NUST Engineering Past Paper-2

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

1. 1

   NUST Engineering Past Paper-2

   Complete the analogy: 'Fear is to Phobia as Anger is to ____'.

   A

   Courage

   B

   Fury

   C

   Mania

   D

   Panic

   Reveal answer
2. 2

   NUST Engineering Past Paper-2

   Complete the sentence with the correct possessive pronoun: 'One should do ___ work honestly.'

   A

   their

   B

   one's

   C

   his

   D

   its

   Reveal answer
3. 3

   NUST Engineering Past Paper-2

   Which option correctly distinguishes between 'Flare' and 'Flair'?

   A

   Flare means a burst of flame or light; Flair means a natural talent or style

   B

   Flare means talent; Flair means a burst of fire

   C

   Both words mean the same thing

   D

   Flare means style; Flair means sudden anger

   Reveal answer
4. 4

   NUST Engineering Past Paper-2

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

   A

   Scarcity

   B

   Poverty

   C

   Affluence

   D

   Misery

   Reveal answer
5. 5

   NUST Engineering Past Paper-2

   Choose the word that is most nearly OPPOSITE in meaning to 'equitable':

   A

   Fair

   B

   Reasonable

   C

   Balanced

   D

   Unjust

   Reveal answer
6. 6

   NUST Engineering Past Paper-2

   Pick the word most nearly OPPOSITE in meaning to 'Abide by':

   A

   Defy

   B

   Obey

   C

   Follow

   D

   Respect

   Reveal answer
7. 7

   NUST Engineering Past Paper-2

   Choose the field whose focus is MOST DISTANT from that of 'Anthropology':

   A

   Astronomy

   B

   Archaeology

   C

   Cultural studies

   D

   Ethnography

   Reveal answer
8. 8

   NUST Engineering Past Paper-2

   Pick the word closest in meaning to 'Beguile':

   A

   Repulse

   B

   Enchant

   C

   Disgust

   D

   Alienate

   Reveal answer
9. 9

   NUST Engineering Past Paper-2

   Pick the option most nearly OPPOSITE in meaning to 'Braggart':

   A

   Showoff

   B

   Narcissist

   C

   Modest person

   D

   Egotist

   Reveal answer
10. 10

    NUST Engineering Past Paper-2

    Pick the option that best defines 'Candid':

    A

    Diplomatic to the point of dishonesty

    B

    Secretive and evasive

    C

    Truthful and straightforward

    D

    Overly emotional

    Reveal answer
11. 11

    NUST Engineering Past Paper-2

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

    A

    Model

    B

    Follow

    C

    Disregard

    D

    Mirror

    Reveal answer
12. 12

    NUST Engineering Past Paper-2

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

    A

    Clear

    B

    Acquit

    C

    Indict

    D

    Vindicate

    Reveal answer
13. 13

    NUST Engineering Past Paper-2

    Pick the term most OPPOSITE in meaning to 'Fiscal':

    A

    Monetary

    B

    Budgetary

    C

    Economic

    D

    Non-financial

    Reveal answer
14. 14

    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
15. 15

    NUST Engineering Past Paper-2

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

    A

    Caper

    B

    Skip

    C

    Trudge

    D

    Romp

    Reveal answer
16. 16

    NUST Engineering Past Paper-2

    Pick the word closest in meaning to 'Imprudent':

    A

    Sensible

    B

    Cautious

    C

    Wise

    D

    Reckless

    Reveal answer
17. 17

    NUST Engineering Past Paper-2

    Pick the word closest in meaning to 'Indomitable':

    A

    Submissive

    B

    Meek

    C

    Unconquerable

    D

    Yielding

    Reveal answer
18. 18

    NUST Engineering Past Paper-2

    Pick the word closest in meaning to 'Lethal':

    A

    Safe

    B

    Harmless

    C

    Benign

    D

    Deadly

    Reveal answer
19. 19

    NUST Engineering Past Paper-16 NUST Engineering Past Paper-2

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

    A

    Alleviate

    B

    Aggravate

    C

    Reduce

    D

    Calm

    Reveal answer
20. 20

    NUST Engineering Past Paper-2

    Pick the option that best defines 'Penurious':

    A

    Indifferent to wealth

    B

    Extremely poor; unwilling to spend money

    C

    Extremely generous

    D

    Moderately wealthy

    Reveal answer
21. 21

    NUST Engineering Past Paper-2

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

    A

    Secure

    B

    Risky

    C

    Shaky

    D

    Uncertain

    Reveal answer
22. 22

    NUST Engineering Past Paper-2

    Pick the option that best defines 'Repeal':

    A

    To temporarily suspend a rule

    B

    To officially revoke or annul a law

    C

    To amend a law by adding provisions

    D

    To officially confirm a law

    Reveal answer
23. 23

    NUST Engineering Past Paper-2

    Pick the option that best defines 'Comparative':

    A

    Entirely independent of context

    B

    Relating to the past only

    C

    Absolute and without reference to other things

    D

    Measured or judged by comparison with something else

    Reveal answer
24. 24

    NUST Engineering Past Paper-2

    Choose the option that gives the correct spelling of the adjective meaning 'relating to a religion':

    A

    Religous

    B

    Religeous

    C

    Relegious

    D

    Religious

    Reveal answer
25. 25

    NUST Engineering Past Paper-2

    Pick the word that means 'the highest point of achievement':

    A

    Marvel

    B

    Accomplishment

    C

    Apex

    D

    Laurel

    Reveal answer
26. 26

    NUST Engineering Past Paper-2

    Pick the correct verb form (tense) to fill the blank: 'She ___ studying for her exams all day.'

