NUST Engineering Past Paper-6

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

1. 1

   NUST Engineering Past Paper-6

   If , what is the equation of its auxiliary circle?

   A

   B

   C

   D

   All of these

   Reveal answer
2. 2

   NUST Engineering Past Paper-6

   If , and are the vertices of triangle , what type of triangle is it?

   A

   Isosceles triangle

   B

   Right Angled triangle

   C

   Equilateral triangle

   D

   No triangle formed

   Reveal answer
3. 3

   NUST Engineering Past Paper-6

   If , find .

   A

   20

   B

   25

   C

   30

   D

   35

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4. 4

   NUST Engineering Past Paper-6

   Find a unit vector along the direction of .

   A

   B

   C

   D

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5. 5

   NUST Engineering Past Paper-6

   What is the coefficient of in the expansion of ?

   A

   B

   0

   C

   D

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6. 6

   NUST Engineering Past Paper-6

   Evaluate .

   A

   B

   C

   D

   None of these

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7. 7

   NUST Engineering Past Paper-6

   Differentiate with respect to .

   A

   B

   C

   D

   None of these

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8. 8

   NUST Engineering Past Paper-6

   A fair die is rolled twice. Find the probability of getting a sum of or .

   A

   B

   C

   D

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9. 9

   NUST Engineering Past Paper-6

   Evaluate .

   A

   B

   C

   D

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10. 10

    NUST Engineering Past Paper-6

    About which line is the graph of symmetric?

    A

    x-axis

    B

    None

    C

    Both axes

    D

    y-axis

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11. 11

    NUST Engineering Past Paper-6

    Find the minimum value of on the interval .

    A

    B

    C

    D

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12. 12

    NUST Engineering Past Paper-6

    If denotes the complement of set (with respect to a universal set ), simplify .

    A

    B

    C

    D

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13. 13

    NUST Engineering Past Paper-6

    Determine the product of the three cube roots of .

    A

    B

    C

    D

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14. 14

    NUST Engineering Past Paper-6

    Determine whether the function (for ) attains a maximum value, and if so, give it.

    A

    B

    C

    No maximum value exists

    D

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15. 15

    NUST Engineering Past Paper-6

    Given , compute .

    A

    B

    C

    None

    D

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16. 16

    NUST Engineering Past Paper-6

    Given and , find for which .

    A

    B

    C

    D

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17. 17

    NUST Engineering Past Paper-6

    Simplify .

    A

    B

    C

    D

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18. 18

    NUST Engineering Past Paper-6

    Evaluate .

    A

    B

    C

    D

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19. 19

    NUST Engineering Past Paper-6

    Find and such that .

    A

    B

    None

    C

    D

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20. 20

    NUST Engineering Past Paper-6

    Suppose is a skew-symmetric matrix and is a symmetric matrix (with defined). Determine .

    A

    B

    C

    D

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21. 21

    NUST Engineering Past Paper-6

    Evaluate .

    A

    B

    C

    D

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22. 22

    NUST Engineering Past Paper-6

    An inscribed angle in a semicircle subtends the diameter. State the measure of .

    A

    45°

    B

    90°

    C

    60°

    D

    30°

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23. 23

    NUST Engineering Past Paper-6

    Evaluate .

    A

    B

    C

    D

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24. 24

    NUST Engineering Past Paper-6

    Evaluate .

    A

    B

    C

    D

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25. 25

    NUST Engineering Past Paper-6

    Determine the complex number satisfying .

    A

    B

    C

    D

    None of these

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26. 26

    NUST Engineering Past Paper-6

    Given and , determine the IMAGINARY part of the product .

    A

    B

    C

    D

    None of these

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27. 27

    NUST Engineering Past Paper-6

    Let be a primitive cube root of unity. Evaluate .

    A

    B

    C

    D

    None of these

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28. 28

    NUST Engineering Past Paper-6

    For any two complex numbers , evaluate in terms of (or ).

    A

    B

    C

    D

    None of these

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29. 29

    NUST Engineering Past Paper-6

    Let for a positive integer . Evaluate .

    A

    B

    C

    D

    None of these

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30. 30

    NUST Engineering Past Paper-6

    Let be a primitive cube root of unity (so ). Evaluate the sum .

    A

    B

    C

    D

    None of these

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31. 31

    NUST Engineering Past Paper-6

    In an arithmetic progression, the th term is and the th term is . Determine the th term.

    A

    B

    C

    D

    None of these

    Reveal answer
32. 32

    NUST Engineering Past Paper-6

    Determine the sum of the first terms of a geometric progression with first term and common ratio .

    A

    B

    C

    D

    None of these

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33. 33

    NUST Engineering Past Paper-6

    A geometric progression has common ratio and sum to infinity . Determine the first term .

    A

    B

    C

    D

    None of these

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34. 34

    NUST Engineering Past Paper-6

    Determine a closed-form expression for the sum of the first EVEN positive integers, i.e., .

