NUST Engineering Past Paper-8

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

1. 1

   NUST Engineering Past Paper-8

   A capacitor stores energy in a:

   A

   Neither

   B

   Magnetic field

   C

   Both electric and magnetic fields

   D

   Electric field

   Reveal answer
2. 2

   NUST Engineering Past Paper-8

   What is the dimensional formula of ?

   A

   B

   C

   D

   Reveal answer
3. 3

   NUST Engineering Past Paper-8

   Which spectral series of hydrogen arises from electron transitions ending at the ground state ()?

   A

   Lyman series

   B

   Pfund series

   C

   Balmer series

   D

   Paschen series

   Reveal answer
4. 4

   NUST Engineering Past Paper-8

   Faraday's law of induction () — including the negative sign (Lenz's law) — is fundamentally a consequence of which conservation law?

   A

   Ohm's Law

   B

   Newton's Law of Motion

   C

   Law of Conservation of Energy

   D

   Law of Conservation of Mass

   Reveal answer
5. 5

   NUST Engineering Past Paper-8

   Identify which type(s) of field a moving electric charge produces.

   A

   Only an electric field

   B

   Both electric and magnetic fields

   C

   Only a magnetic field

   D

   Neither electric nor magnetic field

   Reveal answer
6. 6

   NUST Engineering Past Paper-8

   In a proton-proton fusion chain (such as that powering the Sun), determine the approximate energy released per proton-proton chain event.

   A

   None of the above

   B

   C

   D

   Reveal answer
7. 7

   NUST Engineering Past Paper-8

   State the effect on fluid pressure when the speed of a fluid flowing through a pipe decreases (horizontal flow).

   A

   Becomes zero

   B

   Remains the same

   C

   Increases

   D

   Decreases

   Reveal answer
8. 8

   NUST Engineering Past Paper-8

   Identify the technical term for restricting a transverse wave's oscillations to a single plane.

   A

   Polarization

   B

   Depolarization

   C

   Transformation

   D

   None of these

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9. 9

   NUST Engineering Past Paper-8

   A sound wave has frequency and wavelength . Determine its speed.

   A

   B

   C

   D

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10. 10

    NUST Engineering Past Paper-8

    In the hydrogen atom, an electron makes a transition from to . Identify the spectral series in which the emitted photon falls.

    A

    Balmer series

    B

    Lyman series

    C

    Pfund series

    D

    Paschen series

    Reveal answer
11. 11

    NUST Engineering Past Paper-8

    Describe what occurs at the nuclear level during beta-minus () emission.

    A

    A neutron is converted to a proton and an electron is emitted

    B

    A neutron disappears

    C

    A proton is converted to a neutron

    D

    An electron is absorbed

    Reveal answer
12. 12

    NUST Engineering Past Paper-8

    Identify the scientists who explained different series within the hydrogen atomic spectrum.

    A

    Paschen

    B

    Balmer

    C

    All of them

    D

    Lyman

    Reveal answer
13. 13

    NUST Engineering Past Paper-8

    Determine the angle (above the horizontal) at which a projectile should be launched to achieve maximum horizontal range over level ground (no air resistance).

    A

    B

    C

    D

    Reveal answer
14. 14

    NUST Engineering Past Paper-8

    Identify the thermodynamic quantity that remains constant during an isothermal process.

    A

    Pressure

    B

    Internal Energy

    C

    Temperature

    D

    Volume

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15. 15

    NUST Engineering Past Paper-8

    According to Einstein's theory of relativity, identify the physical quantity whose value is the same in all inertial frames of reference.

    A

    Energy

    B

    Acceleration

    C

    Speed of light

    D

    Mass

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16. 16

    NUST Engineering Past Paper-8

    Identify the Rydberg formula for the wavelengths of spectral lines in the Balmer series of the hydrogen atom.

    A

    B

    C

    D

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17. 17

    NUST Engineering Past Paper-8

    If a uniform metal wire is stretched to TRIPLE its original length (keeping the total volume constant), determine the effect on its electrical resistance.

    A

    9 times the original

    B

    Same

    C

    3 times the original

    D

    of the original

    Reveal answer
18. 18

    NUST Engineering Past Paper-8

    If Earth's radius were reduced while its mass remained the same, determine the corresponding effect on the escape velocity from its surface.

    A

    Decrease

    B

    Remain the same

    C

    Increase

    D

    Double

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19. 19

    NUST Engineering Past Paper-8

    Describe the image always formed by a diverging (concave) lens of a real object placed in front of it.

