NUST Engineering Past Paper-17

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

1. 1

   NUST Engineering Past Paper-17

   We have 2 Red, 2 White and 3 Blue paints. In how many distinct ways can we paint a row of 7 wall panels using one paint per panel?

   A

   210

   B

   420

   C

   105

   D

   60

   Reveal answer
2. 2

   NUST Engineering Past Paper-17

   Find every solution of in the open interval .

   A

   B

   C

   and

   D

   Reveal answer
3. 3

   NUST Engineering Past Paper-17

   Find the value of .

   A

   B

   C

   D

   0

   Reveal answer
4. 4

   NUST Engineering Past Paper-17

   Let . Compute .

   A

   B

   C

   D

   None of these

   Reveal answer
5. 5

   NUST Engineering Past Paper-17

   Find the vertices of the conic .

   A

   B

   C

   D

   None of these

   Reveal answer
6. 6

   NUST Engineering Past Paper-17

   Which of the following is the correct logarithm identity for ?

   A

   B

   C

   D

   None

   Reveal answer
7. 7

   NUST Engineering Past Paper-17

   Find the remainder when is divided by .

   A

   8

   B

   C

   4

   D

   None of these

   Reveal answer
8. 8

   NUST Engineering Past Paper-17

   For the function on , find the number of relative maxima.

   A

   B

   None

   C

   D

   Reveal answer
9. 9

   NUST Engineering Past Paper-17

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

   A

   B

   C

   Not Possible

   D

   Reveal answer
10. 10

    NUST Engineering Past Paper-17

    Evaluate .

    A

    B

    1

    C

    0

    D

    None of these

    Reveal answer
11. 11

    NUST Engineering Past Paper-17

    In a triangle, . Given and , find .

    A

    1

    B

    C

    D

    None of these

    Reveal answer
12. 12

    NUST Engineering Past Paper-17

    Find the area of the triangle in which , , .

    A

    B

    C

    D

    None of these

    Reveal answer
13. 13

    NUST Engineering Past Paper-17

    Evaluate .

    A

    817

    B

    820

    C

    780

    D

    None of these

    Reveal answer
14. 14

    NUST Engineering Past Paper-17

    Compute .

    A

    3

    B

    2

    C

    6

    D

    None of these

    Reveal answer
15. 15

    NUST Engineering Past Paper-17

    Compute .

    A

    16

    B

    C

    D

    None of these

    Reveal answer
16. 16

    NUST Engineering Past Paper-17

    Which of the following is Pascal's identity for binomial coefficients?

    A

    None

    B

    C

    D

    Reveal answer
17. 17

    NUST Engineering Past Paper-17

    What is the range of (principal value)?

    A

    B

    None

    C

    D

    Reveal answer
18. 18

    NUST Engineering Past Paper-17

    What is the domain of ?

    A

    None

    B

    C

    D

    Reveal answer
19. 19

    NUST Engineering Past Paper-17

    Which of the following can serve as a universal set in an appropriate context?

    A

    Points on a plane

    B

    Real numbers

    C

    All of the above

    D

    All people in the world

    Reveal answer
20. 20

    NUST Engineering Past Paper-17

    Find .

    A

    B

    1

    C

    D

    None of these

    Reveal answer
21. 21

    NUST Engineering Past Paper-17

    A sphere is being inflated so that its radius grows at cm/s. At the instant when cm, what is the rate of change of its volume?

    A

    cm/s

    B

    cm/s

    C

    cm/s

    D

    None of these

    Reveal answer
22. 22

    NUST Engineering Past Paper-17

    A circular ripple expands on a pond so that its radius is increasing at the rate cm/s. Find the rate at which its circumference is increasing.

    A

    cm/s

    B

    cm/s

    C

    cm/s

    D

    None of these

    Reveal answer
23. 23

    NUST Engineering Past Paper-17

    Find .

    A

    1

    B

    C

    D

    None of these

    Reveal answer
24. 24

    NUST Engineering Past Paper-17

    For what sign condition on and does represent an ellipse?

    A

    B

    Signs of and are the same

    C

    Signs of and are opposite

    D

    Reveal answer
25. 25

    NUST Engineering Past Paper-17

    If and , find .

    A

    B

    C

    D

    None of these

    Reveal answer
26. 26

    NUST Engineering Past Paper-17

    How many multiples of lie strictly between and ?

    A

    11

    B

    12

    C

    10

    D

    None of these

    Reveal answer
27. 27

    NUST Engineering Past Paper-17

    Find the probability of getting at least heads when a fair coin is tossed times.

    A

    B

    C

    D

    None of these

    Reveal answer
28. 28

    NUST Engineering Past Paper-17

    Compute .

    A

    B

    C

    D

    None of these

    Reveal answer
29. 29

    NUST Engineering Past Paper-17

    Simplify .

    A

    None

    B

    C

    D

    Reveal answer
30. 30

    NUST Engineering Past Paper-17

    Which of the following properties does division of integers (excluding division by zero) satisfy?

    A

    None

    B

    Closed

    C

    Commutative

    D

    Associative

    Reveal answer
31. 31

    NUST Engineering Past Paper-17

    If , find .

