NUST Engineering Past Paper-14

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

1. 1

   NUST Engineering Past Paper-14

   Which of the following conic equations has eccentricity ?

   A

   B

   C

   D

   Reveal answer
2. 2

   NUST Engineering Past Paper-14

   In an equilateral triangle with one side of length m, the points , , are the midpoints of the sides. Find the area of the inner (medial) triangle.

   A

   m

   B

   m

   C

   m

   D

   m

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3. 3

   NUST Engineering Past Paper-14

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

   A

   B

   C

   D

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4. 4

   NUST Engineering Past Paper-14

   Find the sum of the first 30 natural numbers that are divisible by 5.

   A

   2325

   B

   2300

   C

   2350

   D

   None of these

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5. 5

   NUST Engineering Past Paper-14

   Find the maximum value of on the interval .

   A

   B

   C

   D

   1

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6. 6

   NUST Engineering Past Paper-14

   The sum of the cubes of three consecutive integers is always divisible by which of the following?

   A

   Those three numbers

   B

   3

   C

   12

   D

   None

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7. 7

   NUST Engineering Past Paper-14

   Evaluate for constants and .

   A

   B

   C

   D

   None of these

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8. 8

   NUST Engineering Past Paper-14

   For what value of are the vectors , , and coplanar?

   A

   B

   4

   C

   D

   None of these

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9. 9

   NUST Engineering Past Paper-14

   Simplify .

   A

   B

   C

   D

   None of these

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10. 10

    NUST Engineering Past Paper-14

    Evaluate .

    A

    32

    B

    16

    C

    8

    D

    None of these

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11. 11

    NUST Engineering Past Paper-14

    If , find .

    A

    B

    C

    D

    None of these

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12. 12

    NUST Engineering Past Paper-14

    Suppose is continuous on and is an antiderivative of on with and . Compute .

    A

    8

    B

    5

    C

    2

    D

    None of these

    Reveal answer
13. 13

    NUST Engineering Past Paper-14

    Let . Find the value of that makes continuous at .

    A

    B

    C

    D

    None of these

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14. 14

    NUST Engineering Past Paper-14

    Find the equation of the straight line that is parallel to the -axis and passes through the point .

    A

    B

    C

    D

    None of these

    Reveal answer
15. 15

    NUST Engineering Past Paper-14

    How many solutions does the homogeneous system , have?

    A

    Infinite solutions

    B

    Two solutions

    C

    No solution

    D

    One solution

    Reveal answer
16. 16

    NUST Engineering Past Paper-14

    Find the value of .

    A

    B

    4

    C

    D

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17. 17

    NUST Engineering Past Paper-14

    Evaluate (principal value).

    A

    B

    C

    D

    None of these

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18. 18

    NUST Engineering Past Paper-14

    Find the radius of the curve .

    A

    2

    B

    1

    C

    None

    D

    0

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19. 19

    NUST Engineering Past Paper-14

    If , find and .

    A

    B

    C

    D

    None of these

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20. 20

    NUST Engineering Past Paper-14

    Evaluate .

    A

    B

    1

    C

    D

    None of these

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21. 21

    NUST Engineering Past Paper-14

    Suppose both and . Which of the following best describes the local behaviour of at ?

    A

    has an inflection point at

    B

    is continuous at

    C

    is constant

    D

    Can't be determined

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22. 22

    NUST Engineering Past Paper-14

    What is the value of for all valid (i.e., )?

    A

    B

    None

    C

    D

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23. 23

    NUST Engineering Past Paper-14

    Simplify .

    A

    B

    C

    0

    D

    None of these

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24. 24

    NUST Engineering Past Paper-14

    Evaluate .

    A

    B

    C

    D

    None of these

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25. 25

    NUST Engineering Past Paper-14

    If and lies in the third quadrant, find .

    A

    B

    C

    D

    None of these

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26. 26

    NUST Engineering Past Paper-14

    Evaluate .

    A

    B

    C

    D

    None of these

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27. 27

    NUST Engineering Past Paper-14

    Which of the following is an even function?

    A

    B

    C

    D

    None

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28. 28

    NUST Engineering Past Paper-14

    The sides of a 'triangle' are given as 14, 9, 5. Find the size of the largest angle.

    A

    B

    None

    C

    D

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29. 29

    NUST Engineering Past Paper-14

    The cosine of an angle equals . Approximately what is the angle?

    A

    B

    C

    D

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30. 30

    NUST Engineering Past Paper-14

    How many foci and directrices does a hyperbola have?

    A

    One directrix, one focus

    B

    One focus, three directrices

    C

    One directrix, two foci

    D

    Two foci, two directrices

    Reveal answer
31. 31

    NUST Engineering Past Paper-14

    Find the general -th term of the arithmetic sequence .

    A

    B

    C

    D

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32. 32

    NUST Engineering Past Paper-14

    From the integers to , two events are defined: and . What is the probability that or occurs?

