NUST Engineering Past Paper-20

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

1. 1

   NUST Engineering Past Paper-20

   If , then

   A

   8

   B

   10

   C

   7

   D

   9

   Reveal answer
2. 2

   NUST Engineering Past Paper-20

   Evaluate .

   A

   1

   B

   0

   C

   D

   Reveal answer
3. 3

   NUST Engineering Past Paper-20

   If is an equilateral triangle of side m, find the area of its medial (inner) triangle.

   A

   m

   B

   m

   C

   m

   D

   m

   Reveal answer
4. 4

   NUST Engineering Past Paper-20

   Consider the arithmetic progression . Find the value of the first non-negative term.

   A

   3

   B

   1

   C

   7

   D

   0

   Reveal answer
5. 5

   NUST Engineering Past Paper-20

   If , what is the value of ?

   A

   B

   C

   D

   Reveal answer
6. 6

   NUST Engineering Past Paper-20

   If , find .

   A

   12

   B

   9

   C

   11

   D

   20

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7. 7

   NUST Engineering Past Paper-20

   If , find the value of .

   A

   B

   C

   D

   Reveal answer
8. 8

   NUST Engineering Past Paper-20

   Compute the value of .

   A

   B

   C

   D

   Reveal answer
9. 9

   NUST Engineering Past Paper-20

   Write the derivative formula for on its principal domain.

   A

   B

   C

   None of these

   D

   Reveal answer
10. 10

    NUST Engineering Past Paper-20

    Find the derivative of .

    A

    B

    C

    D

    None of these

    Reveal answer
11. 11

    NUST Engineering Past Paper-20

    Using the binomial expansion, approximate to four decimal places.

    A

    ≈ 1.1262

    B

    ≈ 1.0612

    C

    ≈ 1.1200

    D

    ≈ 1.1500

    Reveal answer
12. 12

    NUST Engineering Past Paper-20

    Compute .

    A

    B

    C

    D

    Reveal answer
13. 13

    NUST Engineering Past Paper-20

    Determine the imaginary part of .

    A

    B

    C

    D

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14. 14

    NUST Engineering Past Paper-20

    A fair coin is tossed times. Determine the probability of obtaining at least one head.

    A

    B

    C

    D

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15. 15

    NUST Engineering Past Paper-20

    Find the real part of .

    A

    B

    C

    D

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16. 16

    NUST Engineering Past Paper-20

    A bag holds marbles — blue and green. Five marbles are drawn at random WITHOUT replacement. Which of the following statements MUST be true?

    A

    All 4 blue marbles are picked already

    B

    All 4 green marbles are picked already

    C

    The picked marbles must contain at least 1 blue and 1 green

    D

    The picked marbles must have 2 blue and 2 green

    Reveal answer
17. 17

    NUST Engineering Past Paper-20

    Evaluate .

    A

    B

    C

    D

    Reveal answer
18. 18

    NUST Engineering Past Paper-20

    Determine the value of such that the parallelepiped with edge vectors , , and has volume .

    A

    B

    C

    D

    Reveal answer
19. 19

    NUST Engineering Past Paper-20

    A line has slope . Determine the slope of the line perpendicular to it.

    A

    1/3

    B

    1

    C

    None

    D

    -1/3

    Reveal answer
20. 20

    NUST Engineering Past Paper-20

    Evaluate .

    A

    π/3

    B

    None

    C

    π/4

    D

    1/π

    Reveal answer
21. 21

    NUST Engineering Past Paper-20

    Evaluate .

    A

    √5/4

    B

    None

    C

    1/3

    D

    √14/5

    Reveal answer
22. 22

    NUST Engineering Past Paper-20

    Evaluate for an unspecified real .

    A

    √(p²+3)/p

    B

    p/√(p²+3)

    C

    None

    D

    √(p²/4)

    Reveal answer
23. 23

    NUST Engineering Past Paper-20

    Given that form a geometric progression, identify which of the following triples is also in geometric progression.

    A

    q+r, r+s, s+t

    B

    None

    C

    pq, qr, rs

    D

    p/q, q/r, r/s

    Reveal answer
24. 24

    NUST Engineering Past Paper-20

    If two straight lines have the SAME slope, what is the angle between them?

    A

    0°

    B

    None

    C

    Both

    D

    60°

    Reveal answer
25. 25

    NUST Engineering Past Paper-20

    Two lines are described as 'anti-parallel' (parallel but oriented in opposite directions). What can be said about their slopes?

    A

    Different

    B

    Same

    C

    Reciprocal

    D

    None

    Reveal answer
26. 26

    NUST Engineering Past Paper-20

    Resolve into partial fractions.

    A

    3/(x²−1) + 2/(x−1)

    B

    −1/[3(x+1)] + 1/[4(x−1)]

    C

    1/(x−1) + 1/(x+1)

    D

    None

    Reveal answer
27. 27

    NUST Engineering Past Paper-20

    Among the following expressions, identify the one most closely matching the formula for the orthocentre of a triangle (using vertex weights involving trigonometric ratios of the interior angles).

    A

    (a sinα + b sinβ + c sinγ)/(a+b+c)

    B

    None

    C

    (a tanα + b tanβ + c tanγ)/(a+b+c)

    D

    (ax₁+bx₂+cx₃)/(a+b+c)

    Reveal answer
28. 28

    NUST Engineering Past Paper-20

    Evaluate (two-sided limit).

    A

    0

    B

    None

    C

    1

    D

    Does Not Exist

    Reveal answer
29. 29

    NUST Engineering Past Paper-20

    Evaluate the limit .

    A

    0

    B

    ∞

    C

    None

    D

    1

    Reveal answer
30. 30

    NUST Engineering Past Paper-20

    Evaluate .