    A

    B

    C

    D

    None of these

    Reveal answer
32. 32

    NUST Engineering Past Paper-17

    If , find .

    A

    B

    C

    D

    None of these

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33. 33

    NUST Engineering Past Paper-17

    Find a vector perpendicular to both and .

    A

    B

    C

    D

    None of these

    Reveal answer
34. 34

    NUST Engineering Past Paper-17

    If and lies in the third quadrant, find .

    A

    B

    C

    D

    None of these

    Reveal answer
35. 35

    NUST Engineering Past Paper-17

    Which statement is true about a function that is differentiable at ?

    A

    may or may not be continuous at

    B

    is continuous at

    C

    None

    D

    More information needed

    Reveal answer
36. 36

    NUST Engineering Past Paper-17

    Simplify .

    A

    B

    1

    C

    D

    None of these

    Reveal answer
37. 37

    NUST Engineering Past Paper-17

    Simplify .

    A

    2

    B

    1

    C

    0

    D

    None of these

    Reveal answer
38. 38

    NUST Engineering Past Paper-17

    In how many ways can distinct people be seated around a round table?

    A

    720

    B

    5040

    C

    120

    D

    None of these

    Reveal answer
39. 39

    NUST Engineering Past Paper-17

    Find the equation of the directrix of the parabola .

    A

    B

    C

    D

    None of these

    Reveal answer
40. 40

    NUST Engineering Past Paper-17

    Consider the hyperbola . What special curve does it become when ?

    A

    Point

    B

    Circle

    C

    Both

    D

    None

    Reveal answer
41. 41

    NUST Engineering Past Paper-17

    Which of the following statements are true? (I) Altitudes of a triangle are concurrent. (II) Perpendicular bisectors of the sides meet at the circumcentre. (III) Angle bisectors meet at the incentre.

    A

    I only

    B

    I and II

    C

    II only

    D

    All

    Reveal answer
42. 42

    NUST Engineering Past Paper-17

    A fair coin is tossed times. Find the probability of getting at least one tail.

    A

    B

    C

    D

    None of these

    Reveal answer
43. 43

    NUST Engineering Past Paper-17

    Find the radius of an escribed (ex-)circle of the equilateral triangle whose sides are each units.

    A

    B

    C

    D

    None of these

    Reveal answer
44. 44

    NUST Engineering Past Paper-17

    If , find .

    A

    11

    B

    7

    C

    8

    D

    None of these

    Reveal answer
45. 45

    NUST Engineering Past Paper-17

    For the quadratic , find .

    A

    B

    C

    D

    None of these

    Reveal answer
46. 46

    NUST Engineering Past Paper-17

    For a quadratic with discriminant , write the formula for (the absolute difference of the roots).

    A

    Both

    B

    C

    None

    D

    Reveal answer
47. 47

    NUST Engineering Past Paper-17

    Find the sum of the infinite series .

    A

    B

    C

    4

    D

    None of these

    Reveal answer
48. 48

    NUST Engineering Past Paper-17

    Find the multiplicative inverse of , expressed as an ordered pair .

    A

    B

    C

    D

    None of these

    Reveal answer
49. 49

    NUST Engineering Past Paper-17

    Find the equation of the tangent to the circle at the point .

    A

    B

    C

    D

    None of these

    Reveal answer
50. 50

    NUST Engineering Past Paper-17

    How many tangent lines can be drawn to a circle from a point that lies inside the circle?

    A

    0

    B

    1

    C

    2

    D

    Infinite

    Reveal answer
51. 51

    NUST Engineering Past Paper-17

    Find the centre of the circle .

    A

    B

    C

    D

    None of these

    Reveal answer
52. 52

    NUST Engineering Past Paper-17

    Find the term independent of in the expansion of .

    A

    5670

    B

    C

    D

    None of these

    Reveal answer
53. 53

    NUST Engineering Past Paper-17

    Two forces and act at the point . Compute the magnitude of their combined moment about the point .

    A

    ≈ 16.3

    B

    ≈ 36.4

    C

    20

    D

    None of these

    Reveal answer
54. 54

    NUST Engineering Past Paper-17

    Two fair dice are rolled. Find the probability that both faces show a number divisible by both and .

    A

    B

    C

    D

    None of these

    Reveal answer
55. 55

    NUST Engineering Past Paper-17

    Compute .

    A

    360

    B

    240

    C

    270

    D

    None of these

    Reveal answer
56. 56

    NUST Engineering Past Paper-17

    Find the (positive) geometric mean between and .

    A

    12

    B

    C

    8

    D

    None of these

    Reveal answer
57. 57

    NUST Engineering Past Paper-17

    If , find .

    A

    B

    5

    C

    D

    None of these

    Reveal answer
58. 58

    NUST Engineering Past Paper-17

    Compute .

    A

    B

    C

    D

    None of these

    Reveal answer
59. 59

    NUST Engineering Past Paper-17

    Compute .

    A

    1

    B

    0

    C

    D

    None of these

    Reveal answer
60. 60

    NUST Engineering Past Paper-17

    Find the value of .

    A

    2870

    B

    1240

    C

    2100

    D

    None of these

    Reveal answer
61. 61

    NUST Engineering Past Paper-17

    Find — write the simplified expression.

