IOE Model Paper 1 (100 questions, 140 marks)

Chapter 2 · Full Model Papers · 100 questions in the paper · 12 min read

IOE Model Paper 1 (100 questions, 140 marks)

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

Instructions. Computer-based paper pattern of the IOE B.E./B.Arch. entrance (2083 booklet): 100 questions, 140 marks, 2 hours (120 minutes). Section A has 60 questions of 1 mark; Section B has 40 questions of 2 marks. Each question has four options and one correct answer. A wrong answer costs 10 % of that question's marks: -0.1 in Section A, -0.2 in Section B. Leave a question unanswered to lose nothing. The paper is numbered straight through and is arranged by subject within each section, as in the official model questions. Constants: g=10 m s⁻² unless stated, h=6.63\times10^{-34} J s, e=1.6\times10^{-19} C, N_A=6.02\times10^{23}.

Score yourself: score =(\text{right}\times1+\text{right}_B\times2)-0.1\times\text{wrong}_A-0.2\times\text{wrong}_B. Count from the answer key at the end.

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

The split of questions between subjects within the two sections is not published by IOE; this paper uses the 20+15 / 14+13 / 14+8 / 12+4 distribution that fits 60 + 40 questions and the subject marks 50 / 40 / 30 / 20.

Pacing. 120 minutes for 100 questions is 72 seconds each on average. A sound plan: Section A (60 questions) in 45 minutes, Section B (40) in 60 minutes, 15 minutes for returning to skipped questions.

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

  1. \displaystyle\lim_{x\to0}\frac{\sin5x}{\sin2x} equalsa2/5b1c5/2d5
  2. \dfrac{d}{dx}\ln(\sin x) equalsa\tan xb\cot xc-\cot xd\sec x
  3. \displaystyle\int_0^1\frac{dx}{1+x^2} equalsa\pi/4b\pi/2c1d\pi/8
  4. The sum of the roots of 3x^2-12x+5=0 isa5/3b-4c12d4
  5. The 10th term of the GP 2,6,18,\dots isa39366b19683c59049d13122
  6. The value of ^{10}C_3 isa720b120c210d30
  7. The modulus of 3-4i isa1b7c5d25
  8. The centre of the circle x^2+y^2-4x+6y-12=0 isa(-2,3)b(2,3)c(-2,-3)d(2,-3)
  9. The eccentricity of a parabola isa1b0cless than 1dgreater than 1
  10. The slope of the line 2x-3y+6=0 isa-2/3b3/2c2/3d-3/2
  11. For \vec a=\hat i+2\hat j+3\hat k and \vec b=3\hat i+2\hat j+\hat k, \vec a\cdot\vec b equalsa14b10c6d12
  12. \hat i\times\hat k equalsa\hat jb\hat kc0d-\hat j
  13. The mean of the first 10 natural numbers isa5b5.5c6d10
  14. A die is rolled once. The probability of getting a prime number isa1/3b1/6c1/2d2/3
  15. The general solution of \cos\theta=0 isan\pib2n\picn\pi/2d(2n+1)\pi/2
  16. The value of \sin^{-1}1+\cos^{-1}1 isa\pib0c\pi/2d\pi/4
  17. The range of f(x)=\sin x isa[-1,1]b(-1,1)c\mathrm{R}d[0,1]
  18. The number of subsets of \{a,b,c\} isa6b8c9d7
  19. If I is the 2\times2 identity matrix, |3I| equalsa3b6c9d27
  20. \displaystyle\int_0^2x^2\,dx equalsa8/3b4c2d8