    A

    None

    B

    0

    C

    1/2

    D

    1

    Reveal answer
31. 31

    NUST Engineering Past Paper-20

    Consider the ellipse . Determine the ratio (length of the major axis) : (length of the minor axis).

    A

    √3

    B

    None

    C

    1/√3

    D

    √2

    Reveal answer
32. 32

    NUST Engineering Past Paper-20

    The eccentricity of an ellipse is a numerical measure that describes which geometric property?

    A

    None

    B

    Ovalness

    C

    Measure of circle

    D

    Straightness

    Reveal answer
33. 33

    NUST Engineering Past Paper-20

    By definition, a circle is the set of all points in a plane equidistant from which geometric object?

    A

    None

    B

    Both

    C

    Fixed line

    D

    Fixed point

    Reveal answer
34. 34

    NUST Engineering Past Paper-20

    Given that a parabola has focus and vertex , identify its equation in standard form.

    A

    None

    B

    x²=4(y)(3)

    C

    (x+2)²=4(y−3)

    D

    x²+y=5

    Reveal answer
35. 35

    NUST Engineering Past Paper-20

    Evaluate .

    A

    1

    B

    −1

    C

    0

    D

    None

    Reveal answer
36. 36

    NUST Engineering Past Paper-20

    Given and , identify the quadrant of the Cartesian plane in which the point lies.

    A

    None

    B

    Second

    C

    First

    D

    Third

    Reveal answer
37. 37

    NUST Engineering Past Paper-20

    Among the following functions, identify which has range .

    A

    All

    B

    sinx

    C

    sin2x

    D

    sin4x

    Reveal answer
38. 38

    NUST Engineering Past Paper-20

    Determine the (real) domain of the function .

    A

    ℝ

    B

    [−2, 2]

    C

    ℝ − {−2, 2}

    D

    None

    Reveal answer
39. 39

    NUST Engineering Past Paper-20

    In a quadrilateral, the diagonals are equal in length AND perpendicular to each other. Identify the most specific name for such a quadrilateral.

    A

    Rhombus

    B

    Square

    C

    None

    D

    Rectangle

    Reveal answer
40. 40

    NUST Engineering Past Paper-20

    Let . Determine .

    A

    1/2

    B

    0

    C

    None

    D

    −1

    Reveal answer
41. 41

    NUST Engineering Past Paper-20

    In the general second-degree equation , if and have OPPOSITE SIGNS (with ), what type of conic is represented?

    A

    Ellipse

    B

    Hyperbola

    C

    Parabola

    D

    Circle

    Reveal answer
42. 42

    NUST Engineering Past Paper-20

    For the general second-degree equation in and to represent a PARABOLA, identify the algebraic condition on the coefficients and (with the -coefficient assumed zero).

    A

    A + B = 0

    B

    A = B

    C

    None

    D

    A = −B

    Reveal answer
43. 43

    NUST Engineering Past Paper-20

    Compute the sum of the reciprocals of the four fourth roots of unity.

    A

    1

    B

    None

    C

    2

    D

    0

    Reveal answer
44. 44

    NUST Engineering Past Paper-20

    If are the direction angles of a vector in 3-D space, determine the value of .

    A

    None

    B

    1

    C

    2

    D

    −1

    Reveal answer
45. 45

    NUST Engineering Past Paper-20

    Simplify the expression using a power-reduction identity.

    A

    (1−cos2θ)/2

    B

    (1+cos2θ)/2

    C

    −(1+cos2θ)/2

    D

    −(1−cos2θ)/2

    Reveal answer
46. 46

    NUST Engineering Past Paper-20

    In how many distinct ways can females and males be seated around a circular table?

    A

    B

    C

    D

    None

    Reveal answer
47. 47

    NUST Engineering Past Paper-20

    Compute directly.

    A

    5(6)(11)/16

    B

    5k²

    C

    55

    D

    None

    Reveal answer
48. 48

    NUST Engineering Past Paper-20

    Evaluate the infinite series .

    A

    1/2

    B

    None

    C

    −1/4

    D

    −1/2

    Reveal answer
49. 49

    NUST Engineering Past Paper-20

    Two fair dice are rolled simultaneously three times in succession. Determine the probability that EACH of the three rolls produces a sum of .

    A

    None

    B

    1/729

    C

    1/219

    D

    1/121

    Reveal answer
50. 50

    NUST Engineering Past Paper-20

    Determine the perpendicular distance between the parallel lines and .

    A

    −1/√10

    B

    None

    C

    1/√20

    D

    1/√10

    Reveal answer
51. 51

    NUST Engineering Past Paper-20

    Given , determine .

    A

    None

    B

    sin(x/2)sinx

    C

    −cos(x/2)sinx

    D

    −cos(x)sinx

    Reveal answer
52. 52

    NUST Engineering Past Paper-20

    Given , determine .

    A

    1

    B

    0

    C

    None

    D

    2

    Reveal answer
53. 53

    NUST Engineering Past Paper-20

    For the arithmetic series , identify a closed-form expression for the sum of the first terms.

    A

    None

    B

    n²−2n

    C

    n²+2n

    D

    n³−9n

    Reveal answer
54. 54

    NUST Engineering Past Paper-20

    Compute the dot product .

    A

    2

    B

    None

    C

    6

    D

    4

    Reveal answer
55. 55

    NUST Engineering Past Paper-20

    Given and , find (in ) such that .

    A

    π/3

    B

    π/4

    C

    0

    D

    π/2

    Reveal answer
56. 56

    NUST Engineering Past Paper-20

    Determine the coefficient of in the expansion of .

    A

    (3n)!/[n!(3n−1)]

    B

    None

    C

    3n!/(n!·2)

    D

    3n/21

    Reveal answer
57. 57

    NUST Engineering Past Paper-20

    Simplify the expression .

