NUST Engineering Past Paper-9

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

1. 1

   NUST Engineering Past Paper-9

   Evaluate .

   A

   B

   1

   C

   0

   D

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2. 2

   NUST Engineering Past Paper-9

   Solve . Give the general solution.

   A

   B

   C

   D

   No solution

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3. 3

   NUST Engineering Past Paper-9

   How many solutions does the equation have in the interval ?

   A

   2

   B

   1

   C

   0

   D

   Infinitely many

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4. 4

   NUST Engineering Past Paper-9

   Let . Find .

   A

   B

   C

   D

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5. 5

   NUST Engineering Past Paper-9

   Write the equation of the circle whose centre is and whose radius is .

   A

   B

   C

   D

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6. 6

   NUST Engineering Past Paper-9

   Simplify .

   A

   1

   B

   C

   D

   None of these

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7. 7

   NUST Engineering Past Paper-9

   Classify the geometric series as convergent or divergent.

   A

   None of these

   B

   Divergent series

   C

   Convergent series

   D

   Not a series

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8. 8

   NUST Engineering Past Paper-9

   How many improper subsets does the empty set have?

   A

   1

   B

   0

   C

   2

   D

   None of these

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9. 9

   NUST Engineering Past Paper-9

   Which of the following points lies on the line ?

   A

   B

   C

   D

   None of these

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10. 10

    NUST Engineering Past Paper-9

    An ellipse with eccentricity degenerates into which shape?

    A

    Line

    B

    Parabola

    C

    Circle

    D

    Hyperbola

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11. 11

    NUST Engineering Past Paper-9

    Simplify .

    A

    B

    C

    D

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12. 12

    NUST Engineering Past Paper-9

    Evaluate the scalar expression .

    A

    B

    C

    D

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13. 13

    NUST Engineering Past Paper-9

    Evaluate .

    A

    B

    C

    D

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14. 14

    NUST Engineering Past Paper-9

    If , determine .

    A

    B

    C

    D

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15. 15

    NUST Engineering Past Paper-9

    Given that , determine .

    A

    None of these

    B

    eˣ((1/2)sec²(x/2) − tan(x/2))

    C

    eˣ(tan(x/2) + (1/2)sec²(x/2))

    D

    eˣ(tan(x/2) − (1/2)sec²(x/2))

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16. 16

    NUST Engineering Past Paper-9

    In an arithmetic progression, and . Determine .

    A

    B

    C

    D

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17. 17

    NUST Engineering Past Paper-9

    If form a geometric progression, which of the following triples is also in geometric progression?

    A

    B

    C

    None

    D

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18. 18

    NUST Engineering Past Paper-9

    If the diagonals of a quadrilateral are EQUAL in length AND perpendicular to each other, identify the most specific name of the quadrilateral.

    A

    Rectangle

    B

    Rhombus

    C

    Square

    D

    Parallelogram

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19. 19

    NUST Engineering Past Paper-9

    A shopkeeper has items. Over days, the percentages stolen (of the original total) are . Determine the total number of items stolen.

    A

    B

    C

    D

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20. 20

    NUST Engineering Past Paper-9

    A triangle has area , , . Determine the angle between sides and .

    A

    Not Possible

    B

    C

    D

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21. 21

    NUST Engineering Past Paper-9

    For the conic equation to represent a HYPERBOLA, what condition must hold on and ?

    A

    B

    C

    and have opposite signs

    D

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22. 22

    NUST Engineering Past Paper-9

    The empty set is an IMPROPER subset of which class of sets?

    A

    Only the empty set itself

    B

    Every non-empty set only

    C

    Every set

    D

    No set

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23. 23

    NUST Engineering Past Paper-9

    Solve the quadratic equation .

    A

    B

    C

    D

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24. 24

    NUST Engineering Past Paper-9

    For the series , identify the TRUE statement.

    A

    First term is

    B

    Sum of series is

    C

    Series is not convergent

    D

    Sum

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25. 25

    NUST Engineering Past Paper-9

    Determine the equation of a tangent to the parabola that is perpendicular to the line .

    A

    B

    C

    D

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26. 26

    NUST Engineering Past Paper-9

    In an arithmetic progression, and . Determine the first term .

    A

    B

    C

    D

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27. 27

    NUST Engineering Past Paper-9

    The probability that person A is alive in years is , and that person B is alive is . Assuming the two events are independent, determine the probability that BOTH are alive in years.

    A

    B

    C

    D

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28. 28

    NUST Engineering Past Paper-9

    Find by implicit differentiation from .

    A

    B

    C

    D

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29. 29

    NUST Engineering Past Paper-9

    Convert 1 radian to revolutions of a full circle.

    A

    rev

    B

    rev

    C

    rev

    D

    rev

    Reveal answer
30. 30

    NUST Engineering Past Paper-9

    Determine the DISCRIMINANT of the quadratic equation and use it to classify the roots.

    A

    (real, unequal, rational roots)

    B

    (complex roots)

    C

    (real, irrational)

    D

    (equal roots)

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31. 31

    NUST Engineering Past Paper-9

    Determine the DISCRIMINANT of the quadratic equation and use it to classify the roots.

