IOE Model Paper 2 (100 questions, 140 marks)

Chapter 3 · Full Model Papers · 100 questions in the paper · 11 min read

IOE Model Paper 2 (100 questions, 140 marks)

What the syllabus asks for 1
  • Mathematics 35, Physics 27, Chemistry 22, English 16, with an explained key

Instructions. Same pattern as Model Paper 1: 100 questions, 140 marks, 120 minutes; Section A questions 1–60 carry 1 mark, Section B questions 61–100 carry 2 marks; a wrong answer loses 10 % of the question's marks (-0.1 or -0.2); no penalty for an unanswered question. This paper is a little harder than Paper 1 in Section B and has different questions and numbers throughout. Constants: g=10 m s⁻², N_A=6.02\times10^{23}, R=8.314 J mol⁻¹ K⁻¹.

Subject Section A (1 mark) Section B (2 marks) Questions Marks
Mathematics 1–20 61–75 35 50
Physics 21–34 76–88 27 40
Chemistry 35–48 89–96 22 30
English 49–60 97–100 16 20

Score yourself: score =\text{(1 × right in A)}+\text{(2 × right in B)}-0.1\times\text{wrong in A}-0.2\times\text{wrong in B}. Take the paper in one sitting, then use the answer key below.

Section A — Mathematics (questions 1–20, 1 mark each)

  1. The number of terms in the expansion of (2x-3y)^7 isa7b9c6d8
  2. \dfrac{d}{dx}e^{3x} equalsa3e^{3x}b\frac{1}{3}e^{3x}ce^{3x}d3e^x
  3. The value of \sin75^\circ isa\frac{\sqrt{3}-1}{2\sqrt{2}}b\frac{1}{2}c\frac{\sqrt{3}+1}{2\sqrt{2}}d\frac{\sqrt{3}}{2}
  4. The distance between (1,2) and (4,6) isa7b5c25d3
  5. \displaystyle\int_1^e\frac{dx}{x} equalsa1bec0de-1
  6. The sum of the first 20 natural numbers isa200b190c420d210
  7. The determinant of (det | 2&-1 ; 4&3 |) isa2b6c10d14
  8. The value of i^{-1} isaib-ic1d-1
  9. The equation of the circle with centre at the origin and radius 3 isax^2+y^2=3bx^2+y^2=6cx^2-y^2=9dx^2+y^2=9
  10. The probability of getting at least one tail in two tosses of a fair coin isa3/4b1/4c1/2d1
  11. The derivative of x^3 at x=2 isa6b12c8d3
  12. If \vec a\cdot\vec b=0 for non-zero vectors, then they areaparallelbequalcperpendiculardopposite
  13. The mode of 2,3,3,4,5,3,6 isa3b4c5d2
  14. The value of \cos60^\circ+\sin30^\circ isa0b\frac{1}{2}c\frac{\sqrt{3}}{2}d1
  15. The value of \log_{10}1000 isa2b3c10d1000
  16. The slope of the tangent to y=x^2 at x=1 isa1b4c2d0
  17. If A,B are mutually exclusive with P(A)=0.3 and P(B)=0.4, then P(A\cup B) isa0.12b0.1c0.35d0.7
  18. The focus of the parabola x^2=4y isa(0,1)b(1,0)c(0,4)d(4,0)
  19. The number of diagonals of a hexagon isa6b12c9d15
  20. \displaystyle\lim_{x\to1}\frac{x^2-1}{x-1} equalsa0b2c1d\infty

Section A — Physics (questions 21–34, 1 mark each)

