NUST Engineering Past Paper-4

200 MCQs — Click "Reveal" to see the correct answer.

1. 1

   NUST Engineering Past Paper-4

   Compute .

   A

   B

   C

   D

   None of these

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2. 2

   NUST Engineering Past Paper-4

   Evaluate .

   A

   B

   C

   D

   1

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3. 3

   NUST Engineering Past Paper-4

   Evaluate .

   A

   12

   B

   10

   C

   15

   D

   9

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4. 4

   NUST Engineering Past Paper-4

   If two fair dice are rolled together, what is the probability that the sum of the numbers obtained is a multiple of 5?

   A

   B

   C

   D

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5. 5

   NUST Engineering Past Paper-4

   Determine the equation of the normal to the ellipse at the point .

   A

   B

   C

   D

   None of these

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6. 6

   NUST Engineering Past Paper-4

   If the eccentricity of a conic equals , the conic is:

   A

   Hyperbola

   B

   None of these

   C

   Point

   D

   Circle

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7. 7

   NUST Engineering Past Paper-4

   Two ordinary fair dice and one coin are tossed together. How many distinct outcomes are possible?

   A

   72

   B

   12

   C

   24

   D

   36

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8. 8

   NUST Engineering Past Paper-4

   Determine the area of a triangle whose sides have lengths , , .

   A

   B

   C

   D

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9. 9

   NUST Engineering Past Paper-4

   Evaluate .

   A

   B

   C

   D

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10. 10

    NUST Engineering Past Paper-4

    Evaluate the infinite geometric series .

    A

    B

    Sum not possible

    C

    D

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11. 11

    NUST Engineering Past Paper-4

    Evaluate .

    A

    B

    C

    D

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12. 12

    NUST Engineering Past Paper-4

    Evaluate the definite integral .

    A

    B

    C

    D

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13. 13

    NUST Engineering Past Paper-4

    Among the following quadrilateral/triangle shapes, identify the one in which it is generally NOT possible to inscribe a circle tangent to ALL sides.

    A

    Rectangle

    B

    Triangle

    C

    Parallelogram

    D

    Square

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14. 14

    NUST Engineering Past Paper-4

    Given , determine the product .

    A

    B

    C

    D

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15. 15

    NUST Engineering Past Paper-4

    State the derivative of the inverse-tangent function with respect to .

    A

    B

    C

    D

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16. 16

    NUST Engineering Past Paper-4

    State the geometric relationship between the radius drawn to a point of tangency on a circle and the tangent line at that point.

    A

    Perpendicular to the tangent

    B

    Equal in length to the tangent

    C

    Parallel to the tangent

    D

    The diameter of the circle

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17. 17

    NUST Engineering Past Paper-4

    Evaluate the determinant of the matrix , where is a complex cube root of unity.

    A

    B

    C

    D

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18. 18

    NUST Engineering Past Paper-4

    For , given and , compute the differential .

    A

    B

    C

    D

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19. 19

    NUST Engineering Past Paper-4

    Evaluate .

    A

    B

    C

    D

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20. 20

    NUST Engineering Past Paper-4

    Evaluate .

    A

    B

    C

    D

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21. 21

    NUST Engineering Past Paper-4

    Simplify the trigonometric expression .

    A

    B

    C

    D

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22. 22

    NUST Engineering Past Paper-4

    By the Law of Sines, the ratio in any triangle equals which of the listed quantities (where denotes the circumradius)?

    A

    B

    C

    D

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23. 23

    NUST Engineering Past Paper-4

    Evaluate .

    A

    B

    C

    D

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24. 24

    NUST Engineering Past Paper-4

    If with acute, determine .

    A

    B

    C

    D

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25. 25

    NUST Engineering Past Paper-4

    A fair coin is tossed times. Determine the probability of getting exactly heads.

    A

    B

    C

    D

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26. 26

    NUST Engineering Past Paper-4

    Evaluate .

    A

    B

    C

    D

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27. 27

    NUST Engineering Past Paper-4

    Identify the number that must be added to the set so that the average of the resulting five-element set becomes .

    A

    B

    C

    D

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28. 28

    NUST Engineering Past Paper-4

    Find the derivative of .

    A

    B

    C

    D

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29. 29

    NUST Engineering Past Paper-4

    State the derivative of with respect to on the principal branch.

    A

    B

    C

    D

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30. 30

    NUST Engineering Past Paper-4

    Rewrite the equation in the standard ellipse form .

    A

    B

    C

    D

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31. 31

    NUST Engineering Past Paper-4

    In a triangle, , , and the angle opposite is . Determine the angle opposite .

    A

    B

    C

    D

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32. 32

    NUST Engineering Past Paper-4

    If is a purely imaginary number, determine the smallest positive value of .

    A

    B

    C

    D

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33. 33

    NUST Engineering Past Paper-4

    Evaluate .

    A

    B

    C

    D

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34. 34

    NUST Engineering Past Paper-4

    Evaluate .

    A

    B

    C

    D

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35. 35

    NUST Engineering Past Paper-4

    Determine the product , where is the identity matrix and .