    A

    B

    C

    D

    None of these

    Reveal answer
35. 35

    NUST Engineering Past Paper-6

    Three non-zero numbers are in GEOMETRIC progression. Identify the algebraic relation that must hold between them.

    A

    B

    C

    D

    None of these

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36. 36

    NUST Engineering Past Paper-6

    If are in arithmetic progression (in this order), determine the value of .

    A

    B

    C

    D

    None of these

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37. 37

    NUST Engineering Past Paper-6

    Determine all values of for which the quadratic equation has real and EQUAL roots.

    A

    B

    C

    D

    None of these

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38. 38

    NUST Engineering Past Paper-6

    Determine the roots of the quadratic equation .

    A

    and

    B

    and

    C

    and

    D

    None of these

    Reveal answer
39. 39

    NUST Engineering Past Paper-6

    Let be the roots of the quadratic . Evaluate .

    A

    B

    C

    D

    None of these

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40. 40

    NUST Engineering Past Paper-6

    Determine the PRODUCT of the roots of the quadratic equation .

    A

    B

    C

    D

    None of these

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41. 41

    NUST Engineering Past Paper-6

    Simplify the expression using the sum-to-product identities.

    A

    B

    C

    D

    None of these

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42. 42

    NUST Engineering Past Paper-6

    Given and lies in the THIRD quadrant, determine .

    A

    B

    C

    D

    None of these

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43. 43

    NUST Engineering Past Paper-6

    Simplify the expression using the sum-to-product identities.

    A

    B

    C

    D

    None of these

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44. 44

    NUST Engineering Past Paper-6

    Express as a polynomial in (triple-angle identity).

    A

    B

    C

    D

    None of these

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45. 45

    NUST Engineering Past Paper-6

    Two acute angles and satisfy and (with ). Determine and .

    A

    B

    C

    D

    None of these

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46. 46

    NUST Engineering Past Paper-6

    Using allied-angle identities, simplify .

    A

    B

    C

    D

    Reveal answer
47. 47

    NUST Engineering Past Paper-6

    Determine the RANGE of the real-valued function .

    A

    B

    C

    D

    None of these

    Reveal answer
48. 48

    NUST Engineering Past Paper-6

    In triangle , the sides have lengths , and . Determine the value of (the cosine of the angle opposite side ).

    A

    B

    C

    D

    None of these

    Reveal answer
49. 49

    NUST Engineering Past Paper-6

    An arc on a circle of radius has length . Determine the angle subtended at the centre in RADIANS.

    A

    B

    C

    D

    None of these

    Reveal answer
50. 50

    NUST Engineering Past Paper-6

    Determine the number of solutions of the equation in the interval .

    A

    B

    C

    D

    None of these

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51. 51

    NUST Engineering Past Paper-6

    Determine the derivative .

    A

    B

    C

    D

    None of these

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52. 52

    NUST Engineering Past Paper-6

    If , determine .

    A

    B

    C

    D

    None of these

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53. 53

    NUST Engineering Past Paper-6

    Determine the derivative (assume ).

    A

    B

    C

    D

    None of these

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54. 54

    NUST Engineering Past Paper-6

    If , determine the value of at .

    A

    B

    C

    D

    None of these

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55. 55

    NUST Engineering Past Paper-6

    Determine .

    A

    B

    C

    D

    None of these

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56. 56

    NUST Engineering Past Paper-6

    Determine the CRITICAL points of the function (where ).

    A

    B

    C

    D

    None of these

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57. 57

    NUST Engineering Past Paper-6

    Parametric equations are given by and . Determine in terms of .

    A

    B

    C

    D

    None of these

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58. 58

    NUST Engineering Past Paper-6

    Evaluate the indefinite integral .

    A

    B

    C

    D

    None of these

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59. 59

    NUST Engineering Past Paper-6

    Evaluate the indefinite integral .

    A

    B

    C

    D

    None of these

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60. 60

    NUST Engineering Past Paper-6

    Evaluate the definite integral .

    A

    B

    C

    D

    None of these

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61. 61

    NUST Engineering Past Paper-6

    Evaluate the indefinite integral .

    A

    B

    C

    D

    None of these

    Reveal answer
62. 62

    NUST Engineering Past Paper-6

    Evaluate the indefinite integral .

    A

    B

    C

    D

    None of these

    Reveal answer
63. 63

    NUST Engineering Past Paper-6

    Evaluate the definite integral .

    A

    B

    C

    D

    None of these

    Reveal answer
64. 64

    NUST Engineering Past Paper-6

    Evaluate the indefinite integral .

    A

    B

    C

    D

    None of these

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65. 65

    NUST Engineering Past Paper-6

    Evaluate the indefinite integral .

    A

    B

    C

    D

    None of these

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66. 66

    NUST Engineering Past Paper-6

    Evaluate the limit .