    A

    B

    C

    D

    None of these

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33. 33

    NUST Engineering Past Paper-14

    What is the range of the function ?

    A

    B

    C

    D

    None of these

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34. 34

    NUST Engineering Past Paper-14

    The identity holds for which set of ?

    A

    B

    C

    None

    D

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35. 35

    NUST Engineering Past Paper-14

    Determine the midpoint of the segment joining and .

    A

    B

    C

    D

    None of these

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36. 36

    NUST Engineering Past Paper-14

    If and is the angle between and , simplify .

    A

    None

    B

    C

    D

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37. 37

    NUST Engineering Past Paper-14

    A cricket team of 11 players is to be selected from a panel of 15. If two specified players must always be in the team, in how many ways can the selection be made?

    A

    B

    C

    D

    None of these

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38. 38

    NUST Engineering Past Paper-14

    Implicitly differentiate the equation with respect to to find .

    A

    None of these

    B

    C

    D

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39. 39

    NUST Engineering Past Paper-14

    Compute .

    A

    B

    C

    D

    None of these

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40. 40

    NUST Engineering Past Paper-14

    Two adjacent terms of an infinite geometric series are and , and the series sums to . Find the first term .

    A

    16

    B

    8

    C

    32

    D

    None of these

    Reveal answer
41. 41

    NUST Engineering Past Paper-14

    Find the sum of all binomial coefficients in the expansion of .

    A

    4096

    B

    2048

    C

    1024

    D

    None of these

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42. 42

    NUST Engineering Past Paper-14

    Given with and , determine .

    A

    B

    C

    D

    None of these

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43. 43

    NUST Engineering Past Paper-14

    Solve the compound inequality for (assuming ).

    A

    B

    C

    D

    None of these

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44. 44

    NUST Engineering Past Paper-14

    Classify the sequence defined recursively by and for .

    A

    None

    B

    G.P.

    C

    H.P.

    D

    A.P.

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45. 45

    NUST Engineering Past Paper-14

    Which of the following gives the correct formula for the area of a triangle in terms of two sides and the included angle?

    A

    B

    C

    D

    Reveal answer
46. 46

    NUST Engineering Past Paper-14

    Which expression gives the area of an equilateral triangle of side ?

    A

    B

    C

    None

    D

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47. 47

    NUST Engineering Past Paper-14

    A 12 m ladder is placed against a vertical wall, with its base 6 m from the wall. Find the angle of inclination of the ladder with the ground.

    A

    B

    C

    D

    None of these

    Reveal answer
48. 48

    NUST Engineering Past Paper-14

    Evaluate (note the reversed limits and the singularity at ).

    A

    B

    C

    D

    None

    Reveal answer
49. 49

    NUST Engineering Past Paper-14

    Find , where is a constant.

    A

    B

    C

    D

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50. 50

    NUST Engineering Past Paper-14

    Consider the ellipse . What does this curve become when ?

    A

    Parabola

    B

    Circle

    C

    Hyperbola

    D

    Ellipse

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51. 51

    NUST Engineering Past Paper-14

    Let and . Find the magnitude of .

    A

    0

    B

    1

    C

    D

    None of these

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52. 52

    NUST Engineering Past Paper-14

    Which of the following identities is true for for all valid ?

    A

    B

    C

    D

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53. 53

    NUST Engineering Past Paper-14

    Which of the following expressions equals ?

    A

    B

    All of the above

    C

    D

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54. 54

    NUST Engineering Past Paper-14

    What is the domain of on the real line?

    A

    B

    C

    D

    None

    Reveal answer
55. 55

    NUST Engineering Past Paper-14

    Determine whether the infinite series converges or diverges.

    A

    Diverge

    B

    None

    C

    May diverge

    D

    Converge

    Reveal answer
56. 56

    NUST Engineering Past Paper-14

    A sequence is defined by and for . Find .

    A

    30

    B

    9

    C

    27

    D

    12

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57. 57

    NUST Engineering Past Paper-14

    Which of the following matrices is non-singular?

    A

    B

    C

    D

    Reveal answer
58. 58

    NUST Engineering Past Paper-14

    Find all real roots of (the fourth roots of unity that are real).

    A

    B

    C

    D

    Reveal answer
59. 59

    NUST Engineering Past Paper-14

    Which of the following statements is correct?

    A

    Polynomial with degree one is called linear

    B

    Both

    C

    None

    D

    Polynomial with leading coefficient one is called linear

    Reveal answer
60. 60

    NUST Engineering Past Paper-14

    Which of the following statements about complex numbers is NOT true?

    A

    B

    C

    Both A and B

    D

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61. 61

    NUST Engineering Past Paper-14

    Four points are given as , , , . Find the length of segment .

    A

    9

    B

    C

    D

    None of these

    Reveal answer
62. 62

    NUST Engineering Past Paper-14

    Find the centre of the ellipse .

    A

    B

    C

    D

    None of these

    Reveal answer
63. 63

    NUST Engineering Past Paper-14

    What is the slope of a vertical tangent line to a curve?