    A

    B

    C

    D

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36. 36

    NUST Engineering Past Paper-4

    Given that is a root of , determine the quotient when this polynomial is divided by .

    A

    B

    C

    D

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37. 37

    NUST Engineering Past Paper-4

    Determine the value of such that is a factor of .

    A

    B

    C

    D

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38. 38

    NUST Engineering Past Paper-4

    Evaluate .

    A

    B

    C

    D

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39. 39

    NUST Engineering Past Paper-4

    Determine the total number of solutions of the equation that lie in the interval .

    A

    B

    C

    D

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40. 40

    NUST Engineering Past Paper-4

    Determine the range of .

    A

    B

    C

    D

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41. 41

    NUST Engineering Past Paper-4

    Determine the domain of .

    A

    B

    C

    D

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42. 42

    NUST Engineering Past Paper-4

    If , determine .

    A

    B

    C

    D

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43. 43

    NUST Engineering Past Paper-4

    A circular arc has radius and subtends a central angle . Determine its arc length .

    A

    B

    C

    D

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44. 44

    NUST Engineering Past Paper-4

    If with acute, determine .

    A

    B

    C

    D

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45. 45

    NUST Engineering Past Paper-4

    Evaluate (for , ).

    A

    B

    C

    D

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46. 46

    NUST Engineering Past Paper-4

    Consider the arithmetic progression of complex numbers Identify which of the listed complex numbers is NOT a term of this sequence.

    A

    B

    C

    D

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47. 47

    NUST Engineering Past Paper-4

    For a geometric series with first term and common ratio , find the sum to infinity .

    A

    B

    C

    D

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48. 48

    NUST Engineering Past Paper-4

    Identify which of the listed functions is even for all real values of .

    A

    B

    C

    D

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49. 49

    NUST Engineering Past Paper-4

    Rewrite the circle in standard form by completing the square.

    A

    B

    C

    D

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50. 50

    NUST Engineering Past Paper-4

    An ellipse has foci at , centre at the origin, and semi-major axis . Determine its equation.

    A

    B

    C

    D

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51. 51

    NUST Engineering Past Paper-4

    Evaluate .

    A

    B

    C

    D

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52. 52

    NUST Engineering Past Paper-4

    Find the slope of the line passing through and .

    A

    B

    C

    D

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53. 53

    NUST Engineering Past Paper-4

    For an arithmetic series with and common difference , find .

    A

    B

    C

    D

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54. 54

    NUST Engineering Past Paper-4

    Determine the equation of the directrix of the parabola (with ).

    A

    B

    C

    D

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55. 55

    NUST Engineering Past Paper-4

    Bilal scored marks (out of ) in tests. How many marks does he need on the test to achieve an average of ?

    A

    B

    C

    D

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56. 56

    NUST Engineering Past Paper-4

    Identify the necessary and sufficient property a function must possess in order to have an inverse function on its full codomain.

    A

    One-to-one (bijective)

    B

    Strictly increasing

    C

    Continuous

    D

    Differentiable

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57. 57

    NUST Engineering Past Paper-4

    Evaluate .

    A

    B

    C

    D

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58. 58

    NUST Engineering Past Paper-4

    Vector runs from to . A second vector, parallel and equal in magnitude/direction, has its terminal point at . Determine the initial point of this second vector, expressed as a position vector.

    A

    B

    C

    D

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59. 59

    NUST Engineering Past Paper-4

    If , determine the positive value of .

    A

    B

    C

    D

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60. 60

    NUST Engineering Past Paper-4

    Evaluate the determinant of the matrix , where is a complex cube root of unity.

    A

    B

    C

    D

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61. 61

    NUST Engineering Past Paper-4

    A class has girls and boys. Half the boys and half the girls have brown eyes. If one student is selected at random, determine the probability that the student is a girl OR has brown eyes.

    A

    B

    C

    D

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62. 62

    NUST Engineering Past Paper-4

    Evaluate .

    A

    Infinity (does not exist)

    B

    C

    D

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63. 63

    NUST Engineering Past Paper-4

    Identify the local extremum behaviour of on .

    A

    B

    C

    Does not have a local maximum

    D

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64. 64

    NUST Engineering Past Paper-4

    In the sequence (where each successive term multiplies by an increasing factor), determine the term.

    A

    B

    C

    D

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65. 65

    NUST Engineering Past Paper-4

    Find the perpendicular distance between the parallel lines and .

    A

    B

    C

    D

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66. 66

    NUST Engineering Past Paper-4

    Given and , determine , where is the angle between and .

    A

    B

    C

    D

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67. 67

    NUST Engineering Past Paper-4

    Determine the adjoint (classical adjugate) of the scalar matrix .

    A

    B

    C

    D

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68. 68

    NUST Engineering Past Paper-4

    Determine the derivative of with respect to (where , ).

    A

    B

    C

    D

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69. 69

    NUST Engineering Past Paper-4

    Two positive consecutive integers sum to . Express their product in terms of .