    A

    B

    C

    D

    None of these

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67. 67

    NUST Engineering Past Paper-6

    Evaluate the limit .

    A

    B

    C

    D

    None of these

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68. 68

    NUST Engineering Past Paper-6

    Evaluate the limit .

    A

    B

    C

    D

    None of these

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69. 69

    NUST Engineering Past Paper-6

    Evaluate .

    A

    B

    C

    D

    None of these

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70. 70

    NUST Engineering Past Paper-6

    For two non-zero vectors and , the scalar product satisfies . Identify the geometric relationship between and .

    A

    B

    C

    D

    None of these

    Reveal answer
71. 71

    NUST Engineering Past Paper-6

    Determine the coordinates of the VERTEX of the parabola .

    A

    B

    C

    D

    None of these

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72. 72

    NUST Engineering Past Paper-6

    Determine the eccentricity of the ellipse .

    A

    B

    C

    D

    None of these

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73. 73

    NUST Engineering Past Paper-6

    Determine the perpendicular distance between the parallel lines and .

    A

    B

    C

    D

    None of these

    Reveal answer
74. 74

    NUST Engineering Past Paper-6

    A chord of the circle has its midpoint at the point . Determine the LENGTH of this chord.

    A

    B

    C

    D

    None of these

    Reveal answer
75. 75

    NUST Engineering Past Paper-6

    A committee of members is to be selected from men and women, with EXACTLY MEN and WOMEN. Determine the number of distinct selections.

    A

    B

    C

    D

    None of these

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76. 76

    NUST Engineering Past Paper-6

    Two fair six-sided dice are rolled simultaneously. Determine the probability that the SUM of the two outcomes is .

    A

    B

    C

    D

    None of these

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77. 77

    NUST Engineering Past Paper-6

    A bag contains red balls, green balls and blue balls. One ball is drawn at random. Determine the probability that it is NOT GREEN.

    A

    B

    C

    D

    None of these

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78. 78

    NUST Engineering Past Paper-6

    Determine the domain of the real-valued function .

    A

    B

    C

    D

    None of these

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79. 79

    NUST Engineering Past Paper-6

    In the binomial expansion of , determine the coefficient of the term containing .

    A

    B

    C

    D

    None of these

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80. 80

    NUST Engineering Past Paper-6

    Let be the roots of the quadratic . Determine .

    A

    B

    C

    D

    None of these

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81. 81

    NUST Engineering Past Paper-6

    Determine ALL cube roots of (in the complex plane).

    A

    B

    C

    only

    D

    None of these

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82. 82

    NUST Engineering Past Paper-6

    Determine for .

    A

    B

    C

    D

    None of these

    Reveal answer
83. 83

    NUST Engineering Past Paper-6

    Let be a primitive cube root of unity. Evaluate .

    A

    B

    C

    D

    None of these

    Reveal answer
84. 84

    NUST Engineering Past Paper-6

    In a geometric progression, the th term equals and the th term equals . Determine the first term .

    A

    B

    C

    D

    None of these

    Reveal answer
85. 85

    NUST Engineering Past Paper-6

    Determine a closed-form expression for the sum .

    A

    B

    C

    D

    None of these

    Reveal answer
86. 86

    NUST Engineering Past Paper-6

    Evaluate the limit .

    A

    B

    C

    D

    None of these

    Reveal answer
87. 87

    NUST Engineering Past Paper-6

    Pick the word that describes land suitable for ploughing and growing crops:

    A

    Arable

    B

    Desolate

    C

    Barren

    D

    Fallow

    Reveal answer
88. 88

    NUST Engineering Past Paper-6

    Complete the analogy: 'Clear is to Glass as Transparent is to ____'.

    A

    Cellophane

    B

    Wood

    C

    Brick

    D

    Cloth

    Reveal answer
89. 89

    NUST Engineering Past Paper-6

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

    A

    Diminish

    B

    Aggravate

    C

    Wane

    D

    Subside

    Reveal answer
90. 90

    NUST Engineering Past Paper-6

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

    A

    Dexterous

    B

    Proficient

    C

    Inept

    D

    Nimble

    Reveal answer
91. 91

    NUST Engineering Past Paper-6

    Pick the option that best defines 'Alma mater':

    A

    A future place of work

    B

    The school or university one previously attended

    C

    A childhood home

    D

    A government institution

    Reveal answer
92. 92

    NUST Engineering Past Paper-6

    Pick the word closest in meaning to 'Belittle':

    A

    Praise

    B

    Disparage

    C

    Exalt

    D

    Commend

    Reveal answer
93. 93

    NUST Engineering Past Paper-6

    Pick the word closest in meaning to 'Bleak':

    A

    Vibrant

    B

    Dreary

    C

    Cheerful

    D

    Inviting

    Reveal answer
94. 94

    NUST Engineering Past Paper-6

    Pick the word closest in meaning to 'Blunt' (direct in manner):