    A

    Have been

    B

    Was

    C

    Is

    D

    Has been

    Reveal answer
27. 27

    NUST Engineering Past Paper-2

    Identify the segment containing the grammatical error: 'Neither Jane or John / have confirmed / their attendance / at the conference.'

    A

    At the conference

    B

    Their attendance

    C

    Have confirmed

    D

    Neither Jane or John

    Reveal answer
28. 28

    NUST Engineering Past Paper-2

    Identify the sentence that uses the correct verb tense for a future action.

    A

    They will arrives tomorrow

    B

    They will arrived tomorrow

    C

    They will arriving tomorrow

    D

    They will arrive tomorrow

    Reveal answer
29. 29

    NUST Engineering Past Paper-2

    Identify the tense used in the sentence: 'She had finished her homework before dinner.'

    A

    Past perfect

    B

    Future perfect

    C

    Present perfect

    D

    Past continuous

    Reveal answer
30. 30

    NUST Engineering Past Paper-2

    Pick the synonym of the adjective EXQUISITE.

    A

    Plain

    B

    Ordinary

    C

    Beautiful

    D

    Common

    Reveal answer
31. 31

    NUST Engineering Past Paper-2

    Identify the grammatically correct sentence among the listed options.

    A

    I has been waiting for you

    B

    She is reading a book right now

    C

    He have been studying all day

    D

    They was playing soccer yesterday

    Reveal answer
32. 32

    NUST Engineering Past Paper-2

    Pick the synonym of the phrasal verb ABIDE BY.

    A

    Ignore

    B

    Dispute

    C

    Comply with

    D

    Reject

    Reveal answer
33. 33

    NUST Engineering Past Paper-2

    Pick the antonym of the adjective ARABLE.

    A

    Infertile

    B

    Cultivatable

    C

    Fertile

    D

    Productive

    Reveal answer
34. 34

    NUST Engineering Past Paper-2

    Pick the synonym of the adjective AZURE.

    A

    Emerald

    B

    Sky-blue

    C

    Charcoal

    D

    Crimson

    Reveal answer
35. 35

    NUST Engineering Past Paper-2

    Pick the antonym of the adjective BASE (in the sense of 'morally low or contemptible').

    A

    Immoral

    B

    Mean

    C

    Noble

    D

    Low

    Reveal answer
36. 36

    NUST Engineering Past Paper-2

    Pick the antonym of the adjective CANDID.

    A

    Sincere

    B

    Frank

    C

    Open

    D

    Evasive

    Reveal answer
37. 37

    NUST Engineering Past Paper-2

    Pick the antonym of the adjective IMMUNE.

    A

    Resistant

    B

    Exempt

    C

    Protected

    D

    Susceptible

    Reveal answer
38. 38

    NUST Engineering Past Paper-2

    Pick the antonym of the adjective PERPETUAL.

    A

    Eternal

    B

    Constant

    C

    Intermittent

    D

    Endless

    Reveal answer
39. 39

    NUST Engineering Past Paper-2

    Pick the synonym of the adjective SANGUINE.

    A

    Pale

    B

    Sad

    C

    Gloomy

    D

    Optimistic

    Reveal answer
40. 40

    NUST Engineering Past Paper-2

    Pick the antonym of the adjective VENIAL.

    A

    Forgivable

    B

    Unpardonable

    C

    Excusable

    D

    Minor

    Reveal answer
41. 41

    NUST Engineering Past Paper-2

    Pick the synonym of the adjective ACRIMONIOUS.

    A

    Soft

    B

    Caustic

    C

    Kind

    D

    Sweet

    Reveal answer
42. 42

    NUST Engineering Past Paper-2

    Pick the antonym of the adjective IMPRUDENT.

    A

    Rash

    B

    Foolish

    C

    Wise

    D

    Reckless

    Reveal answer
43. 43

    NUST Engineering Past Paper-2

    Pick the option closest in meaning to the adjective BOORISH.

    A

    Garrulous

    B

    Anachronism

    C

    Impolite

    D

    Courtesy

    Reveal answer
44. 44

    NUST Engineering Past Paper-2

    Choose the option that BEST completes the analogy by preserving the same relational pattern: PERJURY is to TESTIMONY as PLAGIARISM is to ____.

    A

    Writing

    B

    Speech

    C

    Editing

    D

    Reading

    Reveal answer
45. 45

    NUST Engineering Past Paper-2

    A coil produces an induced emf of V when the current through it changes at the rate A/s. Compute the self-inductance of the coil.