    A

    B

    C

    D

    None of these

    Reveal answer
62. 62

    NUST Engineering Past Paper-17

    Find the probability that a randomly chosen three-digit positive integer is divisible by .

    A

    B

    C

    D

    None of these

    Reveal answer
63. 63

    NUST Engineering Past Paper-17

    Simplify for any real .

    A

    B

    C

    D

    None

    Reveal answer
64. 64

    NUST Engineering Past Paper-17

    Simplify for .

    A

    B

    C

    D

    None

    Reveal answer
65. 65

    NUST Engineering Past Paper-17

    Find from the implicit equation .

    A

    B

    C

    D

    None of these

    Reveal answer
66. 66

    NUST Engineering Past Paper-17

    How many diagonals does a regular octagon have?

    A

    20

    B

    16

    C

    12

    D

    None of these

    Reveal answer
67. 67

    NUST Engineering Past Paper-17

    Find the range of .

    A

    B

    C

    D

    None of these

    Reveal answer
68. 68

    NUST Engineering Past Paper-17

    For a -- right triangle, find the exradius opposite the side of length .

    A

    3

    B

    5

    C

    2

    D

    None of these

    Reveal answer
69. 69

    NUST Engineering Past Paper-17

    If , compute .

    A

    B

    100

    C

    D

    None of these

    Reveal answer
70. 70

    NUST Engineering Past Paper-17

    Two fair dice are rolled. What is the probability that the sum of the two upturned faces is ?

    A

    B

    C

    D

    None of these

    Reveal answer
71. 71

    NUST Engineering Past Paper-17

    Compute where is a primitive cube root of unity.

    A

    B

    C

    D

    None of these

    Reveal answer
72. 72

    NUST Engineering Past Paper-17

    Which of the following statements are true? (I) . (II) . (III) .

    A

    II only

    B

    I and II

    C

    I only

    D

    I and III

    Reveal answer
73. 73

    NUST Engineering Past Paper-17

    If is a positive integer, how many terms does the binomial expansion of have?

    A

    B

    C

    None

    D

    Reveal answer
74. 74

    NUST Engineering Past Paper-17

    Find the domain of .

    A

    B

    C

    D

    None of these

    Reveal answer
75. 75

    NUST Engineering Past Paper-17

    Evaluate .

    A

    1

    B

    0

    C

    D

    None of these

    Reveal answer
76. 76

    NUST Engineering Past Paper-17

    Find .

    A

    B

    C

    D

    None of these

    Reveal answer
77. 77

    NUST Engineering Past Paper-17

    Evaluate .

    A

    B

    C

    D

    None of these

    Reveal answer
78. 78

    NUST Engineering Past Paper-17

    Solve the differential equation (one particular solution).

    A

    None

    B

    C

    D

    Reveal answer
79. 79

    NUST Engineering Past Paper-17

    Evaluate .

    A

    B

    C

    D

    None of these

    Reveal answer
80. 80

    NUST Engineering Past Paper-17

    Which of the following triples is/are Pythagorean?

    A

    B

    Both A and B

    C

    D

    Reveal answer
81. 81

    NUST Engineering Past Paper-17

    How many solutions does the system , have?

    A

    1

    B

    C

    0

    D

    2

    Reveal answer
82. 82

    NUST Engineering Past Paper-17

    What is the name of a line drawn from a vertex of a triangle to the midpoint of the opposite side?

    A

    Angle Bisector

    B

    Median

    C

    None

    D

    Right Bisector

    Reveal answer
83. 83

    NUST Engineering Past Paper-17

    Determine whether the vectors and are parallel, perpendicular, or neither.

    A

    Perpendicular

    B

    Parallel

    C

    Neither

    D

    None

    Reveal answer
84. 84

    NUST Engineering Past Paper-17

    Write the equation of the tangent to the parabola at the point on it.

    A

    B

    C

    None

    D

    Reveal answer
85. 85

    NUST Engineering Past Paper-17

    If is tangent to , find when .

    A

    1

    B

    C

    2

    D

    None of these

    Reveal answer
86. 86

    NUST Engineering Past Paper-17

    Find the equations of the asymptotes of the hyperbola .

    A

    B

    C

    D

    None of these

    Reveal answer
87. 87

    NUST Engineering Past Paper-17

    If , find .

    A

    16

    B

    C

    D

    Reveal answer
88. 88

    NUST Engineering Past Paper-17

    Find the foci of .

    A

    B

    C

    D

    None of these

    Reveal answer
89. 89

    NUST Engineering Past Paper-17

    Simplify:

    A

    B

    C

    D

    Reveal answer
90. 90

    NUST Engineering Past Paper-17

    Evaluate .

    A

    B

    C

    D

    Reveal answer
91. 91

    NUST Engineering Past Paper-17

    In an arithmetic progression, and . Determine the -st term.

    A

    B

    C

    D

    None of these

    Reveal answer
92. 92

    NUST Engineering Past Paper-17

    Determine the coefficient of in the binomial expansion of .

    A

    B

    C

    D

    None of these

    Reveal answer
93. 93

    NUST Engineering Past Paper-17

    Evaluate .