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

  1. The SI unit of magnetic flux isateslabweberchenrydgauss
  2. The momentum of a 2 kg body moving at 5 m s⁻¹ isa2.5 kg m s⁻¹b7 kg m s⁻¹c10 kg m s⁻¹d25 kg m s⁻¹
  3. The time period of a seconds pendulum isa2 sb1 sc4 sd0.5 s
  4. If the pressure of a gas is doubled at constant temperature, its volume becomesadoublebfour timeschalfdunchanged
  5. Light travels at 2\times10^8 m s⁻¹ in a medium. Its refractive index isa0.67b1.5c2d3
  6. The equivalent resistance of four 1 Ω resistors in parallel isa4 Ωb1 Ωc0.5 Ωd0.25 Ω
  7. The SI unit of inductance isahenrybfaradctesladohm
  8. At room temperature the speed of sound in air is nearlya34 m s⁻¹b340 m s⁻¹c3400 m s⁻¹d3\times10^8 m s⁻¹
  9. The work function of a metal is 4 eV. The threshold wavelength isa620 nmb155 nmc310 nmd4960 nm
  10. A radioactive sample has a half-life of 20 min. After 1 hour the fraction left isa1/3b1/6c1/9d1/8
  11. The particle emitted in \beta^- decay isaa protonba neutronca helium nucleusdan electron
  12. The kinetic energy of a 1 kg body moving at 2 m s⁻¹ isa2 Jb4 Jc1 Jd0.5 J
  13. The logic gate whose output is 1 only when both inputs are 1 isaORbNANDcANDdXOR
  14. The moment of inertia of a ring of mass M and radius R about its axis isa\frac{1}{2}MR^2b\frac{2}{5}MR^2c\frac{2}{3}MR^2dMR^2

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

  1. The number of electrons in a Cl⁻ ion isa17b18c16d35
  2. The pH of 0.001 M NaOH solution isa3b14c11d10
  3. The IUPAC name of CH₃CH₂OH isaethanolbmethanolcethanaldethanoic acid
  4. The molar mass of CaCO₃ isa40 gb84 gc56 gd100 g
  5. The gas obtained by adding water to calcium carbide isamethanebethenecethynedethane
  6. The oxidation number of sulphur in SO₄²⁻ isa+4b+6c+2d−2
  7. The bond angle in a water molecule is abouta109.5°b120°c104.5°d180°
  8. The catalyst used in the Haber process isaFebPtcNidV₂O₅
  9. The strongest acid among the hydrogen halides isaHFbHClcHBrdHI
  10. The functional group of aldehydes isa–OHb–CHOc–COOHd>C=O
  11. A common ore of iron isahaematitebbauxiteccinnabardgalena
  12. The unit of the rate constant of a first-order reaction isamol L⁻¹ s⁻¹bL mol⁻¹ s⁻¹cmol sds⁻¹
  13. The most electronegative element isaoxygenbfluorinecchlorinednitrogen
  14. The number of σ bonds in methane isa3b5c4d2

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

  1. He ___ to school every day.agoesbgocgoingdgone
  2. The word closest in meaning to "huge" isatinybnarrowcenormousdweak
  3. The opposite of "ancient" isaoldbhistoriccantiquedmodern
  4. She is senior ___ me.atobthancfromdof
  5. The plural of "criterion" isacriterionsbcriteriasccriteriondcriteria
  6. The word "computer" has its primary stress on thea1st syllableb3rd syllablec2nd syllablednone
  7. Which word has the same vowel sound as "feet"?abitbseatcsetdsat
  8. The passive of "The cat ate the fish" is "The fish ___ by the cat."aatebis eatenchas eatendwas eaten
  9. He said, "I am tired." He said that he ___ tired.aisbwerecwasdbe
  10. Which sentence is correct?aEveryone have finished.bEveryone has finished.cEveryone are finished.dEveryone finish.
  11. The idiom "hit the nail on the head" meansabe exactly rightbhurt someonecfaildwork hard
  12. I have not seen him ___ last year.aforbfromcduringdsince