    A

    None

    B

    sec²x · csc²x

    C

    1

    D

    −cotx·tanx/(sinx·cosx)

    Reveal answer
58. 58

    NUST Engineering Past Paper-20

    In an arithmetic progression, and . Determine , the sum of the first terms.

    A

    2500/9

    B

    2700/9

    C

    4000/11

    D

    None

    Reveal answer
59. 59

    NUST Engineering Past Paper-20

    The probability that man A is alive after 10 years is and the probability that man B is alive after 10 years is . Determine the probability that BOTH men are dead after 10 years (assume the events are independent).

    A

    B

    C

    D

    Reveal answer
60. 60

    NUST Engineering Past Paper-20

    Evaluate the telescoping sum .

    A

    C(n, 3)

    B

    None

    C

    C(n+4, 4)

    D

    C(n+3, 4)

    Reveal answer
61. 61

    NUST Engineering Past Paper-20

    A spherical balloon is inflated so that its VOLUME increases at a CONSTANT rate. Describe how the rate of change of its radius behaves with respect to the current radius.

    A

    Constant

    B

    Dependent on radius

    C

    None

    D

    Independent of radius

    Reveal answer
62. 62

    NUST Engineering Past Paper-20

    Given two real numbers satisfying and , which of the following relations MUST always hold?

    A

    x > y

    B

    None

    C

    x = y

    D

    y > x

    Reveal answer
63. 63

    NUST Engineering Past Paper-20

    Identify the value below that lies OUTSIDE the range of .

    A

    0

    B

    None

    C

    −2

    D

    5

    Reveal answer
64. 64

    NUST Engineering Past Paper-20

    Identify the value below that lies OUTSIDE the range of .

    A

    −2

    B

    0

    C

    5

    D

    −0.5

    Reveal answer
65. 65

    NUST Engineering Past Paper-20

    Given the implicit equation , determine .

    A

    y/x · (xy/3x−1)

    B

    (4x−2xy−2y)/(x²+2x)

    C

    3/y · (1+3x/xy)

    D

    None

    Reveal answer
66. 66

    NUST Engineering Past Paper-20

    Classify the series as convergent or divergent.

    A

    Convergent

    B

    Not a series

    C

    Divergent

    D

    Insufficient Data

    Reveal answer
67. 67

    NUST Engineering Past Paper-20

    Determine the additive inverse of the ordered pair (in with componentwise addition).

    A

    None

    B

    (−a, b)

    C

    (a, −b)

    D

    (a, b)

    Reveal answer
68. 68

    NUST Engineering Past Paper-20

    Among the following statements about sets, identify the one that exemplifies the COMMUTATIVE law.

    A

    A∪B = B∪A

    B

    None

    C

    (A∪B)′ = A′∩B′

    D

    A∩B = B∩A

    Reveal answer
69. 69

    NUST Engineering Past Paper-20

    Describe the set of all matrices under the operation of matrix MULTIPLICATION.

    A

    Non-Abelian

    B

    Abelian

    C

    Group

    D

    None

    Reveal answer
70. 70

    NUST Engineering Past Paper-20

    Classify the diagonal matrix with respect to symmetry.

    A

    Symmetric if a = −b

    B

    Both

    C

    Symmetric if a = b

    D

    None

    Reveal answer
71. 71

    NUST Engineering Past Paper-20

    Consider the matrix . For which choices of would the matrix be symmetric or skew-symmetric?

    A

    Both A and B are possible

    B

    Skew-symmetric if k=−2, h=−5, f=−7

    C

    None

    D

    Symmetric if k=2, h=5, f=7

    Reveal answer
72. 72

    NUST Engineering Past Paper-20

    Evaluate when .

    A

    < 0

    B

    Undefined

    C

    > 0

    D

    = 0

    Reveal answer
73. 73

    NUST Engineering Past Paper-20

    Given and , identify which of and is guaranteed to be smaller.

    A

    II (y is smaller)

    B

    Both I and II

    C

    I (x is smaller)

    D

    Neither I nor II

    Reveal answer
74. 74

    NUST Engineering Past Paper-20

    Determine all satisfying .

    A

    45°, 315°

    B

    45°, 135°

    C

    45°, 225°

    D

    None

    Reveal answer
75. 75

    NUST Engineering Past Paper-20

    Comparing the standard form of the Law of Sines with (for a triangle with the side opposite equal to ), determine .

    A

    None

    B

    3

    C

    1

    D

    2

    Reveal answer
76. 76

    NUST Engineering Past Paper-20

    Identify the middle term in the binomial expansion of .

    A

    None

    B

    8th term

    C

    7th term

    D

    6th term

    Reveal answer
77. 77

    NUST Engineering Past Paper-20

    Using the digits in the set at most once each, how many distinct -digit numbers can be formed?

    A

    30

    B

    45

    C

    21

    D

    None

    Reveal answer
78. 78

    NUST Engineering Past Paper-20

    For the sequence (with ), identify the recurrence relation that generates it.

    A

    aₙ = aₙ₋₁ + n

    B

    aₙ = aₙ₋₁ + n + 2

    C

    aₙ = aₙ₋₁ + 2

    D

    None

    Reveal answer
79. 79

    NUST Engineering Past Paper-20

    Write down the Maclaurin series expansion of up to the quadratic term.

    A

    1 + (−3x) + 9x²/2! − ...

    B

    1 + 4x − 9x²/2! + ...

    C

    1 − 4x + 9x²/2! + ...

    D

    None

    Reveal answer
80. 80

    NUST Engineering Past Paper-20

    Identify the value below that CANNOT appear in the range of the function .

    A

    π/4

    B

    −π

    C

    4

    D

    −5

    Reveal answer
81. 81

    NUST Engineering Past Paper-20

    If the slopes of two lines satisfy , how are the lines related geometrically?