    A

    B

    C

    D

    Reveal answer
94. 94

    NUST Engineering Past Paper-17

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

    A

    B

    C

    D

    Reveal answer
95. 95

    NUST Engineering Past Paper-17

    Determine the COEFFICIENT of the th term in the binomial expansion of .

    A

    B

    C

    D

    Reveal answer
96. 96

    NUST Engineering Past Paper-17

    For the monic quadratic , suppose one root is THREE TIMES the other. Determine the resulting algebraic relationship between and .

    A

    B

    C

    D

    Reveal answer
97. 97

    NUST Engineering Past Paper-17

    Pick the option that best captures the meaning of 'Frisky':

    A

    Playful and full of energy

    B

    Sad and withdrawn

    C

    Angry and aggressive

    D

    Lazy and inactive

    Reveal answer
98. 98

    NUST Engineering Past Paper-17

    Complete the analogy: 'Pedestrians are to Sidewalk as Vehicles are to ____'.

    A

    Pavement

    B

    Bridge

    C

    Tunnel

    D

    Road

    Reveal answer
99. 99

    NUST Engineering Past Paper-17

    Identify the correctly worded sentence:

    A

    There are an average of one death every week

    B

    There is an average of one death every week

    C

    There were an average of one death every week

    D

    There was an average of one death every week

    Reveal answer
100. 100

     NUST Engineering Past Paper-17

     Which of the following options spells the word for 'a period of one thousand years' correctly?

     A

     Milenium

     B

     Milennium

     C

     Millennium

     D

     Millenium

     Reveal answer
101. 101

     NUST Engineering Past Paper-17

     Pick the word closest in meaning to 'evocative':

     A

     Dull

     B

     Redolent

     C

     Trivial

     D

     Passive

     Reveal answer
102. 102

     NUST Engineering Past Paper-17

     Pick the option that best defines 'Abide by':

     A

     To challenge authority

     B

     To delay a decision

     C

     To comply with or accept a rule or decision

     D

     To ignore a rule or agreement

     Reveal answer
103. 103

     NUST Engineering Past Paper-17

     Pick the phrase most nearly OPPOSITE in meaning to 'Alma mater':

     A

     Parent school

     B

     Enrollment record

     C

     Future institution

     D

     Graduating institution

     Reveal answer
104. 104

     NUST Engineering Past Paper-17

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

     A

     Obscurity

     B

     Clarity

     C

     Uncertainty

     D

     Doubt

     Reveal answer
105. 105

     NUST Engineering Past Paper-17

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

     A

     Unambiguous

     B

     Cryptic

     C

     Obscure

     D

     Vague

     Reveal answer
106. 106

     NUST Engineering Past Paper-17

     Pick the option that best defines 'Extrovert':

     A

     A person with unpredictable mood swings

     B

     A person who prefers solitude and inner reflection

     C

     A person who avoids public speaking

     D

     An outgoing, socially confident person

     Reveal answer
107. 107

     NUST Engineering Past Paper-17

     Pick the word closest in meaning to 'Fad':

     A

     Craze

     B

     Custom

     C

     Heritage

     D

     Tradition

     Reveal answer
108. 108

     NUST Engineering Past Paper-17

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

     A

     Slowly

     B

     Steadily

     C

     Progressively

     D

     Abruptly

     Reveal answer
109. 109

     NUST Engineering Past Paper-17

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

     A

     Romantic

     B

     Utopian

     C

     Optimistic

     D

     Pragmatic

     Reveal answer
110. 110

     NUST Engineering Past Paper-17

     Pick the option that best defines 'Lethal':

     A

     Mildly irritating

     B

     Capable of causing death

     C

     Temporarily dangerous

     D

     Completely harmless

     Reveal answer
111. 111

     NUST Engineering Past Paper-17

     Pick the word closest in meaning to 'Ominous':

     A

     Foreboding

     B

     Promising

     C

     Encouraging

     D

     Auspicious

     Reveal answer
112. 112

     NUST Engineering Past Paper-17

     Pick the option that best defines 'Perpetual':

     A

     Happening unpredictably

     B

     Lasting only for a brief time

     C

     Occurring once every decade

     D

     Never ending or changing; constant

     Reveal answer
113. 113

     NUST Engineering Past Paper-17

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

     A

     Grandiose

     B

     Conceited

     C

     Humble

     D

     Ostentatious

     Reveal answer
114. 114

     NUST Engineering Past Paper-17

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

     A

     Hopeful

     B

     Pessimistic

     C

     Cheerful

     D

     Buoyant

     Reveal answer
115. 115

     NUST Engineering Past Paper-17

     Pick the option that best defines 'Serenity':

     A

     A feeling of intense excitement

     B

     The state of being calm, peaceful, and untroubled

     C

     A state of extreme agitation

     D

     A condition of constant anxiety

     Reveal answer
116. 116

     NUST Engineering Past Paper-17

     Pick the word closest in meaning to 'Immigrate':

     A

     Exile

     B

     Relocate (to)

     C

     Emigrate

     D

     Depart

     Reveal answer
117. 117

     NUST Engineering Past Paper-17

     Pick the term closest in scale to 'Quintillion':

     A

     Thousand

     B

     Million

     C

     Sextillion

     D

     Billion

     Reveal answer
118. 118

     NUST Engineering Past Paper-17

     Identify the pair below that has the same logical relationship as Sonnet : Poem.