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

  1. Two cards are drawn without replacement from a well-shuffled pack of 52. The probability that both are aces isa1/169b1/221c1/13d4/663
  2. \displaystyle\int_0^{\pi/2}\frac{\cos x}{1+\sin x}dx equalsa1b\ln3c\ln2d\pi/2
  3. The area enclosed between y=x^2 and y=4 isa16/3b32/3c8d16
  4. The solution of x\,dy-y\,dx=0 passing through (1,2) isay=x+1by=x^2+1cy=2/xdy=2x
  5. The length of the chord of x^2+y^2=25 cut off by the line x+y=5 isa10b5c5\sqrt{2}d2\sqrt{5}
  6. For the ellipse 9x^2+25y^2=225, the sum of the distances of any point on it from the two foci isa5b6c8d10
  7. The asymptotes of \dfrac{x^2}{9}-\dfrac{y^2}{16}=1 areay=\pm\frac{4x}{3}by=\pm\frac{3x}{4}cy=\pm\frac{16x}{9}dy=\pm\frac{9x}{16}
  8. The angle between \vec a=\hat i-\hat j+2\hat k and \vec b=2\hat i+\hat j-\hat k isa\cos^{-1}(-\frac{1}{6})b\cos^{-1}(\frac{1}{6})c\cos^{-1}(-\frac{1}{3})d90^\circ
  9. If A=(det | 1&2 ; 2&1 |), the trace of A^2 isa5b8c10d4
  10. The sum of the series 1\cdot2+2\cdot3+3\cdot4+\cdots+10\cdot11 isa385b440c330d550
  11. The coefficient of x^2 in the expansion of (1+2x)^5 isa10b20c80d40
  12. If z=1+i\sqrt{3}, then z^6 equalsa64b-64c32d64i
  13. The minimum value of 2x+\dfrac{8}{x} for x>0 isa4b8c16d10
  14. \displaystyle\lim_{x\to\infty}\frac{x^2+3x}{2x^2-1} equalsa1b3/2c1/2d\infty
  15. The number of distinct arrangements of the letters of MATHEMATICS isa4989600b39916800c9979200d1247400

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

  1. A projectile launched at 45^\circ has a range of 100 m. At the same speed, a launch at 15^\circ gives a range ofa25 mb75 mc50 md100 m
  2. A 0.5 kg ball dropped from 20 m rebounds to 5 m (g=10). The kinetic energy lost in the impact isa25 Jb75 Jc50 Jd100 J
  3. A satellite orbits at 3R above the Earth's surface (R the Earth's radius, \sqrt{gR}=7.9 km s⁻¹). Its orbital speed is abouta7.9 km s⁻¹b5.6 km s⁻¹c1.98 km s⁻¹d3.95 km s⁻¹
  4. A solid cylinder of mass 4 kg rolls without slipping at 2 m s⁻¹. Its total kinetic energy isa12 Jb8 Jc16 Jd6 J
  5. The heat needed to change 1 kg of ice at -10 °C to water at 20 °C is nearly (c_{ice}=2100, c_w=4200 J kg⁻¹ K⁻¹, L_f=336 kJ kg⁻¹)a336 kJb441 kJc420 kJd504 kJ
  6. A Carnot engine with source at 500 K has efficiency 40 %. The efficiency becomes ___ when the sink is lowered to 250 K.a45 %b60 %c50 %d55 %
  7. In Young's experiment slit separation is 0.5 mm, screen distance 1 m and \lambda=500 nm. The 5th bright fringe from the centre is ata1 mmb2.5 mmc10 mmd5 mm
  8. An object is 20 cm from a convex lens of focal length 15 cm. The image distance isa60 cmb30 cmc12 cmd35 cm
  9. A pipe closed at one end is 25 cm long (v=340 m s⁻¹). Its fundamental frequency isa170 Hzb680 Hzc1360 Hzd340 Hz
  10. A 2 µF capacitor charged to 100 V is connected to an uncharged 3 µF capacitor. The common potential isa40 Vb50 Vc60 Vd20 V
  11. An electron (e/m=1.76\times10^{11} C kg⁻¹) moves at 1.76\times10^7 m s⁻¹ perpendicular to a 0.01 T field. The radius of its path isa1 mmb10 cmc1 cmd1 m
  12. A pure inductor of 0.1 H is connected to a 220 V, 50 Hz supply. The rms current is nearlya2.2 Ab7.0 Ac22 Ad0.7 A
  13. A sample initially has 1000 radioactive nuclei with a half-life of 2 h. The number left after 6 h isa250b500c62d125

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

  1. The mass of 5.6 L of CO₂ at STP isa44 gb22 gc11 gd5.5 g
  2. 50 mL of 0.2 M HCl is mixed with 50 mL of 0.1 M NaOH. The pH of the mixture isa1.0b1.3c2.0d0.7
  3. The mass of silver deposited by a current of 1 A in 965 s (\text{Ag}=108) isa1.08 gb0.108 gc10.8 gd108 g
  4. A first-order reaction has a half-life of 10 min. The time for 75 % completion isa10 minb15 minc20 mind30 min
  5. The mass of CO₂ produced by the complete combustion of 4.6 g of ethanol isa8.8 gb4.4 gc17.6 gd2.2 g
  6. A compound C₃H₆O gives a positive iodoform test and does not reduce Tollens' reagent. It isapropanalbpropan-1-olcallyl alcoholdpropanone
  7. The mass of zinc obtained from 194 g of ZnS (M = 97) with complete conversion isa65 gb97 gc130 gd194 g
  8. Which statement about first ionisation energies is correct?aBe < BbN < OcLi > BedMg > Al

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

Read the passage and answer questions 97 and 98.