    A

    Virtual, upright, and diminished

    B

    Real, inverted, and diminished

    C

    Virtual, inverted, and magnified

    D

    Real, upright, and magnified

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20. 20

    NUST Engineering Past Paper-8

    Identify the physicist who first associated a wave nature with material particles (the matter-wave hypothesis).

    A

    Newton

    B

    Einstein

    C

    De Broglie

    D

    Planck

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21. 21

    NUST Engineering Past Paper-8

    Among the listed elements, identify which is a TRANSURANIUM element (atomic number greater than that of uranium, Z=92).

    A

    Cobalt

    B

    Boron

    C

    Hydrogen

    D

    Neptunium

    Reveal answer
22. 22

    NUST Engineering Past Paper-8

    Describe the image formed by the single converging lens used in a simple microscope (a magnifying glass) when the object is placed within the focal length.

    A

    Virtual and diminished

    B

    Real, inverted, and magnified

    C

    Virtual, upright, and magnified

    D

    Virtual and inverted

    Reveal answer
23. 23

    NUST Engineering Past Paper-8

    State the principal factor that determines the intensity of Fresnel diffraction at an observation point behind an aperture.

    A

    The square of the sum of half-period zones

    B

    The number of half-period zones that superpose at the point

    C

    The focal length of the lens used

    D

    The thickness of the obstacle

    Reveal answer
24. 24

    NUST Engineering Past Paper-8

    Identify the physical phenomenon by which voices and sounds can be heard around the edges of obstacles or through open windows even when the source is not directly visible.

    A

    Refraction

    B

    Interference

    C

    Reflection

    D

    Diffraction

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25. 25

    NUST Engineering Past Paper-8

    A circular current loop has its conventional current flowing in the ANTICLOCKWISE direction as viewed by an observer facing it. Identify the direction of the magnetic field at the centre of the loop relative to the observer.

    A

    To the left

    B

    To the right

    C

    Out of the page

    D

    Into the page

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26. 26

    NUST Engineering Past Paper-8

    Describe the acceleration of a particle moving in a circle at constant speed (uniform circular motion).

    A

    Increasing

    B

    Zero

    C

    Constant in magnitude but changing in direction

    D

    Constant in direction but changing in magnitude

    Reveal answer
27. 27

    NUST Engineering Past Paper-8

    Identify the phenomenon known as 'back EMF' in an electric motor.

    A

    Induced EMF due to load

    B

    Self induction

    C

    Resistance EMF

    D

    Mutual induction

    Reveal answer
28. 28

    NUST Engineering Past Paper-8

    When a light wave reflects off the boundary going from an optically rarer medium into a denser medium, identify the phase change that occurs upon reflection.

    A

    Undergoes a 180° phase change

    B

    Undergoes a 270° phase change

    C

    Undergoes a 90° phase change

    D

    Suffers no phase change

    Reveal answer
29. 29

    NUST Engineering Past Paper-8

    Two long parallel metallic wires carry electric currents in the SAME direction. Identify the magnetic force between them.

    A

    Repel each other

    B

    Attract each other

    C

    Remain stationary

    D

    Have no force between them

    Reveal answer
30. 30

    NUST Engineering Past Paper-8

    According to Bohr's model of the hydrogen atom, compare the energy of an electron in an inner orbit with that in an outer orbit.

    A

    Equal

    B

    Greater

    C

    Smaller

    D

    Infinite

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31. 31

    NUST Engineering Past Paper-8

    Determine the approximate escape velocity from the surface of Jupiter.

    A

    B

    C

    D

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32. 32

    NUST Engineering Past Paper-8

    Classify simple harmonic motion (SHM) among the major categories of motion.

    A

    Circular motion

    B

    Oscillatory motion

    C

    Rectilinear motion

    D

    Rotational motion

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33. 33

    NUST Engineering Past Paper-8

    Identify the quantum-optical process by which laser light is produced.

    A

    Stimulated emission

    B

    Reflection

    C

    Absorption

    D

    Spontaneous emission

    Reveal answer
34. 34

    NUST Engineering Past Paper-8

    Classify motion fundamentally — is it absolute or always relative to a reference frame?

    A

    Variable

    B

    Relative

    C

    Absolute

    D

    Uniform

    Reveal answer
35. 35

    NUST Engineering Past Paper-8

    Identify the type of charge present in the depletion region of a PN junction in equilibrium.

    A

    Positive ions

    B

    Negative ions

    C

    Both positive and negative ions

    D

    No charge

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36. 36

    NUST Engineering Past Paper-8

    A wheel starts from rest and reaches an angular velocity of in . Determine its (constant) angular acceleration.

