Model Paper 1

1. (b) — CH₄, NH₃, H₂ and water vapour (boiling water) were sparked; amino acids formed. Free oxygen was deliberately absent: the early atmosphere was reducing.

2. (c) — insect and bird wings do the same job but have different origins (convergent evolution). The other pairs are built on one plan (homologous).

3. (d) — Ramapithecus remains (now referred to Sivapithecus) were found at Tinau Khola, Butwal, in 1980; the first find was in the Siwaliks of India (Lewis, 1932).

4. (a) — the water vascular (ambulacral) system with tube feet is unique to echinoderms (starfish, sea urchin).

5. (c) — notochord, dorsal hollow nerve cord and pharyngeal gill slits are the three chordate features; a vertebral column exists only in vertebrates, not in Amphioxus or tunicates.

6. (b) — flame cells are the protonephridia of flatworms (Planaria, Taenia, Fasciola). Annelids use nephridia.

7. (c) — Ascaris (Aschelminthes) has a pseudocoelom; Taenia is acoelomate, Pheretima is coelomate, Hydra is diploblastic.

8. (b) — microvilli multiply the absorptive surface of the intestine. The trachea has ciliated pseudostratified epithelium, the skin keratinized stratified squamous.

9. (a) — transitional epithelium lines the urinary bladder and ureters; alveoli and Bowman's capsule are simple squamous.

10. (d) — intercalated discs join cardiac fibres so the impulse spreads as one wave.

11. (b) — Haversian systems (osteons) with lamellae and lacunae are typical of mammalian compact bone; cartilage has no blood canals.

12. (c) — sporozoites from the mosquito's salivary glands enter the blood and go to the liver.

13. (d) — P. falciparum causes malignant tertian (cerebral) malaria. P. malariae causes quartan malaria; vivax and ovale cause benign tertian.

14. (a) — segments 14, 15 and 16 form the clitellum. The male genital pores are on segment 18.

15. (b) — the typhlosole is a mid-dorsal fold of the intestinal wall (from segment 26) that increases the absorbing area. Grinding is done by the gizzard.

16. (a) — the frog has 10 pairs of cranial nerves; man has 12.

17. (c) — the venae cavae open into the sinus venosus, which empties into the right auricle.

18. (a) — enterokinase activates trypsinogen to trypsin; pepsinogen is activated by HCl in the stomach.

19. (c) — fatty acids and monoglycerides are resynthesized into fats, packed as chylomicrons and enter the lacteals (lymph).

20. (d) — about 70 % travels as HCO₃⁻ (made by carbonic anhydrase in RBCs), about 20–23 % as carbaminohaemoglobin and about 7 % dissolved.

21. (a) — the respiratory rhythm centre is in the medulla; the pons fine-tunes it.

22. (b) — cardiac output = stroke volume × heart rate = 70 mL × 72 = 5040 mL ≈ 5.0 L min⁻¹.

23. (d) — the SA node in the right atrium generates the impulse; the AV node delays and relays it.

24. (b) — O is IᴼIᴼ, AB is IᴬIᴮ; every child gets Iᴼ from the father and Iᴬ or Iᴮ from the mother, so A (IᴬIᴼ) or B (IᴮIᴼ).

25. (c) — ADH (vasopressin) makes the distal tubule and collecting duct permeable to water via aquaporins.

26. (a) — all the glucose and amino acids and about two-thirds of the water and salt are reabsorbed in the PCT.

27. (d) — about −70 mV, inside negative, kept by the Na⁺–K⁺ pump and the high resting K⁺ permeability. +35 mV is near the peak of an action potential.

28. (b) — the fovea has only cones, packed densely; the blind spot has no photoreceptors at all.

29. (a) — without ADH the kidney cannot concentrate urine: large volumes of dilute urine. Insulin deficiency causes diabetes mellitus.

30. (c) — cretinism: stunted growth and mental retardation. Thyroxine deficiency in the adult is myxoedema.

31. (d) — each primary spermatocyte gives four spermatids by meiosis, each becoming one sperm: 25 × 4 = 100.

32. (d) — the high oestrogen of the late follicular phase triggers an LH surge, and ovulation follows about a day later.

33. (a) — the Widal test detects antibodies against Salmonella typhi antigens.

34. (b) — HIV binds CD4 on helper T cells; their fall below about 200 per mm³ marks AIDS.

35. (c) — IgG is about 75–80 % of serum antibody and the only class that crosses the placenta.

