NUST Engineering Past Paper-10

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

1. 1

   NUST Engineering Past Paper-10

   If the cosine of an angle equals , what is the sine of half of that angle?

   A

   B

   C

   1

   D

   0

   Reveal answer
2. 2

   NUST Engineering Past Paper-10

   What is the probability that a number chosen at random from the first 30 natural numbers is prime?

   A

   B

   C

   D

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3. 3

   NUST Engineering Past Paper-10

   Find the value of that satisfies .

   A

   B

   1

   C

   0

   D

   2

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4. 4

   NUST Engineering Past Paper-10

   A line is given by the parametric equations and . Find its slope.

   A

   B

   2

   C

   D

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5. 5

   NUST Engineering Past Paper-10

   Three vertices of parallelogram are , and . What is the fourth vertex ?

   A

   B

   C

   D

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6. 6

   NUST Engineering Past Paper-10

   Find the distance between the parallel lines and .

   A

   B

   C

   D

   None of these

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7. 7

   NUST Engineering Past Paper-10

   Evaluate .

   A

   B

   C

   D

   None of these

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8. 8

   NUST Engineering Past Paper-10

   Find the area under the curve from to .

   A

   2

   B

   4

   C

   0

   D

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9. 9

   NUST Engineering Past Paper-10

   Find the domain of .

   A

   B

   C

   D

   None of these

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10. 10

    NUST Engineering Past Paper-10

    Find where .

    A

    Undefined (none of these)

    B

    0

    C

    D

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11. 11

    NUST Engineering Past Paper-10

    What is the defining property of a singular matrix?

    A

    A matrix whose determinant is zero

    B

    A matrix whose rows are symmetrical

    C

    A matrix whose determinant is non-zero

    D

    A matrix whose diagonal entries are zero

    Reveal answer
12. 12

    NUST Engineering Past Paper-10

    What is the inverse of the identity matrix ?

    A

    itself

    B

    C

    D

    Zero matrix

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13. 13

    NUST Engineering Past Paper-10

    Identify the point at which the function FAILS to be differentiable.

    A

    All of these

    B

    C

    D

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14. 14

    NUST Engineering Past Paper-10

    Under which of the following conditions on the sets and does ?

    A

    A ⊂ B but A ≠ B

    B

    A and B are disjoint sets

    C

    B ⊂ A but A ≠ B

    D

    All of these

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15. 15

    NUST Engineering Past Paper-10

    If , determine .

    A

    B

    C

    D

    Does not exist

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16. 16

    NUST Engineering Past Paper-10

    Determine the area of a triangle with side lengths , , .

    A

    B

    C

    D

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17. 17

    NUST Engineering Past Paper-10

    Simplify the set expression .

    A

    B

    None

    C

    D

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18. 18

    NUST Engineering Past Paper-10

    Given , determine .

    A

    None

    B

    C

    D

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19. 19

    NUST Engineering Past Paper-10

    Evaluate .

    A

    B

    C

    D

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20. 20

    NUST Engineering Past Paper-10

    Given the IDENTITY matrix , determine .

    A

    B

    C

    D

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21. 21

    NUST Engineering Past Paper-10

    For the infinite series , identify the statement that is NOT TRUE.

    A

    Sum of the series is

    B

    Common ratio is

    C

    It is a Geometric Series

    D

    The series is not convergent

    Reveal answer
22. 22

    NUST Engineering Past Paper-10

    A window has the shape of a rectangle surmounted by a semicircle. The width of the rectangular base is and its height is (with the semicircle's diameter equal to the rectangle's width). Determine the total perimeter of the window.

    A

    None

    B

    C

    D

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23. 23

    NUST Engineering Past Paper-10

    In a triangle, the sides and , and the angle opposite is . Determine the angle opposite .

    A

    B

    C

    D

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24. 24

    NUST Engineering Past Paper-10

    Evaluate .

    A

    B

    C

    D

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25. 25

    NUST Engineering Past Paper-10

    Rewrite the circle in standard form by completing the square.

    A

    B

    C

    D

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26. 26

    NUST Engineering Past Paper-10

    Two positive consecutive integers have sum . Express their product in terms of .

    A

    B

    C

    D

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27. 27

    NUST Engineering Past Paper-10

    In a triangle with sides , , , determine (the sine of the angle opposite side ).

    A

    B

    C

    D

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28. 28

    NUST Engineering Past Paper-10

    Points and are evaluated against the line . Identify the correct statement about their positions.

    A

    lies above and lies below the line

    B

    lies below and lies above the line

    C

    Neither

    D

    Both lie on the same side

    Reveal answer
29. 29

    NUST Engineering Past Paper-10

    State the algebraic condition on the dot product which holds when two non-zero vectors and are ANTI-PARALLEL (i.e., point in exactly opposite directions).

    A

    B

    C

    D

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30. 30

    NUST Engineering Past Paper-10

    If , determine (note ).

    A

    B

    C

    D

    (zero matrix)

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31. 31

    NUST Engineering Past Paper-10

    If , determine the ordered pair .

    A

    B

    C

    D

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32. 32

    NUST Engineering Past Paper-10

    Compute the determinant of .

    A

    B

    C

    D

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33. 33

    NUST Engineering Past Paper-10

    Compute the cofactor of the matrix .

    A

    B

    C

    D

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34. 34

    NUST Engineering Past Paper-10

    If a matrix has , determine the value of .