    A

    B

    C

    D

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70. 70

    NUST Engineering Past Paper-4

    Points and are evaluated against the line . Identify the correct statement about their positions relative to the line.

    A

    and are on opposite sides of the line

    B

    and are on the same side of the line

    C

    Both and lie on the line

    D

    Only lies on the line

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71. 71

    NUST Engineering Past Paper-4

    Evaluate .

    A

    B

    C

    D

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72. 72

    NUST Engineering Past Paper-4

    Find the perpendicular distance between the parallel lines and .

    A

    B

    C

    D

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73. 73

    NUST Engineering Past Paper-4

    In triangle , the area is , angle , and side . Determine side .

    A

    B

    C

    D

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74. 74

    NUST Engineering Past Paper-4

    Let be real numbers and . The vector is perpendicular to . State the algebraic condition that and must satisfy.

    A

    B

    C

    D

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75. 75

    NUST Engineering Past Paper-4

    Determine (for ).

    A

    B

    C

    D

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76. 76

    NUST Engineering Past Paper-4

    Find by implicit differentiation from .

    A

    B

    C

    D

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77. 77

    NUST Engineering Past Paper-4

    For , evaluate .

    A

    B

    C

    D

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78. 78

    NUST Engineering Past Paper-4

    A unit vector lies in the second quadrant and makes an angle of with the negative -axis (measured toward the positive -axis). Determine its -component.

    A

    B

    C

    D

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79. 79

    NUST Engineering Past Paper-4

    Determine the antiderivative of .

    A

    B

    C

    D

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80. 80

    NUST Engineering Past Paper-4

    Determine the principal value of , where .

    A

    B

    C

    D

    None

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81. 81

    NUST Engineering Past Paper-4

    Pick the word closest in meaning to 'Alias':

    A

    Title

    B

    Acronym

    C

    Pseudonym

    D

    Reality

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82. 82

    NUST Engineering Past Paper-4

    Pick the word closest in meaning to 'Acrimonious':

    A

    Bitter

    B

    Cordial

    C

    Serene

    D

    Friendly

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83. 83

    NUST Engineering Past Paper-4

    Pick the word closest in meaning to 'Adroit':

    A

    Awkward

    B

    Inept

    C

    Deft

    D

    Clumsy

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84. 84

    NUST Engineering Past Paper-4

    Pick the word most nearly OPPOSITE in meaning to 'Arable':

    A

    Barren

    B

    Cultivable

    C

    Productive

    D

    Fruitful

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85. 85

    NUST Engineering Past Paper-4

    Pick the option that best defines 'Bawdy':

    A

    Extremely formal and serious

    B

    Dealing with sexual matters in a humorous way

    C

    Overly sad and melancholy

    D

    Relating to children's entertainment

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86. 86

    NUST Engineering Past Paper-4

    Pick the word closest in meaning to 'Bawdy':

    A

    Prim

    B

    Decent

    C

    Ribald

    D

    Refined

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87. 87

    NUST Engineering Past Paper-4

    Pick the word most nearly OPPOSITE in meaning to 'Beguile':

    A

    Lure

    B

    Captivate

    C

    Repel

    D

    Charm

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88. 88

    NUST Engineering Past Paper-4

    Pick the word most nearly OPPOSITE in meaning to 'Belittle':

    A

    Denigrate

    B

    Deprecate

    C

    Demean

    D

    Extol

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89. 89

    NUST Engineering Past Paper-4

    Pick the word most nearly OPPOSITE in meaning to 'Commingle':

    A

    Blend

    B

    Combine

    C

    Segregate

    D

    Merge

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90. 90

    NUST Engineering Past Paper-4

    Pick the option that best defines 'Concede':

    A

    To admit or acknowledge something is true, often reluctantly

    B

    To celebrate a victory

    C

    To argue against evidence

    D

    To firmly deny a claim

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91. 91

    NUST Engineering Past Paper-4

    Pick the word most nearly OPPOSITE in meaning to 'Contradict':

    A

    Corroborate

    B

    Oppose

    C

    Negate

    D

    Deny

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92. 92

    NUST Engineering Past Paper-4

    Pick the word closest in meaning to 'Diligent':

    A

    Industrious

    B

    Careless

    C

    Negligent

    D

    Idle

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93. 93

    NUST Engineering Past Paper-4

    Pick the word closest in meaning to 'Docile':

    A

    Compliant

    B

    Stubborn

    C

    Defiant

    D

    Rebellious

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94. 94

    NUST Engineering Past Paper-4

    Pick the word most nearly OPPOSITE in meaning to 'Flair':

    A

    Knack

    B

    Genius

    C

    Incompetence

    D

    Talent

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95. 95

    NUST Engineering Past Paper-4

    Pick the word closest in meaning to 'Flamboyant':

    A

    Reserved

    B

    Understated

    C

    Ostentatious

    D

    Modest

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96. 96

    NUST Engineering Past Paper-4

    Pick the option that best defines 'Fugitive':