  1. The SI unit of power isajoulebnewtoncwattdpascal
  2. The SI unit of electric field strength isaN C⁻¹bN CcC N⁻¹dJ C
  3. The speed of light in vacuum isa3\times10^6 m s⁻¹b3\times10^7 m s⁻¹c3\times10^9 m s⁻¹d3\times10^8 m s⁻¹
  4. The specific heat capacity of water is nearlya420 J kg⁻¹ K⁻¹b4200 J kg⁻¹ K⁻¹c42000 J kg⁻¹ K⁻¹d42 J kg⁻¹ K⁻¹
  5. A ball is thrown vertically up at 20 m s⁻¹. The maximum height reached isa10 mb40 mc20 md5 m
  6. The current through a 4 Ω resistor connected to 12 V isa3 Ab48 Ac0.33 Ad8 A
  7. The focal length of a plane mirror isazerobequal to its radiuschalf its radiusdinfinite
  8. The frequency of the AC mains supply in Nepal isa60 Hzb50 Hzc100 Hzd25 Hz
  9. The electromagnetic radiation of the shortest wavelength among these isagamma raysbX-rayscultravioletdinfrared
  10. The weight of a 5 kg mass (g=10 m s⁻²) isa5 Nb500 Nc50 Nd0.5 N
  11. The gauge pressure at a depth of 10 m in water (\rho=1000, g=10) isa10^3 Pab10^4 Pac10^6 Pad10^5 Pa
  12. The wavelength of a 680 Hz sound in air (v=340 m s⁻¹) isa2 mb0.5 mc0.25 md1 m
  13. A lens of power +4 D has a focal length ofa25 cmb4 cmc40 cmd2.5 cm
  14. The number of neutrons in ^{238}_{92}U isa92b238c146d330

Section A — Chemistry (questions 35–48, 1 mark each)

  1. The number of neutrons in a ^{14}C atom isa6b8c14d12
  2. The gas liberated at the cathode during the electrolysis of acidified water isaO₂bCl₂cN₂dH₂
  3. The molecular formula of glucose isaC₆H₁₂O₆bC₁₂H₂₂O₁₁cC₂H₅OHdC₆H₆
  4. The hybridisation of sulphur in SF₆ isasp³bsp³dcsp³d²dsp²
  5. Which of these is an alkali metal?aMgbCacAldK
  6. The number of moles in 11.2 L of a gas at STP isa1b0.5c2d0.25
  7. The functional group –COOH is calledacarboxylic acidbaldehydecketonedester
  8. The pH of pure water at 25 °C isa0b14c7d1
  9. The noble gas with the lowest boiling point isaArbHecNedXe
  10. Soap is the sodium salt ofaglycerolbacetic acidcsulphuric acidda fatty acid
  11. The valency of aluminium isa1b2c3d4
  12. Rusting of iron requires oxygen andawaterbnitrogenchydrogendcarbon monoxide
  13. The shape of the methane molecule isaplanarbpyramidalclineardtetrahedral
  14. The metal obtained by the electrolysis of molten alumina isaironbaluminiumccopperdzinc

Section A — English (questions 49–60, 1 mark each)

  1. The books ___ on the table.aisbwascaredhas
  2. The word closest in meaning to "begin" isacommencebendcstopdhide
  3. The opposite of "increase" isagrowbraisecexpandddecrease
  4. He is good ___ drawing.ainbatcondwith
  5. Choose the correct spelling.anecessarybneccessarycnecesarydneccesary
  6. The word "important" has its primary stress on thea1st syllableb3rd syllablec2nd syllablednone
  7. Which word contains the voiceless /θ/ sound?athisbthatcthosedthink
  8. By the time he came, I ___ my homework.afinishbhad finishedchave finisheddfinishing
  9. She said, "I will help you." She said that she ___ help me.awillbcancwouldddid
  10. She prefers tea ___ coffee.atobthancoverdfrom
  11. "Once in a blue moon" meansaevery monthbvery rarelycneverddaily
  12. Neither of the twins ___ here.aarebwerechavedis

Section B — Mathematics (questions 61–75, 2 marks each)