    A

    (real equal roots)

    B

    (real distinct)

    C

    (complex roots)

    D

    (real distinct)

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32. 32

    NUST Engineering Past Paper-9

    Classify the NATURE of the roots of the quadratic equation using the discriminant.

    A

    Complex (imaginary) roots

    B

    Real, equal

    C

    Real, unequal, irrational

    D

    Real, unequal, rational

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33. 33

    NUST Engineering Past Paper-9

    Find the value(s) of for which the quadratic has EQUAL roots.

    A

    B

    C

    D

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34. 34

    NUST Engineering Past Paper-9

    Find ALL values of for which the quadratic has EQUAL roots.

    A

    B

    or

    C

    or

    D

    or

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35. 35

    NUST Engineering Past Paper-9

    Classify the NATURE of the roots of the parametric quadratic (where are real with ).

    A

    Always real and rational

    B

    Always imaginary

    C

    Always irrational

    D

    Always equal

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36. 36

    NUST Engineering Past Paper-9

    Divide the number into two parts such that the SUM of their squares EXCEEDS twice their product by . Determine the two parts.

    A

    and

    B

    and

    C

    and

    D

    and

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37. 37

    NUST Engineering Past Paper-9

    Determine the partial-fraction decomposition of .

    A

    B

    C

    D

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38. 38

    NUST Engineering Past Paper-9

    In the partial-fraction decomposition , determine the value of by the cover-up method.

    A

    B

    C

    D

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39. 39

    NUST Engineering Past Paper-9

    State the FIRST step required when decomposing an IMPROPER rational function (degree of numerator degree of denominator) into partial fractions.

    A

    Polynomial long division to extract a quotient

    B

    Completing the square

    C

    Cross multiplication

    D

    Setting the denominator to zero

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40. 40

    NUST Engineering Past Paper-9

    In the decomposition , determine the value of by the cover-up method at .

    A

    B

    C

    D

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41. 41

    NUST Engineering Past Paper-9

    If FIVE arithmetic means are inserted between and , determine the common difference of the resulting AP.

    A

    B

    C

    D

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42. 42

    NUST Engineering Past Paper-9

    Insert FOUR geometric means between and . State the resulting GP.

    A

    B

    C

    D

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43. 43

    NUST Engineering Past Paper-9

    State the formula for the GEOMETRIC MEAN () between two positive numbers and .

    A

    B

    C

    D

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44. 44

    NUST Engineering Past Paper-9

    For two distinct positive real numbers and , identify the correct CHAIN OF INEQUALITIES among their arithmetic mean (), geometric mean (), and harmonic mean ().

    A

    B

    C

    D

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45. 45

    NUST Engineering Past Paper-9

    State the precise condition under which an INFINITE GEOMETRIC SERIES has a FINITE SUM.

    A

    B

    C

    D

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46. 46

    NUST Engineering Past Paper-9

    Determine how many distinct -letter 'words' (arrangements) can be formed from the letters of the word 'PRIME' if no letter is repeated.

    A

    B

    C

    D

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47. 47

    NUST Engineering Past Paper-9

    A committee of is to be selected from men and women so that the committee contains AT LEAST ONE WOMAN. Determine the number of such committees.

    A

    B

    C

    D

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48. 48

    NUST Engineering Past Paper-9

    Given that , evaluate and express the answer as a binomial coefficient using the SMALLER lower index.

    A

    B

    (uncomputed)

    C

    D

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49. 49

    NUST Engineering Past Paper-9

    In a proof by induction of the identity , after assuming the statement at , state the algebraic equation that the INDUCTIVE STEP produces when adding to both sides.

    A

    B

    C

    D

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50. 50

    NUST Engineering Past Paper-9

    State the GENERAL TERM in the binomial expansion of for non-negative integer .

    A

    B

    C

    D

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51. 51

    NUST Engineering Past Paper-9

    Determine the coefficient of in the binomial expansion of .

    A

    B

    C

    D

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52. 52

    NUST Engineering Past Paper-9

    Determine the th term in the binomial expansion of .

    A

    B

    C

    D

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53. 53

    NUST Engineering Past Paper-9

    Determine the SUM of the coefficients of the EVEN-powered terms in the binomial expansion of .

    A

    B

    C

    D

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54. 54

    NUST Engineering Past Paper-9

    Determine the STANDARD angle in that is COTERMINAL with .

    A

    B

    C

    D

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55. 55

    NUST Engineering Past Paper-9

    If with the terminal arm in the THIRD quadrant, determine .

    A

    B

    C

    D

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56. 56

    NUST Engineering Past Paper-9

    Simplify using a Pythagorean identity.

    A

    B

    C

    D

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57. 57

    NUST Engineering Past Paper-9

    State the set of angles for which is UNDEFINED.

    A

    B

    C

    D

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58. 58

    NUST Engineering Past Paper-9

    Simplify using the cosine addition formulas.

    A

    B

    C

    D

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59. 59

    NUST Engineering Past Paper-9

    Simplify using the sine addition formulas.