    A

    B

    C

    D

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35. 35

    NUST Engineering Past Paper-10

    Determine whether the linear system has a UNIQUE solution, INFINITELY many solutions, or NO solution.

    A

    Infinitely many solutions

    B

    Unique solution

    C

    No solution

    D

    Exactly two solutions

    Reveal answer
36. 36

    NUST Engineering Past Paper-10

    Determine the set of values of for which the linear system has a UNIQUE solution.

    A

    B

    C

    D

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37. 37

    NUST Engineering Past Paper-10

    Determine the LARGER value of for which the quadratic has EQUAL roots.

    A

    B

    C

    D

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38. 38

    NUST Engineering Past Paper-10

    Determine the nature of the roots of the parametric quadratic for real with .

    A

    Depends on (real or complex)

    B

    Always real and rational

    C

    Always imaginary

    D

    Always equal

    Reveal answer
39. 39

    NUST Engineering Past Paper-10

    The quadratic ALWAYS has as a root. Determine its OTHER root in terms of .

    A

    B

    C

    D

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40. 40

    NUST Engineering Past Paper-10

    If are the roots of , determine the quadratic equation whose roots are and .

    A

    B

    C

    D

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41. 41

    NUST Engineering Past Paper-10

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

    A

    B

    C

    D

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42. 42

    NUST Engineering Past Paper-10

    Determine the polynomial QUOTIENT obtained by performing polynomial long division of by (the first step before partial-fraction decomposition).

    A

    B

    C

    D

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43. 43

    NUST Engineering Past Paper-10

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

    A

    B

    C

    D

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44. 44

    NUST Engineering Past Paper-10

    In an arithmetic progression with first term and common difference , determine the SUM of the first terms.

    A

    B

    C

    D

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45. 45

    NUST Engineering Past Paper-10

    If FOUR geometric means are inserted between and , determine the common ratio of the resulting GP.

    A

    B

    C

    D

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46. 46

    NUST Engineering Past Paper-10

    A geometric progression has terms, first term and last term . Determine the common ratio.

    A

    B

    C

    D

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47. 47

    NUST Engineering Past Paper-10

    Evaluate the sum of the infinite series .

    A

    B

    C

    D

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48. 48

    NUST Engineering Past Paper-10

    Determine the TOTAL number of signals that can be made by hoisting different flags, using any number (1, 2, 3, or 4) of them at a time in a vertical sequence.

    A

    B

    C

    D

    Reveal answer
49. 49

    NUST Engineering Past Paper-10

    Determine the number of ways people can be seated in a single row if two PARTICULAR people must sit TOGETHER (next to each other).

    A

    B

    C

    D

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50. 50

    NUST Engineering Past Paper-10

    From men and women, a committee of is to be formed containing EXACTLY women. Determine the number of such committees.

    A

    B

    C

    D

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51. 51

    NUST Engineering Past Paper-10

    If and and the events are INDEPENDENT, determine .

    A

    B

    C

    D

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52. 52

    NUST Engineering Past Paper-10

    A bag contains red balls and blue balls. Two balls are drawn at random WITHOUT REPLACEMENT. Determine the probability that both are BLUE.

    A

    B

    C

    D

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53. 53

    NUST Engineering Past Paper-10

    By mathematical induction one proves that is divisible by for every . Verify the BASE CASE by computing at .

    A

    B

    C

    D

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54. 54

    NUST Engineering Past Paper-10

    Determine the coefficient of in the binomial expansion of .

    A

    B

    C

    D

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55. 55

    NUST Engineering Past Paper-10

    Determine the MIDDLE TERM in the binomial expansion of .

    A

    B

    C

    D

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56. 56

    NUST Engineering Past Paper-10

    Determine the EXACT value of .

    A

    B

    C

    D

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57. 57

    NUST Engineering Past Paper-10

    Using the allied-angle identities, simplify .

    A

    B

    C

    D

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58. 58

    NUST Engineering Past Paper-10

    Using allied-angle identities, simplify .

    A

    B

    C

    D

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59. 59

    NUST Engineering Past Paper-10

    Simplify the expression in terms of functions of and .

    A

    B

    C

    D

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60. 60

    NUST Engineering Past Paper-10

    Simplify the product in terms of squares of and .

    A

    B

    C

    D

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61. 61

    NUST Engineering Past Paper-10

    Express in terms of and (two equivalent half-angle formulas).

    A

    Both and

    B

    only

    C

    only

    D

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62. 62

    NUST Engineering Past Paper-10

    Express in terms of (triple-angle formula for tangent).

    A

    B

    C

    D

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63. 63

    NUST Engineering Past Paper-10

    Express as a polynomial in .

    A

    B

    C

    D

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64. 64

    NUST Engineering Past Paper-10

    Determine the EXACT value of using a sum/difference formula.

    A

    B

    C

    D

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65. 65

    NUST Engineering Past Paper-10

    In triangle , two sides have lengths and , and the included angle is . Determine the length of the third side .

    A

    B

    C

    D

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66. 66

    NUST Engineering Past Paper-10

    State the law of COSINES for a triangle , giving an expression for in terms of and angle .

    A

    B

    C

    D

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67. 67

    NUST Engineering Past Paper-10

    In triangle , , , . Using the law of cosines, express in numerical and trigonometric terms.

    A

    B

    C

    D

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68. 68

    NUST Engineering Past Paper-10

    Determine the value of .