    A

    0.3 H

    B

    0.4 H

    C

    0.5 H

    D

    0.25 H

    Reveal answer
46. 46

    NUST Engineering Past Paper-2

    In Young's double-slit experiment, at what path difference is the -th dark fringe formed?

    A

    B

    C

    D

    Reveal answer
47. 47

    NUST Engineering Past Paper-2

    Compute and write the result with the correct number of significant figures.

    A

    B

    C

    D

    Reveal answer
48. 48

    NUST Engineering Past Paper-2

    Which of the following modifications will leave the fringe pattern in Young's double-slit experiment unchanged?

    A

    Immersing the apparatus in water

    B

    Doubling both the slit separation and screen distance simultaneously

    C

    Increasing the wavelength of light

    D

    Using white light instead of monochromatic light

    Reveal answer
49. 49

    NUST Engineering Past Paper-2

    For an isothermal process on an ideal gas, which of the following statements is FALSE?

    A

    constant

    B

    constant

    C

    D

    None of the above

    Reveal answer
50. 50

    NUST Engineering Past Paper-1 NUST Engineering Past Paper-2

    Identify a typical use of a (semiconductor) diode in electronic circuits.

    A

    Store electrical charge

    B

    Convert DC to AC (inversion)

    C

    Amplify signals

    D

    Convert AC to DC (rectification)

    Reveal answer
51. 51

    NUST Engineering Past Paper-2

    A satellite orbits the Earth in a circular orbit of radius with speed . If the orbital radius is changed to (with the satellite mass unchanged), determine its new orbital speed.

    A

    B

    C

    D

    Reveal answer
52. 52

    NUST Engineering Past Paper-2

    A parallel-plate capacitor has plate area and separation . A dielectric slab of constant fills HALF the gap (the slab is parallel to the plates, occupying thickness ). Determine the effective capacitance.

    A

    B

    C

    D

    Reveal answer
53. 53

    NUST Engineering Past Paper-2

    A body of mass slides DOWN a rough inclined plane of angle with coefficient of kinetic friction . Determine its acceleration down the slope.

    A

    B

    C

    D

    Reveal answer
54. 54

    NUST Engineering Past Paper-2

    Identify how the de Broglie wavelength of an electron accelerated from rest through a potential difference scales with .

    A

    B

    C

    D

    Reveal answer
55. 55

    NUST Engineering Past Paper-2

    Two identical inductors of inductance each are connected in PARALLEL, with no mutual inductance between them. Determine the equivalent inductance.

    A

    B

    C

    D

    Reveal answer
56. 56

    NUST Engineering Past Paper-2

    A proton moves with velocity in a uniform magnetic field . Determine the magnetic force on the proton.

    A

    Zero

    B

    C

    D

    Reveal answer
57. 57

    NUST Engineering Past Paper-2

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

    A

    Halves

    B

    Doubles

    C

    Quadruples

    D

    Remains the same

    Reveal answer
58. 58

    NUST Engineering Past Paper-2

    The radioactive nucleus U decays through a series to Pb. Determine the numbers of and particles emitted, respectively, during this chain.

    A

    6 and 8

    B

    10 and 4

    C

    4 and 10

    D

    8 and 6

    Reveal answer
59. 59

    NUST Engineering Past Paper-2

    A string of length , fixed at both ends, is under tension with linear mass density . Identify the frequency of its third harmonic.

    A

    B

    C

    D

    Reveal answer
60. 60

    NUST Engineering Past Paper-2

    The escape velocity from a planet of mass and radius is . If BOTH the mass and the radius are doubled, determine the new escape velocity.

    A

    B

    C

    D

    Reveal answer
61. 61

    NUST Engineering Past Paper-2

    An ideal gas undergoes ADIABATIC compression. Identify the correct combination of temperature, pressure, and entropy changes.

    A

    Temperature decreases, entropy increases

    B

    Temperature increases, entropy increases

    C

    Temperature increases, entropy remains constant

    D

    Temperature and pressure both decrease

    Reveal answer
62. 62

    NUST Engineering Past Paper-2

    Determine the Compton shift when X-rays scatter from a free electron at angle . (Use the Compton wavelength nm.)

    A

    nm

    B

    nm

    C

    nm

    D

    nm

    Reveal answer
63. 63

    NUST Engineering Past Paper-2

    A resistor is connected in series with a H inductor across a V, Hz AC source. Determine the power factor of the circuit.

    A

    B

    C

    D

    Reveal answer
64. 64

    NUST Engineering Past Paper-2

    In the Bohr model of the hydrogen atom, identify how the radius of the th allowed orbit scales with the principal quantum number .

    A

    B

    C

    D

    Reveal answer
65. 65

    NUST Engineering Past Paper-2

    A particle undergoes SHM with amplitude and angular frequency . At displacement , determine the ratio of kinetic energy to TOTAL energy.

    A

    B

    C

    D

    Reveal answer
66. 66

    NUST Engineering Past Paper-2

    A wire of total resistance is bent into a closed circular ring. Determine the resistance measured between two diametrically opposite ends of the ring.

    A

    B

    C

    D

    Reveal answer
67. 67

    NUST Engineering Past Paper-2

    A photon of wavelength nm strikes a metal surface of work function eV. Determine the maximum kinetic energy of the photoelectrons. (Use eV·nm.)