    A

    2

    B

    1

    C

    D

    0

    Reveal answer
64. 64

    NUST Engineering Past Paper-14

    Evaluate .

    A

    B

    1

    C

    0

    D

    None of these

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65. 65

    NUST Engineering Past Paper-14

    Using the identity , simplify when .

    A

    B

    C

    D

    None of these

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66. 66

    NUST Engineering Past Paper-14

    Evaluate .

    A

    B

    C

    D

    None of these

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67. 67

    NUST Engineering Past Paper-14

    Find the term independent of in the expansion of .

    A

    252

    B

    70

    C

    120

    D

    None of these

    Reveal answer
68. 68

    NUST Engineering Past Paper-14

    Determine the point where the lines and intersect.

    A

    None of these

    B

    C

    D

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69. 69

    NUST Engineering Past Paper-14

    Let and . Find such that .

    A

    B

    C

    D

    None of these

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70. 70

    NUST Engineering Past Paper-14

    If , compute .

    A

    B

    C

    D

    None of these

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71. 71

    NUST Engineering Past Paper-14

    Which area of calculus is primarily used to obtain the equations of the tangent and the normal to a curve?

    A

    None

    B

    Both

    C

    Differential Equation

    D

    Differentiation

    Reveal answer
72. 72

    NUST Engineering Past Paper-14

    Evaluate .

    A

    B

    C

    D

    None of these

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73. 73

    NUST Engineering Past Paper-14

    In a triangle, and . Find the ratio .

    A

    B

    C

    D

    None of these

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74. 74

    NUST Engineering Past Paper-14

    Under what condition does the second-degree equation represent a parabola?

    A

    B

    C

    Both A and B

    D

    Reveal answer
75. 75

    NUST Engineering Past Paper-14

    Determine the period of .

    A

    B

    C

    D

    Reveal answer
76. 76

    NUST Engineering Past Paper-14

    What is the equation of the tangent of slope to the parabola ?

    A

    B

    None

    C

    D

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77. 77

    NUST Engineering Past Paper-14

    Which expression equals ?

    A

    B

    C

    D

    None

    Reveal answer
78. 78

    NUST Engineering Past Paper-14

    Find the imaginary part of .

    A

    B

    1

    C

    0

    D

    2

    Reveal answer
79. 79

    NUST Engineering Past Paper-14

    Which of the following expressions always represents the empty set ?

    A

    Both A/C

    B

    C

    D

    Reveal answer
80. 80

    NUST Engineering Past Paper-14

    If is a root of , find the value of .

    A

    B

    C

    D

    None of these

    Reveal answer
81. 81

    NUST Engineering Past Paper-14

    How many positive integers between 1 and 200 are divisible by 7?

    A

    28

    B

    27

    C

    29

    D

    30

    Reveal answer
82. 82

    NUST Engineering Past Paper-14

    Evaluate .

    A

    B

    C

    D

    Reveal answer
83. 83

    NUST Engineering Past Paper-14

    Which of the following functions is even?

    A

    None

    B

    C

    D

    Reveal answer
84. 84

    NUST Engineering Past Paper-14

    Find for the implicit equation .

    A

    B

    C

    D

    Reveal answer
85. 85

    NUST Engineering Past Paper-14

    Simplify .

    A

    1

    B

    C

    D

    None of these

    Reveal answer
86. 86

    NUST Engineering Past Paper-14

    Find every value of in for which .

    A

    B

    C

    D

    Reveal answer
87. 87

    NUST Engineering Past Paper-14

    Under what condition do the two lines represented by become mutually perpendicular?

    A

    B

    C

    D

    Reveal answer
88. 88

    NUST Engineering Past Paper-14

    If is symmetric () and is skew-symmetric (), simplify .

    A

    None

    B

    C

    D

    Reveal answer
89. 89

    NUST Engineering Past Paper-14

    What is the measure of an angle inscribed in a semicircle (one subtended by a diameter)?

    A

    B

    C

    D

    Reveal answer
90. 90

    NUST Engineering Past Paper-14

    If , find .

    A

    B

    C

    D

    None of these

    Reveal answer
91. 91

    NUST Engineering Past Paper-14

    Find the eccentricity of the hyperbola .

    A

    B

    C

    D

    None of these

    Reveal answer
92. 92

    NUST Engineering Past Paper-14

    Classify the homogeneous linear system .

    A

    None

    B

    Infinite solutions

    C

    Consistent

    D

    Inconsistent

    Reveal answer
93. 93

    NUST Engineering Past Paper-14

    If the -plane is rotated through , what is the equation of the curve in the new coordinates?

    A

    B

    C

    D

    None of these

    Reveal answer
94. 94

    NUST Engineering Past Paper-14

    Simplify .

    A

    B

    C

    D

    Reveal answer
95. 95

    NUST Engineering Past Paper-14

    Two vectors and have magnitudes and respectively. Their resultant is perpendicular to . Determine the angle between and .