36. (d) — tetanus toxoid is inactivated toxin. BCG, OPV and measles vaccines are live attenuated.

37. (a) — amniotic fluid with fetal cells, taken at about 15–20 weeks, is cultured and karyotyped (e.g. Down's syndrome).

38. (c) — Bt makes a crystal (Cry) protein toxic to insect larvae; it is the bio-control agent behind Bt crops.

39. (d) — movement of a whole organism towards light is positive phototaxis; tropism is a growth movement of a fixed organ.

40. (b) — Chitwan National Park was established in 1973 (a World Heritage Site since 1984).

41. (c) — in sucrose the glucose C-1 and fructose C-2 (both anomeric carbons) are joined, so no free carbonyl reduces Fehling's solution. Maltose and lactose are reducing.

42. (b) — the inhibitor competes for the active site; raising the substrate concentration overcomes it.

43. (d) — Whittaker (1969): Monera, Protista, Fungi, Plantae, Animalia. Haeckel added Protista (three kingdoms), Copeland proposed four.

44. (a) — TMV is a rod of protein around single-stranded RNA (about 6400 nucleotides).

45. (c) — gametangial copulation of + and − strains gives a thick-walled zygospore; Mucor is a zygomycete (phycomycete).

46. (b) — one or more spiral, ribbon-shaped chloroplasts with pyrenoids. Cup-shaped is Chlamydomonas, star-shaped Zygnema, reticulate Oedogonium.

47. (a) — in bryophytes the gametophyte is dominant and free-living; the sporophyte (sporogonium) depends on it.

48. (c) — in gymnosperms the endosperm is the female gametophyte, formed before fertilization: haploid. Triploid endosperm is the angiosperm product of double fertilization.

49. (a) — six stamens, four long and two short (tetradynamous), cruciform corolla and siliqua: mustard family.

50. (d) — Liliaceae: P₃₊₃, A₃₊₃, G₍₃₎ superior, trilocular with axile placentation.

51. (b) — sarpagandha (Rauvolfia serpentina) roots yield reserpine, an antihypertensive. Neem is Azadirachta, tulasi Ocimum, ginger Zingiber.

52. (b) — the standing crop of phytoplankton is small at any moment though it reproduces fast, so the biomass of consumers can exceed it. The energy pyramid is always upright.

53. (d) — Nitrosomonas oxidizes NH₃ to NO₂⁻, Nitrobacter oxidizes NO₂⁻ to NO₃⁻. Pseudomonas denitrifies.

54. (c) — 1 DU is a layer of pure ozone 0.01 mm thick at STP; about 300 DU is normal.

55. (a) — crustose lichens secrete acids that weather rock and begin soil formation; mosses follow.

56. (b) — 70S (50S + 30S); eukaryotic cytoplasmic ribosomes are 80S (60S + 40S). Svedberg units do not add.

57. (d) — lysosomes hold acid hydrolases; if the membrane ruptures, the enzymes digest the cell (autolysis).

58. (d) — Singer and Nicolson (1972). Danielli–Davson gave the earlier sandwich model; Robertson the unit membrane.

59. (c) — crossing over happens at pachytene; synapsis starts at zygotene; chiasmata become visible at diplotene.

60. (b) — meiosis I separates homologues: chromosome number halves to 12, but each chromosome still has two sister chromatids until anaphase II.

61. (a) — A = T = 20 %, so G + C = 60 % and C = 30 %.

62. (d) — AUG is the start codon (methionine). UAA, UAG and UGA are stop codons.

63. (c) — AaBb gives four gametes in equal numbers; ab from the recessive parent lets each show: 1 : 1 : 1 : 1.

64. (a) — incomplete dominance: the genotype ratio 1 RR : 2 Rr : 1 rr appears directly as phenotypes.

65. (c) — her father gave her his X carrying the allele, so she is a carrier (XᶜX). Each son gets one of her X chromosomes: probability 1/2.

66. (d) — Klinefelter's (47, XXY): sterile male with some female traits. Turner's is 45, XO; Down's trisomy 21; Edwards' trisomy 18.

67. (b) — monocot stems have many scattered, closed (no cambium) bundles with a bundle sheath; dicot stems have a ring of open bundles.

68. (a) — radial bundles (xylem and phloem on alternate radii) are typical of roots.

69. (d) — large, thin-walled bulliform cells in the upper epidermis of grass leaves make the leaf roll in water stress.

70. (b) — Ψcell = −0.8 + 0.3 = −0.5 MPa, which is higher than −0.6 MPa outside; water moves from higher to lower water potential, out of the cell.