    A

    eV

    B

    eV

    C

    eV

    D

    eV

    Reveal answer
68. 68

    NUST Engineering Past Paper-2

    A Carnot engine operates between K and K. If its work output per cycle is J, determine the heat absorbed from the hot reservoir.

    A

    J

    B

    J

    C

    J

    D

    J

    Reveal answer
69. 69

    NUST Engineering Past Paper-2

    Determine the electric field at a point INSIDE a uniformly charged spherical SHELL of radius , at a distance from the centre.

    A

    Zero

    B

    C

    D

    Reveal answer
70. 70

    NUST Engineering Past Paper-2

    A rigid body, starting from rest, makes complete revolutions in time under uniform angular acceleration. Determine the angular acceleration .

    A

    B

    C

    D

    Reveal answer
71. 71

    NUST Engineering Past Paper-2

    The magnetic energy stored in an inductor carrying current is . If the current is now TRIPLED (with the inductance unchanged), determine the new stored energy.

    A

    B

    C

    D

    Reveal answer
72. 72

    NUST Engineering Past Paper-2

    A ball is thrown vertically upward from the ground with initial speed . Determine the approximate ratio of distances covered during the 1st second and 2nd second of motion (under the standard 'odd-number' rule).

    A

    B

    C

    D

    Reveal answer
73. 73

    NUST Engineering Past Paper-2

    Among the listed hydrogen-atom transitions, identify the one that emits the photon with the HIGHEST energy.

    A

    B

    C

    D

    Reveal answer
74. 74

    NUST Engineering Past Paper-2

    Two point charges and are placed a distance apart. Determine the electric potential at a point on the perpendicular bisector of the line joining them, at distance from the midpoint.

    A

    B

    C

    Zero

    D

    Reveal answer
75. 75

    NUST Engineering Past Paper-2

    A capacitor of capacitance is charged to voltage and then connected (in parallel) to an identical uncharged capacitor of capacitance . Determine the energy dissipated during this process.

    A

    Zero

    B

    C

    D

    Reveal answer
76. 76

    NUST Engineering Past Paper-2

    As an object's height above the Earth's surface increases (with , or alternatively for any using the full form), how does the gravitational potential energy change?

    A

    Remains constant

    B

    Oscillates

    C

    Increases (becomes less negative)

    D

    Decreases (becomes more negative)

    Reveal answer
77. 77

    NUST Engineering Past Paper-2

    A uniform rod of mass and length is pivoted at one end and used as a physical pendulum (small oscillations). With moment of inertia about the pivot, determine the angular frequency.

    A

    B

    C

    D

    Reveal answer
78. 78

    NUST Engineering Past Paper-2

    An ideal step-up transformer has primary turns and secondary turns. If the primary current is A, determine the secondary current.

    A

    A

    B

    A

    C

    A

    D

    A

    Reveal answer
79. 79

    NUST Engineering Past Paper-2

    Determine the work done against gravity to move a mass from the Earth's SURFACE to a height equal to the Earth's radius above the surface (i.e., total radial distance from the center).

    A

    B

    C

    D

    Reveal answer
80. 80

    NUST Engineering Past Paper-2

    An alpha particle (charge ) is accelerated from rest through a potential difference kV. Determine its kinetic energy in eV.

    A

    keV

    B

    keV

    C

    keV

    D

    keV

    Reveal answer
81. 81

    NUST Engineering Past Paper-2

    A circular current loop of radius produces magnetic field at its centre. If the radius is HALVED while keeping the current constant, determine the new field at the centre.

    A

    B

    C

    D

    Reveal answer
82. 82

    NUST Engineering Past Paper-2

    Two coherent waves and superpose. Determine the amplitude of the resultant wave.

    A

    B

    C

    D

    Reveal answer
83. 83

    NUST Engineering Past Paper-2

    A particle of mass and charge enters a uniform magnetic field perpendicular to its velocity, producing circular motion of radius . If the speed is DOUBLED (charge, mass, and field unchanged), determine the new radius.

    A

    B

    C

    D

    Reveal answer
84. 84

    NUST Engineering Past Paper-2

    In (beta-minus) decay, a nucleus emits an electron. Identify the OTHER particle simultaneously emitted, required to conserve lepton number and the continuous energy spectrum.

    A

    A neutrino

    B

    A gamma ray

    C

    A positron

    D

    An antineutrino

    Reveal answer
85. 85

    NUST Engineering Past Paper-2

    Determine the dimensional formula of Planck's constant .

    A

    B

    C

    D

    Reveal answer
86. 86

    NUST Engineering Past Paper-2

    The speed of sound in an ideal gas at temperature is . If the absolute temperature is multiplied by (with the gas unchanged), determine the new speed of sound.

    A

    B

    C

    D

    Reveal answer
87. 87

    NUST Engineering Past Paper-2

    The LYMAN series of the hydrogen spectrum corresponds to transitions ending at which energy level?