    A

    B

    C

    D

    Reveal answer
96. 96

    NUST Engineering Past Paper-14

    Find the derivative of .

    A

    B

    C

    D

    Reveal answer
97. 97

    NUST Engineering Past Paper-14

    If with acute, determine .

    A

    B

    C

    D

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98. 98

    NUST Engineering Past Paper-14

    Pick the option that best defines 'Cacophony':

    A

    Complete silence

    B

    A harsh mixture of discordant sounds

    C

    A soft musical melody

    D

    A pleasing harmony of sounds

    Reveal answer
99. 99

    NUST Engineering Past Paper-14

    Which of the following sentences correctly uses a gerund?

    A

    She to swim every morning.

    B

    She swam very good yesterday.

    C

    She swim in the pool daily.

    D

    Swimming is her favourite hobby.

    Reveal answer
100. 100

     NUST Engineering Past Paper-14

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

     A

     Departure

     B

     Goodbye

     C

     Parting

     D

     Greeting

     Reveal answer
101. 101

     NUST Engineering Past Paper-14

     Pick the option that best defines 'Ambiguous':

     A

     Having a single clear meaning

     B

     Completely false

     C

     Unnecessarily complex

     D

     Open to more than one interpretation

     Reveal answer
102. 102

     NUST Engineering Past Paper-14

     Pick the word closest in meaning to 'Audacious':

     A

     Daring

     B

     Meek

     C

     Cowardly

     D

     Timid

     Reveal answer
103. 103

     NUST Engineering Past Paper-14

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

     A

     Amplify

     B

     Boost

     C

     Supplement

     D

     Diminish

     Reveal answer
104. 104

     NUST Engineering Past Paper-14

     Pick the option that best defines 'Brook' when used as a verb:

     A

     To celebrate enthusiastically

     B

     To tolerate or allow

     C

     To delay indefinitely

     D

     To ignore completely

     Reveal answer
105. 105

     NUST Engineering Past Paper-14

     Pick the word most nearly OPPOSITE in meaning to 'Brook' (tolerate):

     A

     Forbid

     B

     Endure

     C

     Accept

     D

     Permit

     Reveal answer
106. 106

     NUST Engineering Past Paper-14

     Pick the word closest in meaning to 'Concede':

     A

     Contest

     B

     Acknowledge

     C

     Refute

     D

     Deny

     Reveal answer
107. 107

     NUST Engineering Past Paper-14

     Pick the option that best defines 'Contradict':

     A

     To remain silent on an issue

     B

     To assert the opposite of a statement

     C

     To agree after deliberation

     D

     To confirm and support a statement

     Reveal answer
108. 108

     NUST Engineering Past Paper-14

     Pick the word closest in meaning to 'Contradict':

     A

     Confirm

     B

     Validate

     C

     Refute

     D

     Affirm

     Reveal answer
109. 109

     NUST Engineering Past Paper-14

     Pick the option that best defines 'Detention':

     A

     A formal warning issued to a student

     B

     The act of releasing someone from custody

     C

     The process of examining evidence

     D

     The act of keeping someone in official custody

     Reveal answer
110. 110

     NUST Engineering Past Paper-14

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

     A

     Captivity

     B

     Custody

     C

     Liberation

     D

     Imprisonment

     Reveal answer
111. 111

     NUST Engineering Past Paper-14

     Pick the option that best defines 'Egregious':

     A

     Pleasantly surprising

     B

     Average and unremarkable

     C

     Outstandingly good

     D

     Outstandingly bad; shocking

     Reveal answer
112. 112

     NUST Engineering Past Paper-14

     Pick the word closest in meaning to 'Exonerate':

     A

     Indict

     B

     Accuse

     C

     Condemn

     D

     Absolve

     Reveal answer
113. 113

     NUST Engineering Past Paper-14

     Pick the option that best defines 'Expatriate':

     A

     A person living outside their native country

     B

     A government official stationed abroad

     C

     Someone who passionately loves their homeland

     D

     A person who has renounced citizenship

     Reveal answer
114. 114

     NUST Engineering Past Paper-14

     Pick the option that best defines 'Monotonous':

     A

     Varied and stimulating

     B

     Loud and energetic

     C

     Unpredictable and erratic

     D

     Dull, tedious, and repetitively uniform

     Reveal answer
115. 115

     NUST Engineering Past Paper-14

     Pick the word closest in meaning to 'Trifling':

     A

     Substantial

     B

     Significant

     C

     Critical

     D

     Trivial

     Reveal answer
116. 116

     NUST Engineering Past Paper-14

     Pick the option that best defines 'Upbraid':

     A

     To encourage someone quietly

     B

     To praise someone enthusiastically

     C

     To find fault with or scold angrily

     D

     To politely remind someone of a duty

     Reveal answer
117. 117

     NUST Engineering Past Paper-14

     Pick the option that best defines 'Utopian':