71. (c) — hydathodes at the leaf margins release liquid water under root pressure, at night when transpiration is low.

72. (a) — the oxygen-evolving complex of PS II splits water and replaces P680's electrons.

73. (c) — PEP carboxylase fixes CO₂ on PEP in the mesophyll to give oxaloacetate (the first stable product). RuBP is the acceptor of the Calvin cycle in the bundle sheath.

74. (d) — acetyl-CoA (2C) + oxaloacetate (4C) → citric acid (6C), hence "citric acid cycle".

75. (a) — gibberellins cause bolting in rosette plants and can replace a cold or long-day requirement.

76. (b) — 8 nuclei in 7 cells: egg, 2 synergids, 3 antipodals and the central cell with 2 polar nuclei.

77. (c) — Vallisneria (and Zostera) are pollinated by water. Salvia is insect-pollinated, maize wind-pollinated, Ficus by fig wasps.

78. (d) — totipotency is the basis of plant tissue culture. Heterosis is hybrid vigour.

79. (a) — restriction endonucleases cut DNA at specific recognition sites; ligase is the "molecular glue".

80. (b) — the cyanobacterium Anabaena azollae in Azolla's leaf cavities fixes atmospheric nitrogen. Rhizobium lives in legume nodules.

81. (c) — 4.4 g CO₂ = 0.1 mol; each CO₂ holds 2 O atoms, so 0.2 mol O = 0.2 × 6.02 × 10²³ = 1.2 × 10²³ atoms. Option (a) counts only the molecules.

82. (b) — moles: C 40/12 = 3.33, H 6.7/1 = 6.7, O 53.3/16 = 3.33; divide by the smallest (3.33) → C : H : O = 1 : 2 : 1 → CH₂O. (This is the empirical formula of glucose; its molecular formula C₆H₁₂O₆ is a multiple of it.)

83. (d) — a subshell holds 2(2l + 1) electrons; l = 3 (an f subshell) gives 2 × 7 = 14.

84. (c) — l must satisfy 0 ≤ l ≤ n − 1; for n = 2 the largest allowed l is 1, so l = 2 is impossible.

85. (a) — all four have 10 electrons, so size falls as nuclear charge rises: Al (13 p⁺) pulls hardest, F (9 p⁺) least. More protons, same electrons → smaller ion.

86. (b) — S in SF₄ has 4 bond pairs + 1 lone pair (sp³d, trigonal bipyramidal electron geometry); the lone pair occupies an equatorial position, giving the see-saw shape. Square planar would need sp³d² with two lone pairs (as in XeF₄).

87. (d) — in salicylaldehyde the OH and the CHO are ortho neighbours, so the H-bond closes a stable 6-membered ring inside the molecule. Water, ammonia and ethanol bond between molecules. (o-Nitrophenol is the other classic example — it steam-distils while the para isomer does not.)

88. (c) — 2(+1) + 2x + 3(−2) = 0 → x = +2 (an average; the two S atoms are actually in different environments, but the paper asks the average). +4 is sulphite, +6 sulphate.

89. (a) — combined gas law: V₂ = V₁ × (P₁/P₂) × (T₂/T₁) = 200 × (1/0.5) × (400/300) = 533 mL. Temperatures must be in kelvin — using 27/127 gives the distractor (b).

90. (d) — 8 corners × 1/8 + 6 face centres × 1/2 = 1 + 3 = 4. (bcc = 2, simple cubic = 1.)

91. (b) — Kp = Kc(RT)^Δn with Δn = moles of gaseous products − reactants = 2 − 1 = 1.

92. (a) — for AgCl, Ksp = s², so s = √(1.6 × 10⁻¹⁰) = 1.26 × 10⁻⁵ mol L⁻¹. Option (c) wrongly halves Ksp instead of taking the root.

93. (c) — in acid, MnO₄⁻ + 8H⁺ + 5e⁻ → Mn²⁺ + 4H₂O: the change in oxidation number is 5, so the equivalent weight is M/5. (In neutral/faintly alkaline medium Mn goes +7 → +4 and it is M/3.)

94. (d) — for a first-order reaction the half-life is constant: 50 % in 30 min, 75 % (half of what is left again) in the next 30 min → 60 min. Option (b) treats the rate as zero-order.

95. (b) — E°cell = E°cathode − E°anode = (+0.34) − (−0.76) = +1.10 V. Copper reduces (cathode), zinc oxidizes (anode); a positive emf confirms the Daniell cell runs spontaneously as written.