    A

    B

    C

    D

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60. 60

    NUST Engineering Past Paper-9

    Express in TERMS OF ALONE (single-variable double-angle form).

    A

    B

    C

    D

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61. 61

    NUST Engineering Past Paper-9

    Express using the double-angle identity.

    A

    B

    C

    D

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62. 62

    NUST Engineering Past Paper-9

    Determine the fundamental PERIOD of the function .

    A

    B

    C

    D

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63. 63

    NUST Engineering Past Paper-9

    State the DOMAIN of the principal inverse function .

    A

    B

    C

    D

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64. 64

    NUST Engineering Past Paper-9

    Determine the GENERAL solution of the trigonometric equation .

    A

    B

    C

    D

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65. 65

    NUST Engineering Past Paper-9

    Determine the SOLUTION SET of the equation in the interval .

    A

    B

    C

    D

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66. 66

    NUST Engineering Past Paper-9

    Evaluate the limit .

    A

    B

    C

    D

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67. 67

    NUST Engineering Past Paper-9

    Evaluate the limit .

    A

    B

    C

    D

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68. 68

    NUST Engineering Past Paper-9

    Evaluate the limit .

    A

    B

    C

    D

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69. 69

    NUST Engineering Past Paper-9

    Evaluate the limit .

    A

    B

    C

    D

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70. 70

    NUST Engineering Past Paper-9

    State the GENERAL Power Rule for differentiation: for any real exponent .

    A

    B

    C

    D

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71. 71

    NUST Engineering Past Paper-9

    Determine for (and constant base , ).

    A

    B

    C

    D

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72. 72

    NUST Engineering Past Paper-9

    Determine .

    A

    B

    C

    D

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73. 73

    NUST Engineering Past Paper-9

    Determine using the product rule.

    A

    B

    C

    D

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74. 74

    NUST Engineering Past Paper-9

    Determine .

    A

    B

    C

    D

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75. 75

    NUST Engineering Past Paper-9

    If , determine .

    A

    B

    C

    D

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76. 76

    NUST Engineering Past Paper-9

    Determine the largest interval on which the function is strictly INCREASING.

    A

    B

    C

    D

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77. 77

    NUST Engineering Past Paper-9

    Determine the CRITICAL POINTS of the function .

    A

    B

    C

    D

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78. 78

    NUST Engineering Past Paper-9

    Classify the critical point at of the function and state the corresponding extreme value.

    A

    Local maximum of

    B

    Local minimum of

    C

    Local maximum of

    D

    Point of inflection

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79. 79

    NUST Engineering Past Paper-9

    Evaluate the indefinite integral .

    A

    B

    C

    D

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80. 80

    NUST Engineering Past Paper-9

    Evaluate the indefinite integral for .

    A

    B

    C

    D

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81. 81

    NUST Engineering Past Paper-9

    Evaluate the indefinite integral .

    A

    B

    C

    D

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82. 82

    NUST Engineering Past Paper-9

    Evaluate the definite integral .

    A

    B

    C

    D

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83. 83

    NUST Engineering Past Paper-9

    Evaluate the definite integral .

    A

    B

    C

    D

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84. 84

    NUST Engineering Past Paper-9

    State the MIDPOINT formula for the midpoint of the line segment joining and in the Cartesian plane.

    A

    B

    C

    D

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85. 85

    NUST Engineering Past Paper-9

    Determine the SLOPE of the straight line joining the two points and .

    A

    B

    C

    D

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86. 86

    NUST Engineering Past Paper-9

    State the algebraic condition on the slopes and of two non-vertical straight lines so that they are PARALLEL.

    A

    B

    C

    D

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87. 87

    NUST Engineering Past Paper-9

    Determine the solution set of in .

    A

    B

    C

    D

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88. 88

    NUST Engineering Past Paper-9

    If , determine (or give the closed-form pattern).

    A

    B

    C

    D

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89. 89

    NUST Engineering Past Paper-9

    Pick the word that is most nearly OPPOSITE in meaning to 'belittle':

    A

    Ignore

    B

    Scold

    C

    Praise

    D

    Demean

    Reveal answer
90. 90

    NUST Engineering Past Paper-9

    Pick the word closest in meaning to 'Onerous':

    A

    Simple and straightforward

    B

    Joyful and pleasant

    C

    Quick and efficient

    D

    Burdensome and demanding

    Reveal answer
91. 91

    NUST Engineering Past Paper-9

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

    A

    Rough

    B

    Sharp

    C

    Honest

    D

    Dull

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92. 92

    NUST Engineering Past Paper-9

    Complete the sentence: 'He ___ to go to Murree every summer.'