    A

    B

    C

    D

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69. 69

    NUST Engineering Past Paper-10

    Determine the GENERAL solution of the equation .

    A

    B

    C

    D

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70. 70

    NUST Engineering Past Paper-10

    Determine the SOLUTION SET of the equation in .

    A

    B

    C

    D

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71. 71

    NUST Engineering Past Paper-10

    Evaluate the limit .

    A

    B

    C

    D

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72. 72

    NUST Engineering Past Paper-10

    Evaluate the limit .

    A

    B

    C

    D

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73. 73

    NUST Engineering Past Paper-10

    Evaluate the limit .

    A

    B

    C

    D

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74. 74

    NUST Engineering Past Paper-10

    For to have exist, determine the required value of .

    A

    B

    C

    D

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75. 75

    NUST Engineering Past Paper-10

    Define for . By continuity, determine the value that makes continuous at .

    A

    B

    C

    D

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76. 76

    NUST Engineering Past Paper-10

    If , determine the value of at .

    A

    B

    C

    D

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77. 77

    NUST Engineering Past Paper-10

    Determine for on the open interval .

    A

    B

    C

    D

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78. 78

    NUST Engineering Past Paper-10

    If , determine .

    A

    B

    C

    D

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79. 79

    NUST Engineering Past Paper-10

    The function satisfies a second-order linear ODE of the form . Determine the ODE.

    A

    B

    C

    D

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80. 80

    NUST Engineering Past Paper-10

    If and (a Chebyshev-type pair), determine the value of , where primes denote derivatives with respect to .

    A

    B

    C

    D

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81. 81

    NUST Engineering Past Paper-10

    If for constants , determine the value of (an Euler-type expression).

    A

    B

    C

    D

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82. 82

    NUST Engineering Past Paper-10

    Evaluate the indefinite integral for .

    A

    B

    C

    D

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83. 83

    NUST Engineering Past Paper-10

    Evaluate the definite integral .

    A

    B

    C

    D

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84. 84

    NUST Engineering Past Paper-10

    Determine the equation of the tangent line to the parabola at the point where .

    A

    B

    C

    D

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85. 85

    NUST Engineering Past Paper-10

    Determine the equation of the NORMAL to the parabola at the point .

    A

    B

    C

    D

    Reveal answer
86. 86

    NUST Engineering Past Paper-10

    Determine for .

    A

    B

    C

    D

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87. 87

    NUST Engineering Past Paper-10

    Determine the equation of the NORMAL to the ellipse at the point .

    A

    B

    C

    D

    Reveal answer
88. 88

    NUST Engineering Past Paper-10

    A circle passes through the points and , and the -coordinate of its CENTRE is . Determine the equation of the circle.

    A

    B

    C

    D

    Reveal answer
89. 89

    NUST Engineering Past Paper-2 NUST Engineering Past Paper-5 NUST Engineering Past Paper-10

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

    A

    Economical

    B

    Extravagant

    C

    Prudent

    D

    Thrifty

    Reveal answer
90. 90

    NUST Engineering Past Paper-10

    Pick the phrase closest in meaning to 'Alma mater':

    A

    Foster home

    B

    Professional body

    C

    Former school

    D

    Future employer

    Reveal answer
91. 91

    NUST Engineering Past Paper-10

    Pick the word closest in meaning to 'Arduous':

    A

    Strenuous

    B

    Effortless

    C

    Easy

    D

    Trivial

    Reveal answer
92. 92

    NUST Engineering Past Paper-10

    Pick the color most OPPOSITE in shade to 'Azure':

    A

    Indigo

    B

    Teal

    C

    Crimson

    D

    Cobalt

    Reveal answer
93. 93

    NUST Engineering Past Paper-10

    Pick the word closest in meaning to 'Bewildering':

    A

    Illuminating

    B

    Clarifying

    C

    Perplexing

    D

    Simplifying

    Reveal answer
94. 94

    NUST Engineering Past Paper-10

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

    A

    Dissonance

    B

    Euphony

    C

    Noise

    D

    Clamor

    Reveal answer
95. 95

    NUST Engineering Past Paper-10

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

    A

    Yield

    B

    Admit

    C

    Surrender

    D

    Contest

    Reveal answer
96. 96

    NUST Engineering Past Paper-10

    Pick the word closest in meaning to 'Detention':

    A

    Freedom

    B

    Confinement

    C

    Liberation

    D

    Release

    Reveal answer
97. 97

    NUST Engineering Past Paper-10

    Pick the option that best defines 'Efface':

    A

    To make oneself prominent and noticeable

    B

    To strengthen and reinforce

    C

    To decorate a surface

    D

    To erase or remove; to make oneself inconspicuous

    Reveal answer
98. 98

    NUST Engineering Past Paper-10

    Pick the word closest in meaning to 'Expatriate':

    A

    Nationalist

    B

    Emigrant

    C

    Native

    D

    Patriot

    Reveal answer
99. 99

    NUST Engineering Past Paper-10

    Pick the word closest in meaning to 'Fiscal':

    A

    Military

    B

    Social

    C

    Physical

    D

    Financial

    Reveal answer
100. 100

     NUST Engineering Past Paper-10

     Pick the word closest in meaning to 'Hostile':

     A

     Cordial

     B

     Amicable

     C

     Friendly

     D

     Antagonistic

     Reveal answer
101. 101

     NUST Engineering Past Paper-10

     Pick the word closest in meaning to 'Impecunious':