Electric vehicles are quiet and produce no exhaust, but their batteries need metals such as lithium and cobalt, which are mined at a heavy environmental and social cost. Recycling old batteries could reduce the need for new mining, yet today most batteries are not recycled.

  1. The passage is mainly concerned withathe noise of petrol carsbelectric vehicles' benefits and the battery recycling challengecthe low price of lithiumdthe exhaust of electric vehicles
  2. "Today most batteries are not recycled" suggests thatarecycling is completebmining has stoppedcrecycling has room to expanddbatteries last forever
  3. Had I known about the exam, I ___ harder.awould studybwill studycstudieddwould have studied
  4. She suggested that he ___ the doctor.aseebseescsawdseen

Answer key and explanations

Answers — Section A Mathematics (1–20)

1. (c) — \frac{\sin5x}{\sin2x}=\frac{5x}{2x}\cdot\frac{\sin5x/5x}{\sin2x/2x}\to\frac{5}{2}.

2. (b) — \frac{\cos x}{\sin x}.

3. (a) — \tan^{-1}1-\tan^{-1}0=\frac{\pi}{4}.

4. (d) — -\frac{b}{a}=4.

5. (a) — 2\times3^9=2\times19683.

6. (b) — \frac{10\cdot9\cdot8}{6}.

7. (c) — \sqrt{9+16}.

8. (d) — centre (-g,-f)=(2,-3).

9. (a) — by definition.

10. (c) — y=\frac{2}{3}x+2.

11. (b) — 3+4+3.

12. (d) — \hat k\times\hat i=\hat j, so \hat i\times\hat k=-\hat j.

13. (b) — \frac{55}{10}.

14. (c) — primes 2, 3, 5: \frac{3}{6}.

15. (d) — \cos\theta=0 at odd multiples of \frac{\pi}{2}.

16. (c) — \frac{\pi}{2}+0.

17. (a) — closed interval [-1,1].

18. (b) — 2^3.

19. (c) — 3^2\times1.

20. (a) — \frac{8}{3}.

Answers — Section A Physics (21–34)

21. (b) — weber (Wb = T m²).

22. (c) — 2\times5.

23. (a) — T=2 s, l\approx1 m.

24. (c) — PV constant.

25. (b) — \frac{3\times10^8}{2\times10^8}.

26. (d) — \frac{1}{4} Ω.

27. (a) — henry.

28. (b) — about 340 m s⁻¹ at 20 °C.

29. (c) — \frac{1240}{4}=310 nm.

30. (d) — three half-lives: \frac{1}{8}.

31. (d) — an electron (with an antineutrino).

32. (a) — \frac{1}{2}\cdot1\cdot4.

33. (c) — AND.

34. (d) — MR^2 (ring); \frac{1}{2}MR^2 is the disc.

Answers — Section A Chemistry (35–48)

35. (b) — 17 + 1.

36. (c) — pOH 3, pH 11.

37. (a) — two carbons, –OH.

38. (d) — 40+12+48.

39. (c) — CaC₂ + 2H₂O → C₂H₂ + Ca(OH)₂.

40. (b) — x-8=-2.

41. (c) — two lone pairs compress the angle from 109.5°.

42. (a) — iron with a molybdenum promoter.

43. (d) — HI (weakest H–X bond).

44. (b) — –CHO; >C=O is the ketone group.

45. (a) — haematite Fe₂O₃.

46. (d) — rate (mol L⁻¹ s⁻¹) divided by concentration gives s⁻¹.

47. (b) — fluorine, 4.0.

48. (c) — four C–H σ bonds.

Answers — Section A English (49–60)

49. (a) — third-person singular, habitual present.

50. (c) — enormous.

51. (d) — modern.