     A

     Lie : Falsehood

     B

     Ballad : Stanza

     C

     Murder : Crime

     D

     Chapter : Book

     Reveal answer
119. 119

     NUST Engineering Past Paper-17

     Pick the synonym of the adjective BOMBASTIC.

     A

     Meek

     B

     Explosive

     C

     Retaliatory

     D

     Inflated

     Reveal answer
120. 120

     NUST Engineering Past Paper-17

     Pick the correctly spelled noun denoting an elected county law-enforcement officer in the United States.

     A

     Sherrif

     B

     None

     C

     Sherriff

     D

     Sheriff

     Reveal answer
121. 121

     NUST Engineering Past Paper-17

     Pick the antonym of the noun APLOMB.

     A

     Serenity

     B

     Anxiety

     C

     Apathy

     D

     Composure

     Reveal answer
122. 122

     NUST Engineering Past Paper-17

     Pick the synonym of the adjective MANGY.

     A

     Sleek

     B

     Long-limbed

     C

     Voracious

     D

     Shabby

     Reveal answer
123. 123

     NUST Engineering Past Paper-17

     Pick the antonym of the verb VIE.

     A

     Engage

     B

     Pry

     C

     Compete

     D

     Concede

     Reveal answer
124. 124

     NUST Engineering Past Paper-17

     Pick the synonym of the noun CAMEO (in film and theatre).

     A

     Minor role

     B

     Type of fiction

     C

     Funny character

     D

     Sharp tool

     Reveal answer
125. 125

     NUST Engineering Past Paper-17

     Pick the correctly spelled noun denoting miscellaneous articles or equipment associated with a particular activity.

     A

     Paraphernalia

     B

     Paraphernelia

     C

     Parapharnalia

     D

     Parapharnelia

     Reveal answer
126. 126

     NUST Engineering Past Paper-17

     Complete the analogy: Birds is to Aves as ___ is to ___.

     A

     Lizard : Insect

     B

     Man : Homo sapiens

     C

     Whale : Fish

     D

     Fish : Water

     Reveal answer
127. 127

     NUST Engineering Past Paper-17

     Pick the synonym of the verb HARANGUE.

     A

     Perplex

     B

     Console

     C

     Persuade

     D

     Lecture

     Reveal answer
128. 128

     NUST Engineering Past Paper-17

     Pick the synonym of the adjective CRAVEN.

     A

     Resolute

     B

     Courageous

     C

     Audacious

     D

     Timid

     Reveal answer
129. 129

     NUST Engineering Past Paper-17

     Pick the synonym of the adjective TERSE.

     A

     Verbose

     B

     Concise

     C

     None

     D

     Diffuse

     Reveal answer
130. 130

     NUST Engineering Past Paper-17

     Pick the antonym of the noun AXIOM.

     A

     Principle

     B

     Proposition

     C

     Paradox

     D

     Axon

     Reveal answer
131. 131

     NUST Engineering Past Paper-17

     Complete the analogy: Argument is to Debate as ___ is to ___.

     A

     Doe : Stag

     B

     Fight : Contest

     C

     Violence : Peace

     D

     Challenge : Opponent

     Reveal answer
132. 132

     NUST Engineering Past Paper-17

     Pick the synonym of the noun UNDERTAKING.

     A

     Withdrawing

     B

     Renouncing

     C

     All of these

     D

     Upholding

     Reveal answer
133. 133

     NUST Engineering Past Paper-17

     Pick the synonym of the adjective RABID (in its figurative sense).

     A

     Traditional

     B

     Moderate

     C

     Conservative

     D

     Extreme

     Reveal answer
134. 134

     NUST Engineering Past Paper-17

     Complete the analogy: Flag is to Nation as ___ is to ___.

     A

     Emblem : Prosperity

     B

     Insignia : Rank

     C

     Wealth : Prestige

     D

     Honor : Status

     Reveal answer
135. 135

     NUST Engineering Past Paper-17

     Pick the synonym of the adjective MOROSE.

     A

     Melancholy

     B

     Jovial

     C

     Enigmatic

     D

     Radiant

     Reveal answer
136. 136

     NUST Engineering Past Paper-17

     Pick the synonym of the adjective RESTIVE.

     A

     Rebellious

     B

     Friendly

     C

     None

     D

     Docile

     Reveal answer
137. 137

     NUST Engineering Past Paper-17

     Choose the word that BEST completes the sentence: 'The chairman demanded a more ______ analysis of the financial irregularities, rather than the vague summary the auditor had provided.'

     A

     Rigorous

     B

     Regular

     C

     Vehement

     D

     Contradictory

     Reveal answer
138. 138

     NUST Engineering Past Paper-17

     In a common-emitter transistor, the base current is and the collector current is . Find the current gain .

     A

     200

     B

     100

     C

     50

     D

     400

     Reveal answer
139. 139

     NUST Engineering Past Paper-17

     A battery of emf V and internal resistance delivers a current of A to an external circuit. Find the terminal voltage .

