Model Paper 3

Chapter 4 · Full Model Papers · 100 questions in the paper · 12 min read

Model Paper 3

What the syllabus asks for 1
  • 100 questions, Q1-40 English, Q41-90 Mathematics, Q91-100 GK and IT

Full marks: 100. Time: 2 hours. Choose the best answer. One mark each; no negative marking is reported, so answer every question. How to score yourself: marks = number right. This paper tests different questions, numbers and facts from Model Papers 1 and 2.

This paper's question counts
Group Part Questions
A English (1–40) vocabulary 6, idioms and prepositions 6, articles/tenses/agreement 7, voice/narration/tags 5, clauses/conditionals 6, pronouns/modals 5, reading 5 40
B Mathematics (41–90) arithmetic 10, algebra 10, trigonometry 4, coordinate geometry 7, vectors 2, calculus 7, reasoning 10 50
C GK and IT (91–100) Nepal 3, world 2, computer 3, Internet/programming 2 10

Group A — English (questions 1–40)

  1. The synonym of "obstinate" isaflexiblebpolitecstubborndlazy
  2. The antonym of "shallow" isanarrowbdeepcsmalldwide
  3. One word for "a being present everywhere":aomniscientbomnipotentcambitiousdomnipresent
  4. The synonym of "vital" isaessentialbminorclivelydweak
  5. One word for "a person who collects stamps":aphilatelistbnumismatistcarchaeologistdbotanist
  6. The antonym of "expensive" isacostlybrichccheapdvaluable
  7. "To let the cat out of the bag" meansato free a petbto reveal a secret by accidentcto lose a bagdto hunt
  8. He is jealous ___ his brother.aatbwithcfordof
  9. "To put up with" meansato liftbto displaycto refusedto tolerate
  10. This book is similar ___ mine.atobwithcfromdas
  11. "At the eleventh hour" meansavery earlybat nightcat the last momentdslowly
  12. She takes ___ her mother in looks.aupboffcafterdover
  13. He waited for ___ hour.aabthecandno article
  14. We ___ dinner when the guests arrived.ahadbwere havingchave haddare having
  15. Neither of the answers ___ correct.aisbarecweredhave
  16. She ___ in Pokhara for five years now.alivesblivedcis livingdhas been living
  17. The scissors ___ sharp.aarebiscwasdhas
  18. He ___ to the market yesterday.agoesbwentchas gonedgone
  19. The news of the victory ___ welcome.aarebwerecisdhave
  20. The passive of "He is writing a letter" isaA letter is written by him.bA letter is being written by him.cA letter was written by him.dA letter has been written by him.
  21. "He said, 'I live here.'" becomes: He said that he ___ there.alivesbis livingchas liveddlived
  22. It is cold today, ___?aisn't itbis itcdoesn't itdwasn't it
  23. "She said to me, 'Come early.'" becomes: She told me ___ early.acomebthat comecto comedcoming
  24. The passive of "The workers have finished the wall" isaThe wall is finished by the workers.bThe wall has been finished by the workers.cThe wall was finished by the workers.dThe wall had been finished by the workers.
  25. The man ___ I saw yesterday is a doctor.awhosebwhomcwhichdwhere
  26. If I ___ you, I would accept the offer.awerebamcwas beingdbe
  27. I look forward ___ you.ameetbto meetcmetdto meeting
  28. She got her hair ___.acuttingbto cutccutdcuts
  29. Unless you work hard, you ___ succeed.awillbwon'tcwoulddcan
  30. Let him ___.ato gobgoingcgoesdgo
  31. He has ___ patience, so he gets angry quickly.alittleba fewcfewda little
  32. He is junior ___ me.athanbtocfromdof
  33. Scarcely had they arrived ___ it rained.athanbthencthatdwhen
  34. You ___ wear a helmet; it is the law.aneedn'tbmaycmustdshouldn't
  35. Choose the correct sentence.aEach of the boy has a pen.bEach of the boys has a pen.cEach of the boys have a pen.dEach boys has a pen.

Read the passage and answer questions 36–40.

Ranjana joined the school library only after her teacher asked her to find one fact for a project. She found the fact in ten minutes, but the next hour went on a different shelf, where she opened a book on bridges.

By evening she had decided to study engineering. Her father, a bus conductor, had never been inside a library, and he was surprised that a place with no entry fee could change his daughter's plans.