    A

    Is use

    B

    Used

    C

    Use

    D

    Is used

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93. 93

    NUST Engineering Past Paper-9

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

    A

    Apathetic

    B

    Excited

    C

    Fervent

    D

    Enthusiastic

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94. 94

    NUST Engineering Past Paper-9

    Pick the option that best defines 'Audacious':

    A

    Showing a willingness to take bold risks

    B

    Quietly obedient

    C

    Timid and hesitant

    D

    Careful and cautious

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95. 95

    NUST Engineering Past Paper-9

    Pick the option that best defines 'Braggart':

    A

    A person who is excessively generous

    B

    A person who is extremely humble

    C

    A person who boasts about their achievements

    D

    A person who avoids social situations

    Reveal answer
96. 96

    NUST Engineering Past Paper-9

    Pick the word closest in meaning to 'Cacophony':

    A

    Melody

    B

    Discord

    C

    Harmony

    D

    Symphony

    Reveal answer
97. 97

    NUST Engineering Past Paper-9

    Pick the option that best defines 'Evocative':

    A

    Technically precise and accurate

    B

    Completely neutral in tone

    C

    Dull and forgettable

    D

    Bringing strong images or feelings to mind

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98. 98

    NUST Engineering Past Paper-9

    Pick the option that best defines 'Flair':

    A

    A natural talent or aptitude; distinctive style

    B

    A sudden burst of anger

    C

    A complete lack of skill

    D

    A tendency toward laziness

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99. 99

    NUST Engineering Past Paper-9

    Pick the word closest in meaning to 'Neglect':

    A

    Nurture

    B

    Tend

    C

    Cherish

    D

    Disregard

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100. 100

     NUST Engineering Past Paper-9

     Pick the option that best defines 'Ominous':

     A

     Indicating past events

     B

     Giving a reassuring sign of good things to come

     C

     Giving the impression that something bad is about to happen

     D

     Completely neutral and without implication

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101. 101

     NUST Engineering Past Paper-9

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

     A

     Threatening

     B

     Sinister

     C

     Auspicious

     D

     Menacing

     Reveal answer
102. 102

     NUST Engineering Past Paper-9

     Pick the word closest in meaning to 'Pretentious':

     A

     Sincere

     B

     Pompous

     C

     Humble

     D

     Modest

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103. 103

     NUST Engineering Past Paper-9

     Pick the option that best defines 'Sedentary':

     A

     Extremely physically active

     B

     Tending to spend much time seated; inactive

     C

     Moving frequently from place to place

     D

     Enthusiastic about outdoor activities

     Reveal answer
104. 104

     NUST Engineering Past Paper-9

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

     A

     Docile

     B

     Meek

     C

     Yielding

     D

     Dominant

     Reveal answer
105. 105

     NUST Engineering Past Paper-9

     Pick the option that best defines 'Temerity':

     A

     A deep sense of moral responsibility

     B

     Careful planning before taking action

     C

     Excessive confidence or boldness; audacity

     D

     Extreme caution and timidity

     Reveal answer
106. 106

     NUST Engineering Past Paper-9

     Pick the option that best defines 'Trifling':

     A

     Demanding a great deal of attention

     B

     Unimportant; not serious

     C

     Requiring urgent action

     D

     Of great significance and importance

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107. 107

     NUST Engineering Past Paper-9

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

     A

     Improper

     B

     Dignified

     C

     Humiliating

     D

     Shameful

     Reveal answer
108. 108

     NUST Engineering Past Paper-9

     Pick the word closest in meaning to 'Venal':

     A

     Incorruptible

     B

     Honest

     C

     Virtuous

     D

     Corrupt

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109. 109

     NUST Engineering Past Paper-9

     Pick the option that best defines the verb 'abdicate':

     A

     To increase one's authority

     B

     To formally renounce a throne or high office

     C

     To negotiate a peace treaty

     D

     To seize power by force

     Reveal answer
110. 110

     NUST Engineering Past Paper-9

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

     A

     A special talent

     B

     A sign of courage

     C

     A great strength

     D

     A minor weakness or character flaw

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111. 111

     NUST Engineering Past Paper-9

     Pick the preposition that correctly completes: 'All were invited ___ dinner.'

     A

     to

     B

     at

     C

     on

     D

     for

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112. 112

     NUST Engineering Past Paper-9

     Convert to indirect speech: He said, 'I went to school yesterday.'

     A

     He said that he went to school the previous day.

     B

     He said that he goes to school yesterday.

     C

     He told that he had went to school the day before.

     D

     He said that he had gone to school the previous day.

     Reveal answer
113. 113

     NUST Engineering Past Paper-9

     Pick the synonym of the adjective MAGNANIMOUS.

     A

     Loving

     B

     Mean

     C

     Generous

     D

     Loyal

     Reveal answer
114. 114

     NUST Engineering Past Paper-9

     Pick the synonym of the verb EMULATE.

     A

     Imitate

     B

     Likely

     C

     Win

     D

     Enable

     Reveal answer
115. 115

     NUST Engineering Past Paper-9

     Pick the synonym of the verb COZEN.

     A

     Flatter

     B

     Cheat

     C

     Convince

     D

     Ridicule

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116. 116

     NUST Engineering Past Paper-9

     Pick the synonym of the verb REIN (in its figurative sense).

     A

     Overcome

     B

     Pour

     C

     Fling

     D

     Control

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117. 117

     NUST Engineering Past Paper-9

     Pick the synonym of the verb CONSTRUE.

     A

     Interpret

     B

     Confuse

     C

     Scatter

     D

     Unite

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118. 118

     NUST Engineering Past Paper-9

     Pick the synonym of the verb CATAPULT (used figuratively).