    A

    A person who has escaped from captivity or is fleeing from authority

    B

    A government official in exile

    C

    Someone who turns themselves in to authorities

    D

    A person traveling abroad legally

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97. 97

    NUST Engineering Past Paper-4

    Pick the option that best defines 'Gambol':

    A

    To argue about trivial matters

    B

    To run or jump about playfully

    C

    To work continuously without rest

    D

    To walk slowly and solemnly

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98. 98

    NUST Engineering Past Paper-4

    Pick the word closest in meaning to 'Mitigate':

    A

    Alleviate

    B

    Intensify

    C

    Worsen

    D

    Aggravate

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99. 99

    NUST Engineering Past Paper-4

    Pick the word most nearly OPPOSITE in meaning to 'Penurious':

    A

    Pauper

    B

    Indigent

    C

    Opulent

    D

    Destitute

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100. 100

     NUST Engineering Past Paper-4

     Pick the word closest in meaning to 'Sedentary':

     A

     Active

     B

     Energetic

     C

     Inactive

     D

     Vigorous

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101. 101

     NUST Engineering Past Paper-4

     Pick the option that best defines 'Venal':

     A

     Having high moral integrity

     B

     Easily forgiven; minor

     C

     Strictly honest in business

     D

     Open to bribery; corrupt

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102. 102

     NUST Engineering Past Paper-4

     Pick the word closest in meaning to 'Reinforcement':

     A

     Strengthening

     B

     Erosion

     C

     Weakening

     D

     Undermining

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103. 103

     NUST Engineering Past Paper-4

     Pick the option that best defines 'Impressive':

     A

     Easily forgettable

     B

     Evoking admiration through size, quality, or skill

     C

     Below average in quality

     D

     Dull and unremarkable

     Reveal answer
104. 104

     NUST Engineering Past Paper-4

     Pick the word most nearly OPPOSITE in meaning to 'Prevailing':

     A

     Pervasive

     B

     Rare

     C

     Current

     D

     Widespread

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105. 105

     NUST Engineering Past Paper-4

     Pick the term closest in meaning to 'Pedestrians':

     A

     Walkers

     B

     Cyclists

     C

     Motorists

     D

     Commuters

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106. 106

     NUST Engineering Past Paper-4

     Pick the word most nearly OPPOSITE in meaning to 'Common':

     A

     Usual

     B

     Ordinary

     C

     Typical

     D

     Rare

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107. 107

     NUST Engineering Past Paper-4

     Pick the word most nearly OPPOSITE in meaning to 'Clear':

     A

     Transparent

     B

     Obvious

     C

     Obscure

     D

     Apparent

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108. 108

     NUST Engineering Past Paper-4

     Complete the analogy: 'Torso : Arm :: Tree Trunk : ___'.

     A

     Branch

     B

     Bark

     C

     Leaf

     D

     Roots

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109. 109

     NUST Engineering Past Paper-4

     Identify the grammatically correct version of the following sentence among the options:

     A

     Repeated efforts must be made before you give up.

     B

     Before you give up, repeated efforts you must make.

     C

     You must make repeated efforts before you give up.

     D

     Efforts that are repeated must be made before giving up.

     Reveal answer
110. 110

     NUST Engineering Past Paper-4

     Pick the standard collective noun used for a group of fish swimming together.

     A

     Flock

     B

     School

     C

     Herd

     D

     Pack

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111. 111

     NUST Engineering Past Paper-4

     Pick the antonym of the adjective VINDICTIVE.

     A

     Forgiving

     B

     Spiteful

     C

     Revengeful

     D

     Malicious

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112. 112

     NUST Engineering Past Paper-4

     Identify the environment(s) in which AMPHIBIANS live, in keeping with the biological meaning of the word.

     A

     Only in water

     B

     Both on land and in water

     C

     Neither on land nor in water

     D

     Only on land

     Reveal answer
113. 113

     NUST Engineering Past Paper-4

     Pick the option that best captures the meaning of the noun PROCRASTINATION.

     A

     Completing tasks early

     B

     Planning tasks in detail

     C

     Working efficiently ahead of schedule

     D

     Delaying or postponing tasks

     Reveal answer
114. 114

     NUST Engineering Past Paper-4

     Pick the correctly spelled compound noun meaning a man whose occupation involves selling things on behalf of an employer.

     A

     Salemsan

     B

     Salesmann

     C

     Saleesman

     D

     Salesman

     Reveal answer
115. 115

     NUST Engineering Past Paper-4

     Pick the option that best captures the meaning of the adjective LAX.

     A

     Precise and demanding

     B

     Energetic and motivated

     C

     Strict and disciplined

     D

     Not strict; careless or relaxed

     Reveal answer
116. 116

     NUST Engineering Past Paper-4

     Complete the analogy: TAUNT is to CHALLENGE as PLACATE is to ___.

     A

     Anger

     B

     Insult

     C

     Provoke

     D

     Calm

     Reveal answer
117. 117

     NUST Engineering Past Paper-4

     Pick the option that best captures the meaning of the noun EQUIVOCATION.

