Mahanagar Entrance Set-4

 

KMC Scholarship Examination

Full Marks: 100
Time: 2 Hours

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Section A: Mathematics (Q1–Q30)

Each question carries 1 mark.

1. Solve: $2x + 5 = 11$.
   a) 2
   b) 3
   c) 5
   d) 6

2. If HCF of two numbers is 6 and their product is 216, what is their LCM?
   a) 18
   b) 24
   c) 36
   d) 54

3. Mean of 5, 10, 15, 20, 25 is:
   a) 10
   b) 12.5
   c) 15
   d) 20

4. Write the third term of the expansion of $(x+3)^4$.
   a) $54x^2$
   b) $108x^2$
   c) $36x^2$
   d) $81x^2$

5. The value of $0.5^2$ is:
   a) 0.25
   b) 0.5
   c) 0.75
   d) 1.0

6. Find the probability of drawing a king from a pack of 52 cards.
   a) 1/26
   b) 1/13
   c) 1/52
   d) 1/12

7. If $\sin \theta = \frac{4}{5}$, then $\cos \theta = ?$
   a) 3/5
   b) 4/5
   c) 5/4
   d) 9/25

8. Find the area of a circle with radius 7 cm ($\pi=\tfrac{22}{7}$).
   a) 154 cm²
   b) 44 cm²
   c) 49 cm²
   d) 308 cm²

9. The sum of first 10 natural numbers is:
   a) 45
   b) 50
   c) 55
   d) 60

10. Convert 0.375 into fraction.
    a) 3/8
    b) 5/8
    c) 7/8
    d) 9/8

11. Distance between (0,0) and (6,8):
    a) 10
    b) 12
    c) 8
    d) 14

12. If a sphere has diameter 14 cm, its radius is:
    a) 14 cm
    b) 28 cm
    c) 7 cm
    d) 21 cm

13. Find the median of: 7, 5, 9, 3, 11.
    a) 5
    b) 7
    c) 9
    d) 11

14. In △ABC, if ∠A=90°, AB=6 cm, AC=8 cm, then BC=?
    a) 10 cm
    b) 12 cm
    c) 14 cm
    d) 15 cm

15. Express 0.00056 in standard form.
    a) 5.6 × 10⁻⁴
    b) 5.6 × 10⁻³
    c) 56 × 10⁻⁵
    d) 56 × 10⁻³

16. Coefficient of $x^2$ in $(x+2)^3$:
    a) 6
    b) 8
    c) 12
    d) 24

17. The slope of line parallel to y-axis is:
    a) 0
    b) 1
    c) undefined
    d) –1

18. Find the mode of: 2, 4, 4, 5, 6, 6, 6, 7.
    a) 4
    b) 5
    c) 6
    d) 7

19. CI on Rs.1000 for 2 years at 10% p.a. is:
    a) Rs. 200
    b) Rs. 210
    c) Rs. 220
    d) Rs. 250

20. Write the first term of sequence: 12, 24, 48,…
    a) 6
    b) 12
    c) 24
    d) 48

21. The roots of $x^2 – 9 = 0$ are:
    a) 3, –3
    b) 0, 9
    c) –9, 9
    d) none

22. The mean of first 20 natural numbers:
    a) 10
    b) 10.5
    c) 11
    d) 12

23. Find the perimeter of square of area 49 cm².
    a) 21 cm
    b) 28 cm
    c) 14 cm
    d) 35 cm

24. If probability of event is 0.35, then probability of not happening is:
    a) 0.25
    b) 0.45
    c) 0.65
    d) 0.75

25. If sum of first n natural numbers is 55, then n=?
    a) 9
    b) 10
    c) 11
    d) 12

26. The gradient of line passing through (0,0) and (4,8):
    a) 1
    b) 2
    c) 3
    d) 4

27. LCM of 18 and 24 is:
    a) 36
    b) 48
    c) 72
    d) 54

28. The number of diagonals in a hexagon:
    a) 6
    b) 9
    c) 12
    d) 15

29. Find the value of $3^{-2}$.
    a) 9
    b) 1/9
    c) –9
    d) –1/9

30. Which is a quadratic equation?
    a) 3x + 2 = 0
    b) x² + 2x + 1 = 0
    c) x³ – 2 = 0
    d) 5 – x = 0

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Section B: Science (Q31–Q60)

Each question carries 1 mark.

