (a) At the centre of curvature

Answer: Option 1 — At the centre of curvature
With the object at C, the image forms at C itself — real, inverted and the same size as the object.
By the mirror formula, u = −2f gives v = −2f.
Revision note — Image formation by a concave mirror (Class 10)
• Object at infinity → image at F, highly diminished, real, inverted.
• Beyond C → between F and C, diminished, real, inverted.
• At C → at C, same size, real, inverted.
• Between C and F → beyond C, enlarged, real, inverted.
• At F → at infinity, highly enlarged.
• Between P and F → behind the mirror, enlarged, virtual and erect (shaving / make-up mirror).
Also asked from this topic: the image when the object is between C and F (real, inverted, enlarged beyond C); where to keep the face in a shaving mirror (between P and F).
Electricity · Resistance, resistivity and their factors

Q37. Which of the following materials will have the least resistance at room temperature?

  1. (a) Nichrome
  2. (b) Copper
  3. (c) Iron
  4. (d) Aluminum
Answer & solution

Answer: (b) Copper

Answer: Option 2 — Copper
Among the four, copper has the lowest resistivity (about 1.62 × 10^(−8) Ω m), so for the same size it offers the least resistance.
Revision note — Resistivity of materials at 20 °C (NCERT table)
• Silver 1.60 × 10^(−8) Ω m — the best conductor.
• Copper 1.62 × 10^(−8) Ω m — used for household wiring.
• Aluminium 2.63 × 10^(−8) Ω m — used in overhead transmission lines (light and cheap).
• Iron 10.0 × 10^(−8) Ω m.
• Nichrome (Ni–Cr–Mn–Fe alloy) about 100 × 10^(−8) Ω m — heating elements.
• Manganin and constantan — alloys with high resistivity used in standard resistors.
Do not mix these up
• Copper vs aluminium — aluminium is used for long transmission lines because it is lighter and cheaper, not because it conducts better; copper conducts better.
Also asked from this topic: the wire with lower resistance between copper and iron of the same size (copper); why copper is used in household wiring (low resistance).
Magnetism and Magnetic Effects of Current · Magnetic field and field lines

Q38. Which of the following options is INCORRECT with relation to the given statement?The magnetic field lines of a bar magnet may be drawn using:

  1. (a) another bar magnet
  2. (b) wood particles
  3. (c) iron filings
  4. (d) a magnetic compass
Answer & solution

Answer: (b) wood particles

Answer: Option 2 — wood particles
Wood is a non-magnetic material, so its particles do not line up along a magnetic field.
Iron filings and a compass needle are magnetic, so they show the field pattern.
Revision note — Magnetic field lines
• Field lines of a bar magnet are traced with iron filings or by marking the positions of a compass needle step by step.
• Outside the magnet the lines run from the north pole to the south pole; inside, from south to north — they are closed curves.
• No two field lines ever cross — at one point the field has only one direction.
• Where lines are closer together, the field is stronger — crowded near the poles.
• The tangent to a field line gives the field's direction; a compass needle points along it.
• SI unit of magnetic field: tesla (T).
Also asked from this topic: what closely spaced field lines show (a stronger magnetic field); the shape of field lines inside a current-carrying solenoid (parallel straight lines).
Electricity · Resistors in series and parallel

Q39. Which of the following is correct with regard to resistances in a series circuit?

  1. (a) Total resistance is equal to the sum of all individual resistances.
  2. (b) Total resistance is equal to the product of all resistances.
  3. (c) Total resistance is less than any individual resistance.
  4. (d) Total resistance is inversely proportional to each resistance.
Answer & solution

Answer: (a) Total resistance is equal to the sum of all individual resistances.

Answer: Option 1 — Total resistance is equal to the sum of all individual resistances.
In series the same current passes through each resistor one after another.
So the resistances add up: R = R_(1) + R_(2) + R_(3).
Revision note — Series and parallel combinations
• Series — same current through every resistor; the potential difference divides among them.
• Series total resistance is greater than the largest single resistance.
• Parallel — same potential difference across each resistor; the current divides.
• Parallel: 1/R = 1/R_(1) + 1/R_(2) + 1/R_(3) — total is less than the smallest resistance.
• Domestic wiring uses parallel — each appliance gets full voltage and can be switched independently.
• In series, if one bulb fuses the whole circuit breaks.
Do not mix these up
• Series vs parallel — series keeps current the same; parallel keeps voltage the same.
Also asked from this topic: why resistors are joined in series (to increase total resistance and limit current); current when 3 Ω, 2 Ω and 1 Ω in series are joined to 9 V (1.5 A).
Light - Reflection and Mirrors · Concave mirror - image formation and uses

Q40. How can you experimentally determine the focal length of a concave mirror?