     A

     Penurious

     B

     Affluent

     C

     Prosperous

     D

     Wealthy

     Reveal answer
102. 102

     NUST Engineering Past Paper-10

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

     A

     Indigent

     B

     Destitute

     C

     Affluent

     D

     Penniless

     Reveal answer
103. 103

     NUST Engineering Past Paper-10

     Pick the option that best defines 'Pretentious':

     A

     Attempting to impress by claiming importance or merit

     B

     Completely unaware of social norms

     C

     Genuinely modest and humble

     D

     Open and honest about one's abilities

     Reveal answer
104. 104

     NUST Engineering Past Paper-10

     Pick the word closest in meaning to 'Serenity':

     A

     Turmoil

     B

     Chaos

     C

     Tranquility

     D

     Agitation

     Reveal answer
105. 105

     NUST Engineering Past Paper-10

     Pick the word closest in meaning to 'Submissive':

     A

     Dominant

     B

     Defiant

     C

     Assertive

     D

     Compliant

     Reveal answer
106. 106

     NUST Engineering Past Paper-10

     Pick the option that best defines 'Transient':

     A

     Affecting a wide geographic area

     B

     Permanent and unchanging

     C

     Deeply rooted and stable

     D

     Lasting for a very short time; temporary

     Reveal answer
107. 107

     NUST Engineering Past Paper-10

     Pick the word closest in meaning to 'Sensitive':

     A

     Unfeeling

     B

     Callous

     C

     Perceptive

     D

     Indifferent

     Reveal answer
108. 108

     NUST Engineering Past Paper-10

     Pick the word closest in meaning to 'Frisky':

     A

     Drowsy

     B

     Sluggish

     C

     Lively

     D

     Lethargic

     Reveal answer
109. 109

     NUST Engineering Past Paper-10

     Identify the scientific discipline devoted to the study of human beings, their cultures, and societies.

     A

     Biology

     B

     Anthropology

     C

     Psychology

     D

     Sociology

     Reveal answer
110. 110

     NUST Engineering Past Paper-10

     Complete the analogy: 'Sculptor : Studio :: Physician : ___'.

     A

     Infirmary

     B

     Library

     C

     Pharmacy

     D

     Laboratory

     Reveal answer
111. 111

     NUST Engineering Past Paper-10

     Pick the option that best defines 'indomitable':

     A

     Easily discouraged or defeated

     B

     Impossible to subdue or conquer

     C

     Very talkative and outgoing

     D

     Reluctant to take risks

     Reveal answer
112. 112

     NUST Engineering Past Paper-10

     Pick the word closest in meaning to 'Attire':

     A

     Adorn

     B

     Acquire

     C

     Attract

     D

     Garment

     Reveal answer
113. 113

     NUST Engineering Past Paper-10

     Identify the meaning of the idiom 'TO HAVE A BRUSH WITH.'

     A

     To start painting

     B

     To be impressed

     C

     To have good and pleasing terms

     D

     To have a brief or slight encounter

     Reveal answer
114. 114

     NUST Engineering Past Paper-10

     Identify the meaning of the idiom 'TO THROW DOWN THE GLOVE.'

     A

     To resort to wrong tactics

     B

     To reject the prize

     C

     To accept defeat

     D

     To offer a challenge

     Reveal answer
115. 115

     NUST Engineering Past Paper-10

     Identify the meaning of the idiom 'TO TALK SHOP.'

     A

     To talk reasonably

     B

     To talk nonsense

     C

     To discuss professional matters at a social occasion

     D

     To abuse someone

     Reveal answer
116. 116

     NUST Engineering Past Paper-10

     Identify the meaning of the idiom 'TO BEAR THE PALM.'

     A

     To endure something

     B

     To accept defeat

     C

     To win reward

     D

     To challenge

     Reveal answer
117. 117

     NUST Engineering Past Paper-10

     Pick the verb pair that completes: 'The petrol warning light ___ on when I ___ the garage.'

     A

     flashes / will be reaching

     B

     is going to flash / will reach

     C

     flashed / have reached

     D

     had been flashing / reached

     Reveal answer
118. 118

     NUST Engineering Past Paper-10

     Pick the phrasal verb that best completes: 'Nobody can ___ Piyush because of his strange behaviour.'

     A

     get through

     B

     get along

     C

     get away

     D

     get over

     Reveal answer
119. 119

     NUST Engineering Past Paper-10

     Pick the adjective phrase that completes: 'The reconstruction of ancient buildings is ___ work that requires expert knowledge.'

     A

     a simple

     B

     a rapid

     C

     a painstaking

     D

     an effortless

     Reveal answer
120. 120

     NUST Engineering Past Paper-10

     Pick the adjective that best completes: 'The scientist was ___ in her research; she worked without rest for days.'

     A

     casual

     B

     negligent

     C

     relentless

     D

     indifferent

     Reveal answer
121. 121

     NUST Engineering Past Paper-10

     Identify the correction needed in: 'There are not many men who are so famous that they are frequently referred to by their signatures only.'

     A

     signatures

     B

     middle names

     C

     pictures

     D

     initials

     Reveal answer
122. 122

     NUST Engineering Past Paper-10

     Pick the corrected version of: 'Neither of the two boys have done their homework.'

     A

     Neither of the two boys have done his homework.