     A

     Relating to a realistic and achievable plan

     B

     Relating to historical events

     C

     Relating to economic prosperity

     D

     Relating to an ideal, perfect but impractical society

     Reveal answer
118. 118

     NUST Engineering Past Paper-14

     Pick the option that best defines 'Reinforcement':

     A

     The weakening of a structure or belief

     B

     The process of gradually reducing effort

     C

     The removal of existing supports

     D

     The process of strengthening or supporting something

     Reveal answer
119. 119

     NUST Engineering Past Paper-14

     Pick the term closest in meaning to 'Postmortem':

     A

     Autopsy

     B

     Prophylactic

     C

     Antenatal

     D

     Pre-operative

     Reveal answer
120. 120

     NUST Engineering Past Paper-14

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

     A

     Susceptible

     B

     Shielded

     C

     Exempt

     D

     Protected

     Reveal answer
121. 121

     NUST Engineering Past Paper-14

     Pick the option that best defines 'Clear' (as an adjective):

     A

     Obscure and hard to understand

     B

     Complex and ambiguous

     C

     Clouded and uncertain

     D

     Easy to perceive, understand, or interpret

     Reveal answer
122. 122

     NUST Engineering Past Paper-14

     Pick the option that best functions as an antonym (opposite in meaning) of the word ACCURACY.

     A

     Correctness

     B

     Consistency

     C

     Precision

     D

     Error

     Reveal answer
123. 123

     NUST Engineering Past Paper-14

     Pick the option that most accurately defines the verb FULMINATE.

     A

     Support

     B

     Approve

     C

     Praise

     D

     Protest strongly

     Reveal answer
124. 124

     NUST Engineering Past Paper-14

     Pick the option that most accurately defines the verb VILIFY.

     A

     Respect

     B

     Praise

     C

     Defame

     D

     Honor

     Reveal answer
125. 125

     NUST Engineering Past Paper-14

     Pick the option that most accurately captures the meaning of the adjective SANGUINE.

     A

     Pessimistic

     B

     Gloomy

     C

     Depressed

     D

     Hopeful

     Reveal answer
126. 126

     NUST Engineering Past Paper-14

     Pick the option that most accurately defines the verb OBVIATE.

     A

     Cause

     B

     Encourage

     C

     Prevent

     D

     Create

     Reveal answer
127. 127

     NUST Engineering Past Paper-14

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

     A

     Thorough

     B

     Detailed

     C

     Superficial

     D

     Careful

     Reveal answer
128. 128

     NUST Engineering Past Paper-14

     Pick the option that most accurately describes someone who is INTRANSIGENT.

     A

     Stubborn

     B

     Flexible

     C

     Adaptable

     D

     Compromising

     Reveal answer
129. 129

     NUST Engineering Past Paper-14

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

     A

     Genuine

     B

     False

     C

     Authentic

     D

     Real

     Reveal answer
130. 130

     NUST Engineering Past Paper-14

     Pick the option that most accurately defines the verb PLACATE.

     A

     Provoke

     B

     Anger

     C

     Calm

     D

     Irritate

     Reveal answer
131. 131

     NUST Engineering Past Paper-14

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

     A

     Doubtful

     B

     Skeptical

     C

     Easily deceived

     D

     Suspicious

     Reveal answer
132. 132

     NUST Engineering Past Paper-14

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

     A

     Convenient

     B

     Inappropriate

     C

     Disadvantageous

     D

     Impractical

     Reveal answer
133. 133

     NUST Engineering Past Paper-14

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

     A

     Personal

     B

     Direct

     C

     Firsthand

     D

     Experienced through others

     Reveal answer
134. 134

     NUST Engineering Past Paper-14

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

     A

     Generous

     B

     Petty

     C

     Selfish

     D

     Mean

     Reveal answer
135. 135

     NUST Engineering Past Paper-14

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

     A

     Active

     B

     Energetic

     C

     Busy

     D

     Lazy

     Reveal answer
136. 136

     NUST Engineering Past Paper-14

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

     A

     Verbose

     B

     Quiet

     C

     Chatty

     D

     Talkative

     Reveal answer
137. 137

     NUST Engineering Past Paper-14

     Pick the synonym of the verb ABHOR.

     A

     Admire

     B

     Fancy

     C

     Favor

     D

     Abominate

     Reveal answer
138. 138

     NUST Engineering Past Paper-14

     In simple harmonic motion (SHM), the maximum displacement of a particle from its equilibrium position is called its:

     A

     Phase

     B

     Frequency

     C

     Amplitude

     D

     Time period

     Reveal answer
139. 139

     NUST Engineering Past Paper-14

     A block of mass kg sits on a frictionless surface, attached to a spring of stiffness N/m. The block is pulled m from equilibrium and released from rest. Find its maximum speed during the resulting oscillation.

     A

     2 m/s

     B

     1 m/s

     C

     m/s

     D

     0.2 m/s

     Reveal answer
140. 140

     NUST Engineering Past Paper-14

     On a frictionless surface, a kg block is connected to a spring with N/m. It is displaced m from equilibrium and released. Determine the maximum speed achieved.