  1. (a) Measure the angle of reflection.
  2. (b) Measure the distance between the mirror and the image of a distant object formed by it.
  3. (c) Measure the diameter of the mirror.
  4. (d) Measure the distance between the pole and the centre of curvature.
Answer & solution

Answer: (b) Measure the distance between the mirror and the image of a distant object formed by it.

Answer: Option 2 — Measure the distance between the mirror and the image of a distant object formed by it.
Rays from a distant object (a far tree, the Sun) arrive almost parallel to the principal axis.
A concave mirror brings parallel rays to a point at its principal focus, so the sharp image on a screen lies at F.
The mirror-to-screen distance is therefore the focal length.
Revision note — Concave mirror and focal length
• Object at infinity ⇒ image at F, real, inverted and highly diminished (point-sized).
• Focal length f = R/2, where R is the radius of curvature; F lies midway between P and C.
• Object at C ⇒ image at C, real, inverted, same size.
• Object between P and F ⇒ image virtual, erect, magnified, behind the mirror (shaving / make-up mirror).
• Concave mirrors converge light, so they are used in solar furnaces, torches / headlights (bulb at F) and by dentists.
• Sign convention: f of a concave mirror is negative.
Do not mix these up
• Focal length vs radius of curvature — the pole-to-C distance is R = 2f, not f.
Also asked from this topic: why concave mirrors are used in solar furnaces (they converge sunlight to the focus); object position for a virtual, erect, magnified image (between P and F).

Medieval History (1)

Mughal Empire · Humayun and Sher Shah Suri

Q41. Who among the following was the ruler of Gujarat when Humayun attacked the kingdom in 1532?

  1. (a) Sikandar Shah
  2. (b) Zafar Khan Muzaffar
  3. (c) Muzaffar Shah ll
  4. (d) Bahadur Shah
Answer & solution

Answer: (d) Bahadur Shah

Answer: Option 4 — Bahadur Shah
Bahadur Shah of the Muzaffarid dynasty ruled Gujarat (1526–1537).
His growing power and his shelter to Humayun's rivals led Humayun to march against him.
Humayun defeated him at Mandsaur and took Mandu and Champaner (1535).
Revision note — Humayun's reign (1530–1540, 1555–1556)
• Eldest son of Babur; succeeded in 1530; built the city Dinpanah in Delhi.
• Campaign against Bahadur Shah of Gujarat (1532–1535): Mandu and Champaner captured, but Gujarat soon lost again.
• Defeated by Sher Khan (Sher Shah Suri) at Chausa (1539) and Kannauj / Bilgram (1540); went into exile in Persia.
• Regained Delhi after the Battle of Sirhind (1555) with Persian help.
• Died in 1556 after a fall from the stairs of his library Sher Mandal in Purana Qila; Humayun's Tomb built by his widow Hamida Banu Begum.
• His sister Gulbadan Begum wrote Humayun-nama.
Do not mix these up
• Bahadur Shah of Gujarat vs Bahadur Shah Zafar — the first fought Humayun in the 1530s; Zafar was the last Mughal emperor, leader of the 1857 revolt.
Also asked from this topic: who founded the Sur Empire after defeating Humayun (Sher Shah Suri); the battles of Humayun's defeat (Chausa 1539, Kannauj 1540).

Geography (2)

India - Location, Physiography and Neighbours · Himalayas - ranges and peaks

Q42. Which of the following statements are correct with respect to Arunachal Himalaya?Statement 1: These extend from the east of the Bhutan Himalayas up to the Diphu pass in the east.Statement 2: The general direction of the mountain range is from southwest to northeast.Statement 3: Some of the important mountain peaks of the region are K2 and Annapurna.Statement 4: These ranges are dissected by fast-flowing rivers from the north to the south, forming deep gorges.