     A

     8.2 V

     B

     9.8 V

     C

     9 V

     D

     10 V

     Reveal answer
140. 140

     NUST Engineering Past Paper-17

     What is the net electric charge of a p-type semiconductor?

     A

     Negative

     B

     Neutral

     C

     Positive

     D

     Cannot be determined

     Reveal answer
141. 141

     NUST Engineering Past Paper-17

     A capacitor of capacitance is charged to a potential of V. Determine the energy stored.

     A

     J

     B

     J

     C

     J

     D

     J

     Reveal answer
142. 142

     NUST Engineering Past Paper-17

     A body of mass kg moving with velocity m/s collides head-on with a stationary body of mass kg. The two bodies stick together. Determine their common velocity after the collision.

     A

     m/s

     B

     m/s

     C

     m/s

     D

     m/s

     Reveal answer
143. 143

     NUST Engineering Past Paper-17

     In an electric circuit, the power dissipated in a resistor when a current flows through it is . If the current is now doubled while stays the same, what is the new power dissipated?

     A

     B

     C

     D

     Reveal answer
144. 144

     NUST Engineering Past Paper-17

     Determine the work required to rotate a magnetic dipole of moment from equilibrium (parallel to the external field ) to the antiparallel orientation (180 to ).

     A

     B

     C

     Zero

     D

     Reveal answer
145. 145

     NUST Engineering Past Paper-17

     In quantum mechanics, what physical information does the wave function encode?

     A

     The exact position of the particle

     B

     The energy of the particle directly

     C

     The probability amplitude; gives the probability density

     D

     The exact momentum of the particle

     Reveal answer
146. 146

     NUST Engineering Past Paper-17

     A train approaches a platform observer at . Determine the relativistic Lorentz factor for the train.

     A

     B

     C

     D

     Reveal answer
147. 147

     NUST Engineering Past Paper-17

     For a small sphere falling through a viscous fluid, how does the terminal velocity scale with the sphere's radius ?

     A

     B

     C

     D

     Reveal answer
148. 148

     NUST Engineering Past Paper-17

     In a Compton scattering experiment, at what scattering angle of the outgoing photon is the wavelength shift maximum?

     A

     B

     C

     D

     Reveal answer
149. 149

     NUST Engineering Past Paper-17

     Identify the correct expression for the self-inductance of a long solenoid with turns per unit length, cross-sectional area , and length carrying current .

     A

     B

     C

     D

     Reveal answer
150. 150

     NUST Engineering Past Paper-17

     A man of mass kg stands on a weighing scale in a vertical elevator. The scale reads N. Taking m/s, determine the magnitude and direction of the elevator's acceleration.

     A

     m/s² downward

     B

     Zero

     C

     m/s² upward

     D

     m/s² upward

     Reveal answer
151. 151

     NUST Engineering Past Paper-17

     Identify the formula relating the power of a lens (in diopters) to its focal length (in metres).

     A

     B

     C

     D

     Reveal answer
152. 152

     NUST Engineering Past Paper-17

     Two capacitors F and F are connected in series across a V supply. Determine the voltage across .

     A

     V

     B

     V

     C

     V

     D

     V

     Reveal answer
153. 153

     NUST Engineering Past Paper-17

     A projectile is launched on level ground with initial speed . The maximum horizontal range (achieved at the optimum launch angle of ) is given by which expression?

     A

     B

     C

     D

     Reveal answer
154. 154

     NUST Engineering Past Paper-17

     Identify the magnetic-field magnitude at the centre of a single circular loop of radius carrying a steady current .

     A

     B

     C

     D

     Reveal answer
155. 155

     NUST Engineering Past Paper-17

     Using the Bohr model, determine the ratio of the energy of the first excited state () to the energy of the ground state () of the hydrogen atom.

     A

     B

     C

     D

     Reveal answer
156. 156

     NUST Engineering Past Paper-17

     Bernoulli's equation, applied along a streamline of an incompressible, non-viscous fluid, represents which fundamental conservation principle?

     A

     Conservation of energy for fluid flow

     B

     Newton's second law for fluids

     C

     Conservation of mass for fluid flow

     D

     Conservation of momentum

     Reveal answer
157. 157

     NUST Engineering Past Paper-17

     Identify the balance condition for a Wheatstone bridge with resistors , , , in the four arms.

     A

     B

     C

     D

     Reveal answer
158. 158

     NUST Engineering Past Paper-17

     Identify the physical reason why a glass prism produces dispersion of white light into its constituent colours.

     A

     Light is reflected from the surface

     B

     The prism absorbs certain frequencies

     C

     White light undergoes total internal reflection

     D

     Different wavelengths of light have different refractive indices

     Reveal answer
159. 159

     NUST Engineering Past Paper-17

     For a body of mass attached to a spring of stiffness and oscillating with amplitude , identify the restoring force at displacement from equilibrium.

     A

     B

     C

     D

     Reveal answer
160. 160

     NUST Engineering Past Paper-17

     Arrange the three principal nuclear radiations in order of INCREASING penetrating power (i.e., least penetrating first).