     A

     Expressing agreement openly

     B

     Using ambiguous or misleading language to avoid commitment

     C

     Speaking with clarity and directness

     D

     Stating facts in an aggressive manner

     Reveal answer
118. 118

     NUST Engineering Past Paper-4

     Fill the blank with the best descriptive adjective: 'His ___ features reminded me of the missing links.'

     A

     Euphemistic

     B

     Simian

     C

     Skin

     D

     Vicarious

     Reveal answer
119. 119

     NUST Engineering Past Paper-4

     Pick the sentence with the correct English ordering of cumulative adjectives preceding a noun.

     A

     I bought new white Suzuki Swift.

     B

     I bought Swift white Suzuki new.

     C

     I bought Suzuki new white Swift.

     D

     I bought white new Suzuki Swift.

     Reveal answer
120. 120

     NUST Engineering Past Paper-4 NUST Engineering Past Paper-6

     Pick the synonym of the adjective NEFARIOUS.

     A

     Virtuous

     B

     Gentle

     C

     Honest

     D

     Wicked

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121. 121

     NUST Engineering Past Paper-4

     Pick the synonym of the verb BEGUILE (in its everyday sense).

     A

     Frighten

     B

     Repel

     C

     Charm

     D

     Bore

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122. 122

     NUST Engineering Past Paper-4

     Cloze: Pick the pair of words that best fills the blanks in 'She had her ___ [nature], which covered her ___ personality.'

     A

     Mischievous, unseen

     B

     Silent, cheerful

     C

     Hidden, bitter

     D

     Obvious, pleasant

     Reveal answer
123. 123

     NUST Engineering Past Paper-4

     Pick the option that best captures the meaning of the verb ENTHRALL.

     A

     Bore

     B

     Frighten

     C

     Captivate

     D

     Repel

     Reveal answer
124. 124

     NUST Engineering Past Paper-4

     As a verb, BROOK has a specific meaning. Pick the option that best captures it.

     A

     Avoid

     B

     Celebrate

     C

     Ignore

     D

     Tolerate

     Reveal answer
125. 125

     NUST Engineering Past Paper-4

     In Young's double-slit setup, monochromatic light of wavelength nm illuminates two slits separated by mm, with the screen at m. Find the fringe width.

     A

     5 mm

     B

     10 mm

     C

     2 mm

     D

     0.5 mm

     Reveal answer
126. 126

     NUST Engineering Past Paper-4

     Three point charges are placed on a line: at the left, at the right, and at the midpoint between them. For the net force on to be zero, what value (sign and magnitude) must take?

     A

     B

     C

     D

     Reveal answer
127. 127

     NUST Engineering Past Paper-19 NUST Engineering Past Paper-4

     The conclusion that the luminiferous ether does NOT exist as a medium permeating space is most directly supported by which of the following?

     A

     Coulomb's Law

     B

     Newton's Laws of Motion

     C

     Faraday's Law

     D

     Michelson-Morley Experiment

     Reveal answer
128. 128

     NUST Engineering Past Paper-4

     If the mass of a simple pendulum bob is changed from to , what effect does this have on the time period of oscillation?

     A

     Increase

     B

     Decrease

     C

     Become double

     D

     Remain the same

     Reveal answer
129. 129

     NUST Engineering Past Paper-4

     Identify the unit in the following list that is NOT one of the seven SI base units.

     A

     m²

     B

     A

     C

     K

     D

     cd

     Reveal answer
130. 130

     NUST Engineering Past Paper-4

     A vertical force of N is applied to lift an object to a height of m over a time of s. Determine the work done by this force.

     A

     J

     B

     J

     C

     J

     D

     J

     Reveal answer
131. 131

     NUST Engineering Past Paper-4

     Identify the law of thermodynamics that explains why a refrigerator REQUIRES external work input in order to move heat from a cold reservoir to a hot reservoir.

     A

     Third law of thermodynamics

     B

     First law of thermodynamics

     C

     Zeroth law of thermodynamics

     D

     Second law of thermodynamics

     Reveal answer
132. 132

     NUST Engineering Past Paper-4

     When a body falling through a viscous medium has reached its TERMINAL velocity, identify the net force acting on it.

     A

     Downward

     B

     Zero

     C

     None of these

     D

     Upward

     Reveal answer
133. 133

     NUST Engineering Past Paper-20 NUST Engineering Past Paper-4

     Which spectral series of the hydrogen atom lies in the VISIBLE region of the electromagnetic spectrum?

     A

     Brackett series

     B

     Lyman series

     C

     Paschen series

     D

     Balmer series

     Reveal answer
134. 134

     NUST Engineering Past Paper-4

     Identify the SI unit of the universal gravitational constant .

     A

     B

     C

     D

     Reveal answer
135. 135

     NUST Engineering Past Paper-1 NUST Engineering Past Paper-4

     Two equal, like point charges are placed at points I and III on a straight line. At which point does the net electric field vanish?

     A

     At point III

     B

     At point II (the midpoint)

     C

     Between I and III (somewhere in between)

     D

     At point I

     Reveal answer
136. 136

     NUST Engineering Past Paper-1 NUST Engineering Past Paper-4

     Identify the physical quantity for which the RADIAN is the SI supplementary (derived) unit.