Later he began to walk to the library with her on Saturdays.

  1. What made Ranjana join the library?aher father's adviceba school rulecher teacher's request to find a factda prize
  2. The next hour she spent reading aboutabridgesbbusesclibrariesdfees
  3. By evening she had decided toabecome a teacherbleave schoolcdrive busesdstudy engineering
  4. Her father was surprised that a libraryawas so far awaybwith no entry fee could change his daughter's planscwas so largedhad no books
  5. Ranjana's father's work wasabus conductorbengineercteacherdlibrarian

Group B — Mathematics (questions 41–90)

  1. 12.5 % of 480 isa48b60c64d72
  2. The HCF of 18 and 27 isa9b3c54d18
  3. An article is sold for Rs 920 at a 15 % profit. Its cost price isaRs 780bRs 820cRs 770dRs 800
  4. A marked price of Rs 2,000 with a 20 % discount gives a selling price ofaRs 1,800bRs 1,400cRs 1,600dRs 1,500
  5. A can do a job in 20 days and B in 30 days. Together they takea10 daysb25 daysc12 daysd50 days
  6. A boat goes at 12 km/h in still water and the stream flows at 3 km/h. Downstream it covers 45 km ina2 hb3 hc4 hd5 h
  7. A speed of 15 m/s equalsa54 km/hb45 km/hc60 km/hd36 km/h
  8. The curved surface area of a cone of radius 3 cm and height 4 cm isa12\pi cm²b24\pi cm²c9\pi cm²d15\pi cm²
  9. The volume of a sphere of radius 3 cm isa12\pi cm³b27\pi cm³c36\pi cm³d108\pi cm³
  10. Rs 400 is divided in the ratio 5:7:8. The largest share isaRs 160bRs 140cRs 100dRs 120
  11. Of 80 students, 50 like mathematics, 45 like science and 25 like both. The number who like neither isa0b5c20d10
  12. If f(x)=x^2-3, then f(-2) isa-7b7c1d-1
  13. If \alpha,\beta are the roots of x^2-4x+3=0, then \alpha^2+\beta^2 isa10b16c7d13
  14. If 2^x=64, then x isa5b6c7d32
  15. The 3rd term of the GP 5, 10, … isa15b20c25d40
  16. The sum of the first 15 natural numbers isa105b135c150d120
  17. The determinant of [[2, 0], [0, 5]] isa7b0c10d25
  18. The value of {}^7C_3 isa35b21c210d42
  19. The value of \frac{5!}{3!} isa2b60c15d20
  20. The probability of exactly one head in two tosses of a fair coin isa\frac{1}{4}b\frac{1}{2}c\frac{3}{4}d1
  21. The value of \tan45^\circ+\cot45^\circ isa0b1c2d\sqrt{2}
  22. The value of \cos90^\circ+\sin90^\circ isa0b2c-1d1
  23. If \cos\theta=\frac{4}{5}, then \cos2\theta isa\frac{8}{5}b\frac{7}{25}c\frac{24}{25}d\frac{1}{5}
  24. From a point 20 m from a tower the angle of elevation of its top is 60°. The height of the tower isa20\sqrt{3} mb20 mc40 md\frac{20}{\sqrt{3}} m
  25. The slope of the line 4x-2y=7 isa-2b2c4d\frac{1}{2}
  26. The x-intercept of 3x+4y=12 isa3b12c4d1
  27. The distance between (0,0) and (5,12) isa13b17c7d169
  28. The distance of (1,2) from 4x+3y+5=0 isa15b1c5d3
  29. The radius of x^2+y^2-4x-6y-12=0 isa5b25c12d7
  30. The focus of x^2=12y isa(3,0)b(0,12)c(0,3)d(12,0)
  31. The length of the major axis of \frac{x^2}{36}+\frac{y^2}{16}=1 isa12b6c8d4
  32. For \mathbf{a}=3\mathbf{i}-\mathbf{j} and \mathbf{b}=\mathbf{i}+2\mathbf{j}, \mathbf{a}\cdot\mathbf{b} isa5b1c-1d0
  33. The magnitude of \mathbf{i}+2\mathbf{j}+2\mathbf{k} isa5b9c3d1
  34. \lim_{x\to2}\frac{x^3-8}{x-2} equalsa8b4c6d12
  35. The derivative of x^3+3x^2 at x=1 isa4b6c12d9
  36. The derivative of \tan x at x=0 isa1b0cinfinited-1
  37. The slope of the tangent to y=x^2+1 at x=3 isa3b6c10d9
  38. \int_1^{e^2}\frac{1}{x}\,dx equalsa1bec2de^2
  39. \int e^{2x}\,dx equalsa2e^{2x}+Cbe^{2x}+Cc\frac{e^x}{2}+Cd\frac{e^{2x}}{2}+C
  40. \int_0^13x^2\,dx equalsa1b3c0d2
  41. The next number in 2, 6, 18, 54 isa108b162c216d148
  42. The next letter in A, D, G, J isaMbLcNdK
  43. If TEA is coded 26 (the sum of letter positions), CAT is codeda22b26c24d27
  44. A person facing north turns right, right and then left. He now facesanorthbsouthcwestdeast
  45. Sita is 8th from the left and 12th from the right in a row. The row hasa19 personsb20 personsc21 personsd18 persons
  46. The angle between the hands of a clock at 2:00 isa30°b90°c60°d120°
  47. Which of these is a leap year?a2026b2100c1900d2032
  48. 5 March 2026 was a Thursday. 27 March 2026, the day the new Prime Minister took oath, was aaThursdaybFridaycSaturdaydWednesday
  49. The number of rectangles of all sizes in a 2 × 3 grid of squares isa12b15c18d21
  50. My mother's sister's husband is myaunclebbrother-in-lawccousindnephew