     A

     3 m/s

     B

     1 m/s

     C

     2 m/s

     D

     m/s

     Reveal answer
141. 141

     NUST Engineering Past Paper-14

     Given that the electric potential at a distance from a point charge is , what is the magnitude (and direction for ) of the electric field at that point?

     A

     (radially outward for positive )

     B

     C

     D

     Reveal answer
142. 142

     NUST Engineering Past Paper-14

     In a laser, stimulated emission requires the incident photon's energy to satisfy which condition?

     A

     Is greater than the transition energy

     B

     Is less than the transition energy

     C

     Equals the transition energy of the excited atom

     D

     Can be any value

     Reveal answer
143. 143

     NUST Engineering Past Paper-14

     An object moves in uniform circular motion. How much work does the centripetal force do over one full revolution?

     A

     B

     Zero

     C

     Maximum

     D

     Reveal answer
144. 144

     NUST Engineering Past Paper-14

     Estimate the ratio of the electric force to the gravitational force between two electrons separated by some distance .

     A

     B

     C

     D

     Reveal answer
145. 145

     NUST Engineering Past Paper-14

     A wheel of radius m starts from rest and uniformly accelerates to rad/s in s. How far does a point on the rim travel during this interval?

     A

     30 m

     B

     15 m

     C

     60 m

     D

     75 m

     Reveal answer
146. 146

     NUST Engineering Past Paper-14

     For which of the following thermodynamic processes is the entropy change of the system equal to zero?

     A

     Irreversible adiabatic compression

     B

     Isothermal expansion of ideal gas

     C

     Free expansion of gas into vacuum

     D

     Reversible adiabatic process

     Reveal answer
147. 147

     NUST Engineering Past Paper-14

     For which of the following nuclei is the binding energy per nucleon largest?

     A

     Hydrogen (H)

     B

     Iron (Fe)

     C

     Helium (He)

     D

     Uranium (U)

     Reveal answer
148. 148

     NUST Engineering Past Paper-14

     A glass prism of refractive index has an apex (refracting) angle of . Write the equation that determines its minimum deviation angle .

     A

     B

     C

     D

     Reveal answer
149. 149

     NUST Engineering Past Paper-14

     A wire of length , cross-sectional area and Young's modulus is stretched by a tensile force . Write the expression for the elastic potential energy stored in the wire.

     A

     B

     C

     D

     Reveal answer
150. 150

     NUST Engineering Past Paper-14

     Which of the following quantities associated with sound is a scalar?

     A

     Intensity

     B

     Velocity of sound

     C

     Particle velocity

     D

     Displacement of medium particles

     Reveal answer
151. 151

     NUST Engineering Past Paper-14

     A Carnot refrigerator works between cold and hot reservoirs at C and C respectively. Find its coefficient of performance (COP).

     A

     ≈ 10.2

     B

     ≈ 9

     C

     ≈ 0.1

     D

     ≈ 0.9

     Reveal answer
152. 152

     NUST Engineering Past Paper-14

     Write the expression for the momentum carried by a photon of wavelength .

     A

     B

     C

     D

     Reveal answer
153. 153

     NUST Engineering Past Paper-14

     A projectile is launched at above the horizontal with initial speed . Find the ratio of its maximum height to its horizontal range.

     A

     B

     C

     D

     Reveal answer
154. 154

     NUST Engineering Past Paper-14

     In the photoelectric effect, doubling the intensity of the incident light (without changing its frequency) doubles which of the following quantities?

     A

     Number of photoelectrons emitted per second

     B

     Maximum kinetic energy of photoelectrons

     C

     Threshold frequency

     D

     Stopping potential

     Reveal answer
155. 155

     NUST Engineering Past Paper-14

     What is the impedance of an ideal series LC circuit at its resonance frequency?

     A

     B

     Maximum

     C

     D

     Zero (in ideal case) or minimum

     Reveal answer
156. 156

     NUST Engineering Past Paper-14

     Which physical quantities determine the time period of a simple pendulum (in the small-amplitude limit)?

     A

     Amplitude and length

     B

     Mass and amplitude

     C

     Length and gravitational acceleration only

     D

     Length, mass, and gravitational acceleration

     Reveal answer
157. 157

     NUST Engineering Past Paper-14

     According to Gauss's law, the total electric flux through a closed surface in vacuum is equal to which of the following?

     A

     B

     C

     D

     Reveal answer
158. 158

     NUST Engineering Past Paper-14

     For an NPN transistor in the active region, which of the following correctly relates the emitter, base, and collector currents?

     A

     B

     C

     D

     Reveal answer
159. 159

     NUST Engineering Past Paper-14

     Two conducting spheres of radii and with are connected by a thin wire. Once equilibrium is reached, which sphere carries the larger surface charge density?

     A

     The larger sphere

     B

     The smaller sphere

     C

     Depends on initial charge

     D

     Both are equal

     Reveal answer
160. 160

     NUST Engineering Past Paper-14

     If the absolute temperature of a blackbody is tripled, by what factor does the power radiated per unit area change?