96. (a) — ΔG = ΔH − TΔS < 0 needs T > ΔH/ΔS = 30000/100 = 300 K. With both ΔH and ΔS positive, the reaction is spontaneous only at high temperature.

97. (c) — 25 % left = two half-lives (100 → 50 → 25): 2 × 5730 = 11460 years.

98. (d) — O₃ + 2KI + H₂O → 2KOH + I₂ + O₂; the liberated iodine turns starch blue. Ozone acts as the oxidizing agent; nothing "reduces to iodide" — iodide is already the reduced form.

99. (b) — acidity rises down the group as the H–X bond weakens (HI easiest to break) and the larger anion spreads its charge; HF is the weakest despite being most polar, and it is only partially ionized in water.

100. (a) — Cu + 2H₂SO₄ → CuSO₄ + SO₂ + 2H₂O. Hot concentrated H₂SO₄ is an oxidizing acid: it is itself reduced to SO₂. Dilute H₂SO₄ does not attack copper at all (Cu is below H in the electrochemical series).

101. (c) — CO (and N₂O, H₂O) neither turn litmus nor form salts with acids or bases: neutral. CO₂ and SO₂ are acidic (give H₂CO₃, H₂SO₃ in water); CaO is basic.

102. (d) — flux + gangue (the rocky impurity) → slag, a fusible mass that floats and is tapped off, e.g. CaO (flux) + SiO₂ (acidic gangue) → CaSiO₃ (slag) in iron smelting.

103. (b) — the Downs cell electrolyzes a molten NaCl–CaCl₂ mixture (about 60 % : 40 %) at ~600 °C; CaCl₂ depresses the melting point from 801 °C and improves conductivity. Aqueous NaCl would give H₂ at the cathode instead of Na (the discharge potential of Na⁺ exceeds that of water).

104. (a) — Mn²⁺ is 3d⁵: five unpaired electrons. Fe²⁺ (3d⁶) has four, Cu²⁺ (3d⁹) one, Zn²⁺ (3d¹⁰) none. (Fe³⁺, also d⁵, ties with Mn²⁺ — it is deliberately not among the options.)

105. (c) — galvanization = a zinc coat. Zinc is more electropositive than iron, so even if the coat is scratched it corrodes sacrificially and the iron stays safe. Tin does the opposite: a scratched tin coat makes the iron rust faster.

106. (c) — the pump is an ATPase that pushes 3 Na⁺ out and 2 K⁺ in against their gradients per ATP hydrolysed — active transport, the basis of the resting membrane potential. The numbers are the classic 3 : 2.

107. (a) — Minamata disease: methyl mercury from a chemical plant's effluent, biomagnified through fish. Cadmium caused itai-itai disease; lead and arsenic have their own syndromes but not this one.

108. (c) — the longest chain has 5 carbons (pentane); numbering from either end puts the methyls on C-2 and C-3 → 2,3-dimethylpentane. Option (a) numbers from the wrong end; (b) does not choose the longest chain.

109. (b) — lactic acid, CH₃–CH(OH)–COOH, has a chiral carbon bonded to four different groups (H, OH, CH₃, COOH), so it exists as two enantiomers (the muscle form and the sour-milk form). Glycine has two H atoms on its α-carbon — achiral.

110. (d) — tertiary > secondary > primary > methyl: every extra alkyl group donates electrons (+I effect) and hyperconjugates, dispersing the positive charge.

111. (a) — peroxides make the addition go by a free-radical mechanism, so Br adds to the end carbon (anti-Markovnikov): CH₃CH₂CH₂Br. Without peroxide the ionic addition follows Markovnikov and gives 2-bromopropane. The peroxide effect is shown by HBr only — not HCl or HI.

112. (c) — iso-octane is the 100-point anti-knock reference; n-heptane, which knocks badly, is the 0-point reference.

113. (b) — a terminal alkyne has an acidic ≡C–H and gives a white precipitate of silver acetylide (RC≡CAg) with ammoniacal AgNO₃; an internal alkyne has no such H and does not react. Bromine water and KMnO₄ are decolorized by both.

114. (d) — SN1 rate follows carbocation stability: the tert-butyl cation (3°) forms most easily. (In SN2 the order reverses — methyl chloride is fastest — because of steric crowding.)

115. (a) — light-catalysed oxidation by air converts CHCl₃ to phosgene (COCl₂), a deadly gas; the dark bottle excludes light, the full bottle excludes air, and ethanol converts any phosgene formed to harmless diethyl carbonate.