     A

     Contain

     B

     Shoot

     C

     Control

     D

     Restrain

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119. 119

     NUST Engineering Past Paper-9

     Pick the synonym of the verb FOMENT.

     A

     Extirpate

     B

     Abrade

     C

     Provoke

     D

     Isolate

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120. 120

     NUST Engineering Past Paper-9

     Pick the synonym of the adjective PREDOMINANT.

     A

     Important

     B

     Assurance

     C

     Vague

     D

     Lovable

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121. 121

     NUST Engineering Past Paper-9

     Pick the synonym of the verb EXTRICATE.

     A

     Pull

     B

     Complicate

     C

     Free

     D

     Tie

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122. 122

     NUST Engineering Past Paper-9

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

     A

     Indulge

     B

     Serve

     C

     Tolerate

     D

     Taste

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123. 123

     NUST Engineering Past Paper-9

     Pick the antonym of the noun ACCELERATION (used in the sense of 'speeding up').

     A

     Retrogression

     B

     Progress

     C

     Transgression

     D

     Retardation

     Reveal answer
124. 124

     NUST Engineering Past Paper-9

     Pick the antonym of the adjective BENEVOLENT.

     A

     Kind

     B

     Charitable

     C

     Malevolent

     D

     Generous

     Reveal answer
125. 125

     NUST Engineering Past Paper-9

     Pick the antonym of the adjective ZEALOUS.

     A

     Enthusiastic

     B

     Apathetic

     C

     Passionate

     D

     Fervent

     Reveal answer
126. 126

     NUST Engineering Past Paper-16 NUST Engineering Past Paper-9

     Pick the antonym of the noun PAUCITY.

     A

     Shortage

     B

     Need

     C

     Lack

     D

     Sufficiency

     Reveal answer
127. 127

     NUST Engineering Past Paper-9

     Identify the single-word term for a person who is against the established government and seeks to abolish it.

     A

     Defeatist

     B

     Truant

     C

     Anarchist

     D

     Sycophant

     Reveal answer
128. 128

     NUST Engineering Past Paper-9

     Identify the single-word term for the killing of one's own brother or sister.

     A

     Patricide

     B

     Infanticide

     C

     Homicide

     D

     Fratricide

     Reveal answer
129. 129

     NUST Engineering Past Paper-9

     Identify the meaning of the idiom 'To end in smoke.'

     A

     To become very popular

     B

     To catch fire

     C

     To cause pollution

     D

     To be destroyed or ruined

     Reveal answer
130. 130

     NUST Engineering Past Paper-9

     Identify the meaning of the idiom 'To set the Thames on fire.'

     A

     To do a heroic deed

     B

     To destroy with fire

     C

     To achieve something amazing and praiseworthy

     D

     To wreak evil on something

     Reveal answer
131. 131

     NUST Engineering Past Paper-9

     Identify the meaning of the idiom 'Cheek by jowl.'

     A

     Side by side

     B

     Face to face

     C

     Proportionately

     D

     Close together

     Reveal answer
132. 132

     NUST Engineering Past Paper-9

     How must a high resistance be connected to a galvanometer to convert it into a voltmeter?

     A

     Parallel then series

     B

     Parallel

     C

     Series then parallel

     D

     Series

     Reveal answer
133. 133

     NUST Engineering Past Paper-9

     A long solenoid has length , cross-sectional area , total turns , and carries current , producing magnetic field inside. If the length is HALVED (with , , and unchanged), what is the new magnetic field?

     A

     B

     C

     D

     Reveal answer
134. 134

     NUST Engineering Past Paper-9

     For a parallel-plate capacitor, the plate area and the plate separation are BOTH doubled simultaneously (with the dielectric unchanged). How does the capacitance change?

     A

     Becomes double

     B

     Becomes four times

     C

     Becomes half

     D

     Remains same

     Reveal answer
135. 135

     NUST Engineering Past Paper-9

     Among the SI prefixes nano (n), atto (a), pico (p), and femto (f), identify the one representing the SMALLEST factor.

     A

     pico

     B

     femto

     C

     nano

     D

     atto

     Reveal answer
136. 136

     NUST Engineering Past Paper-9

     Identify the correct form of the First Law of Thermodynamics specialised to an ADIABATIC process, with the sign convention that is the work done BY the system.

     A

     B

     C

     D

     Reveal answer
137. 137

     NUST Engineering Past Paper-9

     For a simple harmonic oscillator, determine the kinetic energy at the maximum displacement (amplitude) point.

     A

     Maximum

     B

     Half of total mechanical energy

     C

     Zero

     D

     Equal to potential energy

     Reveal answer
138. 138

     NUST Engineering Past Paper-9

     A point charge moves with velocity relative to an observer. Identify which field(s) it produces in the surrounding space.

     A

     Only an electric field

     B

     Neither

     C

     Only a magnetic field

     D

     Both an electric field and a magnetic field

     Reveal answer
139. 139

     NUST Engineering Past Paper-9

     Identify the correct statement from the postulates and consequences of special relativity.