    A

    Tactful

    B

    Subtle

    C

    Forthright

    D

    Diplomatic

    Reveal answer
95. 95

    NUST Engineering Past Paper-6

    Pick the word closest in meaning to 'Bona fide':

    A

    Authentic

    B

    Fraudulent

    C

    Counterfeit

    D

    Dubious

    Reveal answer
96. 96

    NUST Engineering Past Paper-6

    Pick the word closest in meaning to 'Commingle':

    A

    Isolate

    B

    Mingle

    C

    Segregate

    D

    Separate

    Reveal answer
97. 97

    NUST Engineering Past Paper-6

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

    A

    Sociable

    B

    Outgoing

    C

    Gregarious

    D

    Introvert

    Reveal answer
98. 98

    NUST Engineering Past Paper-6

    Pick the option that best defines 'Hostile':

    A

    Neutral and detached

    B

    Unfriendly; showing opposition or aggression

    C

    Warmly welcoming

    D

    Openly cooperative

    Reveal answer
99. 99

    NUST Engineering Past Paper-6

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

    A

    Effortless

    B

    Demanding

    C

    Laborious

    D

    Taxing

    Reveal answer
100. 100

     NUST Engineering Past Paper-6

     Pick the word closest in meaning to 'Temperate':

     A

     Excessive

     B

     Moderate

     C

     Extreme

     D

     Immoderate

     Reveal answer
101. 101

     NUST Engineering Past Paper-6

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

     A

     Restrained

     B

     Calm

     C

     Intemperate

     D

     Mild

     Reveal answer
102. 102

     NUST Engineering Past Paper-6

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

     A

     Scold

     B

     Chide

     C

     Censure

     D

     Commend

     Reveal answer
103. 103

     NUST Engineering Past Paper-6

     Pick the option that best defines 'Pedestrians':

     A

     Drivers of motorized vehicles

     B

     People who are walking, especially in an urban area

     C

     Passengers on public transport

     D

     Workers employed in construction

     Reveal answer
104. 104

     NUST Engineering Past Paper-6

     Pick the option that best defines 'bonanza':

     A

     A sudden and very large profit or stroke of good fortune

     B

     A type of wild plant

     C

     A state of extreme poverty

     D

     A formal legal agreement

     Reveal answer
105. 105

     NUST Engineering Past Paper-6

     Pick the option that best defines 'coherence':

     A

     Logical and consistent connection or unity

     B

     Extreme stubbornness

     C

     A state of confusion or disorder

     D

     A sudden burst of energy

     Reveal answer
106. 106

     NUST Engineering Past Paper-6

     Choose the option that gives the correct spelling of the adverb meaning 'by chance; unintentionally':

     A

     Accidentaly

     B

     Acidentally

     C

     Accidentlly

     D

     Accidentally

     Reveal answer
107. 107

     NUST Engineering Past Paper-6

     Pick the word most nearly OPPOSITE in meaning to 'Ferocious'.

     A

     Gentle

     B

     Fierce

     C

     Wild

     D

     Belittle

     Reveal answer
108. 108

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

     Pick the synonym of the adjective NEFARIOUS.

     A

     Virtuous

     B

     Gentle

     C

     Honest

     D

     Wicked

     Reveal answer
109. 109

     NUST Engineering Past Paper-6

     Pick the word that grammatically completes: 'Our country is a spiritual country, theirs ___ religious.'

     A

     is

     B

     also

     C

     have

     D

     are

     Reveal answer
110. 110

     NUST Engineering Past Paper-6

     Pick the preposition that best completes: 'Our sir teaches Mathematics ___ English.'

     A

     beside

     B

     both

     C

     besides

     D

     across

     Reveal answer
111. 111

     NUST Engineering Past Paper-6

     Pick the prepositional phrase that completes: 'Please, come ___ the bathroom.'

     A

     over

     B

     out of

     C

     in

     D

     on

     Reveal answer
112. 112

     NUST Engineering Past Paper-6

     Pick the preposition that completes: 'Please, don't laugh ___ those beggars.'

     A

     at

     B

     against

     C

     for

     D

     from

     Reveal answer
113. 113

     NUST Engineering Past Paper-6

     Pick the verb form that completes: 'Please, stop ___ so many mistakes.'

     A

     makes

     B

     make

     C

     to make

     D

     making

     Reveal answer
114. 114

     NUST Engineering Past Paper-6

     Pick the verb form that completes: 'She ___ her husband for 15 minutes.'

     A

     beats

     B

     has been beating

     C

     has been beaten

     D

     is beating

     Reveal answer
115. 115

     NUST Engineering Past Paper-6

     Pick the verb form that completes: 'The English ___ English.'

     A

     spoke

     B

     speak

     C

     is spoken

     D

     spoken

     Reveal answer
116. 116

     NUST Engineering Past Paper-6

     Pick the preposition that completes: 'The rain comes ___ the clouds.'