     A

     Solid angle

     B

     Plane angle

     C

     Luminous flux

     D

     Intensity of light

     Reveal answer
137. 137

     NUST Engineering Past Paper-4

     Determine the dimensional formula of the coefficient of viscosity .

     A

     B

     C

     D

     Reveal answer
138. 138

     NUST Engineering Past Paper-4

     Determine the number of significant figures in the measurement .

     A

     3

     B

     7

     C

     4

     D

     6

     Reveal answer
139. 139

     NUST Engineering Past Paper-4

     Determine the magnitude of .

     A

     7

     B

     6

     C

     5

     D

     8

     Reveal answer
140. 140

     NUST Engineering Past Paper-4

     Compute the dot product for and .

     A

     B

     2

     C

     0

     D

     14

     Reveal answer
141. 141

     NUST Engineering Past Paper-4

     An object starts from rest and travels m in s under UNIFORM acceleration. Determine its final velocity.

     A

     m/s

     B

     m/s

     C

     m/s

     D

     m/s

     Reveal answer
142. 142

     NUST Engineering Past Paper-4

     A ball is projected from level ground at to the horizontal with initial speed m/s. Taking m/s, determine the maximum height reached.

     A

     m

     B

     m

     C

     m

     D

     m

     Reveal answer
143. 143

     NUST Engineering Past Paper-4

     A block slides down a FRICTIONLESS incline of angle . Determine its acceleration along the slope (take m/s).

     A

     m/s²

     B

     m/s²

     C

     m/s²

     D

     m/s²

     Reveal answer
144. 144

     NUST Engineering Past Paper-4

     A kg person climbs stairs of height m in s. Taking m/s, determine the power generated.

     A

     W

     B

     W

     C

     W

     D

     W

     Reveal answer
145. 145

     NUST Engineering Past Paper-4

     A horizontal force of N pushes a kg box through m on a horizontal surface with coefficient of kinetic friction . Taking m/s, determine the NET work done on the box.

     A

     J

     B

     J

     C

     J

     D

     J

     Reveal answer
146. 146

     NUST Engineering Past Paper-4

     Determine the moment of inertia of a uniform thin rod of mass and length about an axis through one end, perpendicular to the rod.

     A

     B

     C

     D

     Reveal answer
147. 147

     NUST Engineering Past Paper-4

     If the Earth's mass were doubled while its radius remained the same, how would the surface gravitational acceleration change?

     A

     Halves

     B

     Quadruples

     C

     Doubles

     D

     Remains the same

     Reveal answer
148. 148

     NUST Engineering Past Paper-4

     Compare the orbital speed of a satellite at a height equal to the Earth's radius (i.e., orbital radius ) with the orbital speed of a satellite just above the Earth's surface.

     A

     Same

     B

     2 times smaller

     C

     4 times smaller

     D

     times smaller

     Reveal answer
149. 149

     NUST Engineering Past Paper-4

     Water flows through a horizontal pipe. At a CONSTRICTION (narrowed section), according to Bernoulli's principle, how do the speed and pressure of the flow change?

     A

     Pressure decreases, speed increases

     B

     Both increase

     C

     Both decrease

     D

     Pressure increases, speed increases

     Reveal answer
150. 150

     NUST Engineering Past Paper-4

     In simple harmonic motion, the restoring force is directly proportional to which quantity?

     A

     Velocity

     B

     Acceleration

     C

     Displacement

     D

     Mass

     Reveal answer
151. 151

     NUST Engineering Past Paper-4

     A spring of constant N/m is compressed by cm. Determine the elastic potential energy stored.

     A

     J

     B

     J

     C

     J

     D

     J

     Reveal answer
152. 152

     NUST Engineering Past Paper-4

     For a string of length fixed at both ends, identify the wavelength of the FUNDAMENTAL standing-wave mode.

     A

     B

     C

     D

     Reveal answer
153. 153

     NUST Engineering Past Paper-4

     Identify the correct mathematical expression of the FIRST law of thermodynamics (sign convention: = work done BY the system).

     A

     for isothermal processes

     B

     constant

     C

     Entropy always increases

     D

     Reveal answer
154. 154

     NUST Engineering Past Paper-4

     Identify the electric potential at a point at distance from a point charge (with at infinity).

     A

     B

     C

     D

     Reveal answer
155. 155

     NUST Engineering Past Paper-4

     Identify the energy stored in a capacitor of capacitance holding charge .

     A

     B

     C

     D

     Reveal answer
156. 156

     NUST Engineering Past Paper-4

     Kirchhoff's Current Law (KCL) states that the algebraic sum of currents at any junction is zero. This is fundamentally a consequence of which conservation law?

     A

     Conservation of charge

     B

     Conservation of energy

     C

     Newton's laws

     D

     Faraday's law

     Reveal answer
157. 157

     NUST Engineering Past Paper-4

     To convert a galvanometer into an AMMETER, what type of resistance should be connected and in what configuration?