     A

     81

     B

     27

     C

     9

     D

     3

     Reveal answer
161. 161

     NUST Engineering Past Paper-14

     Water flowing in a pipe speeds up by a factor of 4 when the pipe's radius is halved. Which principle of fluid mechanics is this a direct consequence of?

     A

     Pascal's law

     B

     The equation of continuity:

     C

     Stokes' law

     D

     Bernoulli's equation alone

     Reveal answer
162. 162

     NUST Engineering Past Paper-14

     An object is placed exactly at the centre of curvature () of a concave mirror. Describe the image formed.

     A

     Between focus and mirror, virtual

     B

     At infinity

     C

     At the center of curvature, real, inverted, and same size

     D

     At focus, virtual and magnified

     Reveal answer
163. 163

     NUST Engineering Past Paper-14

     In the photoelectric effect, how is the stopping potential related to the incident-light frequency ? (Let be the work function.)

     A

     B

     C

     D

     Reveal answer
164. 164

     NUST Engineering Past Paper-14

     A particle of charge and mass moves in a uniform magnetic field . Write the expression for its cyclotron frequency .

     A

     B

     C

     D

     Reveal answer
165. 165

     NUST Engineering Past Paper-14

     A diffraction grating has 500 lines per mm. When illuminated with light of wavelength nm, what is the approximate angle of the first-order principal maximum?

     A

     ≈ 17.5°

     B

     ≈ 36.9°

     C

     30°

     D

     45°

     Reveal answer
166. 166

     NUST Engineering Past Paper-14

     A radioactive sample contains undecayed nuclei and has decay constant . Write the instantaneous rate of decay of the sample.

     A

     B

     C

     D

     Reveal answer
167. 167

     NUST Engineering Past Paper-14

     On which thermodynamic variable does the internal energy of an ideal gas depend solely?

     A

     Pressure only

     B

     Volume only

     C

     Pressure and volume

     D

     Temperature

     Reveal answer
168. 168

     NUST Engineering Past Paper-14

     In a transverse standing wave on a string fixed at both ends, what is the distance between two consecutive nodes?

     A

     B

     C

     D

     Reveal answer
169. 169

     NUST Engineering Past Paper-14

     Starting from rest, a body slides down a rough inclined plane of length tilted at angle above the horizontal, with kinetic-friction coefficient . Write the expression for its speed at the bottom of the incline.

     A

     B

     C

     D

     Reveal answer
170. 170

     NUST Engineering Past Paper-14

     Pair production is the process by which a sufficiently energetic gamma-ray photon creates which of the following?

     A

     Two electrons

     B

     An electron-positron pair

     C

     A proton-antiproton pair

     D

     A neutron and antineutron

     Reveal answer
171. 171

     NUST Engineering Past Paper-14

     What can be said about the angular momentum of a planet that follows an elliptical orbit around the Sun?

     A

     Is maximum at perihelion

     B

     Varies continuously

     C

     Is maximum at aphelion

     D

     Remains constant throughout the orbit

     Reveal answer
172. 172

     NUST Engineering Past Paper-14

     Estimate the energy carried by a photon of frequency Hz. Use Js.

     A

     J

     B

     J

     C

     J

     D

     J

     Reveal answer
173. 173

     NUST Engineering Past Paper-14

     In simple harmonic motion, what is the phase difference between displacement and acceleration?

     A

     B

     C

     0

     D

     Reveal answer
174. 174

     NUST Engineering Past Paper-14

     On what does the critical angle for total internal reflection (TIR) primarily depend?

     A

     The wavelength of light only

     B

     The intensity of light

     C

     The angle of incidence

     D

     The refractive indices of both media

     Reveal answer
175. 175

     NUST Engineering Past Paper-14

     Write the standard expression for the magnetic force per unit length acting between two long parallel wires carrying currents and , separated by a distance .

     A

     B

     C

     D

     Reveal answer
176. 176

     NUST Engineering Past Paper-14

     Give the formula for the speed of a transverse wave on a string of linear mass density stretched under tension .

     A

     B

     C

     D

     Reveal answer
177. 177

     NUST Engineering Past Paper-14

     Identify the majority charge carriers in the base region of a PNP transistor.

     A

     Electrons

     B

     Ions

     C

     Photons

     D

     Holes

     Reveal answer
178. 178

     NUST Engineering Past Paper-14

     A perfect blackbody at K emits peak radiation at wavelength . When its temperature is raised to K, find the new peak wavelength.

     A

     B

     C

     D

     Reveal answer
179. 179

     NUST Engineering Past Paper-14

     Potassium has a work function of eV. Find the longest wavelength of light able to eject photoelectrons from it. (Take eVnm.)

     A

     ≈ 539 nm

     B

     ≈ 248 nm

     C

     1240 nm

     D

     2300 nm

     Reveal answer
180. 180

     NUST Engineering Past Paper-14

     The first law of thermodynamics is . What does it reduce to for an isobaric (constant-pressure) process?