31. Unit of work is:
    a) Newton
    b) Joule
    c) Watt
    d) Pascal

32. Blood is pumped by:
    a) Lungs
    b) Heart
    c) Kidney
    d) Brain

33. The lens used to correct myopia:
    a) Convex
    b) Concave
    c) Cylindrical
    d) Plano-convex

34. Chemical formula of ammonium chloride is:
    a) NH₄Cl
    b) NaCl
    c) KCl
    d) NH₃

35. Device used to measure current:
    a) Ammeter
    b) Voltmeter
    c) Galvanometer
    d) Rheostat

36. Which one is a renewable energy source?
    a) Coal
    b) Petroleum
    c) Wind
    d) Natural gas

37. The process of separation of pure liquid from solution by heating:
    a) Filtration
    b) Distillation
    c) Evaporation
    d) Sedimentation

38. The SI unit of pressure is:
    a) Watt
    b) Pascal
    c) Joule
    d) Newton

39. Which vitamin prevents rickets?
    a) A
    b) B
    c) C
    d) D

40. Which gas turns lime water milky?
    a) CO₂
    b) O₂
    c) N₂
    d) H₂

41. Which plant tissue transports water?
    a) Xylem
    b) Phloem
    c) Parenchyma
    d) Collenchyma

42. Sound cannot travel through:
    a) Water
    b) Air
    c) Vacuum
    d) Metal

43. Catalyst used in preparation of oxygen from potassium chlorate:
    a) HCl
    b) MnO₂
    c) CuSO₄
    d) NaOH

44. Acid found in lemon:
    a) Lactic acid
    b) Citric acid
    c) Acetic acid
    d) Sulphuric acid

45. An example of exothermic reaction:
    a) Burning of fuel
    b) Photosynthesis
    c) Electrolysis of water
    d) Melting of ice

46. Which planet is known as the "Red Planet"?
    a) Venus
    b) Jupiter
    c) Mars
    d) Saturn

47. Electric power is measured in:
    a) Joule
    b) Watt
    c) Newton
    d) Ampere

48. Photosynthesis requires:
    a) CO₂ + water + sunlight
    b) O₂ + water + sunlight
    c) H₂ + sunlight
    d) CO₂ + nitrogen + sunlight

49. Process of conversion of liquid into gas at all temperature:
    a) Boiling
    b) Evaporation
    c) Condensation
    d) Sublimation

50. Which element is found in proteins?
    a) Nitrogen
    b) Calcium
    c) Phosphorus
    d) Potassium

51. The speed of light in vacuum is:
    a) 3×10⁸ m/s
    b) 3×10⁶ m/s
    c) 3×10⁴ m/s
    d) 3×10² m/s

52. Which law states: "Mass is neither created nor destroyed"?
    a) Boyle’s law
    b) Dalton’s law
    c) Law of conservation of mass
    d) Ohm’s law

53. Which organ purifies blood?
    a) Lungs
    b) Heart
    c) Kidney
    d) Brain

54. Which type of energy is produced in solar cells?
    a) Heat
    b) Sound
    c) Chemical
    d) Electrical

55. Rusting of iron is:
    a) Oxidation
    b) Reduction
    c) Neutralization
    d) Catalysis

56. The SI unit of force is:
    a) Joule
    b) Watt
    c) Newton
    d) Dyne

57. The number of chromosomes in human body cell:
    a) 23
    b) 46
    c) 92
    d) 24

58. Example of non-metal:
    a) Iron
    b) Sodium
    c) Sulphur
    d) Copper

59. The structural unit of life is:
    a) Cell
    b) Tissue
    c) Organ
    d) Organ system

60. Instrument used to measure temperature:
    a) Barometer
    b) Thermometer
    c) Hydrometer
    d) Ammeter

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Section C: English (Q61–Q90)

Each question carries 1 mark.

61. Choose the correct synonym of rapid:
    a) slow
    b) quick
    c) steady
    d) weak

62. The antonym of victory is:
    a) win
    b) defeat
    c) joy
    d) success

63. Select the correct spelling:
    a) Occurance
    b) Occurrence
    c) Ocurence
    d) Occurence

64. Identify the adverb: She sings beautifully.
    a) she
    b) sings
    c) beautifully
    d) none

65. Which is a passive voice?
    a) He plays football.
    b) Football is played by him.
    c) He is playing football.
    d) He will play football.

66. Fill in the blank: The train _____ at 6 pm tomorrow.
    a) leave
    b) leaves
    c) left
    d) leaving

67. Choose the correct article: She bought ____ orange.
    a) a
    b) an
    c) the
    d) no article

68. One who studies stars is called:
    a) biologist
    b) astrologer
    c) astronomer
    d) historian

69. Identify the preposition: The book is on the table.
    a) book
    b) on
    c) is
    d) table

70. Reported speech: He said, "I am busy."
    a) He said that he is busy.
    b) He said that I was busy.
    c) He said that he was busy.
    d) He said that he busy.