    A

    B

    C

    D

    Reveal answer
88. 88

    NUST Engineering Past Paper-2

    A uniform electric field acts in a region. A charge is displaced from to m. Determine the work done by the electric field.

    A

    B

    C

    D

    Reveal answer
89. 89

    NUST Engineering Past Paper-2

    At what DEPTH below the Earth's surface does the gravitational acceleration equal HALF its surface value?

    A

    B

    C

    D

    Reveal answer
90. 90

    NUST Engineering Past Paper-2

    A metal has photoelectric threshold frequency . If light of frequency is incident, determine the maximum kinetic energy of the emitted electrons.

    A

    B

    C

    D

    Reveal answer
91. 91

    NUST Engineering Past Paper-2

    A toroid (torus-shaped solenoid) has total turns, mean radius , and carries current . Identify the magnetic field strength inside the toroidal core.

    A

    B

    C

    D

    Reveal answer
92. 92

    NUST Engineering Past Paper-2

    In a SERIES RLC AC circuit at RESONANCE, determine the impedance.

    A

    Equal to

    B

    Equal to

    C

    Maximum

    D

    Equal to

    Reveal answer
93. 93

    NUST Engineering Past Paper-2

    In simple harmonic motion, identify the physical quantities that are MAXIMUM at the equilibrium position.

    A

    Potential energy and acceleration

    B

    Displacement and restoring force

    C

    Speed and kinetic energy

    D

    Speed and potential energy

    Reveal answer
94. 94

    NUST Engineering Past Paper-2

    Identify the primary role of moderators in a nuclear fission reactor.

    A

    They increase the speed of neutrons

    B

    They prevent chain reactions

    C

    They absorb all excess neutrons

    D

    They slow down fast neutrons through elastic collisions

    Reveal answer
95. 95

    NUST Engineering Past Paper-2

    The refractive index of glass is . Determine the critical angle for total internal reflection at a glass-to-air interface.

    A

    B

    C

    D

    Reveal answer
96. 96

    NUST Engineering Past Paper-2

    In the Bohr model of hydrogen, with angular momentum , identify how the kinetic energy of the electron in the th orbit scales with .

    A

    B

    C

    D

    Reveal answer
97. 97

    NUST Engineering Past Paper-2

    A W incandescent bulb operates at V. Determine its approximate operating resistance.

    A

    B

    C

    D

    Reveal answer
98. 98

    NUST Engineering Past Paper-2

    Determine the wavelength of the FIRST line (red, ) of the Balmer series of hydrogen, given the Rydberg constant m.

    A

    nm

    B

    nm

    C

    nm

    D

    nm

    Reveal answer
99. 99

    NUST Engineering Past Paper-2

    A particle moves in a circle of radius with constant angular velocity . Determine its centripetal acceleration.

    A

    B

    C

    D

    Reveal answer
100. 100

     NUST Engineering Past Paper-2

     Under FORWARD BIAS, how does the depletion layer of a p-n junction diode change?

     A

     Increases in width

     B

     Remains unchanged

     C

     Disappears completely

     D

     Decreases in width

     Reveal answer
101. 101

     NUST Engineering Past Paper-2

     Identify the orbital period of a satellite in a circular orbit at height above the Earth's surface, given Earth's radius and surface gravity .

     A

     B

     C

     D

     Reveal answer
102. 102

     NUST Engineering Past Paper-2

     A source of sound of frequency moves toward a stationary observer with speed , in a medium where the sound speed is . Determine the Doppler frequency SHIFT observed by the listener.

     A

     B

     C

     D

     Reveal answer
103. 103

     NUST Engineering Past Paper-2

     In a perfectly elastic collision between a moving ball of mass (incident) and a stationary ball of mass , identify the condition for the FRACTION of kinetic energy transferred to be MAXIMUM.

     A

     B

     C

     D

     Reveal answer
104. 104

     NUST Engineering Past Paper-2

     Identify the statement that correctly captures Lenz's law of electromagnetic induction.

     A

     The induced current is in the same direction as the changing flux

     B

     Induced EMF equals the rate of change of current

     C

     The induced current opposes the change in magnetic flux that caused it

     D

     The induced EMF is proportional to the current

     Reveal answer
105. 105

     NUST Engineering Past Paper-2

     A gas initially at K is heated to K (at constant volume, say). Determine the ratio of its new rms molecular speed to the original.

     A

     Halved

     B

     Quadrupled

     C

     Tripled

     D

     Doubled

     Reveal answer
106. 106

     NUST Engineering Past Paper-2

     Identify the correct condition for principal maxima at angle for light of wavelength falling on a diffraction grating with slits per metre.

     A

     B

     C

     D

     where

     Reveal answer
107. 107

     NUST Engineering Past Paper-2

     A transformer has primary turns and secondary turns, connected to a V AC source. Determine the secondary voltage and identify whether the transformer steps up or steps down.

     A

     V; step-down

     B

     V; step-down

     C

     V; isolation

     D

     V; step-up

     Reveal answer
108. 108

     NUST Engineering Past Paper-2

     A radioactive sample has half-life . Determine the fraction of the original nuclei remaining after a time interval of .