52. (a) — senior to (Latin comparatives take to).

53. (d) — criteria.

54. (c) — com-PU-ter.

55. (b) — /iː/ in feet and seat.

56. (d) — simple past passive.

57. (c) — am → was.

58. (b) — everyone is singular.

59. (a) — to say exactly the right thing.

60. (d) — since + point of time.

Answers — Section B Mathematics (61–75)

61. (b) — \frac{4}{52}\cdot\frac{3}{51}=\frac{1}{221}.

62. (c) — [\ln(1+\sin x)]_0^{\pi/2}=\ln2.

63. (b) — 2\int_0^2(4-x^2)dx=2(8-\frac{8}{3})=\frac{32}{3}.

64. (d) — \frac{dy}{y}=\frac{dx}{x}, y=Cx; C=2.

65. (c) — distance from the origin \frac{5}{\sqrt{2}}; chord =2\sqrt{25-\frac{25}{2}}=5\sqrt{2}.

66. (d) — \frac{x^2}{25}+\frac{y^2}{9}=1, 2a=10.

67. (a) — y=\pm\frac{b}{a}x=\pm\frac{4}{3}x.

68. (a) — \vec a\cdot\vec b=2-1-2=-1, |\vec a||\vec b|=6.

69. (c) — A^2=(det | 5&4 ; 4&5 |), trace 10.

70. (b) — \frac{n(n+1)(n+2)}{3}=\frac{10\cdot11\cdot12}{3}=440.

71. (d) — ^5C_2\cdot2^2=10\times4.

72. (a) — z=2e^{i\pi/3}, z^6=64e^{2\pi i}=64.

73. (b) — AM–GM: 2x+\frac{8}{x}\ge2\sqrt{16}=8.

74. (c) — ratio of leading coefficients.

75. (a) — \frac{11!}{2!\,2!\,2!} (M, A, T repeat).

Answers — Section B Physics (76–88)

76. (c) — R\propto\sin2\theta: \sin30^\circ/\sin90^\circ=\frac{1}{2}.

77. (b) — mg\Delta h=0.5\times10\times15=75 J.

78. (d) — orbit radius 4R: v=\sqrt{\frac{gR^2}{4R}}=\frac{7.9}{2}.

79. (a) — \frac{3}{4}Mv^2=\frac{3}{4}\times4\times4=12 J.

80. (b) — 21000+336000+84000=441000 J.

81. (c) — T_2=300 K; 1-\frac{250}{500}=50\%.

82. (d) — \beta=\frac{\lambda D}{d}=1 mm; 5\beta=5 mm.

83. (a) — \frac{1}{v}=\frac{1}{15}-\frac{1}{20}=\frac{1}{60}.

84. (d) — \frac{v}{4L}=\frac{340}{1}.

85. (a) — V=\frac{200}{5}=40 V.

86. (c) — r=\frac{v}{(e/m)B}=\frac{1.76\times10^7}{1.76\times10^{11}\times0.01}=10^{-2} m.

87. (b) — X_L=2\pi\times50\times0.1=31.4 Ω; I=\frac{220}{31.4}=7.0 A.

88. (d) — three half-lives: \frac{1000}{8}=125.

Answers — Section B Chemistry (89–96)

89. (c) — \frac{5.6}{22.4}=0.25 mol \times44=11 g.

90. (b) — excess H⁺ =0.010-0.005=0.005 mol in 0.1 L =0.05 M; pH =1.3.

91. (a) — Q=965 C =0.01 F; 0.01\times108=1.08 g.

92. (c) — 75 % completion is two half-lives.

93. (a) — 0.1 mol C₂H₅OH gives 0.2 mol CO₂ =8.8 g.

94. (d) — propanone (CH₃CO–) gives iodoform; it is a ketone and does not reduce Tollens' reagent.

95. (c) — 2 mol ZnS gives 2 mol Zn =130 g.

96. (d) — Mg (3s²) > Al (3p¹); the others are reversed (Be > B, N > O, Be > Li).

Answers — Section B English (97–100)

97. (b) — benefits, then the mining and recycling challenge.

98. (c) — if most are not recycled, recycling can still expand.

99. (d) — third conditional (Had I known … I would have studied).

100. (a) — suggest that + subject + base verb.