     A

     B

     C

     D

     Reveal answer
161. 161

     NUST Engineering Past Paper-17

     If an AC signal of frequency is fed into a full-wave rectifier, what is the fundamental frequency of the output ripple?

     A

     B

     C

     D

     Reveal answer
162. 162

     NUST Engineering Past Paper-17

     Determine the potential difference required to accelerate a proton from rest so that its de Broglie wavelength becomes Å m. (Use kg, J·s, C.)

     A

     V

     B

     V

     C

     V

     D

     V

     Reveal answer
163. 163

     NUST Engineering Past Paper-17

     What does the conservation of baryon number require in any allowed particle reaction?

     A

     The total baryon number before and after reaction remains constant

     B

     Mass is conserved

     C

     Energy is conserved but baryon number may change

     D

     The total charge is conserved

     Reveal answer
164. 164

     NUST Engineering Past Paper-17

     For a spring-mass oscillator with mass and spring constant , if both and are HALVED, how does the time period change?

     A

     Remains the same

     B

     times

     C

     Halves

     D

     Doubles

     Reveal answer
165. 165

     NUST Engineering Past Paper-17

     Which physical mechanism is most directly responsible for the energy released when two deuterium nuclei fuse to form helium-3 and a neutron?

     A

     The mass defect converted via

     B

     Chemical bonding energy

     C

     Coulomb repulsion energy

     D

     Kinetic energy of incident particles

     Reveal answer
166. 166

     NUST Engineering Past Paper-17

     A uniform resistance wire of resistance is cut into equal pieces, which are then connected together in parallel. Determine the effective resistance of the parallel combination.

     A

     B

     C

     D

     Reveal answer
167. 167

     NUST Engineering Past Paper-17

     Identify the oscillation frequency of a second's pendulum.

     A

     Hz

     B

     Hz

     C

     Hz

     D

     Hz

     Reveal answer
168. 168

     NUST Engineering Past Paper-17

     According to the principle of superposition for waves, what is the displacement at a point where two waves overlap?

     A

     The waves always cancel

     B

     Energy doubles

     C

     The resultant displacement is the algebraic sum of individual displacements

     D

     The wave with higher amplitude dominates

     Reveal answer
169. 169

     NUST Engineering Past Paper-17

     A heat engine absorbs J of heat from the hot reservoir per cycle and rejects J to the cold reservoir. Determine its thermal efficiency.

     A

     B

     C

     D

     Reveal answer
170. 170

     NUST Engineering Past Paper-17

     For an ideal DIATOMIC gas, identify the ratio of specific heats .

     A

     B

     C

     D

     Reveal answer
171. 171

     NUST Engineering Past Paper-17

     When light traveling in a less-dense medium reflects off a boundary with a DENSER medium, what is the phase change of the reflected ray?

     A

     (no change)

     B

     (phase reversal)

     C

     D

     Reveal answer
172. 172

     NUST Engineering Past Paper-17

     Identify the rotational kinetic energy of a rigid body that has moment of inertia and is spinning with angular velocity .

     A

     B

     C

     D

     Reveal answer
173. 173

     NUST Engineering Past Paper-17

     A W monochromatic light bulb emits light of wavelength nm. Estimate the number of photons emitted per second. (Take J·s, m/s.)

     A

     B

     C

     D

     Reveal answer
174. 174

     NUST Engineering Past Paper-17

     If the separation between two point charges is DOUBLED (with the charges unchanged), what happens to the Coulomb force between them?

     A

     4 times larger

     B

     2 times larger

     C

     Quarter

     D

     Half

     Reveal answer
175. 175

     NUST Engineering Past Paper-17

     When two sound waves of nearby frequencies and superpose to produce beats, what is the beat frequency?

     A

     B

     C

     D

     Reveal answer
176. 176

     NUST Engineering Past Paper-17

     A bullet of mass g moving at m/s embeds itself in a stationary block of mass kg resting on a frictionless surface. Determine the common velocity of the bullet-block system immediately after impact.

     A

     m/s

     B

     m/s

     C

     m/s

     D

     m/s

     Reveal answer
177. 177

     NUST Engineering Past Paper-17

     In an ideal LC circuit undergoing free oscillations, at what point in the cycle is the current through the inductor at its maximum value?

     A

     The capacitor is fully charged

     B

     The charge on the capacitor is zero (energy fully in inductor)

     C

     The capacitor is half-charged

     D

     The inductor has maximum voltage across it

     Reveal answer
178. 178

     NUST Engineering Past Paper-17

     A cyclist takes a circular track of radius at constant speed . Identify the banking angle that allows the turn to be negotiated without relying on friction.

     A

     B

     C

     D

     Reveal answer
179. 179

     NUST Engineering Past Paper-17

     A coil has self-inductance . Identify the induced back-EMF when the current through it changes at the rate .

     A

     B

     C

     D

     Reveal answer
180. 180

     NUST Engineering Past Paper-17

     For total internal reflection to occur at the interface between an optically denser and a less dense medium, what condition must the angle of incidence satisfy?

     A

     Less than the critical angle

     B

     Greater than the critical angle

     C

     Exactly

     D

     Equal to the critical angle

     Reveal answer
181. 181

     NUST Engineering Past Paper-17

     In a cathode-ray oscilloscope (CRO), what does the 'time-base' setting control?