     A

     Low resistance in series

     B

     High resistance in parallel

     C

     Low resistance in parallel

     D

     High resistance in series

     Reveal answer
158. 158

     NUST Engineering Past Paper-4

     Identify the force per unit length between two long parallel wires carrying currents and , separated by distance .

     A

     B

     C

     D

     Reveal answer
159. 159

     NUST Engineering Past Paper-4

     An AC generator operates at frequency Hz. Determine its angular frequency .

     A

     rad/s

     B

     rad/s

     C

     rad/s

     D

     rad/s

     Reveal answer
160. 160

     NUST Engineering Past Paper-4

     Determine the RMS (root-mean-square) value of an AC voltage whose PEAK amplitude is .

     A

     B

     C

     D

     Reveal answer
161. 161

     NUST Engineering Past Paper-4

     In Young's double-slit experiment with m, mm, and nm, determine the fringe width.

     A

     mm

     B

     mm

     C

     mm

     D

     mm

     Reveal answer
162. 162

     NUST Engineering Past Paper-4

     A thin converging lens has focal length cm. Determine its optical power in diopters.

     A

     D

     B

     D

     C

     D

     D

     D

     Reveal answer
163. 163

     NUST Engineering Past Paper-4

     Identify the approximate wavelength range of VISIBLE light.

     A

     – μm

     B

     – nm

     C

     – nm

     D

     – nm

     Reveal answer
164. 164

     NUST Engineering Past Paper-4

     Identify the MAXIMUM Compton wavelength shift, attained for back-scattering at .

     A

     B

     C

     D

     Reveal answer
165. 165

     NUST Engineering Past Paper-4

     Identify the approximate minimum escape speed from the Earth's surface.

     A

     km/s

     B

     km/s

     C

     km/s

     D

     km/s

     Reveal answer
166. 166

     NUST Engineering Past Paper-4

     State the formula given by Torricelli's theorem for the speed of efflux of an ideal liquid from a small orifice at depth below the free surface in a large tank.

     A

     B

     C

     D

     Reveal answer
167. 167

     NUST Engineering Past Paper-4

     Polarization (the property of having a preferred oscillation direction) is observed only for which type of wave?

     A

     Longitudinal waves

     B

     All waves

     C

     Transverse waves

     D

     Sound waves

     Reveal answer
168. 168

     NUST Engineering Past Paper-4

     Identify the condition for the FIRST DARK fringe in single-slit Fraunhofer diffraction (slit width , wavelength , observation angle ).

     A

     B

     C

     D

     Reveal answer
169. 169

     NUST Engineering Past Paper-4

     Two equal charges experience Coulomb force in vacuum. If a dielectric of constant now fills the space between them (with the separation unchanged), determine the new force.

     A

     B

     C

     D

     Reveal answer
170. 170

     NUST Engineering Past Paper-4

     A wire of resistance is stretched to DOUBLE its original length, while the volume is conserved (so the cross-section reduces accordingly). Determine the new resistance.

     A

     B

     C

     D

     Reveal answer
171. 171

     NUST Engineering Past Paper-4

     Identify the magnetic field at the CENTRE of a single circular loop of radius carrying current .

     A

     B

     C

     D

     Reveal answer
172. 172

     NUST Engineering Past Paper-4

     A bar magnet falls vertically through a horizontal conducting ring. Describe what the ring does to the falling magnet as the magnet ENTERS the ring.

     A

     No force acts

     B

     The ring repels the magnet

     C

     The ring becomes permanently magnetized

     D

     The ring attracts the magnet

     Reveal answer
173. 173

     NUST Engineering Past Paper-4

     Determine the ionization energy of the hydrogen atom (the energy needed to remove the ground-state electron to infinity).

     A

     eV

     B

     eV

     C

     eV

     D

     eV

     Reveal answer
174. 174

     NUST Engineering Past Paper-4

     An ideal transformer has primary turns, secondary turns, and primary current A. Determine the secondary current.

     A

     A

     B

     A

     C

     A

     D

     A

     Reveal answer
175. 175

     NUST Engineering Past Paper-4

     Using Einstein's mass-energy equivalence , determine the energy released by the complete conversion of g of matter.

     A

     J

     B

     J

     C

     J

     D

     J

     Reveal answer
176. 176

     NUST Engineering Past Paper-4

     Determine the output of a logical OR gate with inputs and .

     A

     B

     0

     C

     1

     D

     Undefined

     Reveal answer
177. 177

     NUST Engineering Past Paper-4

     Determine the approximate barrier potential (cut-in voltage) of a forward-biased silicon p-n junction diode at room temperature.

     A

     V

     B

     V

     C

     V

     D

     V

     Reveal answer
178. 178

     NUST Engineering Past Paper-4

     State the de Broglie relation between a particle's wavelength and its momentum .

     A

     B

     C

     D

     Reveal answer
179. 179

     NUST Engineering Past Paper-4

     A radioactive substance has half-life years. Determine the fraction of the original sample remaining after years.