116. (c) — hydroboration adds H–BH₂ across the double bond with boron to the less-substituted carbon (anti-Markovnikov), and oxidation replaces B with OH → propan-1-ol. Acid-catalysed hydration would give propan-2-ol.

117. (b) — the phenoxide ion delocalizes its negative charge into the ring (resonance structures at o and p carbons), so it is stable and phenol gives up H⁺ readily. Ethoxide has no such stabilization — the charge stays localized on O.

118. (d) — formaldehyde: no alkyl groups to push electrons onto the carbonyl carbon and no steric hindrance, so the nucleophile attacks most easily. Order: HCHO > CH₃CHO > CH₃COCH₃; benzaldehyde is further slowed by resonance stabilization of its C=O.

119. (a) — benzaldehyde has no α-hydrogen, so in concentrated base two molecules disproportionate: one is reduced to the alcohol, the other oxidized to the salt — the Cannizzaro reaction. Aldehydes with α-H (e.g. acetaldehyde) give aldol condensation instead.

120. (c) — the iodoform test is positive for a CH₃CO– group (methyl ketones) or CH₃CH(OH)– (which is first oxidized to it). Acetone (CH₃COCH₃) qualifies; benzophenone and formaldehyde have no CH₃CO; methanol has no CH₃CH(OH) — ethanol does.

121. (b) — each electronegative Cl pulls electron density away from the O–H bond (−I effect), stabilizing the anion; three Cl atoms beat two beat one. Trichloroacetic acid is one of the strongest simple carboxylic acids.

122. (d) — RMgX + H₂O → R–H + Mg(OH)X: the reagent is such a strong base that even water's weak acidity destroys it, which is why it is made in dry ether. "Making alkanes" is actually a use of this reaction.

123. (a) — in water: 2° > 1° > 3° > NH₃. Alkyl groups raise basicity (+I) but crowding and weaker hydration of the substituted ammonium ion lower it; for the methylamines the two effects balance with dimethylamine on top. (In the gas phase the order is simply 3° > 2° > 1°.)

124. (c) — RNH₂ + CHCl₃ + 3KOH → R–N≡C (isocyanide, foul smell) + 3KCl + 3H₂O. Only primary amines react — the test distinguishes them from 2° and 3° amines.

125. (b) — Haber: N₂ + 3H₂ ⇌ 2NH₃ (Fe catalyst, ~450–500 °C, 150–250 atm); Ostwald: NH₃ → HNO₃; Contact: SO₂ → SO₃ → H₂SO₄; Solvay: NaCl + NH₃ + CO₂ → Na₂CO₃.

126. (d) — Teflon is addition-polymerized tetrafluoroethylene, (CF₂=CF₂)n; the very strong C–F bonds make it chemically inert and non-stick. Vinyl chloride gives PVC; styrene gives polystyrene.

127. (a) — cobalt-60 γ-rays for radiotherapy. Carbon-14 dates fossils, sodium-24 traces blood flow and detects leaks, phosphorus-32 treats polycythemia and traces fertilizer uptake.

128. (c) — the fused mass's NaCN + FeSO₄ route makes ferrocyanide, which with Fe³⁺ gives ferro-ferricyanide Fe₄[Fe(CN)₆]₃ — Prussian blue. [Fe(H₂O)₅NO]²⁺ is the brown ring (nitrate); Fe(CNS)₃ is the blood-red colour of iron with thiocyanate.

129. (b) — nitrate + fresh FeSO₄, then concentrated H₂SO₄ down the side of the tube: a brown ring of [Fe(H₂O)₅NO]²⁺ at the junction confirms NO₃⁻.

130. (d) — Ca²⁺ brick red; Na golden yellow, K lilac (seen through cobalt glass), Ba apple green, Cu bluish green. Flame colours are a quick analytical test for the alkali and alkaline-earth metals.

131. (b) — from Newton's law of viscous flow, F = ηA(dv/dx): η = F/(A dv/dx) → [MLT⁻²]/([L²][T⁻¹]) = [ML⁻¹T⁻¹]. (Surface tension is [MT⁻²]; momentum [MLT⁻¹] is the distractor (a).)

132. (c) — fall time t = √(2h/g) = √(2×20/10) = 2 s; horizontal range = 10 × 2 = 20 m. The two motions are independent — the horizontal speed never affects the time of fall.

133. (a) — impulse = change of momentum = m(v − u) with the rebound opposite in sign: 0.1 × (10 − (−10)) = 2 N s. Forgetting the direction change gives the distractor 1 N s.