     A

     B

     C

     D

     Reveal answer
109. 109

     NUST Engineering Past Paper-2

     A body is projected HORIZONTALLY from a height of m with speed m/s. Taking m/s, determine the time to hit the ground.

     A

     s

     B

     s

     C

     s

     D

     s

     Reveal answer
110. 110

     NUST Engineering Past Paper-2

     State the standard conversion factor: inch equals how many centimetres?

     A

     B

     C

     None

     D

     Reveal answer
111. 111

     NUST Engineering Past Paper-2

     A ball is thrown at an angle of to the horizontal. To reach another player it must cover a horizontal range of . Determine the launch speed (use ).

     A

     B

     C

     D

     Reveal answer
112. 112

     NUST Engineering Past Paper-2

     The product , where is mass, is radius, and is angular acceleration, has the same dimensions as which physical quantity?

     A

     Linear momentum

     B

     Force

     C

     Torque

     D

     Linear acceleration

     Reveal answer
113. 113

     NUST Engineering Past Paper-2

     In Compton scattering, the incident wavelength is and the scattered wavelength is . Given the Compton wavelength , determine the scattering angle .

     A

     B

     C

     D

     Reveal answer
114. 114

     NUST Engineering Past Paper-2

     Find the value of .

     A

     B

     C

     D

     None of these

     Reveal answer
115. 115

     NUST Engineering Past Paper-2

     Which of the following functions has period ?

     A

     B

     C

     D

     Reveal answer
116. 116

     NUST Engineering Past Paper-2

     For with roots satisfying , find .

     A

     4

     B

     5

     C

     2

     D

     6

     Reveal answer
117. 117

     NUST Engineering Past Paper-2

     Simplify .

     A

     B

     C

     D

     Reveal answer
118. 118

     NUST Engineering Past Paper-2

     Find the largest angle of a triangle whose sides are , , and .

     A

     ≈ 126.87°

     B

     120°

     C

     135°

     D

     90°

     Reveal answer
119. 119

     NUST Engineering Past Paper-2

     Determine the value of .

     A

     B

     C

     D

     Reveal answer
120. 120

     NUST Engineering Past Paper-2

     Simplify .

     A

     B

     C

     D

     Reveal answer
121. 121

     NUST Engineering Past Paper-2

     Insert TWO arithmetic means between and .

     A

     B

     C

     D

     Reveal answer
122. 122

     NUST Engineering Past Paper-2

     Evaluate .

     A

     B

     C

     D

     Reveal answer
123. 123

     NUST Engineering Past Paper-2

     Given that , determine .

     A

     B

     C

     D

     Reveal answer
124. 124

     NUST Engineering Past Paper-2

     A single card is drawn at random from a standard -card deck. Determine the probability that the drawn card is EITHER a spade OR an ace (or both).

     A

     B

     C

     D

     Reveal answer
125. 125

     NUST Engineering Past Paper-2

     Determine the middle term of the binomial expansion .

     A

     None of these

     B

     6th term

     C

     8th term

     D

     7th term

     Reveal answer
126. 126

     NUST Engineering Past Paper-2

     Evaluate .

     A

     None of these

     B

     C

     D

     Reveal answer
127. 127

     NUST Engineering Past Paper-2

     Determine the coefficient of the term in the binomial expansion of .

     A

     B

     C

     D

     None

     Reveal answer
128. 128

     NUST Engineering Past Paper-2

     Simplify the expression .

     A

     B

     C

     D

     Reveal answer
129. 129

     NUST Engineering Past Paper-2

     Compare the asymptotic growth of and for large positive .

     A

     They are always equal

     B

     Depends on the value of

     C

     is always greater

     D

     is always greater

     Reveal answer
130. 130

     NUST Engineering Past Paper-2

     Simplify .

     A

     B

     C

     D

     Reveal answer
131. 131

     NUST Engineering Past Paper-2

     Evaluate .

     A

     B

     C

     None

     D

     Reveal answer
132. 132

     NUST Engineering Past Paper-2

     If the sample-space outcomes corresponding to events and satisfy , how should the events and be classified?

     A

     Disjoint

     B

     None

     C

     Mutually Exclusive

     D

     Overlapping

     Reveal answer
133. 133

     NUST Engineering Past Paper-2

     Determine which term in the binomial expansion of is INDEPENDENT of .

     A

     term

     B

     term

     C

     term

     D

     None of these

     Reveal answer
134. 134

     NUST Engineering Past Paper-2

     Determine the range of the function .

     A

     B

     C

     D

     Reveal answer
135. 135

     NUST Engineering Past Paper-2

     For the sequence , determine the term.

     A

     B

     C

     D

     None

     Reveal answer
136. 136

     NUST Engineering Past Paper-2

     Find such that .

     A

     B

     C

     D

     None

     Reveal answer
137. 137

     NUST Engineering Past Paper-2

     A rectangle has perimeter . If denotes the length of one side, express its area as a function of .

     A

     B

     C

     None

     D

     Reveal answer
138. 138

     NUST Engineering Past Paper-2

     Given , , , determine .

     A

     B

     C

     None

     D

     Reveal answer
139. 139

     NUST Engineering Past Paper-2

     Partition into two real numbers so that the sum of their squares is minimum.