71. Change into comparative: She is tall.
    a) taller
    b) tallest
    c) more tall
    d) most tall

72. Fill in the blank: He has been working _____ morning.
    a) since
    b) for
    c) in
    d) from

73. Plural of "child" is:
    a) childs
    b) children
    c) childs’
    d) childes

74. Which sentence is interrogative?
    a) She is dancing.
    b) Are you ready?
    c) He plays cricket.
    d) It is raining.

75. Identify the verb: The baby cried loudly.
    a) baby
    b) cried
    c) loudly
    d) the

76. The opposite of brave:
    a) coward
    b) strong
    c) bold
    d) proud

77. Which is correct:
    a) He don’t know me.
    b) He doesn’t know me.
    c) He isn’t know me.
    d) He not know me.

78. Change into past tense: They go to school.
    a) They goed to school.
    b) They gone to school.
    c) They went to school.
    d) They goes to school.

79. Fill in the blank: This book is _____ than that one.
    a) good
    b) best
    c) better
    d) well

80. Choose correct question tag: He is a teacher, ____?
    a) isn’t he
    b) is he
    c) wasn’t he
    d) does he

81. Antonym of ancient:
    a) old
    b) new
    c) antique
    d) historic

82. Which is an exclamatory sentence?
    a) What a beautiful day!
    b) Where are you going?
    c) She sings well.
    d) I am reading.

83. One word for: A place where books are kept.
    a) library
    b) museum
    c) laboratory
    d) kitchen

84. Choose correct preposition: He is good ____ mathematics.
    a) at
    b) in
    c) on
    d) for

85. Change into passive: She wrote a letter.
    a) A letter wrote by her.
    b) A letter was written by her.
    c) A letter is written by her.
    d) A letter writes by her.

86. Opposite of rise:
    a) stand
    b) fall
    c) sit
    d) run

87. Find the noun: Honesty is the best policy.
    a) honesty
    b) best
    c) policy
    d) both a & c

88. Past participle of drink:
    a) drank
    b) drunk
    c) drinks
    d) drinking

89. Fill in: He is fond _____ music.
    a) on
    b) in
    c) of
    d) for

90. Which is a correct sentence?
    a) She don’t like tea.
    b) She doesn’t like tea.
    c) She not like tea.
    d) She isn’t like tea.

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Section D: General Knowledge (Q91–Q100)

Each carries 1 mark.

91. National flower of Nepal:
    a) Sunflower
    b) Rhododendron
    c) Lotus
    d) Jasmine

92. The largest continent is:
    a) Africa
    b) Asia
    c) Europe
    d) America

93. The author of Muna Madan:
    a) Bhanubhakta
    b) Laxmi Prasad Devkota
    c) Motiram Bhatta
    d) Balkrishna Sama

94. UNO headquarters is in:
    a) London
    b) Paris
    c) New York
    d) Geneva

95. First woman to climb Mt. Everest:
    a) Junko Tabei
    b) Pasang Lhamu Sherpa
    c) Mira Rai
    d) Aruna Lama

96. Currency of Bangladesh is:
    a) Rupee
    b) Taka
    c) Ringgit
    d) Yen

97. Who discovered gravity?
    a) Albert Einstein
    b) Isaac Newton
    c) Galileo Galilei
    d) C.V. Raman

98. The Sugauli Treaty was signed in:
    a) 1816 AD
    b) 1846 AD
    c) 1768 AD
    d) 1950 AD

99. The smallest bone in human body:
    a) Stapes
    b) Femur
    c) Tibia
    d) Humerus

100. First President of Nepal:
     a) Girija Prasad Koirala
     b) Dr. Ram Baran Yadav
     c) Pushpa Kamal Dahal
     d) Bidya Devi Bhandari

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Answer Key 

Mathematics (Q1–Q30):
1b, 2c, 3c, 4a, 5a, 6b, 7a, 8a, 9c, 10a, 11a, 12c, 13b, 14a, 15a, 16a, 17c, 18c, 19b, 20b, 21a, 22b, 23c, 24c, 25c, 26b, 27b, 28c, 29b, 30b

Science (Q31–Q60):
31b, 32b, 33b, 34a, 35a, 36c, 37b, 38b, 39d, 40a, 41a, 42c, 43b, 44b, 45a, 46c, 47b, 48a, 49b, 50a, 51a, 52c, 53c, 54d, 55a, 56c, 57b, 58c, 59a, 60b

English (Q61–Q90):
61b, 62b, 63b, 64c, 65b, 66b, 67b, 68c, 69b, 70c, 71a, 72a, 73b, 74b, 75b, 76a, 77b, 78c, 79c, 80a, 81b, 82a, 83a, 84a, 85b, 86b, 87d, 88b, 89c, 90b

General Knowledge (Q91–Q100):
91b, 92b, 93b, 94c, 95a, 96b, 97b, 98a, 99a, 100b