     A

     The speed of light is not absolute

     B

     Momentum is not conserved

     C

     None of the above

     D

     Time is not absolute (time dilation occurs)

     Reveal answer
140. 140

     NUST Engineering Past Paper-9

     A black body radiates total power at temperature with the peak emission at wavelength . If the temperature changes such that the new peak occurs at , determine the new total radiated power in terms of .

     A

     B

     C

     D

     Reveal answer
141. 141

     NUST Engineering Past Paper-9

     State the type of thermodynamic process from which Laplace's correction to Newton's formula for the speed of sound is derived.

     A

     Adiabatic change

     B

     Isothermal change

     C

     Isochoric change

     D

     Isobaric change

     Reveal answer
142. 142

     NUST Engineering Past Paper-9

     Among the listed pairs of physical quantities, identify the pair that does NOT have identical dimensions.

     A

     Angular momentum and Planck's constant

     B

     Work and torque

     C

     Impulse and momentum

     D

     Moment of inertia and moment of force

     Reveal answer
143. 143

     NUST Engineering Past Paper-9

     In an ideal step-up transformer, if the alternating voltage at the secondary is increased relative to the primary, describe the corresponding behaviour of the secondary alternating current.

     A

     Will increase

     B

     Will decrease

     C

     None of the above

     D

     Will not change

     Reveal answer
144. 144

     NUST Engineering Past Paper-9

     By Gauss's law, the electric flux through a closed surface does NOT depend on which of the following factors?

     A

     Nature of charge

     B

     Charge enclosed

     C

     Shape of surface

     D

     Medium

     Reveal answer
145. 145

     NUST Engineering Past Paper-9

     If a radioactive sample has decayed to of its original amount, determine the number of half-lives that have elapsed.

     A

     B

     C

     D

     Reveal answer
146. 146

     NUST Engineering Past Paper-9

     A stretched string long has a fundamental frequency of . If its length is reduced to without changing the tension or linear density, determine the new fundamental frequency.

     A

     B

     C

     D

     Reveal answer
147. 147

     NUST Engineering Past Paper-9

     By Faraday's law, describe what happens to the induced EMF in a coil if the rate of decrease of magnetic flux is doubled (i.e. flux changes twice as fast).

     A

     Becomes zero

     B

     Doubles

     C

     Triples

     D

     Becomes

     Reveal answer
148. 148

     NUST Engineering Past Paper-9

     Identify the physical quantity whose SI unit equals .

     A

     Electric potential

     B

     Electric field

     C

     Magnetic field strength

     D

     Electric charge

     Reveal answer
149. 149

     NUST Engineering Past Paper-9

     Determine the dimensional formula for the MODULUS OF ELASTICITY (e.g. Young's modulus).

     A

     B

     C

     D

     Reveal answer
150. 150

     NUST Engineering Past Paper-9

     Identify which of the listed equivalences is correct for .

     A

     milligrams

     B

     1000 grams

     C

     2.2 pounds

     D

     All are correct

     Reveal answer
151. 151

     NUST Engineering Past Paper-9

     State the formula for the Compton wavelength shift when a photon scatters off a stationary electron through angle .

     A

     B

     C

     D

     Reveal answer
152. 152

     NUST Engineering Past Paper-9

     Determine the INITIAL acceleration of an object the moment after it is dropped (released from rest) in free fall near the Earth's surface (ignoring air resistance).

     A

     Depends on mass

     B

     Infinite

     C

     Equal to gravitational acceleration

     D

     Zero

     Reveal answer
153. 153

     NUST Engineering Past Paper-9

     Identify the particle family to which the neutron belongs in the Standard Model classification.

     A

     Baryons

     B

     None

     C

     Mesons

     D

     Leptons

     Reveal answer
154. 154

     NUST Engineering Past Paper-9

     Identify the physical quantity whose dimensions are .

     A

     Momentum

     B

     Energy

     C

     Power

     D

     Force

     Reveal answer
155. 155

     NUST Engineering Past Paper-9

     According to Bohr's model of the atom, identify the physical quantity whose quantization keeps electrons in stable orbits.

     A

     Electric charge

     B

     Gravitational force

     C

     Radius

     D

     Angular momentum

     Reveal answer
156. 156

     NUST Engineering Past Paper-9

     State the primary role of the MODERATOR in a nuclear fission reactor.

     A

     Slow down neutrons

     B

     Reflect neutrons

     C

     Increase neutron energy

     D

     Absorb neutrons

     Reveal answer
157. 157

     NUST Engineering Past Paper-9

     State the SI unit of torque.

     A

     kg·m/s

     B

     N·m

     C

     J/s

     D

     kg·m²/s²

     Reveal answer
158. 158

     NUST Engineering Past Paper-9

     Determine the work done by gravity on a small mass placed at the very centre of the Earth (ignoring rotation, treating Earth as a uniform sphere).

     A

     Infinite

     B

     Minimum

     C

     Zero

     D

     Maximum

     Reveal answer
159. 159

     NUST Engineering Past Paper-9

     Identify the medium in which electric current flows due to the motion of BOTH positive and negative ions.