  1. Two fair dice are thrown. The probability that the sum is 8 isa1/6b5/36c1/9d7/36
  2. \displaystyle\int_0^1xe^{x^2}dx equalsae-1be/2c(e+1)/2d(e-1)/2
  3. The area under y=\sin x from x=0 to x=\pi isa2b1c4d\pi
  4. The solution of \dfrac{dy}{dx}=2xy isay=Cx^2by=C+x^2cy=Ce^{x^2}dy=e^{2x}+C
  5. The line y=2x+c touches the parabola y^2=4x when c equalsa1b\frac{1}{2}c2d4
  6. The eccentricity of \dfrac{x^2}{16}+\dfrac{y^2}{7}=1 isa9/16b7/16c3/5d3/4
  7. The plane through (1,1,1) with normal vector (2,-1,3) isa2x-y+3z=4b2x-y+3z=6c2x+y-3z=0dx+y+z=3
  8. For \vec a=2\hat i+\hat j-\hat k and \vec b=\hat i-\hat j+2\hat k, |\vec a\times\vec b| isa\sqrt{11}b5c\sqrt{35}d\sqrt{26}
  9. For A=(det | 2&1 ; 5&3 |), the element in the second row, first column of A^{-1} isa5b-3c2d-5
  10. The sum 1^2+2^2+\cdots+10^2 equalsa330b385c440d3025
  11. A committee of 3 is formed from 4 boys and 3 girls with at least one girl. The number of ways isa31b35c28d34
  12. If |z-2|=|z+2|, the point z lies onathe real axisba circlecthe line x=2dthe imaginary axis
  13. The maximum value of f(x)=-x^2+4x+1 isa4b5c1d3
  14. \displaystyle\lim_{x\to0}\frac{1-\cos2x}{x^2} equalsa1b4c2d\frac{1}{2}
  15. If \alpha,\beta are the roots of x^2-5x+6=0, then \alpha^3+\beta^3 equalsa19b27c35d125

Section B — Physics (questions 76–88, 2 marks each)

  1. A stone is thrown horizontally at 15 m s⁻¹ from a cliff 80 m high. It lands at a horizontal distance ofa40 mb80 mc60 md120 m
  2. A spring of constant 400 N m⁻¹ is compressed by 10 cm. The energy stored isa4 Jb20 Jc0.2 Jd2 J
  3. A wire extends by 1 mm under a 10 N load. Within the elastic limit, a 25 N load extends it bya1.5 mmb2.5 mmc4 mmd10 mm
  4. A 1000 W heater warms 0.5 kg of water at 20 °C for 2 minutes with no loss. The final temperature is nearlya77 °Cb57 °Cc97 °Cd40 °C
  5. A gas absorbs 500 J of heat and does 200 J of work. The change in its internal energy isa700 Jb200 Jc300 Jd100 J
  6. The critical angle of a medium is 30^\circ. Its refractive index isa1.5b1.41c1.73d2
  7. A thin prism of angle 4^\circ and n=1.5 gives a deviation ofa2^\circb4^\circc1^\circd6^\circ
  8. A concave mirror has focal length 10 cm. An object at 15 cm gives an image ata30 cmb6 cmc25 cmd150 cm
  9. An open organ pipe 0.5 m long (v=340 m s⁻¹) has a second harmonic of frequencya340 Hzb510 Hzc1020 Hzd680 Hz
  10. Charges +2\ \muC and -2\ \muC are 10 cm apart in air. The force between them isa36 Nb3.6 Nc0.36 Nd360 N
  11. A battery of emf 12 V and internal resistance 1 Ω is connected to a 5 Ω resistor. The terminal voltage isa12 Vb11 Vc10 Vd2 V
  12. An ideal transformer steps 220 V down to 22 V and delivers 5 A. The primary current isa5 Ab50 Ac0.05 Ad0.5 A
  13. Photons of energy 4.5 eV eject electrons with a stopping potential of 2 V. The work function isa6.5 eVb2 eVc2.5 eVd4.5 eV

Section B — Chemistry (questions 89–96, 2 marks each)