     B

     No correction required.

     C

     Neither of the two boys had done their homework.

     D

     Neither of the two boys has done his homework.

     Reveal answer
123. 123

     NUST Engineering Past Paper-10

     Sentence Improvement: 'She could not help but to laugh at his joke.' Pick the corrected version.

     A

     She could not help herself to laugh at his joke.

     B

     She could not help laughing at his joke.

     C

     No correction required.

     D

     She could not help but laughing at his joke.

     Reveal answer
124. 124

     NUST Engineering Past Paper-10

     Arrange the sentence fragments in the correct order to form a coherent sentence: (1) He was punished (2) because he lied (3) by his teacher (4) to his parents.

     A

     2-4-1-3

     B

     1-3-2-4

     C

     3-1-2-4

     D

     1-2-4-3

     Reveal answer
125. 125

     NUST Engineering Past Paper-10

     Pick the noun that best completes: 'The ambassador presented his ___ to the Foreign Minister.'

     A

     credence

     B

     credibility

     C

     credentials

     D

     accreditation

     Reveal answer
126. 126

     NUST Engineering Past Paper-10

     Identify the meaning of the idiom 'TO SHOW ONE'S TEETH.'

     A

     To be humble

     B

     To ridicule

     C

     To act in an angry or threatening manner

     D

     To face difficulties

     Reveal answer
127. 127

     NUST Engineering Past Paper-10

     Identify the meaning of the idiom 'GET DOWN TO BRASS TACKS.'

     A

     To get into the thick of a problem

     B

     To start considering basic facts or practical details

     C

     To start an argument

     D

     To begin talking plainly

     Reveal answer
128. 128

     NUST Engineering Past Paper-10

     Identify the meaning of the idiom 'BUILT UPON SAND.'

     A

     Constructed near a beach

     B

     Without secure foundations; liable to collapse

     C

     Based on inexperience

     D

     Resting on immature ideas

     Reveal answer
129. 129

     NUST Engineering Past Paper-10

     Identify the meaning of the idiom 'TO BE AT DAGGERS DRAWN.'

     A

     To be a bitter enemy

     B

     To be in a state of extreme unfriendliness

     C

     To threaten one

     D

     To be frightened

     Reveal answer
130. 130

     NUST Engineering Past Paper-10

     Identify the meaning of the idiom 'THE SEAMY SIDE OF LIFE.'

     A

     The exciting parts of life

     B

     The glamorous side of life

     C

     The sordid, base, or unpleasant parts of life

     D

     The working side of life

     Reveal answer
131. 131

     NUST Engineering Past Paper-10

     Identify the meaning of the idiom 'TO GIVE CHAPTER AND VERSE.'

     A

     To make publicity of a thing

     B

     To eulogize the qualities of a thing

     C

     To tell all the details without missing anything

     D

     To attach artificial value to a thing

     Reveal answer
132. 132

     NUST Engineering Past Paper-10

     Identify the meaning of the idiom 'TO SET PEOPLE BY THE EARS.'

     A

     To insult and disgrace people

     B

     To cause a group of people to engage in a squabble or dispute

     C

     To box the people

     D

     To punish heavily

     Reveal answer
133. 133

     NUST Engineering Past Paper-10

     Which physical quantity has dimensional formula ?

     A

     Momentum

     B

     Force

     C

     Pressure

     D

     Energy

     Reveal answer
134. 134

     NUST Engineering Past Paper-10

     Given that the charge of a particle becomes and the accelerating voltage becomes , determine the new de Broglie wavelength (original wavelength is ).

     A

     B

     C

     D

     Reveal answer
135. 135

     NUST Engineering Past Paper-10

     Which of the following factors does NOT influence the capacitance of a parallel-plate capacitor?

     A

     Dielectric

     B

     Geometry of capacitor

     C

     Voltage across capacitor

     D

     Distance between the plates

     Reveal answer
136. 136

     NUST Engineering Past Paper-10

     Determine the dimensional formula for mechanical work (or energy).

     A

     B

     C

     D

     Reveal answer
137. 137

     NUST Engineering Past Paper-10

     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 in which direction) should an umbrella be tilted from the vertical to best block the rain?

     A

     towards south

     B

     towards north

     C

     towards north

     D

     towards south

     Reveal answer
138. 138

     NUST Engineering Past Paper-10

     Identify the physical reason the Sun appears red during sunrise and sunset.

     A

     Red light is scattered more than other colours

     B

     The sun's temperature drops at sunrise and sunset

     C

     Blue light is scattered more by the atmosphere, leaving red light to dominate

     D

     The sun emits red light only at those times

     Reveal answer
139. 139

     NUST Engineering Past Paper-10

     A person inside a lift notices that their apparent weight is decreasing relative to their normal weight. Identify the motion of the lift consistent with this observation.

     A

     Upward with constant velocity

     B

     At rest

     C

     Upward with acceleration

     D

     Downward (accelerating downward)

     Reveal answer
140. 140

     NUST Engineering Past Paper-10

     If the mass of a spring-mass oscillator is increased to while the spring constant remains , determine the effect on its time period.

     A

     Doubles

     B

     Halves

     C

     Quadruples

     D

     Unchanged

     Reveal answer
141. 141

     NUST Engineering Past Paper-10

     If the current through an inductor is reduced to one-third of its original value, determine the factor by which the stored magnetic energy changes.