Group C — General Knowledge and IT (questions 91–100)

  1. The capital of Lumbini Province isaButwalbNepalgunjcBhairahawadDeukhuri
  2. The Aadikavi of Nepali literature isaBhanubhakta AcharyabLaxmi Prasad DevkotacLekhnath PaudyaldParijat
  3. The ODI Cricket World Cup 2023 was won byaIndiabAustraliacEnglanddNew Zealand
  4. The United Nations was founded ina1919b1939c1945d1955
  5. Which of these is application software?aMS WordbLinuxcBIOSdWindows
  6. One kilobyte equalsa100 bytesb1,000 bytesc512 bytesd1,024 bytes
  7. The binary form of decimal 9 isa1010b1001c1100d0110
  8. The HTML tag for a line break isa<p>b<h1>c<br>d<a>
  9. SMTP is used toasend e-mailbreceive e-mailctransfer filesdbrowse web pages
  10. Bcc in e-mail stands foraBlack copybBasic carbon copycBlind computer copydBlind carbon copy

Answer key and explanations

Answers — Group A English (1–40)

1. (c) — obstinate means stubborn.

2. (b) — deep is the opposite of shallow.

3. (d) — omnipresent; omniscient is all-knowing.

4. (a) — vital means essential.

5. (a) — philatelist; a numismatist collects coins.

6. (c) — cheap.

7. (b) — to reveal a secret by accident.

8. (d) — jealous of.

9. (d) — put up with means tolerate.

10. (a) — similar to.

11. (c) — at the last moment.

12. (c) — take after means resemble.

13. (c) — "hour" begins with a vowel sound.

14. (b) — an action in progress when the guests arrived.

15. (a) — "neither of" takes a singular verb.

16. (d) — "now" with "for five years": present perfect continuous.

17. (a) — scissors is plural.

18. (b) — "yesterday" needs the simple past.

19. (c) — "the news" is singular.

20. (b) — present continuous passive.

21. (d) — simple present shifts to simple past.

22. (a) — positive statement, negative tag.

23. (c) — a command becomes told + to.

24. (b) — present perfect passive.

25. (b) — "whom" is the object of "saw".

26. (a) — "were" in the second conditional.

27. (d) — look forward to + -ing.

28. (c) — have/get something done.

29. (b) — "unless you work" = if you do not work.

30. (d) — let + bare verb.

31. (a) — "little patience" has a negative sense.

32. (b) — junior to.

33. (d) — scarcely … when.

34. (c) — obligation: must.

35. (b) — "each of the boys" + singular verb.

36. (c) — "only after her teacher asked her".

37. (a) — "a book on bridges".

38. (d) — "decided to study engineering".

39. (b) — "a place with no entry fee could change his daughter's plans".

40. (a) — "a bus conductor".

Answers — Group B Mathematics (41–90)

41. (b) — 480 ÷ 8 = 60.

42. (a) — 18 = 2·3², 27 = 3³: HCF 9.

43. (d) — 920 ÷ 1.15 = 800.