  1. The volume of 0.5 M HCl needed to neutralise 0.1 mol of Ca(OH)₂ isa200 mLb100 mLc400 mLd800 mL
  2. The pH of 0.05 M H₂SO₄ (treated as fully dissociated) isa1.3b1.0c2.0d0.7
  3. Given E^\circ(\text{Zn}^{2+}/\text{Zn})=-0.76 V and E^\circ(\text{Ag}^+/\text{Ag})=+0.80 V, the standard cell potential of the Zn–Ag cell isa0.04 Vb0.84 Vc1.10 Vd1.56 V
  4. A first-order reaction has k=0.0693 min⁻¹. Its half-life isa1 minb100 minc10 mind0.1 min
  5. The mass of NaOH needed to prepare 500 mL of 0.2 M solution isa4 gb8 gc2 gd40 g
  6. Which compound gives a silver mirror with Tollens' reagent?aacetonebethanalcethanoldpropan-2-ol
  7. The number of atoms in 0.1 mol of CO₂ isa6.02\times10^{22}b3.0\times10^{23}c6.02\times10^{23}d1.8\times10^{23}
  8. Roasting 2 mol of HgS gives mercury of mass (Hg = 200.6)a100.3 gb200.6 gc401.2 gd602 g

Section B — English (questions 97–100, 2 marks each)

Read the passage and answer questions 97 and 98.

A bridge rarely fails because steel is weak. It fails because loads, corrosion and fatigue act together over many years. Engineers therefore inspect bridges regularly and replace parts before they reach the end of their life.

  1. The main idea of the passage is thatasteel is a weak materialbbridges never failcengineers avoid steeldbridge failure is a combined, long-term process that inspection can prevent
  2. The passage implies that regular inspectionais unnecessaryballows parts to be replaced before they failccauses corrosiondincreases the loads
  3. Neither the teacher nor the students ___ ready.awerebiscwasdhas
  4. If I ___ you, I would apologise.aambwascweredbe

Answer key and explanations

Answers — Section A Mathematics (1–20)

1. (d) — n+1=8.

2. (a) — chain rule.

3. (c) — \sin(45^\circ+30^\circ)=\frac{\sqrt{3}+1}{2\sqrt{2}}.

4. (b) — \sqrt{9+16}.

5. (a) — [\ln x]_1^e.

6. (d) — \frac{20\cdot21}{2}.

7. (c) — 2\cdot3-(-1)\cdot4=10.

8. (b) — \frac{1}{i}=-i.

9. (d) — x^2+y^2=r^2.

10. (a) — 1-\frac{1}{4}.

11. (b) — 3x^2=12.

12. (c) — zero dot product.

13. (a) — 3 occurs three times.

14. (d) — \frac{1}{2}+\frac{1}{2}.

15. (b) — 10^3=1000.

16. (c) — 2x=2.

17. (d) — exclusive events add: 0.3+0.4.

18. (a) — x^2=4ay with a=1.

19. (c) — \frac{6\cdot3}{2}.

20. (b) — \frac{x^2-1}{x-1}=x+1\to2.

Answers — Section A Physics (21–34)

21. (c) — watt (J s⁻¹).

22. (a) — N C⁻¹ (= V m⁻¹).

23. (d) — 3\times10^8.

24. (b) — 4200.

25. (c) — \frac{u^2}{2g}=\frac{400}{20}.

26. (a) — \frac{12}{4}.

27. (d) — a plane mirror has R=\infty.

28. (b) — 50 Hz.

29. (a) — gamma rays.

30. (c) — mg=50 N.

31. (d) — \rho gh=1000\times10\times10.

32. (b) — \frac{340}{680}.

33. (a) — f=\frac{1}{P}=0.25 m.

34. (c) — 238-92.

Answers — Section A Chemistry (35–48)

35. (b) — 14-6.

36. (d) — hydrogen at the cathode, oxygen at the anode.

37. (a) — C₆H₁₂O₆.

38. (c) — six bond pairs: sp³d².

39. (d) — potassium.

40. (b) — \frac{11.2}{22.4}.

41. (a) — carboxyl group.

42. (c) — neutral.

43. (b) — helium.

44. (d) — soap is the sodium (or potassium) salt of a long-chain fatty acid.

45. (c) — three.

46. (a) — iron + oxygen + water.