     A

     Remains the same

     B

     One-third

     C

     One-ninth

     D

     Tripled

     Reveal answer
142. 142

     NUST Engineering Past Paper-10

     Among the listed quantities, identify the one that is NOT a fixed physical constant of nature.

     A

     Relativity constant

     B

     Speed of electromagnetic waves

     C

     None of the above

     D

     Gravitational constant

     Reveal answer
143. 143

     NUST Engineering Past Paper-10

     A storage battery of EMF and internal resistance is being CHARGED by an external source. State the relationship between its terminal potential difference and its EMF during charging.

     A

     B

     C

     D

     None of these

     Reveal answer
144. 144

     NUST Engineering Past Paper-10

     Determine the work done by Earth's gravitational force on a satellite that moves in a stable CIRCULAR orbit around the Earth in one complete revolution.

     A

     Zero

     B

     Minimum

     C

     Infinite

     D

     Maximum

     Reveal answer
145. 145

     NUST Engineering Past Paper-10

     A travelling sinusoidal wave is reflected normally from a rigid boundary, producing a reflected wave . Determine the resultant wave produced by their superposition.

     A

     B

     C

     D

     Reveal answer
146. 146

     NUST Engineering Past Paper-10

     Among the listed scenarios, identify the situation in which the law of conservation of linear momentum DOES NOT hold.

     A

     Closed systems

     B

     None of the above

     C

     Elastic collision

     D

     Inelastic collision

     Reveal answer
147. 147

     NUST Engineering Past Paper-10

     For a projectile traversing a parabolic trajectory under gravity alone (no air resistance), identify the quantity that stays CONSTANT throughout the motion.

     A

     Kinetic energy

     B

     Horizontal component of velocity

     C

     Total energy

     D

     Vertical component of velocity

     Reveal answer
148. 148

     NUST Engineering Past Paper-10

     A car of mass carrying passengers of each decelerates uniformly from to in . Determine the magnitude of the retarding force acting on the car.

     A

     B

     C

     D

     Reveal answer
149. 149

     NUST Engineering Past Paper-10

     A uniform metallic wire of length and resistance is cut into three equal segments. Determine the resistivity of each resulting segment.

     A

     One half

     B

     Double

     C

     One fourth

     D

     The same

     Reveal answer
150. 150

     NUST Engineering Past Paper-10

     A bipolar junction transistor has an emitter region doped as N-type semiconductor. Identify the corresponding transistor configuration.

     A

     PNP

     B

     Either

     C

     None

     D

     NPN

     Reveal answer
151. 151

     NUST Engineering Past Paper-10

     A magnetic dipole initially aligned along an external magnetic field is rotated through , doing work against the field. Determine the magnitude of the torque that must be applied to hold the dipole in this new position.

     A

     B

     C

     D

     Reveal answer
152. 152

     NUST Engineering Past Paper-10

     State the total solid angle subtended at the centre of a sphere by its complete surface area, and identify the correct SI unit.

     A

     steradian

     B

     steradian

     C

     steradian

     D

     radian

     Reveal answer
153. 153

     NUST Engineering Past Paper-10

     Identify the fundamental conceptual distinction between MASS and WEIGHT of an object.

     A

     Mass is always less than weight

     B

     None of the above

     C

     Weight is a force; mass is not

     D

     Both are the same

     Reveal answer
154. 154

     NUST Engineering Past Paper-10

     State the SI unit of angular acceleration of a rotating rigid body.

     A

     Radian per second

     B

     None

     C

     Radian

     D

     Radian per second

     Reveal answer
155. 155

     NUST Engineering Past Paper-10

     A Carnot heat engine operating between a hot source and a cold sink at has efficiency . Determine by how many kelvin the source temperature must be raised so that the efficiency increases to , keeping the sink temperature fixed.

     A

     B

     C

     D

     Reveal answer
156. 156

     NUST Engineering Past Paper-10

     In Young's double-slit experiment with monochromatic light and equally illuminated identical slits, identify the nature of the CENTRAL fringe of the resulting interference pattern.

     A

     Dark

     B

     Neutral

     C

     Sometimes bright, sometimes dark

     D

     Bright

     Reveal answer
157. 157

     NUST Engineering Past Paper-10

     A body of mass changes its velocity from to in . Determine the magnitude and sign of the net force acting on it.

     A

     B

     C

     D

     Reveal answer
158. 158

     NUST Engineering Past Paper-10

     A charged particle in a uniform electric field experiences a force . Determine the new force experienced if its charge is reduced to ONE-THIRD of its original value (field unchanged).

     A

     Tripled

     B

     Unchanged

     C

     One-third

     D

     One-ninth

     Reveal answer
159. 159

     NUST Engineering Past Paper-10

     A constant force of is applied to a body initially at rest for . Determine its final speed.

     A

     B

     C

     D

     Reveal answer
160. 160

     NUST Engineering Past Paper-10

     Applying Kirchhoff's voltage law to a series circuit containing a resistor , a capacitor holding charge , and a battery of EMF (with current flowing), identify the correct loop equation.

     A

     B

     C

     D

     Reveal answer
161. 161

     NUST Engineering Past Paper-10

     Identify the physical law that states stress is proportional to strain within the elastic limit of a deformable solid.