134. (d) — P = work/time = mgh/t = 100 × 9.8 × 10 / 20 = 490 W.

135. (c) — no external torque acts, so angular momentum L = Iω is conserved: I doubles → ω halves. (The kinetic energy ½Iω² also halves — the "missing" energy is spent in the inelastic grab.)

136. (b) — Bernoulli: p + ½ρv² + ρgh = constant along a streamline; at the same height a faster stream is a lower-pressure stream. This lift/pressure trade drives aeroplane lift, the Bunsen burner and a spinning ball's swing.

137. (d) — T = 2π√(l/g); with l fixed, T ∝ 1/√g. On the moon T = 2 × √6 ≈ 4.9 s — the pendulum swings nearly 2.5 times slower. A pendulum clock taken to the moon loses time.

138. (a) — for the frictionless design speed, tan θ = v²/(rg) = 400/(100 × 10) = 0.4. On a banked road the normal reaction's horizontal component supplies the centripetal force.

139. (c) — v_e = √(2GM/R) ∝ √(M/R): factor √(2 ÷ ½) = √4 = 2, so 2 × 11.2 = 22.4 km s⁻¹.

140. (b) — Y = FL/(AΔL) = (98 × 2)/(10⁻⁶ × 10⁻³) = 1.96 × 10¹¹ Pa — a steel-like value. Watch the conversions: 1 mm² = 10⁻⁶ m², 1 mm = 10⁻³ m.

141. (d) — Stefan–Boltzmann: E = σT⁴, so E₂/E₁ = 2⁴ = 16.

142. (a) — Wien's law: λ_m = b/T = 2.9 × 10⁻³/6000 = 4.83 × 10⁻⁷ m = 483 nm — in the blue-green, near the peak of the sun's spectrum, which is why our eyes are most sensitive there.

143. (c) — Δl = lαΔT = 1 × 2 × 10⁻⁵ × 100 = 2 × 10⁻³ m = 2 mm.

144. (b) — melt the ice: 100 × 80 = 8000 cal, then warm the water: 100 × 1 × 20 = 2000 cal; total 10000 cal = 10 kcal. Option (a) forgets the warming stage.

145. (d) — v_rms ∝ √T, so doubling v needs T₂ = 4T₁ = 4 × 300 = 1200 K = 927 °C. The trap is doubling the Celsius reading (54 °C) instead of the kelvin temperature.

146. (a) — first law: ΔU = Q − W = 200 − 150 = +50 J (Q in is positive, W done by the gas is positive).

147. (c) — η = 1 − T₂/T₁ = 1 − 300/400 = 0.25 = 25 %. Temperatures must be absolute; no real engine between these reservoirs can beat this.

148. (b) — a closed pipe sounds odd harmonics with fundamental f = v/4L = 340/(4 × 0.5) = 170 Hz. An open pipe of the same length would give v/2L = 340 Hz.

149. (d) — source approaching a stationary listener: f' = f·v/(v − v_s) = 500 × 340/320 = 531.25 ≈ 531 Hz. Approaching raises the pitch; the distractor 472 Hz is the receding case (v + v_s).

150. (a) — level in dB = 10 log₁₀(I/I₀); a factor 10 in intensity adds exactly 10 dB. (A factor 10 in pressure amplitude would add 20 dB.)

151. (c) — mirror formula with the Cartesian sign convention: 1/v + 1/u = 1/f → 1/v = 1/(−10) − 1/(−15) = −1/30 → v = −30 cm: real, inverted, 30 cm in front of the mirror, magnified ×2 (the object lies between F and C).

152. (d) — sin C = 1/μ = 1/1.5 = 0.667 → C = 41.8° ≈ 42°. Angles of incidence above this inside the glass are totally internally reflected — the principle of optical fibres.

153. (a) — lenses in contact add powers: P = +5 − 3 = +2 D, so f = 100/2 = +50 cm — still a converging combination.

154. (b) — β = λD/d = (600 × 10⁻⁹ × 1)/10⁻³ = 6 × 10⁻⁴ m = 0.6 mm.

155. (c) — Brewster's law: tan p = μ = 1.732 = √3 → p = 60°. At this angle the reflected ray is completely plane-polarized and reflected and refracted rays are 90° apart.

156. (d) — 1/R = 1/2 + 1/3 + 1/6 = (3 + 2 + 1)/6 = 1 → R = 1 Ω. A parallel combination is always smaller than the smallest member.