     A

     The frequency of input signal

     B

     The horizontal sweep of the electron beam

     C

     The vertical deflection

     D

     The brightness of the spot

     Reveal answer
182. 182

     NUST Engineering Past Paper-17

     State what the net work done on an object equals, according to the work-energy theorem.

     A

     The change in its kinetic energy

     B

     The change in its total mechanical energy

     C

     The product of force and time

     D

     The change in its potential energy

     Reveal answer
183. 183

     NUST Engineering Past Paper-17

     A conducting rod of length moves with velocity perpendicular to a uniform magnetic field of strength . Determine the induced motional EMF across the rod.

     A

     B

     C

     D

     Reveal answer
184. 184

     NUST Engineering Past Paper-17

     In a Young's double-slit experiment, if the wavelength of the illuminating light is INCREASED while the slit spacing and screen distance remain fixed, how does the fringe separation change?

     A

     Becomes zero

     B

     Remains the same

     C

     Increases

     D

     Decreases

     Reveal answer
185. 185

     NUST Engineering Past Paper-17

     Describe the configuration of the electric field lines produced by an ISOLATED positive point charge.

     A

     Are parallel and uniform

     B

     Are circular around the charge

     C

     Converge toward the charge

     D

     Radiate outward from the charge

     Reveal answer
186. 186

     NUST Engineering Past Paper-17

     A string fixed at both ends is set to vibrate in its FOURTH harmonic (third overtone). Determine the number of antinodes in the standing wave.

     A

     3

     B

     2

     C

     1

     D

     4

     Reveal answer
187. 187

     NUST Engineering Past Paper-17

     In pair annihilation of an electron with a positron (both at rest), what are the typical end products?

     A

     Two electrons

     B

     One gamma-ray photon

     C

     Two gamma-ray photons

     D

     A neutron and proton

     Reveal answer
188. 188

     NUST Engineering Past Paper-17

     Determine the impedance of a series RL circuit driven by an AC source, with and inductive reactance .

     A

     B

     C

     D

     Reveal answer
189. 189

     NUST Engineering Past Paper-17

     Inside a uniform-density solid sphere of radius , how does the gravitational field magnitude at radial distance () vary with ?

     A

     (increases linearly)

     B

     Constant

     C

     D

     Reveal answer
190. 190

     NUST Engineering Past Paper-17

     Identify the equivalent spring constant when TWO identical springs are arranged in PARALLEL (both supporting the same load between common end-points).

     A

     Half the individual spring constant

     B

     The sum of individual spring constants

     C

     Equal to one spring constant

     D

     The harmonic mean

     Reveal answer
191. 191

     NUST Engineering Past Paper-17

     Estimate the rest-mass energy of an electron, given kg.

     A

     keV

     B

     eV

     C

     MeV

     D

     MeV

     Reveal answer
192. 192

     NUST Engineering Past Paper-17

     A converging (convex) glass lens with focal length in air is now fully immersed in water (). What happens to its focal length?

     A

     Becomes negative (diverging)

     B

     Decreases (becomes more converging)

     C

     Increases (becomes less converging)

     D

     Remains the same

     Reveal answer
193. 193

     NUST Engineering Past Paper-17

     A deuteron (, ) and an alpha particle (, ) are accelerated from rest through the same potential difference. Determine the ratio of their de Broglie wavelengths.

     A

     B

     C

     D

     Reveal answer
194. 194

     NUST Engineering Past Paper-17

     Determine the output of a logical AND gate when its inputs are and .

     A

     B

     C

     Indeterminate

     D

     Reveal answer
195. 195

     NUST Engineering Past Paper-17

     An open organ pipe of length resonates in its fundamental mode. Identify the wavelength of the corresponding standing wave.

     A

     B

     C

     D

     Reveal answer
196. 196

     NUST Engineering Past Paper-17

     Determine the SI dimensional formula of the permittivity of free space, .

     A

     B

     C

     D

     Reveal answer
197. 197

     NUST Engineering Past Paper-17

     An object is placed exactly at the focal point of a concave mirror. Where is its image formed?

     A

     Behind the mirror

     B

     Infinity

     C

     The center of curvature

     D

     At the mirror surface

     Reveal answer
198. 198

     NUST Engineering Past Paper-17

     A stretched string of length cm has fundamental frequency Hz. If the vibrating length is reduced to cm with the tension (and linear mass density) unchanged, determine the new fundamental frequency.

     A

     Hz

     B

     Hz

     C

     Hz

     D

     Hz

     Reveal answer
199. 199

     NUST Engineering Past Paper-17

     In a Young's double-slit setup, the fringe width is mm. If the slit separation is now TRIPLED (with the screen distance and wavelength unchanged), determine the new fringe width.

     A

     mm

     B

     mm

     C

     mm

     D

     mm

     Reveal answer
200. 200

     NUST Engineering Past Paper-17

     An electron initially in the orbit of a hydrogen atom de-excites to lower levels. Identify the spectral series in which the highest-energy emitted photon falls.

     A

     Lyman

     B

     Pfund

     C

     Balmer

     D

     Paschen

     Reveal answer