47. (d) — four bond pairs.

48. (b) — Hall–Héroult process.

Answers — Section A English (49–60)

49. (c) — plural subject books.

50. (a) — commence.

51. (d) — decrease.

52. (b) — good at.

53. (a) — necessary (one c, two s).

54. (c) — im-POR-tant.

55. (d) — think has /θ/; this, that, those have /ð/.

56. (b) — the earlier past action takes the past perfect.

57. (c) — will → would.

58. (a) — prefer … to.

59. (b) — very rarely.

60. (d) — neither of + singular verb.

Answers — Section B Mathematics (61–75)

61. (b) — (2,6), (3,5), (4,4), (5,3), (6,2): \frac{5}{36}.

62. (d) — u=x^2: \frac{1}{2}[e^u]_0^1=\frac{e-1}{2}.

63. (a) — [-\cos x]_0^\pi=2.

64. (c) — \frac{dy}{y}=2x\,dx.

65. (b) — c=\frac{a}{m} with a=1, m=2.

66. (d) — e=\sqrt{1-\frac{7}{16}}=\frac{3}{4}.

67. (a) — 2(x-1)-(y-1)+3(z-1)=0\Rightarrow2x-y+3z=4.

68. (c) — \vec a\times\vec b=(1,-5,-3), magnitude \sqrt{35}.

69. (d) — |A|=1; A^{-1}=(det | 3&-1 ; -5&2 |).

70. (b) — \frac{10\cdot11\cdot21}{6}=385.

71. (a) — ^7C_3-{}^4C_3=35-4.

72. (d) — equal distance from 2 and -2: x=0.

73. (b) — vertex at x=2: -4+8+1=5.

74. (c) — \frac{1-\cos2x}{x^2}=\frac{2\sin^2x}{x^2}\to2.

75. (c) — roots 2 and 3: 8+27.

Answers — Section B Physics (76–88)

76. (c) — t=\sqrt{\frac{2\times80}{10}}=4 s; x=15\times4.

77. (d) — \frac{1}{2}\times400\times0.01=2 J.

78. (b) — extension is proportional to load: 1\times2.5.

79. (a) — Q=1000\times120=120000 J; \Delta T=\frac{120000}{0.5\times4200}=57.1 °C; final 77 °C.

80. (c) — \Delta U=Q-W=300 J.

81. (d) — n=\frac{1}{\sin30^\circ}=2.

82. (a) — (n-1)A=0.5\times4.

83. (a) — \frac{1}{v}=\frac{1}{10}-\frac{1}{15}=\frac{1}{30}.

84. (d) — f_2=\frac{2v}{2L}=\frac{340}{0.5}=680 Hz.

85. (b) — \frac{9\times10^9\times4\times10^{-12}}{0.01}=3.6 N (attractive).

86. (c) — I=\frac{12}{6}=2 A; V=12-2=10 V.

87. (d) — power is conserved: I_p=5\times\frac{22}{220}.

88. (c) — \phi=h f-eV_s=4.5-2.

Answers — Section B Chemistry (89–96)

89. (c) — 0.1 mol Ca(OH)₂ gives 0.2 mol OH⁻, needing 0.2 mol HCl =\frac{0.2}{0.5}=0.4 L.

90. (b) — [\text{H}^+]=2\times0.05=0.1 M.

91. (d) — 0.80-(-0.76)=1.56 V.

92. (c) — \frac{0.693}{0.0693}.

93. (a) — 0.5\times0.2\times40=4 g.

94. (b) — ethanal (an aldehyde); ketones and alcohols do not respond.

95. (d) — 0.1\times3\times6.02\times10^{23}=1.8\times10^{23}.

96. (c) — HgS + O₂ → Hg + SO₂; 2\times200.6.

Answers — Section B English (97–100)

97. (d) — loads, corrosion and fatigue together, over years, and inspection prevents failure.

98. (b) — "replace parts before they reach the end of their life".

99. (a) — verb agrees with the nearer subject students.

100. (c) — second conditional uses were.