    A

    Anti-parallel

    B

    Parallel

    C

    None

    D

    Both

    Reveal answer
82. 82

    NUST Engineering Past Paper-20

    Evaluate the scalar .

    A

    0

    B

    None

    C

    k̂

    D

    î

    Reveal answer
83. 83

    NUST Engineering Past Paper-20

    Evaluate the integral .

    A

    B

    C

    D

    Reveal answer
84. 84

    NUST Engineering Past Paper-20

    In how many distinct ways can females and males be seated around a circular table such that no two of the same sex sit next to each other (alternating arrangement)?

    A

    B

    C

    D

    None

    Reveal answer
85. 85

    NUST Engineering Past Paper-20

    Two forces and act at the point . Determine the magnitude of the moment (torque) of these forces about the point .

    A

    None

    B

    C

    D

    Reveal answer
86. 86

    NUST Engineering Past Paper-20

    Transform the equation by translating the origin to the new point . Determine the resulting equation in the new coordinates .

    A

    B

    C

    D

    None of these

    Reveal answer
87. 87

    NUST Engineering Past Paper-20

    Find the coefficient of in the expansion of .

    A

    B

    C

    D

    None of these

    Reveal answer
88. 88

    NUST Engineering Past Paper-20

    Evaluate (or estimate) .

    A

    B

    C

    D

    Series is not convergent

    Reveal answer
89. 89

    NUST Engineering Past Paper-20

    Two vertices of a rectangle are and . Identify which of the listed points CANNOT serve as another vertex of the rectangle.

    A

    B

    C

    D

    Reveal answer
90. 90

    NUST Engineering Past Paper-20

    If , evaluate .

    A

    B

    C

    D

    Reveal answer
91. 91

    NUST Engineering Past Paper-20

    Evaluate .

    A

    B

    C

    D

    Reveal answer
92. 92

    NUST Engineering Past Paper-20

    In the residue classes modulo , determine the multiplicative inverse of .

    A

    B

    C

    D

    Reveal answer
93. 93

    NUST Engineering Past Paper-20

    If and the partial sums satisfy (for all , where denotes the sum of the first terms), determine the sum of the first terms.

    A

    B

    C

    D

    None of these

    Reveal answer
94. 94

    NUST Engineering Past Paper-20

    Identify the statement that is NOT true regarding the series .

    A

    It is a Geometric Series

    B

    Common ratio is

    C

    The series is not convergent

    D

    Sum of the series is

    Reveal answer
95. 95

    NUST Engineering Past Paper-20

    Determine how many solutions has in the interval .

    A

    B

    C

    D

    Infinite

    Reveal answer
96. 96

    NUST Engineering Past Paper-20

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

    A

    B

    C

    D

    Reveal answer
97. 97

    NUST Engineering Past Paper-20

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

    A

    To increase rapidly

    B

    To lessen or reduce in intensity

    C

    To celebrate loudly

    D

    To confuse someone

    Reveal answer
98. 98

    NUST Engineering Past Paper-20

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

    A

    Dry

    B

    Humid

    C

    Freezing

    D

    Boiling

    Reveal answer
99. 99

    NUST Engineering Past Paper-20

    Read the scenario and pick the most reasonable inference. Ali ran into the meeting room, panicked, apologising to his boss for intruding.

    A

    Ali was angry at his boss

    B

    Ali was running late

    C

    Ali was sick

    D

    Ali did not want to attend the meeting

    Reveal answer
100. 100

     NUST Engineering Past Paper-20

     Which option spells the rotating part of an electric motor correctly?

     A

     Armeture

     B

     Armatuer

     C

     Armature

     D

     Armiture

     Reveal answer
101. 101

     NUST Engineering Past Paper-20

     Choose the pair whose relationship is most similar to 'Concert : Symphony':

     A

     Stage : Drama

     B

     Music : Orchestra

     C

     Exhibition : Painting

     D

     Accompaniment : Melody

     Reveal answer
102. 102

     NUST Engineering Past Paper-20

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

     A

     Revoked

     B

     Enacted

     C

     Repealed

     D

     Nullified

     Reveal answer
103. 103

     NUST Engineering Past Paper-20

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

     A

     Distant

     B

     Affable

     C

     Cold

     D

     Reserved

     Reveal answer
104. 104

     NUST Engineering Past Paper-20

     Pick the option that best defines 'Anthropology':

     A

     The study of celestial bodies

     B

     The study of human societies, cultures, and evolution

     C

     The study of animal behavior

     D

     The study of ancient languages

     Reveal answer
105. 105

     NUST Engineering Past Paper-20

     Choose the field whose focus is closest to that of 'Anthropology':

     A

     Botany

     B

     Sociology

     C

     Astronomy

     D

     Geology

     Reveal answer
106. 106

     NUST Engineering Past Paper-20

     Pick the word closest in meaning to 'Bashful':

     A

     Brazen

     B

     Bold

     C

     Timid

     D

     Assertive

     Reveal answer
107. 107

     NUST Engineering Past Paper-20

     Pick the word most nearly OPPOSITE in meaning to 'Blunt' (direct in manner):

     A

     Tactful

     B

     Abrupt

     C

     Brusque

     D

     Curt

     Reveal answer
108. 108

     NUST Engineering Past Paper-20

     Pick the word closest in meaning to 'Extrovert':

     A

     Loner

     B

     Recluse

     C

     Socialite

     D

     Hermit

     Reveal answer
109. 109

     NUST Engineering Past Paper-20

     Pick the option that best defines 'Gradually':