44. (c) — 2000 × 0.8 = 1,600.

45. (c) — 20 × 30 / 50 = 12.

46. (b) — downstream speed 15 km/h; 45/15 = 3 h.

47. (a) — 15 × 18/5 = 54.

48. (d) — slant height 5, π × 3 × 5 = 15π.

49. (c) — (4/3)π × 27 = 36π.

50. (a) — 400/20 = 20 per part; 8 × 20 = 160.

51. (d) — union = 70, neither = 80 − 70 = 10.

52. (c) — 4 − 3 = 1.

53. (a) — 4² − 2 × 3 = 10.

54. (b) — 64 = 2⁶.

55. (b) — 5 × 2² = 20.

56. (d) — 15 × 16 / 2 = 120.

57. (c) — 2 × 5 − 0.

58. (a) — 7·6·5 / 6 = 35.

59. (d) — 5 × 4 = 20.

60. (b) — HT or TH: 2/4.

61. (c) — 1 + 1.

62. (d) — 0 + 1.

63. (b) — 2(16/25) − 1 = 7/25.

64. (a) — 20 tan 60° = 20√3.

65. (b) — y = 2x − 7/2.

66. (c) — set y = 0: x = 4.

67. (a) — 5-12-13 triple.

68. (d) — |4 + 6 + 5| / 5 = 3.

69. (a) — g = −2, f = −3: √(4 + 9 + 12) = 5.

70. (c) — 4a = 12, a = 3.

71. (a) — 2a = 12.

72. (b) — 3 − 2 = 1.

73. (c) — √(1 + 4 + 4) = 3.

74. (d) — 3 × 2² = 12.

75. (d) — 3x² + 6x at 1 = 9.

76. (a) — sec²0 = 1.

77. (b) — 2x at 3 = 6.

78. (c) — ln e² = 2.

79. (d) — divide by the inner coefficient 2.

80. (a) — [x³] from 0 to 1.

81. (b) — multiply by 3.

82. (a) — every third letter: J → M.

83. (c) — 3 + 1 + 20.

84. (d) — north → east → south → east.

85. (a) — 8 + 12 − 1.

86. (c) — 2 × 30°.

87. (d) — 2032 is divisible by 4; 2100 and 1900 are not leap years.

88. (b) — 22 days = 3 weeks + 1 day, so Friday.

89. (c) — C(3,2) × C(4,2) = 3 × 6.

90. (a) — a mother's sister's husband is an uncle.

Answers — Group C General Knowledge and IT (91–100)

91. (d) — Deukhuri.

92. (a) — Bhanubhakta Acharya.

93. (b) — Australia.

94. (c) — 1945.

95. (a) — MS Word; the others are system software.

96. (d) — 2¹⁰ = 1,024.

97. (b) — 8 + 1.

98. (c) — <br>.

99. (a) — SMTP sends mail.

100. (d) — blind carbon copy.

Score sheet and error analysis

Use the figures and steps below after you finish the paper. Mark your sheet with the answer key, enter the group scores, then work through the error log.

diagram
Figure 4.1. Answer-key balance of Model Paper 3. Each bar counts how many correct answers are a, b, c or d in a group. The cell reads the 100-letter key and checks the group sizes (40, 50, 10) and the totals a=27, b=24, c=25, d=24; the longest run of one repeated letter is 3. A balanced key means a pattern guess cannot replace knowledge, so answer each question on its merits.

diagram
Figure 4.2. Score sheet for Model Paper 3. Each group has its question count, time budget (English 30 min, Mathematics 70, GK and IT 5, checking 15) and seconds per question, which the cell computes. The right-hand boxes are blank for your own score. The illustrative targets (English 32, Mathematics 35, GK and IT 8, total 75) are study goals chosen by NEBians, not a TU pass mark or cut-off.

  1. Score each group separately and compare with the target boxes in Fig 4.2. A low group tells you which units to revisit first.
  2. Write an error log line for every miss: question number, the cause (formula, arithmetic slip, grammar rule, never learnt) and the unit that fixes it.
  3. Redo each missed question after two days, without looking at the explanation. A question you can now solve is fixed; one you cannot goes back into the log.
  4. Check your time: if Mathematics took more than 70 minutes, practise skipping and returning (Fig 4.2).
  5. Do not read patterns into the key (Fig 4.1). The letters are spread across a, b, c and d.