     A

     Metals

     B

     Gases

     C

     Both

     D

     None

     Reveal answer
160. 160

     NUST Engineering Past Paper-9

     In projectile motion (no air resistance), state the condition on the velocity components at the moment of maximum height.

     A

     Equal in both axes

     B

     Maximum in y-axis

     C

     Zero in y-axis

     D

     Maximum in x-axis

     Reveal answer
161. 161

     NUST Engineering Past Paper-9

     A heat engine absorbs from a hot source and rejects to the cold sink per cycle. Determine its thermal efficiency.

     A

     B

     C

     D

     Reveal answer
162. 162

     NUST Engineering Past Paper-9

     Identify which of the listed devices operates on the principle of electromagnetic induction (Faraday's law).

     A

     Electric Generator

     B

     Electric Motor

     C

     Battery

     D

     Electric Fan

     Reveal answer
163. 163

     NUST Engineering Past Paper-9

     Identify the thermodynamic process in which the volume of the gas remains constant.

     A

     Adiabatic

     B

     Isobaric

     C

     Isothermal

     D

     Isochoric

     Reveal answer
164. 164

     NUST Engineering Past Paper-9

     A simple pendulum has total mechanical energy . Determine its kinetic energy at the mean (equilibrium) position.

     A

     B

     C

     D

     Reveal answer
165. 165

     NUST Engineering Past Paper-9

     In Young's double-slit experiment with fringe width , determine the new fringe width if the wavelength of light is TRIPLED while all other parameters (slit separation, screen distance) are kept fixed.

     A

     B

     C

     D

     Reveal answer
166. 166

     NUST Engineering Past Paper-9

     State the SI unit of electric potential (and potential difference / EMF).

     A

     Joule

     B

     Ampere

     C

     Coulomb

     D

     Volt

     Reveal answer
167. 167

     NUST Engineering Past Paper-9

     Describe what happens to the wavelength of sound waves reaching a stationary listener when the source of sound moves TOWARD the listener (Doppler effect).

     A

     Remains the same

     B

     Increases

     C

     Doubles

     D

     Decreases

     Reveal answer
168. 168

     NUST Engineering Past Paper-9

     State the formula for the electric energy stored in a capacitor with capacitance and voltage across its plates.

     A

     B

     C

     D

     Reveal answer
169. 169

     NUST Engineering Past Paper-9

     Identify the property that determines the minimum energy required to liberate an electron from a metal surface.

     A

     Work function

     B

     Power

     C

     Wavelength

     D

     Work

     Reveal answer
170. 170

     NUST Engineering Past Paper-9

     Based on quantum mechanics, identify the description that best captures the fundamental level of nature.

     A

     Deterministic

     B

     Both

     C

     None

     D

     Probabilistic

     Reveal answer
171. 171

     NUST Engineering Past Paper-9

     Identify the factor(s) on which the horizontal range of a projectile depends (in the absence of air resistance, on level ground).

     A

     Both angle and velocity of projection

     B

     Angle of projection

     C

     Mass of projectile

     D

     Velocity of projection

     Reveal answer
172. 172

     NUST Engineering Past Paper-9

     A constant force moves an object from the origin to the position . Determine the work done.

     A

     units

     B

     unit

     C

     units

     D

     units

     Reveal answer
173. 173

     NUST Engineering Past Paper-9

     Identify the property of a system that ENTROPY most directly measures.

     A

     Energy

     B

     Disorder

     C

     Work

     D

     Temperature

     Reveal answer
174. 174

     NUST Engineering Past Paper-9

     Three vectors of equal magnitude act along the three sides of an equilateral triangle, taken in order (head-to-tail). Determine the magnitude of their resultant.

     A

     B

     C

     D

     Reveal answer
175. 175

     NUST Engineering Past Paper-9

     In the SHM equation , given and , determine the approximate value of (in degrees) for the first such instant.

     A

     B

     C

     D

     Reveal answer
176. 176

     NUST Engineering Past Paper-9

     In the 'Well of Death' carnival stunt, a motorbike rides along the vertical inner wall of a cylindrical drum. Identify the force that prevents the bike from sliding down.

     A

     Centripetal force

     B

     Normal force

     C

     Gravitational force

     D

     Centrifugal force

     Reveal answer
177. 177

     NUST Engineering Past Paper-9

     For a telescope in normal adjustment with angular magnification , state the relationship between the focal lengths of the objective and the eyepiece.

     A

     Focal length of objective is four times the focal length of the eyepiece

     B

     Focal length of eyepiece is four times the focal length of the objective

     C

     Telescope cannot have a magnification of four

     D

     Focal length of both lenses are equal

     Reveal answer
178. 178

     NUST Engineering Past Paper-9

     State the behaviour of angular momentum for a rotating body when the net external torque acting on it is zero.

     A

     Unstable

     B

     Zero

     C

     Variable

     D

     Constant

     Reveal answer
179. 179

     NUST Engineering Past Paper-9

     State the type of motion produced by a couple (two equal, opposite, non-collinear forces).

     A

     Linear and rotational motion

     B

     Purely linear motion

     C

     Purely rotational motion

     D

     No motion

     Reveal answer
180. 180

     NUST Engineering Past Paper-9

     Pick the correct statement among the listed options about stationary (standing) waves.