  1. (a) Statements 2, 3 and 4 are correct.
  2. (b) Statements 1, 2 and 3 are correct.
  3. (c) Statements 1, 2 and 4 are correct.
  4. (d) Only statements 2 and 3 are correct.
Answer & solution

Answer: (c) Statements 1, 2 and 4 are correct.

Answer: Option 3 — Statements 1, 2 and 4 are correct.
Statement 3 is wrong: K2 is in the Karakoram and Annapurna is in Nepal.
The main peaks of the Arunachal Himalaya are Kangtu and Namcha Barwa.
Revision note — Arunachal Himalaya
• Extends from the east of the Bhutan Himalaya up to the Diphu pass in the east.
• General direction of the ranges: south-west to north-east.
• Fast rivers cut the ranges from north to south, forming deep gorges.
• The Brahmaputra flows through a deep gorge after crossing Namcha Barwa.
• Main rivers: Kameng, Subansiri, Dihang, Dibang, Lohit.
• Tribes from west to east: Monpa, Daphla, Abor, Mishmi, Nishi, Nagas; jhumming (shifting cultivation) is practised.
Do not mix these up
• Direction of the Himalaya — NW–SE in Kashmir and Himachal, east–west in Nepal and Sikkim, SW–NE in Arunachal, north–south in Manipur and Mizoram.
Also asked from this topic: the tri-junction of India, China and Myanmar in eastern Arunachal Pradesh (Diphu Pass); the peak marking the eastern end of the Great Himalaya (Namcha Barwa).
India - Transport and Communication · Inland waterways

Q43. Which of the following waterways is located on the Tapi river?

  1. (a) NW-1
  2. (b) NW-10
  3. (c) NW-91
  4. (d) NW-100
Answer & solution

Answer: (d) NW-100

Answer: Option 4 — NW-100
National Waterway 100 is on the Tapi (Tapti) river, declared under the National Waterways Act, 2016.
Revision note — National Waterways of India
• The National Waterways Act, 2016 raised the number of national waterways from 5 to 111.
• NW-1: Ganga–Bhagirathi–Hooghly, Prayagraj to Haldia (about 1,620 km, the longest).
• NW-2: Brahmaputra, Sadiya to Dhubri (891 km); NW-3: West Coast Canal (Kerala).
• NW-4: Krishna–Godavari system with canals; NW-5: Brahmani–Mahanadi delta with East Coast Canal.
• NW-10 is on the Amba river and NW-91 on the Shastri river–Jaigad creek (both Maharashtra); the Narmada is NW-73.
• National waterways are developed and regulated by the Inland Waterways Authority of India (IWAI), set up in 1986, headquarters Noida.
Do not mix these up
• Tapi vs Narmada — both flow west to the Arabian Sea; Tapi is NW-100, Narmada is NW-73.
Also asked from this topic: the river system of National Waterway 1 (Ganga–Bhagirathi–Hooghly); the body that develops and regulates national waterways (Inland Waterways Authority of India).

Modern History (1)

Rise of Nationalism and Indian National Congress · Foundation of the INC (1885)

Q44. The first President of the Indian National Congress was __________.

  1. (a) Womesh Chandra Banerjee
  2. (b) Ras Behari Bose
  3. (c) Dada Bhai Naoroji
  4. (d) Gopal Krishna Gokhale
Answer & solution

Answer: (a) Womesh Chandra Banerjee

Answer: Option 1 — Womesh Chandra Banerjee
Womesh Chandra Bonnerjee, a Calcutta barrister, presided over the first session of the Indian National Congress at Bombay in December 1885.
Revision note — Early Congress
• The INC was founded in 1885 by A. O. Hume, a retired British civil servant.
• First session: 28–31 December 1885, Gokuldas Tejpal Sanskrit College, Bombay, with 72 delegates; it was shifted from Pune because of cholera.
• 2nd session 1886, Calcutta — president Dadabhai Naoroji (first Parsi president).
• 3rd session 1887, Madras — Badruddin Tyabji (first Muslim president).
• 4th session 1888, Allahabad — George Yule (first British president).
• First woman president Annie Besant (1917, Calcutta); first Indian woman president Sarojini Naidu (1925, Kanpur).
Do not mix these up
• Founder vs first president — A. O. Hume founded the Congress; W. C. Bonnerjee was its first president.
Also asked from this topic: the city of the first INC session (Bombay); the first Muslim president of the INC (Badruddin Tyabji); the first woman president of the INC (Annie Besant).
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