     A

     In a slow and steady manner over time

     B

     In a random and unpredictable way

     C

     All at once; suddenly

     D

     In an immediate and dramatic fashion

     Reveal answer
110. 110

     NUST Engineering Past Paper-20 NUST Engineering Past Paper-1

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

     A

     Extinguish

     B

     Inflame

     C

     Stir

     D

     Arouse

     Reveal answer
111. 111

     NUST Engineering Past Paper-20

     Pick the word closest in meaning to 'Nefarious':

     A

     Villainous

     B

     Honorable

     C

     Admirable

     D

     Virtuous

     Reveal answer
112. 112

     NUST Engineering Past Paper-20

     Pick the option that best defines 'Neglect':

     A

     To deliberately reward someone

     B

     To enthusiastically take on new duties

     C

     To fail to give proper care or attention

     D

     To pay careful attention to

     Reveal answer
113. 113

     NUST Engineering Past Paper-20

     Pick the option that best defines 'Obviate':

     A

     To announce something publicly

     B

     To make a problem worse

     C

     To remove a need or difficulty; to prevent

     D

     To delay a decision

     Reveal answer
114. 114

     NUST Engineering Past Paper-20

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

     A

     Brief

     B

     Permanent

     C

     Ephemeral

     D

     Momentary

     Reveal answer
115. 115

     NUST Engineering Past Paper-20

     Pick the option that best defines 'Undignified':

     A

     Composed and decorous in manner

     B

     Reserved and well-mannered

     C

     Extremely formal and proper

     D

     Appearing foolish or lacking in dignity

     Reveal answer
116. 116

     NUST Engineering Past Paper-20

     Pick the term that represents a number vastly SMALLER than 'Quintillion':

     A

     Sextillion

     B

     Thousand

     C

     Googol

     D

     Septillion

     Reveal answer
117. 117

     NUST Engineering Past Paper-20

     Pick the option that best defines 'hooligan':

     A

     A formal title of respect

     B

     A type of migratory bird

     C

     A violent or rowdy troublemaker

     D

     A polite and well-mannered person

     Reveal answer
118. 118

     NUST Engineering Past Paper-20

     Pick the antonym of the verb MITIGATE.

     A

     Alleviate

     B

     Reduce

     C

     Aggravate

     D

     Calm

     Reveal answer
119. 119

     NUST Engineering Past Paper-20

     Identify the single-word adjective used to describe land that is fit or suitable for growing crops.

     A

     Desolate

     B

     Arable

     C

     Fallow

     D

     Barren

     Reveal answer
120. 120

     NUST Engineering Past Paper-20

     Pick the option closest in meaning to the adjective MONOTONOUS.

     A

     Varied

     B

     Tedious

     C

     Vibrant

     D

     Exciting

     Reveal answer
121. 121

     NUST Engineering Past Paper-20

     Pick the option closest in meaning to the adjective TRANSIENT.

     A

     Eternal

     B

     Temporary

     C

     Permanent

     D

     Constant

     Reveal answer
122. 122

     NUST Engineering Past Paper-20

     Pick the closest opposite of the verb NEGLECT.

     A

     Attend

     B

     Overlook

     C

     Ignore

     D

     Abandon

     Reveal answer
123. 123

     NUST Engineering Past Paper-20

     Pick the antonym of the adjective SUBMISSIVE.

     A

     Passive

     B

     Obedient

     C

     Assertive

     D

     Timid

     Reveal answer
124. 124

     NUST Engineering Past Paper-20

     Complete the analogy: Rain is to Drenched as ___ is to ___.

     A

     Wind : Dusty

     B

     Sun : Cold

     C

     Fire : Warm

     D

     Snow : Frozen

     Reveal answer
125. 125

     NUST Engineering Past Paper-20

     Pick the correctly spelled adverb meaning 'in a violent or aggressively intense manner.'

     A

     Fiercely

     B

     Fiersely

     C

     Fiercly

     D

     Fierceley

     Reveal answer
126. 126

     NUST Engineering Past Paper-20

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

     A

     To be an omen of a future event

     B

     To travel quickly

     C

     To rest comfortably

     D

     To argue strongly

     Reveal answer
127. 127

     NUST Engineering Past Paper-20

     Pick the most natural emphatic phrase to fill the blank: 'Who ___ would like to buy such a haunted house?'

     A

     Under the sun

     B

     In heaven

     C

     On Earth

     D

     In the world

     Reveal answer
128. 128

     NUST Engineering Past Paper-20

     Complete the analogy: Fear is to Phobia as Anger is to ___.

     A

     Fury

     B

     Courage

     C

     Mania

     D

     Panic

     Reveal answer
129. 129

     NUST Engineering Past Paper-20

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

     A

     To lie down and rest

     B

     To give a false impression of something

     C

     To believe strongly in an idea

     D

     To confirm the truth of something

     Reveal answer
130. 130

     NUST Engineering Past Paper-20

     Pick the correctly spelled noun denoting the rotating component of an electric motor (or the part of a generator with the windings).

     A

     Armeture

     B

     Armature

     C

     Armiture

     D

     Armatuor

     Reveal answer
131. 131

     NUST Engineering Past Paper-20

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

     A

     To frighten someone greatly

     B

     To charm or enchant someone, sometimes deceitfully

     C

     To punish someone for wrongdoing

     D

     To teach someone a new skill

     Reveal answer
132. 132

     NUST Engineering Past Paper-20

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

     A

     Coming from an external source

     B

     Unimportant and irrelevant

     C

     Added artificially from outside

     D

     Belonging naturally and essentially to something

     Reveal answer
133. 133

     NUST Engineering Past Paper-20

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

     A

     Naturally built in or inherent

     B

     Deep and meaningful

     C

     Rare and extraordinary

     D

     Coming from outside; not essential

     Reveal answer
134. 134

     NUST Engineering Past Paper-20

     Identify the grammatically correct sentence among the variants involving the relative pronoun 'who/whom.'