     A

     Energy is transmitted in one direction only

     B

     All particles have the same amplitude

     C

     There are points with zero amplitude

     D

     The particles in the wave move along the wave

     Reveal answer
181. 181

     NUST Engineering Past Paper-9

     When a wave passes from one medium into another, identify which of its properties must change.

     A

     Frequency

     B

     None of these

     C

     Speed

     D

     Amplitude

     Reveal answer
182. 182

     NUST Engineering Past Paper-9

     State the least count of a standard Vernier calliper.

     A

     1 mm

     B

     All of these

     C

     0.001 m

     D

     0.01 cm

     Reveal answer
183. 183

     NUST Engineering Past Paper-9

     Identify the physical quantity whose dimensions match those of Planck's constant .

     A

     Angular momentum

     B

     Angular frequency

     C

     Energy

     D

     Power

     Reveal answer
184. 184

     NUST Engineering Past Paper-9

     Among the listed devices, identify which does NOT primarily work on the principle of electromagnetic induction.

     A

     Transformer

     B

     Radio

     C

     Mutual Inductor

     D

     TV

     Reveal answer
185. 185

     NUST Engineering Past Paper-9

     In circular motion, if the radius of the circular path is increased by , determine the effect on the TANGENTIAL acceleration of a particle moving along it.

     A

     Decreases by 25%

     B

     Remains the same

     C

     Cannot be determined

     D

     Increases by 25%

     Reveal answer
186. 186

     NUST Engineering Past Paper-9

     A bar magnet is positioned along the axis of a circular coil. State the condition(s) under which a current is induced in the coil.

     A

     None of these

     B

     Both A and B

     C

     Magnet is moved towards or away with constant speed

     D

     Magnet is moved towards or away with varying speed

     Reveal answer
187. 187

     NUST Engineering Past Paper-9

     In Young's double-slit experiment, if the inter-slit distance is reduced (to approach ), describe the effect on the fringe spacing on the screen.

     A

     Increase

     B

     Remain constant

     C

     Cannot be determined

     D

     Decrease

     Reveal answer
188. 188

     NUST Engineering Past Paper-9

     Identify the SI unit used to measure the electrical capacitance of a capacitor.

     A

     Farad

     B

     Volt

     C

     Ampere

     D

     Ohm

     Reveal answer
189. 189

     NUST Engineering Past Paper-9

     Identify the conservation law that underlies the phenomenon of electromagnetic induction.

     A

     Charge

     B

     Energy

     C

     Momentum

     D

     Mass

     Reveal answer
190. 190

     NUST Engineering Past Paper-9

     Per Newton's second law, identify the type of acceleration that a net unbalanced force generates on a particle.

     A

     Linear acceleration

     B

     None

     C

     Rotational acceleration

     D

     Both

     Reveal answer
191. 191

     NUST Engineering Past Paper-9

     Three resistors , , are connected in series across a battery. Identify the resistor that dissipates the maximum power.

     A

     B

     C

     D

     All dissipate the same power

     Reveal answer
192. 192

     NUST Engineering Past Paper-9

     Identify the direction in which the instantaneous acceleration of a particle performing simple harmonic motion always points.

     A

     None of these

     B

     Extremes

     C

     Away from center

     D

     Mean position

     Reveal answer
193. 193

     NUST Engineering Past Paper-9

     Among the listed physical quantities, identify the one whose SI unit is equivalent to .

     A

     Pressure

     B

     Work

     C

     Energy density

     D

     Force

     Reveal answer
194. 194

     NUST Engineering Past Paper-9

     For a particle in uniform circular motion at constant speed, determine how its angular velocity changes when the orbital radius is doubled.

     A

     Doubled

     B

     Halved

     C

     One-fourth

     D

     Unchanged

     Reveal answer
195. 195

     NUST Engineering Past Paper-9

     An X-ray photon of wavelength is scattered by a free electron at a scattering angle . Determine the Compton shift .

     A

     B

     C

     D

     Reveal answer
196. 196

     NUST Engineering Past Paper-9

     Among the listed regions of the electromagnetic spectrum, identify the one whose individual photons carry the GREATEST energy.

     A

     Ultraviolet rays

     B

     Visible light

     C

     X-rays

     D

     Gamma rays

     Reveal answer
197. 197

     NUST Engineering Past Paper-9

     Two point charges experience an electrostatic force . Determine the new force when the separation between them is tripled (charges held constant).

     A

     One-third

     B

     One-sixth

     C

     One-ninth

     D

     Nine times

     Reveal answer
198. 198

     NUST Engineering Past Paper-9

     Identify the orientation between two non-zero vectors for which their scalar (dot) product becomes negative.

     A

     In the same direction

     B

     Parallel

     C

     Perpendicular

     D

     Anti-parallel

     Reveal answer
199. 199

     NUST Engineering Past Paper-9

     State the standard formula for the HORIZONTAL RANGE of a projectile launched from level ground at an angle above the horizontal with initial speed (neglecting air resistance).

     A

     B

     C

     D

     Reveal answer