157. (a) — at balance P/Q = l/(100 − l) = 40/60 = 2/3. The metre bridge is the Wheatstone bridge with a 100 cm wire for the two ratio arms.

158. (c) — an ammeter needs a shunt: a low resistance in parallel that carries most of the current, keeping the total resistance small so the meter does not disturb the circuit. (A voltmeter is the opposite: a high resistance in series.)

159. (b) — F = BIL sin θ = 0.5 × 2 × 0.4 × 1 = 0.4 N (θ = 90°). Fleming's left-hand rule gives the direction.

160. (d) — B = μ₀NI/(2r) = (4π × 10⁻⁷ × 100 × 2)/(2 × 0.1) = 1.257 × 10⁻³ ≈ 1.26 × 10⁻³ T. Forgetting the N turns gives distractor (a).

161. (a) — above the Curie temperature thermal agitation breaks the domain alignment and the substance becomes paramagnetic; it turns ferromagnetic again on cooling. (Iron: 1043 K.)

162. (c) — Faraday: ε = N dΦ/dt = 500 × 0.01/0.1 = 50 V.

163. (b) — an ideal transformer conserves power: V_s/V_p = N_s/N_p = 1/20, so I_s = I_p × (N_p/N_s) = 1 × 20 = 20 A. Step down the voltage, step up the current.

164. (d) — f₀ = 1/(2π√(LC)) = 1/(2π√(10⁻³ × 10⁻⁶)) = 1/(2π × 3.16 × 10⁻⁵) ≈ 5033 Hz ≈ 5 kHz. At resonance X_L = X_C, impedance is minimum (just R) and current maximum.

165. (a) — F = (9 × 10⁹ × 2 × 10⁻⁶ × 3 × 10⁻⁶)/(0.3)² = 54 × 10⁻³/0.09 = 0.6 N, repulsive (like charges).

166. (c) — E = q/(4πε₀r²) = 9 × 10⁹ × 10⁻⁶/9 = 1000 V m⁻¹. (The potential at that point is 3000 V — E falls as 1/r², V as 1/r.)

167. (b) — Gauss's law counts only the enclosed charge: Φ = q/ε₀ through the whole closed surface, however it is shaped. Each of the six symmetric faces takes q/6ε₀ — but the question asks the total.

168. (d) — filling the gap with a dielectric multiplies the capacitance by K: C' = 4 × 10 = 40 pF. (If the battery stays connected Q rises too; if isolated, V falls to V/4.)

169. (a) — Millikan's oil-drop experiment (1909) balanced charged drops between plates and found every charge to be a multiple of e = 1.6 × 10⁻¹⁹ C — charge is quantized. Thomson measured e/m; Rutherford found the nucleus; Franck–Hertz confirmed discrete atomic energy levels.

170. (c) — e/m = 1.76 × 10¹¹ C kg⁻¹, from deflecting cathode rays in crossed E and B fields. Options (a) and (b) are e and m themselves — three numbers every candidate must know cold.

171. (b) — Einstein's equation: K_max = hc/λ − W = 1240/400 − 2.1 = 3.1 − 2.1 = 1.0 eV. Option (a) is the photon energy alone — the work function must come off first.

172. (d) — E_n = −13.6/n² eV: E₁ = −13.6, E₂ = −3.4; ΔE = 13.6 − 3.4 = 10.2 eV — the Lyman-α photon. Ionization from the ground state is the full 13.6 eV.

173. (a) — λ = h/mv = 6.63 × 10⁻³⁴/(9.1 × 10⁻³¹ × 10⁶) = 7.3 × 10⁻¹⁰ m ≈ 7.3 Å — the scale of X-rays and atomic spacings, which is why electrons can diffract from crystals.

174. (c) — BE = Δm × 931.5 = 0.0303 × 931.5 ≈ 28.2 MeV (≈ 7.05 MeV per nucleon — the peak of stability sits near iron at ~8.8 MeV/nucleon). 200 MeV (b) is the energy per uranium fission.

175. (b) — 30 days = three half-lives: 1 → 1/2 → 1/4 → 1/8 left undecayed (the other 7/8 has decayed).

176. (d) — cadmium (and boron) absorb neutrons strongly; sliding the control rods in or out sets the multiplication factor at exactly 1. The moderator (heavy water, graphite) — not cadmium — slows the neutrons.

177. (a) — boron has 3 valence electrons: each B atom creates a hole (an acceptor level), and holes are the majority carriers → p-type. A group V dopant (P, As) would give n-type.