     A

     B

     None

     C

     D

     Reveal answer
140. 140

     NUST Engineering Past Paper-2

     A square is inscribed in a circle of diameter . Determine the area of the square.

     A

     B

     C

     None

     D

     Reveal answer
141. 141

     NUST Engineering Past Paper-2

     Determine (in degrees, with ) such that .

     A

     B

     C

     None

     D

     Reveal answer
142. 142

     NUST Engineering Past Paper-2

     If the surface area of a cube equals half its volume, determine the side length .

     A

     B

     C

     None

     D

     Reveal answer
143. 143

     NUST Engineering Past Paper-2

     Find the equation of the perpendicular bisector of the segment joining and .

     A

     B

     C

     D

     None

     Reveal answer
144. 144

     NUST Engineering Past Paper-2

     Find the eccentricity of the ellipse .

     A

     B

     None

     C

     D

     Reveal answer
145. 145

     NUST Engineering Past Paper-2

     If the point lies strictly to the right of the -axis, determine the sign condition on .

     A

     B

     C

     D

     Reveal answer
146. 146

     NUST Engineering Past Paper-2

     Identify the vertical asymptote(s) of .

     A

     B

     None

     C

     No real value

     D

     Reveal answer
147. 147

     NUST Engineering Past Paper-2

     Convert to radians (to two decimal places).

     A

     None

     B

     C

     D

     Reveal answer
148. 148

     NUST Engineering Past Paper-2

     Identify the values of for which is undefined.

     A

     B

     None

     C

     D

     Reveal answer
149. 149

     NUST Engineering Past Paper-2

     Points , , form a right-angled triangle with the right angle at . Determine .

     A

     B

     None

     C

     D

     Reveal answer
150. 150

     NUST Engineering Past Paper-2

     Given a triangle with sides , compute the sine of its smallest interior angle.

     A

     None

     B

     C

     D

     Reveal answer
151. 151

     NUST Engineering Past Paper-2

     Two fair six-sided dice are rolled. Determine the probability that the sum of the two faces equals .

     A

     B

     C

     D

     None

     Reveal answer
152. 152

     NUST Engineering Past Paper-2

     Use the periodicity of cosine to simplify .

     A

     B

     C

     D

     None

     Reveal answer
153. 153

     NUST Engineering Past Paper-2

     Evaluate .

     A

     B

     C

     D

     None

     Reveal answer
154. 154

     NUST Engineering Past Paper-2

     Find the real part of .

     A

     B

     C

     None

     D

     Reveal answer
155. 155

     NUST Engineering Past Paper-2

     Consider the two complex cube roots of unity, and . Identify the property they do NOT satisfy with respect to each other.

     A

     Additive inverses

     B

     Both A and B

     C

     Multiplicative inverses

     D

     Squares of each other

     Reveal answer
156. 156

     NUST Engineering Past Paper-2

     Five distinguishable biscuits are distributed to three children. In how many ways can the distribution be made so that no child receives more than two biscuits?

     A

     B

     C

     D

     None

     Reveal answer
157. 157

     NUST Engineering Past Paper-2

     Given defined on all real numbers, determine its inverse .

     A

     B

     C

     None

     D

     Reveal answer
158. 158

     NUST Engineering Past Paper-2

     Classify the monotonic behaviour of on — does it increase, decrease, or remain constant?

     A

     Remains the same

     B

     Increases

     C

     None

     D

     Decreases

     Reveal answer
159. 159

     NUST Engineering Past Paper-2

     Suppose . Determine .

     A

     B

     C

     None

     D

     Reveal answer
160. 160

     NUST Engineering Past Paper-2

     Two fair dice are rolled three times in succession. Determine the probability that the sum of the two faces equals on every one of the three rolls.

     A

     B

     C

     D

     None

     Reveal answer
161. 161

     NUST Engineering Past Paper-2

     Compute .

     A

     None

     B

     C

     D

     Reveal answer
162. 162

     NUST Engineering Past Paper-2

     Given , evaluate .

     A

     B

     None

     C

     D

     Reveal answer
163. 163

     NUST Engineering Past Paper-2

     Determine the side length of a cube whose surface area equals one-fourth of its volume.

     A

     B

     None

     C

     D

     Reveal answer
164. 164

     NUST Engineering Past Paper-2

     Line is parallel to line . If has slope and has -intercept , determine the point where crosses the -axis.

     A

     B

     Never cuts

     C

     None

     D

     Reveal answer
165. 165

     NUST Engineering Past Paper-2

     Eliminate the parameter from and to express the relation between and .

     A

     B

     C

     None

     D

     Reveal answer
166. 166

     NUST Engineering Past Paper-2

     State the limit-based definition of the derivative of at the point .

     A

     B

     C

     None

     D

     Reveal answer
167. 167

     NUST Engineering Past Paper-2

     Given , , and , determine .

     A

     B

     C

     D

     None

     Reveal answer
168. 168

     NUST Engineering Past Paper-2

     Among the following, identify the function that is its own inverse (an involution).