     A

     B

     C

     D

     Reveal answer
181. 181

     NUST Engineering Past Paper-14

     A projectile is launched with initial speed at an angle above the horizontal. Determine its speed at the highest point of the trajectory.

     A

     B

     Zero

     C

     D

     Reveal answer
182. 182

     NUST Engineering Past Paper-14

     Which of the following subatomic particles has zero electric charge and (essentially) zero rest mass?

     A

     Neutron

     B

     Photon

     C

     Positron

     D

     Neutrino

     Reveal answer
183. 183

     NUST Engineering Past Paper-14

     For a current-carrying conductor in a magnetic field, . The force on the conductor is minimum (in fact zero) when:

     A

     B

     C

     D

     Reveal answer
184. 184

     NUST Engineering Past Paper-14

     An electron in a hydrogen atom undergoes a transition from to . Find the approximate wavelength of the photon emitted. Use m.

     A

     ≈ 102.6 nm

     B

     ≈ 121.6 nm

     C

     ≈ 656 nm

     D

     ≈ 91 nm

     Reveal answer
185. 185

     NUST Engineering Past Paper-14

     A rod with proper length moves lengthwise at speed past a stationary observer. According to special relativity, what length does the observer measure?

     A

     B

     C

     D

     Reveal answer
186. 186

     NUST Engineering Past Paper-14

     The magnetic flux through a coil of turns changes from to over a time interval . Write the expression for the induced EMF in the coil.

     A

     B

     C

     D

     Reveal answer
187. 187

     NUST Engineering Past Paper-14

     What is the molar specific heat at constant volume, , for a diatomic ideal gas (at temperatures where only translation and rotation are excited)?

     A

     B

     C

     D

     Reveal answer
188. 188

     NUST Engineering Past Paper-14

     A converging lens has focal length . An object is placed at a distance of from the lens. Where is the image formed?

     A

     on the other side

     B

     on the other side

     C

     on the other side

     D

     on the other side

     Reveal answer
189. 189

     NUST Engineering Past Paper-14

     For an adiabatic process of an ideal gas (with ), which of the following relations is correct?

     A

     constant

     B

     constant

     C

     constant

     D

     constant

     Reveal answer
190. 190

     NUST Engineering Past Paper-14

     The ground-state energy of the hydrogen atom is eV. How much energy must be supplied to excite a hydrogen atom from the ground state to the level?

     A

     12.75 eV

     B

     13.6 eV

     C

     10.2 eV

     D

     0.85 eV

     Reveal answer
191. 191

     NUST Engineering Past Paper-14

     A truck of mass kg accelerates uniformly from rest to m/s in s. Find the average net force on it.

     A

     6250 N

     B

     3125 N

     C

     2000 N

     D

     50000 N

     Reveal answer
192. 192

     NUST Engineering Past Paper-14

     Why does the electrical conductivity of an intrinsic semiconductor increase with temperature?

     A

     More electron-hole pairs are thermally generated

     B

     The bandgap increases

     C

     Electron mobility increases

     D

     Lattice vibrations decrease

     Reveal answer
193. 193

     NUST Engineering Past Paper-14

     Point charges C and C lie on a line cm apart. Locate the point along this line (outside the segment, near ) where the net electric field is zero.

     A

     20 cm beyond

     B

     40 cm beyond

     C

     10 cm between the charges

     D

     30 cm beyond

     Reveal answer
194. 194

     NUST Engineering Past Paper-14

     Find the rms value of the alternating current amperes.

     A

     A

     B

     8 A

     C

     4 A

     D

     A

     Reveal answer
195. 195

     NUST Engineering Past Paper-14

     State Heisenberg's uncertainty relation between position and the corresponding momentum component .

     A

     B

     C

     D

     Reveal answer
196. 196

     NUST Engineering Past Paper-14

     A bar magnet is rotated through from its equilibrium orientation in a uniform field , performing work . What torque must now be applied to hold it in place at ?

     A

     B

     C

     D

     Reveal answer
197. 197

     NUST Engineering Past Paper-14

     Water flows at speed through a main pipe of inner diameter , then exits through identical small holes (each of diameter ) into a second chamber. Find the speed of the water emerging from each small hole.

     A

     B

     C

     D

     Reveal answer
198. 198

     NUST Engineering Past Paper-14

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

     A

     ≈ 33.3%

     B

     ≈ 40%

     C

     ≈ 50%

     D

     ≈ 66.7%

     Reveal answer
199. 199

     NUST Engineering Past Paper-14

     A positively charged proton moves to the right with through a uniform magnetic field directed out of the page. Determine the direction of the magnetic force on the proton.

     A

     Downward ()

     B

     Upward ()

     C

     To the left ()

     D

     To the right ()

     Reveal answer
200. 200

     NUST Engineering Past Paper-14

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

     A

     B

     C

     D

     Reveal answer