178. (c) — NAND gives 0 only for 11; every other input pair gives 1. (NOR gives 1 only for 00.) NAND and NOR are the universal gates — any logic function can be built from either alone.

179. (b) — proton = uud (charge ⅔ + ⅔ − ⅓ = +1); neutron = udd (⅔ − ⅓ − ⅓ = 0). Beta decay is literally a d quark turning into a u quark.

180. (d) — the recession speed–distance proportionality (v = H₀d, from galactic redshifts) is the observational foundation of the expanding-universe picture and the Big Bang theory.

181. (c) — north then east makes a right angle: distance from home = √(3² + 4²) = √25 = 5 km (the classic 3-4-5 right triangle). Option (a) adds the two legs, which is the path walked, not the displacement.

182. (a) — "the only daughter of my mother" can only be the woman herself; so the man's mother is the woman — she is his mother. Work backwards from the speaker, one phrase at a time.

183. (c) — every letter moves +1: N→O, E→F, P→Q, A→B, L→M. So I→J, N→O, D→E, I→J, A→B: JOEJB.

184. (b) — 27 = 3³, 64 = 4³, 125 = 5³ are perfect cubes; 100 is not (it is 10²). Classification questions ask for the property the other three share.

185. (c) — total = left position + right position − 1 = 12 + 8 − 1 = 19 (Sita is counted in both positions, so subtract her once).

186. (a) — with expenditure fixed, consumption ∝ 1/price: the cut needed = (rise)/(100 + rise) × 100 = 25/125 × 100 = 20 %. Check: 100 × 1 → 125 × 0.8 = 100. ✔

187. (d) — for two equal halves the average speed is the harmonic mean 2xy/(x + y) = 2 × 30 × 60/90 = 40 km h⁻¹, not the arithmetic mean 45. Check: 120 km journey → 2 h + 1 h = 3 h → 120/3 = 40. ✔

188. (b) — let CP of one pen = Re 1. CP of 16 pens = 16; SP of 16 = CP of 20 = 20. Gain = 4 on a cost of 16 → 4/16 × 100 = 25 %. The gain is always reckoned on the cost of the sold quantity (16 pens), not on 20 — that is where option (a) comes from.

189. (c) — one day's work: 1/12 + 1/24 = 3/24 = 1/8 → together they finish in 8 days.

190. (a) — let the son be x: father = 3x. After 10 years 3x + 10 = 2(x + 10) → x = 10. Check: 10 and 30 now; 20 and 40 in ten years — exactly double. ✔

191. (d) — the terms are n(n + 1): 1×2, 2×3, 3×4, 4×5, 5×6, so next is 6×7 = 42. Equivalently the differences rise 4, 6, 8, 10, 12.

192. (b) — every letter advances 6 places: B→H→N→V, D→J→P→X, F→L→R→Z. The next term is VXZ.

193. (c) — from 1 to 26 January is 25 days; 25 = 3 weeks + 4 days, so the weekday advances by 4: Thursday → Friday → Saturday → Sunday → Monday.

194. (a) — angle = |30H − 5.5M| = |30 × 3 − 5.5 × 40| = |90 − 220| = 130°. The minute hand has passed the hour hand; 120° (b) is the angle at 4:00-style thinking that ignores the hour hand's 40-minute creep.

195. (d) — the third number is the product of the first two: 2×3 = 6, 4×5 = 20, so 3×7 = 21.

196. (b) — opposite faces of a standard die add to 7: top = 7 − 4 = 3.

197. (c) — a vertical mirror reverses left-right; the image is identical to the original when every letter has a vertical line of symmetry and the word reads the same reversed. M, O and M each mirror into themselves and MOM is a palindrome — so MOM is unchanged. N, E, P, A, I, D, T, H, S all tilt or flip the wrong way.

198. (a) — two folds stack the sheet into 4 layers; one punch goes through all 4, and each unfolding mirrors the holes across its fold line: 1 → 2 → 4 holes.

199. (d) — count by size: 9 squares of 1×1, 4 of 2×2, 1 of 3×3 → 9 + 4 + 1 = 14. In an n × n grid the total is 1² + 2² + … + n²; here 1 + 4 + 9 = 14.

200. (b) — 27 small cubes = a 3 × 3 × 3 cut. One-face-painted cubes are the centres of the six faces → 6. (Corners: 8 with three faces; edge middles: 12 with two faces; the single central cube: unpainted. 6 + 8 + 12 + 1 = 27 ✔.)