     A

     He was the one to who I gave the book

     B

     He was the one to whom I gave the book

     C

     He was the one who I gave the book

     D

     He was the one whom I gave the book

     Reveal answer
135. 135

     NUST Engineering Past Paper-20

     Fill the blank with the correct verb form: 'Neither the players nor the coach ___ satisfied with the final score of the game.'

     A

     Has been

     B

     Were

     C

     Have been

     D

     Was

     Reveal answer
136. 136

     NUST Engineering Past Paper-20

     Identify the segment containing the grammatical error: 'whom do you believe / was responsible for / the mistake in the report / that caused so much confusion?'

     A

     Whom do you believe

     B

     Was responsible for

     C

     That caused so much confusion

     D

     The mistake in the report

     Reveal answer
137. 137

     NUST Engineering Past Paper-20

     What is the approximate value of the escape velocity from the Moon's surface? (Take m/s and m.)

     A

     ≈ 2.4 km/s

     B

     ≈ 11.2 km/s

     C

     ≈ 9.8 km/s

     D

     ≈ 7.9 km/s

     Reveal answer
138. 138

     NUST Engineering Past Paper-20

     Identify the correct dimensional formula for the modulus of elasticity.

     A

     B

     C

     D

     Reveal answer
139. 139

     NUST Engineering Past Paper-20

     Among the four fundamental interactions of nature, identify the WEAKEST.

     A

     Strong nuclear force

     B

     Weak nuclear force

     C

     Electromagnetic force

     D

     Gravitational force

     Reveal answer
140. 140

     NUST Engineering Past Paper-20

     A radioactive element has half-life . Determine its effective half-life AFTER half-lives have elapsed.

     A

     T

     B

     3T

     C

     2T

     D

     4T

     Reveal answer
141. 141

     NUST Engineering Past Paper-20

     Among the listed optical phenomena, identify the one that most clearly distinguishes the TRANSVERSE-wave nature of light from other wave types.

     A

     Rarefaction

     B

     Reflection

     C

     Polarization

     D

     Diffraction

     Reveal answer
142. 142

     NUST Engineering Past Paper-20 NUST Engineering Past Paper-1

     Express the SI unit 'joule' (J) in terms of the SI unit 'watt' (W).

     A

     Watt/meter

     B

     Watt-meter

     C

     Watt/second

     D

     Watt-second

     Reveal answer
143. 143

     NUST Engineering Past Paper-20

     Two batteries, of EMF V and V, are connected in series such that the positive terminal of the V battery is wired to the NEGATIVE terminal of the V battery. A resistor is connected across the combination. Find the voltage across the resistor (assume negligible internal resistance).

     A

     12 V

     B

     10 V

     C

     6 V

     D

     8 V

     Reveal answer
144. 144

     NUST Engineering Past Paper-20

     Among the following, identify the wave that propagates as a LONGITUDINAL wave.

     A

     Light waves

     B

     X-rays

     C

     Sound waves

     D

     Radio waves

     Reveal answer
145. 145

     NUST Engineering Past Paper-20

     Which of the following statements correctly characterise the work done by the gravitational field?

     A

     Zero for a closed path

     B

     Depends only on vertical displacement

     C

     Negative when moving upward

     D

     All of these

     Reveal answer
146. 146

     NUST Engineering Past Paper-20

     Identify the dimensional formula for WORK (or equivalently energy).

     A

     B

     C

     D

     Reveal answer
147. 147

     NUST Engineering Past Paper-20

     On a transverse travelling wave, what is the distance between a crest and the adjacent (next) trough?

     A

     B

     C

     D

     Reveal answer
148. 148

     NUST Engineering Past Paper-20

     On which thermodynamic principle does a refrigerator operate?

     A

     Third law of thermodynamics

     B

     Second law of thermodynamics

     C

     Zeroth law of thermodynamics

     D

     First law of thermodynamics

     Reveal answer
149. 149

     NUST Engineering Past Paper-20

     Einstein's first postulate of special relativity states that, in an inertial frame of reference, the laws of physics behave how?

     A

     All laws are always applicable

     B

     None of these

     C

     All laws are not applicable

     D

     Laws may or may not be applicable

     Reveal answer
150. 150

     NUST Engineering Past Paper-20

     To convert a galvanometer into a voltmeter, a high resistance is connected in which configuration?

     A

     Series

     B

     Series then parallel

     C

     Parallel

     D

     Parallel then series

     Reveal answer
151. 151

     NUST Engineering Past Paper-20

     Among the following factors, which one does NOT affect the capacitance of a parallel-plate capacitor?

     A

     Voltage across capacitor

     B

     Dielectric

     C

     Geometry of capacitor

     D

     Distance between the plates

     Reveal answer
152. 152

     NUST Engineering Past Paper-20

     Among the following devices/technologies, identify the one that is NOT a major application of electromagnetic INDUCTION.

     A

     Television

     B

     Telephone

     C

     Transformer

     D

     Radio

     Reveal answer
153. 153

     NUST Engineering Past Paper-20

     Classify electric flux in terms of its character (scalar vs. vector) and the type of field it summarises.

     A

     Vector quantity of vector field

     B

     Scalar quantity of vector field

     C

     Scalar quantity of scalar field

     D

     Vector quantity of scalar field

     Reveal answer
154. 154

     NUST Engineering Past Paper-20

     Identify the physical quantity represented by the expression (mass , speed , length ).

     A

     Momentum lost

     B

     Momentum transferred

     C

     Force applied

     D

     Pressure

     Reveal answer
155. 155

     NUST Engineering Past Paper-20

     Identify the physical quantity whose SI unit is (newton per coulomb).