     A

     from

     B

     in

     C

     under

     D

     near

     Reveal answer
117. 117

     NUST Engineering Past Paper-6

     Pick the participial phrase that completes: 'The ship ___, Robinson arrived on the island.'

     A

     having broken

     B

     has broken

     C

     having been broken

     D

     had been broken

     Reveal answer
118. 118

     NUST Engineering Past Paper-6

     Pick the modal phrase that best completes: 'The stars ___ counted.'

     A

     cannot be

     B

     must

     C

     can

     D

     can be

     Reveal answer
119. 119

     NUST Engineering Past Paper-6

     Pick the correct tag question to complete: 'Chirag hardly ever cooks, ___?'

     A

     does he

     B

     he doesn't

     C

     isn't he

     D

     doesn't he

     Reveal answer
120. 120

     NUST Engineering Past Paper-6

     Pick the verb form that completes: 'He ___ for you all day. He's still waiting.'

     A

     waits

     B

     waited

     C

     had waited

     D

     has waited

     Reveal answer
121. 121

     NUST Engineering Past Paper-6

     Pick the response that correctly completes: 'Did the company test the equipment yesterday? Yes, it ___.'

     A

     has been tested

     B

     was tested

     C

     had tested

     D

     tested

     Reveal answer
122. 122

     NUST Engineering Past Paper-6

     Identify the tense used in the question: 'What are you going to wear to the party tonight?'

     A

     Simple Future

     B

     Future Perfect

     C

     Simple Present

     D

     Present Continuous

     Reveal answer
123. 123

     NUST Engineering Past Paper-6

     Pick the correct articles to fill the blanks: 'Children recited a poem in ___ honour of ___ Prime Minister.'

     A

     no article, the

     B

     the, a

     C

     an, the

     D

     a, the

     Reveal answer
124. 124

     NUST Engineering Past Paper-6

     Convert to passive voice: 'The boy laughed at the beggar.' Pick the correct passive sentence.

     A

     The beggar was laughed by the boy.

     B

     The beggar was laughed at by the boy.

     C

     The beggar was being laughed by the boy.

     D

     The beggar was being laughed at by the boy.

     Reveal answer
125. 125

     NUST Engineering Past Paper-6

     Convert to active voice: 'Our task had been completed before sunset.' Pick the correct active sentence.

     A

     We completed our task before sunset.

     B

     We had completed our task before sunset.

     C

     We have completed our task before sunset.

     D

     We complete our task before sunset.

     Reveal answer
126. 126

     NUST Engineering Past Paper-6

     Convert the passive question to active voice: 'Has your question been answered?'

     A

     Your question has been answered.

     B

     Did you answer your question?

     C

     Has someone answered your question?

     D

     Have you answered your question?

     Reveal answer
127. 127

     NUST Engineering Past Paper-6

     Convert to indirect speech: He said, 'The mice will play when the cat is away.'

     A

     He said that the mice will play when the cat is away.

     B

     He said that the mice would play when the cat would be away.

     C

     He said that the mice shall play, when the cat is away.

     D

     He said that the mice would play when the cat was away.

     Reveal answer
128. 128

     NUST Engineering Past Paper-6

     Convert to indirect speech: The employer said to the workman, 'I cannot pay you higher wages.'

     A

     The employer told the workman that he could not be paid higher wages.

     B

     The employer told the workman that he could not pay him higher wages.

     C

     The employer warned the workman that he cannot pay him higher wages.

     D

     The employer forbade the workman to pay higher wages.

     Reveal answer
129. 129

     NUST Engineering Past Paper-6

     Convert to indirect speech: He asked his servant, 'Why are you so lazy today?'

     A

     He asked his servant why he was so lazy that day.

     B

     He asked his servant why was he so lazy that day.

     C

     He asked his servant why he was being so lazy that day.

     D

     He asked his servant why he had been so lazy that day.

     Reveal answer
130. 130

     NUST Engineering Past Paper-6

     Convert to indirect speech: Rajan said, 'O that I were a child again!'

     A

     Rajan said that he was a child again.

     B

     Rajan told that he were a child again.

     C

     Rajan exclaimed that he were a child again.

     D

     Rajan strongly wished that he were a child again.

     Reveal answer
131. 131

     NUST Engineering Past Paper-6

     Pick the synonym of the verb ADMONISH.

     A

     Punish

     B

     Reprimand

     C

     Dismiss

     D

     Curse

     Reveal answer
132. 132

     NUST Engineering Past Paper-6

     Choose the word that BEST completes the sentence: 'Her response to the criticism was so ______ that it left her opponents speechless and unable to formulate any counter-arguments.'

     A

     Trenchant

     B

     Tepid

     C

     Candid

     D

     Ambiguous

     Reveal answer
133. 133

     NUST Engineering Past Paper-6

     If the Earth's radius were doubled (with mass kept constant), how would the acceleration due to gravity at the surface change?