     A

     Hooke's Law

     B

     Ohm's Law

     C

     Faraday's Law

     D

     Newton's Law

     Reveal answer
162. 162

     NUST Engineering Past Paper-10

     Identify the front-panel control on a cathode-ray oscilloscope (CRO) that determines the BRIGHTNESS of the displayed spot.

     A

     Intensity control

     B

     Trigger control

     C

     Time base control

     D

     Focus control

     Reveal answer
163. 163

     NUST Engineering Past Paper-10

     State the value of the scalar (dot) product of two non-zero vectors that are MUTUALLY PERPENDICULAR.

     A

     One

     B

     Maximum

     C

     Zero

     D

     Negative

     Reveal answer
164. 164

     NUST Engineering Past Paper-10

     An electric motor lifts a cage of mass through a vertical height of in . If the motor's efficiency is , determine the input electrical power required (use ).

     A

     B

     C

     D

     Reveal answer
165. 165

     NUST Engineering Past Paper-10

     Describe the magnitude of the fluid drag (viscous friction) acting on an object that has attained TERMINAL VELOCITY while falling through a fluid.

     A

     Zero

     B

     Decreasing

     C

     Maximum

     D

     Minimum

     Reveal answer
166. 166

     NUST Engineering Past Paper-10

     Determine the AVERAGE value of a sinusoidal alternating current taken over one complete cycle.

     A

     Maximum

     B

     Positive

     C

     0

     D

     Constant

     Reveal answer
167. 167

     NUST Engineering Past Paper-10

     A coil of turns experiences a magnetic flux change of in . Determine the magnitude of the induced EMF.

     A

     B

     C

     D

     Reveal answer
168. 168

     NUST Engineering Past Paper-10

     State the words for which the acronym LASER stands.

     A

     Light Amplification by Stimulated Emission of Radiation

     B

     Light Amplification by Static Emission of Radiation

     C

     Light Application by Stimulated Emission of Rays

     D

     Laser Amplification by Stimulated Emission of Radiation

     Reveal answer
169. 169

     NUST Engineering Past Paper-10

     Among the listed SI units, identify the one that is a DERIVED unit (not a base SI unit).

     A

     Joule (J)

     B

     Mole (mol)

     C

     Kilogram (kg)

     D

     Second (s)

     Reveal answer
170. 170

     NUST Engineering Past Paper-10

     Determine the DIMENSIONAL FORMULA for POWER (energy per unit time).

     A

     B

     C

     D

     Reveal answer
171. 171

     NUST Engineering Past Paper-10

     In an ISOLATED SYSTEM (no external interactions), identify which conservation law(s) HOLD for the system.

     A

     Both momentum and energy (and angular momentum)

     B

     Only momentum

     C

     Only mass

     D

     Only energy

     Reveal answer
172. 172

     NUST Engineering Past Paper-10

     In UNIFORM CIRCULAR motion (constant speed, constant radius), identify the kinematic quantity that CONTINUOUSLY changes DIRECTION.

     A

     Linear velocity vector

     B

     Speed

     C

     Angular velocity

     D

     Magnitude of centripetal force

     Reveal answer
173. 173

     NUST Engineering Past Paper-10

     A stone whirled on a string in a horizontal circle has the STRING BREAK. Describe the SUBSEQUENT motion of the stone (neglecting gravity for the brief instant).

     A

     Moves in a straight line tangent to the circle

     B

     Moves outward along the former string direction

     C

     Stops immediately

     D

     Continues circular motion

     Reveal answer
174. 174

     NUST Engineering Past Paper-10

     Identify the factor(s) on which the RESISTANCE of a uniform metallic wire DEPENDS.

     A

     Material, length and cross-sectional area

     B

     Only applied voltage

     C

     Only current flowing through it

     D

     Only material's nature

     Reveal answer
175. 175

     NUST Engineering Past Paper-10

     A charged ideal capacitor has charge on one plate. Determine the NET (algebraic) charge on the capacitor as a whole.

     A

     B

     C

     D

     Reveal answer
176. 176

     NUST Engineering Past Paper-10

     State the approximate KNEE (cut-in) voltage for a GERMANIUM PN-junction diode at room temperature.

     A

     V

     B

     V

     C

     V

     D

     V

     Reveal answer
177. 177

     NUST Engineering Past Paper-10

     In the visible spectrum, identify the colour with the SHORTEST wavelength (highest frequency).

     A

     Green

     B

     Blue

     C

     Red

     D

     Violet

     Reveal answer
178. 178

     NUST Engineering Past Paper-10

     State LENZ'S LAW for the direction of the induced electromotive force (EMF) in a conducting loop.

     A

     Always flow clockwise

     B

     Flow in the direction of the external magnetic field

     C

     Oppose the change in magnetic flux that caused it

     D

     Increase the magnetic flux through the conductor

     Reveal answer
179. 179

     NUST Engineering Past Paper-10

     State the PRIMARY function of a TRANSFORMER in electrical-power applications.

     A

     To amplify current

     B

     To store electrical energy

     C

     To convert AC to DC

     D

     To change the voltage level of an AC supply

     Reveal answer
180. 180

     NUST Engineering Past Paper-10

     Four books are stacked on top of each other with individual weights of , , , and . Determine the NET downward force exerted on the table by the stack.

     A

     B

     C

     D

     Reveal answer
181. 181

     NUST Engineering Past Paper-10

     State the definition of IMPULSE in mechanics.