     A

     B

     None

     C

     D

     Reveal answer
169. 169

     NUST Engineering Past Paper-2

     Two chords and of a circle meet at an interior point . Given , , , determine .

     A

     B

     C

     D

     None

     Reveal answer
170. 170

     NUST Engineering Past Paper-2

     Identify the equation of a line whose slope is and whose -intercept is .

     A

     Both

     B

     C

     D

     None

     Reveal answer
171. 171

     NUST Engineering Past Paper-2

     From a group of men, a committee of must be formed that always includes two specific individuals. Determine the number of such committees.

     A

     None

     B

     C

     D

     Reveal answer
172. 172

     NUST Engineering Past Paper-2

     Determine the maximum value of on the interval .

     A

     None

     B

     C

     D

     Reveal answer
173. 173

     NUST Engineering Past Paper-2

     Identify the point in the Cartesian plane that lies on both coordinate axes at the same time.

     A

     B

     C

     D

     None

     Reveal answer
174. 174

     NUST Engineering Past Paper-2

     Identify the axis or point of symmetry of the curve .

     A

     -axis

     B

     None

     C

     Origin

     D

     -axis

     Reveal answer
175. 175

     NUST Engineering Past Paper-2

     Classify the parity of the function — is it even, odd, neither, or none of these?

     A

     Odd

     B

     Neither

     C

     Even

     D

     None

     Reveal answer
176. 176

     NUST Engineering Past Paper-2

     Given , determine the cofactor of the entry .

     A

     B

     C

     D

     Reveal answer
177. 177

     NUST Engineering Past Paper-2

     If and , determine .

     A

     None

     B

     C

     D

     Reveal answer
178. 178

     NUST Engineering Past Paper-2

     Simplify .

     A

     B

     C

     None

     D

     Reveal answer
179. 179

     NUST Engineering Past Paper-2

     State the range of the principal-valued inverse-tangent function .

     A

     B

     None

     C

     D

     Reveal answer
180. 180

     NUST Engineering Past Paper-2

     If two sets and satisfy , what does this force about (or )?

     A

     B

     C

     D

     None

     Reveal answer
181. 181

     NUST Engineering Past Paper-2

     Find the - and -intercepts of the line .

     A

     B

     C

     None

     D

     Reveal answer
182. 182

     NUST Engineering Past Paper-2

     Compute correct to three decimal places.

     A

     B

     C

     None

     D

     Reveal answer
183. 183

     NUST Engineering Past Paper-2

     Approximate to three decimal places.

     A

     B

     None

     C

     D

     Reveal answer
184. 184

     NUST Engineering Past Paper-2

     Classify the monotonicity behaviour of .

     A

     Decreasing on

     B

     None

     C

     Increasing on

     D

     Increasing on

     Reveal answer
185. 185

     NUST Engineering Past Paper-2

     Find the maximum value of on its natural domain.

     A

     None

     B

     C

     D

     Reveal answer
186. 186

     NUST Engineering Past Paper-2

     Let be a complex cube root of unity. Identify which value of satisfies uniquely among the listed options.

     A

     B

     C

     None

     D

     Reveal answer
187. 187

     NUST Engineering Past Paper-2

     From a group of men and women, a committee of size must be formed with exactly women. How many such committees are possible?

     A

     B

     C

     None

     D

     Reveal answer
188. 188

     NUST Engineering Past Paper-2

     Identify the local extrema of .

     A

     Local minima

     B

     local maxima

     C

     None

     D

     local minima

     Reveal answer
189. 189

     NUST Engineering Past Paper-2

     Two fair six-sided dice are rolled. Determine the probability that the sum of the two faces is at most .

     A

     B

     C

     D

     None

     Reveal answer
190. 190

     NUST Engineering Past Paper-2

     Identify the term of the sequence

     A

     B

     C

     D

     None of these

     Reveal answer
191. 191

     NUST Engineering Past Paper-2

     Determine the equation of the parabola whose directrix is the line and whose focus is at .

     A

     B

     C

     D

     None of these

     Reveal answer
192. 192

     NUST Engineering Past Paper-2

     Given the recurrence with , compute .

     A

     B

     C

     D

     None of these

     Reveal answer
193. 193

     NUST Engineering Past Paper-2

     A classroom has left-hand and right-hand chairs (total seats). Two students are seated at random. Compute the probability that both occupy right-hand chairs.

     A

     B

     C

     None of these

     D

     Reveal answer
194. 194

     NUST Engineering Past Paper-2

     Given , determine .

     A

     B

     None of these

     C

     D

     Reveal answer
195. 195

     NUST Engineering Past Paper-2

     Given , evaluate .

     A

     B

     None of these

     C

     D

     Reveal answer
196. 196

     NUST Engineering Past Paper-2

     Given , determine .

     A

     B

     C

     D

     None of these

     Reveal answer
197. 197

     NUST Engineering Past Paper-2

     Evaluate .

     A

     B

     C

     D

     Reveal answer
198. 198

     NUST Engineering Past Paper-2

     Compute the determinant of the cyclic cube-root-of-unity matrix .

     A

     B

     C

     D

     Reveal answer