    A

    B

    C

    D

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37. 37

    NUST Engineering Past Paper-8

    A stretched string of length has tension and linear mass density . Determine the frequency of its second harmonic.

    A

    B

    C

    D

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38. 38

    NUST Engineering Past Paper-8

    An electron and a proton are projected with the same velocity perpendicular to a uniform magnetic field. Identify which suffers the greater deflection (smaller radius of curvature).

    A

    Electron

    B

    Both will suffer equal deflection

    C

    None

    D

    Proton

    Reveal answer
39. 39

    NUST Engineering Past Paper-8

    Identify the property of an object that acts as the source of its gravitational pull.

    A

    Charge

    B

    Spin

    C

    All of the above

    D

    Matter

    Reveal answer
40. 40

    NUST Engineering Past Paper-8

    Two forces each of magnitude act on a point. If the magnitude of their resultant is also , determine the angle between them.

    A

    B

    C

    D

    Reveal answer
41. 41

    NUST Engineering Past Paper-8

    Two water pipes connected to the same supply have inner diameters and . By the continuity equation, compare the flow speeds.

    A

    times the speed in the wider pipe

    B

    times

    C

    Twice the wider-pipe speed

    D

    Half the wider-pipe speed

    Reveal answer
42. 42

    NUST Engineering Past Paper-8

    State the condition (in terms of path difference) for constructive interference of two coherent light waves of wavelength .

    A

    B

    C

    D

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43. 43

    NUST Engineering Past Paper-8

    A parallel-plate capacitor has its plate separation TRIPLED and its plate area reduced to ONE-THIRD. Determine the corresponding change in its capacitance.

    A

    Decreased to

    B

    Increased times

    C

    Doubled

    D

    Remains the same

    Reveal answer
44. 44

    NUST Engineering Past Paper-8

    Identify the fundamental physical principle on which a transformer operates.

    A

    Ohm's Law

    B

    Ampere's Law

    C

    Lenz's Law

    D

    Faraday's Law of Electromagnetic Induction

    Reveal answer
45. 45

    NUST Engineering Past Paper-8

    Identify the standard physical mechanism used to produce X-rays in medical imaging tubes.

    A

    Nuclear fission

    B

    Stimulated emission

    C

    Bombarding a metal target with high-energy electrons

    D

    Radioactive decay

    Reveal answer
46. 46

    NUST Engineering Past Paper-8

    In the radioactive decay chain , determine how many and particles are emitted in total.

    A

    6 electrons and 8 protons

    B

    and

    C

    4 protons and 8 neutrons

    D

    and

    Reveal answer
47. 47

    NUST Engineering Past Paper-8

    Identify the elastic property defined as the ratio of volumetric strain to volumetric stress.

    A

    Shear modulus

    B

    Compressibility

    C

    Young's modulus

    D

    Bulk modulus

    Reveal answer
48. 48

    NUST Engineering Past Paper-8

    Once the Space Shuttle is in free-fall orbit around Earth, determine the force exerted by the seat on an astronaut sitting in it.

    A

    Zero

    B

    C

    D

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49. 49

    NUST Engineering Past Paper-8

    Determine the minimum distance to a reflecting surface required to hear a CLEAR echo (using the standard physiology threshold of separation between original and reflected sound).

    A

    66 m

    B

    10 m

    C

    16.5 m

    D

    33 m

    Reveal answer
50. 50

    NUST Engineering Past Paper-8

    Identify the room characteristic that improves audibility (reduced echo / good speech clarity).

    A

    Room with curtains

    B

    Tunnel

    C

    Straight wall

    D

    Curved wall

    Reveal answer
51. 51

    NUST Engineering Past Paper-8

    State the frequency of a seconds pendulum (a pendulum whose period equals seconds).

    A

    0.5 Hz

    B

    None

    C

    1 Hz

    D

    2 Hz

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52. 52

    NUST Engineering Past Paper-8

    Identify the thermodynamically correct statement among the listed options.

    A

    Entropy of a system always increases

    B

    Heat can flow from cold to hot spontaneously

    C

    Energy can be created

    D

    All energy becomes work

    Reveal answer
53. 53

    NUST Engineering Past Paper-8

    Identify the kind of material that undergoes significant plastic deformation before breaking under tensile stress.