     A

     Rate of change of energy

     B

     Mass times acceleration

     C

     Product of force and time

     D

     Force divided by time

     Reveal answer
182. 182

     NUST Engineering Past Paper-10

     State the formula for the GRAVITATIONAL POTENTIAL ENERGY between two point masses and separated by distance (zero of taken at infinity).

     A

     B

     C

     D

     Reveal answer
183. 183

     NUST Engineering Past Paper-10

     To use a galvanometer-based AVOMETER as an AMMETER (current-measuring device), describe how the galvanometer should be modified and connected in the circuit.

     A

     In series with the load, with a low-resistance shunt in parallel with the galvanometer

     B

     In parallel with the load

     C

     In series with the load with a high series multiplier

     D

     Directly across the power supply

     Reveal answer
184. 184

     NUST Engineering Past Paper-10

     To use a galvanometer-based AVOMETER as a VOLTMETER (voltage-measuring device), describe how the galvanometer should be modified and connected in the circuit.

     A

     In parallel with the load, with a high-resistance multiplier in series with the galvanometer

     B

     In series with the load

     C

     In series with a low resistance

     D

     Directly across the battery terminals only

     Reveal answer
185. 185

     NUST Engineering Past Paper-10

     Describe the behaviour of a PN-junction diode under REVERSE BIAS (below breakdown).

     A

     The depletion region narrows and current increases

     B

     It has low resistance and allows large current to flow

     C

     Forward current increases exponentially

     D

     It has a very high resistance and essentially blocks current

     Reveal answer
186. 186

     NUST Engineering Past Paper-10

     Identify the THREE PRIMARY types of radioactive emission studied in nuclear decay.

     A

     Alpha (), Beta (), and Gamma () particles

     B

     Electrons and Protons only

     C

     Neutrons and Mesons only

     D

     Photons and Quarks

     Reveal answer
187. 187

     NUST Engineering Past Paper-10

     State the relationship between the CENTRIPETAL ACCELERATION of a particle in circular motion, its angular speed , and the radius of the circle.

     A

     B

     C

     D

     Reveal answer
188. 188

     NUST Engineering Past Paper-10

     Describe the COMPTON EFFECT (Compton scattering) and what it demonstrated about the nature of light.

     A

     Bending of light around obstacles

     B

     Emission of electrons from a surface when exposed to light of sufficient frequency

     C

     Emission of light when electrons recombine

     D

     Absorption of photons by a nucleus

     Reveal answer
189. 189

     NUST Engineering Past Paper-10

     A body moves in a circle of radius with constant speed . Determine the magnitude of its centripetal acceleration.

     A

     B

     C

     D

     Reveal answer
190. 190

     NUST Engineering Past Paper-10

     State the dimensional formula corresponding to the physical quantity called LINEAR MOMENTUM.

     A

     B

     C

     D

     Reveal answer
191. 191

     NUST Engineering Past Paper-10

     A capacitor of capacitance holds charge on its plates. State the formula for the ENERGY stored in the capacitor in terms of and .

     A

     B

     C

     D

     Reveal answer
192. 192

     NUST Engineering Past Paper-10

     Two resistors made of the SAME material are compared. Resistor 1 has THREE TIMES the length AND TWICE the cross-sectional area of resistor 2. Determine the ratio .

     A

     B

     C

     D

     Reveal answer
193. 193

     NUST Engineering Past Paper-10

     A force of acts on a body for . Determine the resulting change in the body's velocity.

     A

     B

     C

     D

     Reveal answer
194. 194

     NUST Engineering Past Paper-10

     In the photoelectric effect with incident light above the threshold frequency, describe the effect of INCREASING the FREQUENCY (not intensity) of the incident light on the photoelectrons.

     A

     Double the number of emitted electrons per second

     B

     Increase the threshold frequency

     C

     Double the maximum kinetic energy of emitted electrons

     D

     Double the stopping potential

     Reveal answer
195. 195

     NUST Engineering Past Paper-10

     A transformer has primary turns and secondary turns. If the primary voltage is , determine the secondary voltage (assume an ideal transformer).

     A

     B

     C

     D

     Reveal answer
196. 196

     NUST Engineering Past Paper-10

     When a (electron) particle is emitted in nuclear -decay, state the CHANGES in the parent nucleus's MASS NUMBER () and ATOMIC NUMBER ().

     A

     Mass , Atomic

     B

     Mass , Atomic

     C

     Mass , Atomic

     D

     Mass , Atomic

     Reveal answer
197. 197

     NUST Engineering Past Paper-10

     A particle moves in a circle of radius with angular speed . State the magnitude of its TANGENTIAL (linear) SPEED.

     A

     B

     C

     D

     Reveal answer
198. 198

     NUST Engineering Past Paper-10

     Describe the behaviour of a PN-junction diode under FORWARD BIAS (above the knee voltage).

     A

     The depletion region widens and only a small leakage current flows

     B

     The depletion region narrows and large forward current flows

     C

     The depletion region stays the same and no current flows

     D

     The diode has zero resistance

     Reveal answer
199. 199

     NUST Engineering Past Paper-10

     According to Lenz's Law, describe the direction of the induced current in a coil when the NORTH pole of a bar magnet is PULLED OUT of the coil (away from it).

     A

     Attract the magnet to accelerate it into the coil

     B

     Have no effect on the magnet

     C

     Create a magnetic field that repels the approaching magnet

     D

     Reverse direction once the magnet is fully inside

     Reveal answer