     A

     Electric flux

     B

     Electric field

     C

     Magnetic flux

     D

     Magnetic field

     Reveal answer
156. 156

     NUST Engineering Past Paper-20

     Identify the form of the First Law of Thermodynamics specialised to an ADIABATIC process (with denoting the work done BY the system).

     A

     B

     C

     D

     Reveal answer
157. 157

     NUST Engineering Past Paper-20

     Identify the SI unit of impulse.

     A

     B

     C

     D

     Reveal answer
158. 158

     NUST Engineering Past Paper-20

     A solenoid carries current and has cross-sectional area with total turns and initial length , producing magnetic field inside. If the length is DOUBLED (with , , and unchanged), determine the new magnetic field.

     A

     B

     C

     D

     Reveal answer
159. 159

     NUST Engineering Past Paper-20

     An ideal transformer can step up voltage and current (at the cost of the other). Identify the quantity a transformer CANNOT step up.

     A

     Voltage

     B

     Current

     C

     Energy

     D

     None

     Reveal answer
160. 160

     NUST Engineering Past Paper-20

     A force of magnitude N applied at a point m from the origin produces a torque of N·m about the origin. Determine the angle between the force and the position vector (moment arm).

     A

     B

     C

     D

     Reveal answer
161. 161

     NUST Engineering Past Paper-20

     A ball resting on the Earth's surface is lifted vertically to some height. How does its gravitational potential energy change?

     A

     Remains constant

     B

     Decreases

     C

     None of these

     D

     Increases

     Reveal answer
162. 162

     NUST Engineering Past Paper-20

     Among the SI prefixes nano, atto, pico, and femto, identify the one representing the SMALLEST factor.

     A

     femto

     B

     atto

     C

     pico

     D

     nano

     Reveal answer
163. 163

     NUST Engineering Past Paper-20

     A charged capacitor (with battery disconnected) initially has air between its plates. The air is replaced with a diamond slab (a high-permittivity dielectric). What happens to the voltage across the capacitor?

     A

     None

     B

     Decrease

     C

     Increase

     D

     Remain same

     Reveal answer
164. 164

     NUST Engineering Past Paper-20

     Identify an alternative name commonly used for the 'back EMF' produced by a changing current in an inductor.

     A

     Induced emf

     B

     None

     C

     Positive emf

     D

     Negative emf

     Reveal answer
165. 165

     NUST Engineering Past Paper-20

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

     A

     10 J

     B

     250 J

     C

     100 J

     D

     50 J

     Reveal answer
166. 166

     NUST Engineering Past Paper-20

     An excited hydrogen-atom electron transitions to the FIRST excited state (). Identify the spectral series of the emitted photon.

     A

     Balmer series

     B

     Paschen series

     C

     Pfund series

     D

     Bracket series

     Reveal answer
167. 167

     NUST Engineering Past Paper-20

     In a double-slit setup, the slit separation is and the screen is at distance cm. Using the standard small-angle approximation, determine the position of the 2ND-order bright fringe.

     A

     2 cm from the center of the screen

     B

     1 cm from the center of the screen

     C

     4 cm from the center of the screen

     D

     None of these

     Reveal answer
168. 168

     NUST Engineering Past Paper-20

     Why can an electron microscope resolve finer detail than an optical (light) microscope?

     A

     Electron has more intensity than photon

     B

     Electron has less wavelength than photon

     C

     Electron is a charged particle while photon is not

     D

     None of these

     Reveal answer
169. 169

     NUST Engineering Past Paper-20

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

     A

     Becomes double

     B

     Becomes four times

     C

     Remains same

     D

     Becomes half

     Reveal answer
170. 170

     NUST Engineering Past Paper-20

     For a gamma-ray photon with energy MeV interacting with matter, identify the DOMINANT interaction.

     A

     Photoelectric effect

     B

     All of these

     C

     Pair production

     D

     Compton effect

     Reveal answer
171. 171

     NUST Engineering Past Paper-20

     Identify a valid SI unit for momentum.

     A

     N s

     B

     J s

     C

     N m

     D

     kg m/s²

     Reveal answer
172. 172

     NUST Engineering Past Paper-20

     Equal forces are applied to objects of the SAME size (volume) but different materials. Identify the material whose object accelerates the most.

     A

     Brass

     B

     Iron

     C

     Wood

     D

     None

     Reveal answer
173. 173

     NUST Engineering Past Paper-20

     Among the four fundamental forces of nature, identify the WEAKEST.

     A

     Gravitational force

     B

     Strong nuclear force

     C

     Weak nuclear force

     D

     Electromagnetic force

     Reveal answer
174. 174

     NUST Engineering Past Paper-20

     A horizontal loop of area sits in a uniform magnetic field pointing EAST, whose magnitude is INCREASING. The plane of the loop is perpendicular to . Determine the direction of the magnetic field produced by the induced current inside the loop.

     A

     North

     B

     East

     C

     West

     D

     South

     Reveal answer
175. 175

     NUST Engineering Past Paper-20

     A radioactive element has half-life . After half-lives have elapsed, what is the effective half-life?

     A

     B

     C

     D

     Reveal answer
176. 176

     NUST Engineering Past Paper-20

     Identify the most precise thermodynamic definition of 'heat'.

     A

     Amount of energy transferred from cold to hot body

     B

     Amount of energy transferred from hot to cold body

     C

     Internal energy

     D

     Thermal energy

     Reveal answer
177. 177

     NUST Engineering Past Paper-20

     Two like charges are at fixed separation. Compare the magnitude of the Coulomb repulsion in AIR with that in OIL (a dielectric).

     A

     Equal to 1

     B

     Less than 1

     C

     Greater than 1

     D

     Equal to zero

     Reveal answer
178. 178

     NUST Engineering Past Paper-20

     Identify the type of rectification performed by a bridge-rectifier circuit.