     A

     Increase

     B

     None of the above

     C

     Decrease

     D

     Remain same

     Reveal answer
134. 134

     NUST Engineering Past Paper-6

     If the same force is applied to four equal-sized balls made of different materials, which one experiences the smallest acceleration?

     A

     Aluminium

     B

     Brass

     C

     Wood

     D

     Iron

     Reveal answer
135. 135

     NUST Engineering Past Paper-6

     When an avometer (multimeter) is used as an ammeter, what is the correct way to connect it in the circuit and what range should be chosen?

     A

     In series, with the lowest resistance range selected

     B

     In parallel, with the lowest resistance range selected

     C

     In series, with the highest resistance range selected

     D

     In parallel, with the highest resistance range selected

     Reveal answer
136. 136

     NUST Engineering Past Paper-6

     Identify the material from the following list that is most effective as a magnetic shield (i.e., diverts external magnetic field lines around a region).

     A

     Cobalt

     B

     Copper

     C

     Iron

     D

     Nickel

     Reveal answer
137. 137

     NUST Engineering Past Paper-6

     A charged capacitor (isolated from any battery) 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

     Increase

     B

     Decrease

     C

     None

     D

     Remain same

     Reveal answer
138. 138

     NUST Engineering Past Paper-6

     Identify the SI unit of impulse.

     A

     N m

     B

     N s

     C

     D

     J/s

     Reveal answer
139. 139

     NUST Engineering Past Paper-6

     For a stretched wire, if the LINEAR MASS DENSITY is doubled while the tension is held constant, how does the fundamental frequency of vibration change?

     A

     B

     C

     D

     Reveal answer
140. 140

     NUST Engineering Past Paper-6

     For a particle undergoing SHM with amplitude and angular frequency , determine the ratio .

     A

     B

     C

     D

     Reveal answer
141. 141

     NUST Engineering Past Paper-6

     In Young's double-slit experiment, the fringe width in air is . If the entire apparatus is immersed in a liquid of refractive index , determine the new fringe width.

     A

     B

     C

     D

     Reveal answer
142. 142

     NUST Engineering Past Paper-6

     Two vectors and have magnitudes and respectively. If their resultant has magnitude , determine the angle between them.

     A

     B

     C

     D

     Reveal answer
143. 143

     NUST Engineering Past Paper-6

     A Carnot engine operates between reservoirs at K and K. If it absorbs J of heat per cycle from the hot reservoir, determine the work done per cycle.

     A

     J

     B

     J

     C

     J

     D

     J

     Reveal answer
144. 144

     NUST Engineering Past Paper-6

     A point charge is placed at the CENTRE of a cube. Determine the total electric flux through the entire (closed) cube surface.

     A

     B

     C

     D

     Reveal answer
145. 145

     NUST Engineering Past Paper-6

     In a series RLC AC circuit at RESONANCE, determine the phase difference between the current and the applied voltage.

     A

     B

     C

     D

     Reveal answer
146. 146

     NUST Engineering Past Paper-6

     A radioactive sample has half-life days. Determine the fraction of the original sample remaining undecayed after days.

     A

     B

     C

     D

     Reveal answer
147. 147

     NUST Engineering Past Paper-6

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

     A

     B

     C

     D

     Reveal answer
148. 148

     NUST Engineering Past Paper-6

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

     A

     B

     C

     D

     Reveal answer
149. 149

     NUST Engineering Past Paper-6

     A particle moves in a circular path of radius with CONSTANT angular velocity . Determine its TANGENTIAL acceleration.

     A

     B

     C

     D

     Reveal answer
150. 150

     NUST Engineering Past Paper-6

     In a photoelectric experiment, the stopping potential is for incident light of frequency . If the frequency is DOUBLED, determine the new stopping potential. (Use work function .)

     A

     B

     C

     D

     Reveal answer
151. 151

     NUST Engineering Past Paper-6

     An electron in the ground state of hydrogen has energy eV. Determine the IONIZATION energy.

     A

     eV

     B

     eV

     C

     eV

     D

     eV

     Reveal answer
152. 152

     NUST Engineering Past Paper-6

     An ideal transformer has primary turns and secondary turns. If the primary voltage is V, determine the secondary voltage.

     A

     V

     B

     V

     C

     V

     D

     V

     Reveal answer
153. 153

     NUST Engineering Past Paper-6

     Determine the time period of a simple pendulum of length inside a lift that is accelerating UPWARD with acceleration .

     A

     B

     C

     D

     Reveal answer
154. 154

     NUST Engineering Past Paper-6

     A body of mass moving with velocity collides elastically (1-D) with a stationary body of mass . Determine the FRACTION of kinetic energy transferred to the second body.

     A

     B

     C

     D

     Reveal answer
155. 155

     NUST Engineering Past Paper-6

     Determine the value of for an ideal DIATOMIC gas at HIGH temperature (where vibrational degrees of freedom are also active).