     A

     B

     C

     D

     Reveal answer
180. 180

     NUST Engineering Past Paper-4

     Identify the threshold wavelength for the photoelectric effect from a metal with work function .

     A

     B

     C

     D

     Reveal answer
181. 181

     NUST Engineering Past Paper-4

     Heisenberg's uncertainty principle places a fundamental limit on the product of uncertainties in WHICH pair of conjugate physical quantities?

     A

     Position and momentum

     B

     Energy and power

     C

     Mass and acceleration

     D

     Position and velocity

     Reveal answer
182. 182

     NUST Engineering Past Paper-4

     Identify the part of the electromagnetic spectrum in which the LYMAN series of hydrogen lies.

     A

     Ultraviolet region

     B

     Visible region

     C

     X-ray region

     D

     Infrared region

     Reveal answer
183. 183

     NUST Engineering Past Paper-4

     Determine the quality factor of a series RLC circuit at resonance (resonant angular frequency ).

     A

     B

     C

     D

     Reveal answer
184. 184

     NUST Engineering Past Paper-4

     In Young's double-slit experiment, the screen distance is DOUBLED and simultaneously the slit separation is HALVED. Determine how the fringe width changes.

     A

     Doubles

     B

     Remains same

     C

     Becomes 4 times

     D

     Halves

     Reveal answer
185. 185

     NUST Engineering Past Paper-4

     Identify the hydrostatic gauge pressure at depth below the free surface of a fluid of density (with surface at atmospheric pressure).

     A

     B

     C

     D

     Reveal answer
186. 186

     NUST Engineering Past Paper-4

     Identify the nuclear reaction in which LIGHT nuclei combine to release energy.

     A

     Pair production

     B

     Beta decay

     C

     Nuclear fission

     D

     Nuclear fusion

     Reveal answer
187. 187

     NUST Engineering Past Paper-4

     For which element is the binding energy per nucleon HIGHEST?

     A

     Helium

     B

     Uranium

     C

     Iron

     D

     Hydrogen

     Reveal answer
188. 188

     NUST Engineering Past Paper-4

     Identify the Bohr quantization condition on the angular momentum of an electron in the -th orbit.

     A

     B

     C

     D

     Reveal answer
189. 189

     NUST Engineering Past Paper-4

     A spring-mass oscillator has spring constant N/m and mass kg. Determine its natural frequency .

     A

     Hz

     B

     Hz

     C

     Hz

     D

     Hz

     Reveal answer
190. 190

     NUST Engineering Past Paper-4

     A Carnot engine operates between a hot reservoir at K and a cold reservoir at K. Determine its efficiency.

     A

     B

     C

     D

     Reveal answer
191. 191

     NUST Engineering Past Paper-4

     Determine the capacitance of a parallel-plate capacitor with plate area m and plate separation mm (vacuum between plates). Use F/m.

     A

     pF

     B

     pF

     C

     pF

     D

     pF

     Reveal answer
192. 192

     NUST Engineering Past Paper-4

     Identify the cyclotron frequency (in Hz) of a proton (mass , charge ) moving in a uniform magnetic field of magnitude .

     A

     B

     C

     D

     Reveal answer
193. 193

     NUST Engineering Past Paper-4

     Among the following motions, identify the one that is NOT an example of simple harmonic motion.

     A

     Earth revolving around the Sun

     B

     Oscillations in an LC circuit

     C

     Mass-spring system

     D

     Simple pendulum (small angle)

     Reveal answer
194. 194

     NUST Engineering Past Paper-4

     A magnetic field of T is perpendicular to a straight wire of length m carrying current A. Determine the magnetic force on the wire.

     A

     N

     B

     N

     C

     N

     D

     N

     Reveal answer
195. 195

     NUST Engineering Past Paper-4

     Describe the current flow through a p-n junction diode under REVERSE bias.

     A

     A very small leakage current

     B

     No current at all

     C

     A large current

     D

     Only alternating current

     Reveal answer
196. 196

     NUST Engineering Past Paper-4

     If the universal gravitational constant is tripled, determine the corresponding effect on the surface gravitational acceleration on Earth.

     A

     Remain the same

     B

     Triple

     C

     Become one-third

     D

     Become nine times

     Reveal answer
197. 197

     NUST Engineering Past Paper-4

     In simple harmonic motion, if the total mechanical energy is reduced to one-fourth its original value, determine the corresponding change in amplitude .

     A

     becomes

     B

     becomes

     C

     becomes

     D

     remains unchanged

     Reveal answer
198. 198

     NUST Engineering Past Paper-4

     A spring-mass system has total mechanical energy and amplitude . Determine the spring constant .

     A

     B

     C

     D

     Reveal answer
199. 199

     NUST Engineering Past Paper-4

     In SHM with spring constant , mass , and maximum speed , compute the maximum acceleration.

     A

     B

     C

     D

     None of the above

     Reveal answer
200. 200

     NUST Engineering Past Paper-4

     When the measurements and are added together, determine how many significant figures the result should be reported with.

     A

     B

     C

     D

     Reveal answer