     A

     Half wave

     B

     Full wave

     C

     Both

     D

     None

     Reveal answer
179. 179

     NUST Engineering Past Paper-20

     Among the following modifications, identify the one that INCREASES the sensitivity of a moving-coil galvanometer.

     A

     Decreasing number of turns

     B

     None

     C

     Decreasing the magnetic field

     D

     Increasing area

     Reveal answer
180. 180

     NUST Engineering Past Paper-20

     Identify which of the following source pairings respectively produce an electric force and a magnetic force.

     A

     Gravitational field

     B

     Stationary charge, moving charge

     C

     Magnetic field, Electric field

     D

     Moving charge, stationary charge

     Reveal answer
181. 181

     NUST Engineering Past Paper-20

     Identify the type of semiconductor material used in the construction of a transistor.

     A

     Intrinsic semi-conductor

     B

     None of these

     C

     Both

     D

     Extrinsic semi-conductor

     Reveal answer
182. 182

     NUST Engineering Past Paper-20

     A body falling through a viscous medium reaches its TERMINAL velocity. Identify the net force acting on it at that point.

     A

     Upward

     B

     Zero

     C

     Downward

     D

     None of these

     Reveal answer
183. 183

     NUST Engineering Past Paper-20

     The phenomenon of POLARIZATION is observable for light. What does this demonstrate about the nature of light?

     A

     Light is transverse

     B

     Light is a wave

     C

     Light is longitudinal

     D

     All of these

     Reveal answer
184. 184

     NUST Engineering Past Paper-20

     Among the following options, identify the approximate value of the escape velocity from Saturn's surface.

     A

     35.5 km/s

     B

     4.25 km/s

     C

     11.2 km/s

     D

     59.5 km/s

     Reveal answer
185. 185

     NUST Engineering Past Paper-20

     Identify how much heat enters or leaves a system during an ADIABATIC thermodynamic process.

     A

     A lot

     B

     None of these

     C

     No

     D

     Little

     Reveal answer
186. 186

     NUST Engineering Past Paper-20

     Rain falls vertically downward at m/s. A person walks horizontally from north to south at m/s. In the person's reference frame, by what angle (and toward which direction) should an umbrella be tilted from the vertical to best block the rain?

     A

     towards north

     B

     towards south

     C

     towards south

     D

     towards north

     Reveal answer
187. 187

     NUST Engineering Past Paper-20

     A long straight wire carries conventional current directly OUT of the page. Determine the direction of the magnetic field circling the wire as viewed from the same side as the reader.

     A

     Away from wire radially outward

     B

     Clockwise

     C

     Anti-clockwise

     D

     Into the page

     Reveal answer
188. 188

     NUST Engineering Past Paper-20

     For an ideal gas undergoing an ISOTHERMAL process, if both the number of moles AND the volume are doubled simultaneously (, ), what is the new pressure ?

     A

     B

     C

     D

     Reveal answer
189. 189

     NUST Engineering Past Paper-20

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

     A

     Zero

     B

     Half of total mechanical energy

     C

     Maximum

     D

     Equal to potential energy

     Reveal answer
190. 190

     NUST Engineering Past Paper-20

     For an orthonormal right-handed basis (analogous to ), determine the magnitude of .

     A

     0

     B

     2

     C

     1

     D

     Reveal answer
191. 191

     NUST Engineering Past Paper-20

     A free neutron (outside any nucleus) is unstable and undergoes spontaneous beta decay. Identify the products of this decay.

     A

     A proton, an electron, and an antineutrino

     B

     Two protons and an electron

     C

     An alpha particle

     D

     A proton and a gamma ray

     Reveal answer
192. 192

     NUST Engineering Past Paper-20

     For a spring-mass oscillator with period , if BOTH the mass and the spring constant are halved (, ), determine the new time period.

     A

     B

     C

     D

     Reveal answer
193. 193

     NUST Engineering Past Paper-20

     Identify the physical quantity whose dimensions match those of the expression (permittivity area / distance).

     A

     Charge

     B

     Capacitance

     C

     Inductance

     D

     Resistance

     Reveal answer
194. 194

     NUST Engineering Past Paper-20

     Identify the material that is most effective as a magnetic shield (channelling external magnetic field lines around a protected region).

     A

     Co (Cobalt)

     B

     Fe (Soft Iron)

     C

     Ni (Nickel)

     D

     Cu (Copper)

     Reveal answer
195. 195

     NUST Engineering Past Paper-20

     A vector has magnitude and makes an angle of with the positive -axis (in the first quadrant of the -plane). Express in component form.

     A

     B

     C

     D

     Reveal answer
196. 196

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

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

     A

     Brackett series

     B

     Lyman series

     C

     Paschen series

     D

     Balmer series

     Reveal answer
197. 197

     NUST Engineering Past Paper-20

     In a perfectly elastic 1-D collision of two objects of EQUAL mass, object 1 has velocity m/s and object 2 is at rest. Determine the velocities of the two objects after collision.

     A

     First object stops; second moves at 3 m/s

     B

     First moves at 3 m/s; second stops

     C

     Both move at 1.5 m/s

     D

     Both move at 3 m/s

     Reveal answer
198. 198

     NUST Engineering Past Paper-20

     Determine the gravitational field at the EXACT centre of a uniform-density Earth.

     A

     Zero

     B

     Half of surface gravity

     C

     Maximum

     D

     Equal to surface gravity

     Reveal answer
199. 199

     NUST Engineering Past Paper-20

     In Young's double-slit experiment, the slit separation is DECREASED (with screen distance and wavelength fixed). How does the fringe width change?

     A

     Remain unchanged

     B

     Decrease

     C

     Increase

     D

     Become zero

     Reveal answer