     A

     B

     C

     D

     Reveal answer
156. 156

     NUST Engineering Past Paper-6

     Two long parallel wires carrying currents and in opposite directions experience a (repulsive) force per unit length . If BOTH currents are doubled (directions unchanged), determine the new force per unit length.

     A

     B

     C

     D

     Reveal answer
157. 157

     NUST Engineering Past Paper-6

     In the Bohr model of hydrogen, determine the angular momentum of an electron in the SECOND orbit.

     A

     B

     C

     D

     Reveal answer
158. 158

     NUST Engineering Past Paper-6

     A converging lens of focal length cm forms a REAL image at cm from the lens. Determine the object distance.

     A

     cm

     B

     cm

     C

     cm

     D

     cm

     Reveal answer
159. 159

     NUST Engineering Past Paper-6

     A transistor amplifier has current gain . If the base current changes by A, determine the change in collector current.

     A

     mA

     B

     mA

     C

     A

     D

     A

     Reveal answer
160. 160

     NUST Engineering Past Paper-6

     A metal has work function eV. Determine the threshold wavelength for photoelectric emission. (Use eV·nm.)

     A

     nm

     B

     nm

     C

     nm

     D

     nm

     Reveal answer
161. 161

     NUST Engineering Past Paper-6

     A particle executes SHM with time period . Determine the time taken to travel from the mean (equilibrium) position to a displacement of HALF the amplitude.

     A

     B

     C

     D

     Reveal answer
162. 162

     NUST Engineering Past Paper-6

     Determine the dimensional formula of Planck's constant .

     A

     B

     C

     D

     Reveal answer
163. 163

     NUST Engineering Past Paper-6

     In an electromagnetic wave propagating in vacuum, describe the geometric relationship between the electric field , the magnetic field , and the direction of propagation.

     A

     Parallel to each other but perpendicular to propagation direction

     B

     Perpendicular to each other and to the direction of propagation

     C

     Parallel to each other and to the direction of propagation

     D

     Perpendicular to each other but parallel to propagation direction

     Reveal answer
164. 164

     NUST Engineering Past Paper-6

     Two capacitors F and F are connected in series across a V battery. Determine the potential difference across .

     A

     V

     B

     V

     C

     V

     D

     V

     Reveal answer
165. 165

     NUST Engineering Past Paper-6

     For which nuclide is the binding energy per nucleon MAXIMUM?

     A

     Helium

     B

     Hydrogen

     C

     Uranium-238

     D

     Iron-56

     Reveal answer
166. 166

     NUST Engineering Past Paper-6

     A projectile is launched with initial speed at angle . Determine the RADIUS of curvature of its trajectory at the highest point.

     A

     B

     C

     D

     Reveal answer
167. 167

     NUST Engineering Past Paper-6

     Determine the dimensional formula for the coefficient of viscosity .

     A

     B

     C

     D

     Reveal answer
168. 168

     NUST Engineering Past Paper-6

     In a nuclear fission reaction, approximately of the mass of the reactants is converted to energy. Determine the energy released from the fission of kg of fissile material.

     A

     J

     B

     J

     C

     J

     D

     J

     Reveal answer
169. 169

     NUST Engineering Past Paper-6

     An object weighs N on Earth. Determine its weight on a planet that has HALF Earth's radius but TWICE Earth's density.

     A

     N

     B

     N

     C

     N

     D

     N

     Reveal answer
170. 170

     NUST Engineering Past Paper-6

     Determine the FIRST excitation energy of the hydrogen atom (energy required for the transition from the ground state to the first excited state ).

     A

     eV

     B

     eV

     C

     eV

     D

     eV

     Reveal answer
171. 171

     NUST Engineering Past Paper-6

     A string of length fixed at both ends vibrates in its SECOND harmonic. Determine the wavelength of the standing wave.

     A

     B

     C

     D

     Reveal answer
172. 172

     NUST Engineering Past Paper-6

     For molecules of an ideal gas at temperature , identify the correct ordering of the most probable speed , the average speed , and the root-mean-square speed .

     A

     B

     C

     D

     Reveal answer
173. 173

     NUST Engineering Past Paper-6

     Identify the resonance condition for a series LCR AC circuit.

     A

     B

     C

     D

     Reveal answer
174. 174

     NUST Engineering Past Paper-6

     Identify the SI unit of magnetic flux .

     A

     Gauss

     B

     Henry

     C

     Tesla

     D

     Weber

     Reveal answer
175. 175

     NUST Engineering Past Paper-6

     A particle's position vector is (SI units). Determine the magnitude of its acceleration at s.

     A

     m/s²

     B

     m/s²

     C

     m/s²

     D

     m/s²

     Reveal answer
176. 176

     NUST Engineering Past Paper-6

     A cell of EMF and internal resistance delivers current to an external resistance . Determine the potential difference across the cell's terminals.

     A

     B

     C

     D

     Reveal answer
177. 177

     NUST Engineering Past Paper-6

     A hollow sphere and a solid sphere of the SAME radius and mass roll without slipping down an inclined plane. Determine the ratio of their accelerations .

     A

     B

     C

     D

     Reveal answer
178. 178

     NUST Engineering Past Paper-6

     According to Bohr's correspondence principle, in what limit do quantum-mechanical predictions reduce to classical-mechanics predictions?

     A

     Low velocities

     B

     Small quantum numbers

     C

     High energies

     D

     Large quantum numbers

     Reveal answer
179. 179

     NUST Engineering Past Paper-6

     Identify the relation between the decay constant of a radioactive nuclide and its half-life .

     A

     B

     C

     D

     Reveal answer
180. 180

     NUST Engineering Past Paper-6

     Two coherent sources emit waves with intensities in the ratio . Determine the ratio of maximum to minimum intensity in their interference pattern.

     A

     B

     C

     D

     Reveal answer
181. 181

     NUST Engineering Past Paper-6

     Estimate the typical order of magnitude of the band-gap energy in a SEMICONDUCTOR.

     A

     eV

     B

     eV

     C

     eV

     D

     eV

     Reveal answer
182. 182

     NUST Engineering Past Paper-6

     Determine the force between two point charges and separated by distance in a medium of dielectric constant .

     A

     B

     C

     D

     Reveal answer
183. 183

     NUST Engineering Past Paper-6

     For a body in UNIFORM circular motion (constant speed), which of the following physical quantities remains CONSTANT?

     A

     Velocity

     B

     Momentum

     C

     Kinetic energy

     D

     Acceleration

     Reveal answer
184. 184

     NUST Engineering Past Paper-6

     Determine the maximum possible efficiency of a heat engine operating between reservoirs at K and K.

     A

     B

     C

     D

     Reveal answer
185. 185

     NUST Engineering Past Paper-6

     Identify the fundamental factor that limits the RESOLVING power of an optical microscope.

     A

     Focal length of objective

     B

     Wavelength of light used

     C

     Magnification

     D

     Numerical aperture

     Reveal answer
186. 186

     NUST Engineering Past Paper-6

     A uniform wire of total resistance is bent into a closed circular ring. Determine the resistance measured between two DIAMETRICALLY OPPOSITE points.

     A

     B

     C

     D

     Reveal answer
187. 187

     NUST Engineering Past Paper-6

     An electron accelerated from rest through potential difference has de Broglie wavelength . If is DOUBLED, determine the new wavelength.

     A

     B

     C

     D

     Reveal answer
188. 188

     NUST Engineering Past Paper-6

     Determine the magnitude of the torque on a magnetic dipole of moment placed in a uniform magnetic field , with angle between the moment and the field.

     A

     B

     C

     D

     Reveal answer
189. 189

     NUST Engineering Past Paper-6

     For an ideal gas at temperature , determine the average translational kinetic energy PER MOLECULE.

     A

     B

     C

     D

     Reveal answer
190. 190

     NUST Engineering Past Paper-6

     A spring of force constant is cut into TWO equal halves. Determine the force constant of each half.

     A

     B

     C

     D

     Reveal answer
191. 191

     NUST Engineering Past Paper-6

     A particle of mass and charge enters a uniform magnetic field with velocity perpendicular to the field. Determine the radius of its circular path.

     A

     B

     C

     D

     Reveal answer
192. 192

     NUST Engineering Past Paper-6

     Determine the power factor of a series LCR AC circuit AT RESONANCE.

     A

     B

     C

     D

     Reveal answer
193. 193

     NUST Engineering Past Paper-6

     On a charged conductor in electrostatic equilibrium, where is the surface charge density HIGHEST?

     A

     Regions of smallest radius of curvature

     B

     Regions of largest radius of curvature

     C

     Flat surfaces

     D

     Everywhere uniform

     Reveal answer
194. 194

     NUST Engineering Past Paper-6

     Determine the time constant of an RC circuit with and F.

     A

     s

     B

     s

     C

     s

     D

     s

     Reveal answer
195. 195

     NUST Engineering Past Paper-6

     In a Compton-scattering event, identify the scattering angle of the photon at which the wavelength shift is MAXIMUM.

     A

     B

     C

     D

     Reveal answer
196. 196

     NUST Engineering Past Paper-6

     Determine the gravitational potential energy of a body of mass at height above the Earth's surface (radius , Earth's mass ), measured RELATIVE to the surface as zero.

     A

     B

     C

     D

     Reveal answer
197. 197

     NUST Engineering Past Paper-6

     Identify the value of for an ideal MONATOMIC gas.

     A

     B

     C

     D

     Reveal answer
198. 198

     NUST Engineering Past Paper-6

     Using the relation , calculate the power delivered when a constant force acts on an object moving at in the direction of .

     A

     B

     C

     D

     Reveal answer