    A

    Plastic substance

    B

    Brittle substance

    C

    All of these

    D

    Ductile substance

    Reveal answer
54. 54

    NUST Engineering Past Paper-8

    A photon of energy interacts with matter. Identify which photon-matter interaction process is most likely to dominate at this energy.

    A

    Compton effect

    B

    Photoelectric effect

    C

    None of these

    D

    Pair production

    Reveal answer
55. 55

    NUST Engineering Past Paper-8

    Determine the path difference (in terms of wavelength ) between two consecutive nodes in a standing wave on a string or in a pipe.

    A

    B

    C

    D

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56. 56

    NUST Engineering Past Paper-8

    Identify how a sustained nuclear-fission chain reaction is controlled inside a reactor.

    A

    Controlling the fissionable material

    B

    Controlling the number of neutrons

    C

    Controlling the number of electrons

    D

    Controlling the number of protons

    Reveal answer
57. 57

    NUST Engineering Past Paper-8

    A projectile is launched at angle such that its maximum height equals its horizontal range . Determine .

    A

    B

    C

    D

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58. 58

    NUST Engineering Past Paper-8

    A body is thrown vertically downward and its speed at the top of the trajectory is GREATER than its speed at the ground. Determine the sign of the acceleration (taking 'downward' as the negative direction).

    A

    Negative

    B

    Zero

    C

    Constant

    D

    Positive

    Reveal answer
59. 59

    NUST Engineering Past Paper-8

    A particle moves in a vertical circle. At the position where the string makes with the vertical, the tension is ; at , the tension is . Compare and .

    A

    None

    B

    C

    D

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60. 60

    NUST Engineering Past Paper-8

    Four resistors form a balanced Wheatstone bridge when . If and are interchanged and balance is restored with , determine the original value of .

    A

    B

    C

    D

    Reveal answer
61. 61

    NUST Engineering Past Paper-8

    A simple pendulum is suspended from the ceiling of a lift. If the lift is allowed to fall FREELY (i.e. in free fall), describe what happens to the pendulum's oscillation.

    A

    None of these

    B

    Acceleration becomes zero

    C

    Time period becomes zero

    D

    Vibration is stopped

    Reveal answer
62. 62

    NUST Engineering Past Paper-8

    A pipe of internal diameter feeds water into a second section that has outlet holes, each of diameter . If the water speed in the first pipe is , determine the speed of water emerging from each outlet hole.

    A

    B

    C

    D

    Reveal answer
63. 63

    NUST Engineering Past Paper-8

    Two charged bodies are connected by a conductor. State the condition under which NO current flows between them.

    A

    Density

    B

    Capacity

    C

    Potential

    D

    Charge

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64. 64

    NUST Engineering Past Paper-8

    Among the following physical quantities, identify the one whose SI units differ from the units of the other three.

    A

    Rate of change of momentum

    B

    Young's modulus Area

    C

    Weight

    D

    Density Volume Velocity

    Reveal answer
65. 65

    NUST Engineering Past Paper-8

    A simple harmonic oscillator has period and total energy . If the amplitude is TRIPLED, describe the corresponding changes in and .

    A

    Period unchanged, energy becomes

    B

    Period and energy both triple

    C

    Period unchanged, energy unchanged

    D

    Period triples, energy unchanged

    Reveal answer
66. 66

    NUST Engineering Past Paper-8

    Among the listed reactions, identify which releases the most energy per unit mass of fuel consumed.

    A

    Fission reaction

    B

    Thermal reaction

    C

    Chemical reaction

    D

    Fusion reaction

    Reveal answer
67. 67

    NUST Engineering Past Paper-8

    In an electron–positron PAIR ANNIHILATION event (at rest), identify the products that are produced.

    A

    A neutron and a proton

    B

    A neutrino only

    C

    An alpha particle

    D

    Two gamma ray photons ()

    Reveal answer
68. 68

    NUST Engineering Past Paper-8

    State the formula for the instantaneous POWER delivered by a force acting on an object moving with velocity .

    A

    B

    (i.e., )

    C

    D

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69. 69

    NUST Engineering Past Paper-8

    A simple pendulum has a time period of . Determine its new time period when its length is increased to TIMES the original length.

    A

    B

    C

    D

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70. 70

    NUST Engineering Past Paper-8

    If and , find .

    A

    B

    C

    D

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71. 71

    NUST Engineering Past Paper-8

    Two vectors are and . If , find .

    A

    B

    2

    C

    0

    D

    6

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72. 72

    NUST Engineering Past Paper-8

    Simplify .

    A

    B

    C

    D

    0

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73. 73

    NUST Engineering Past Paper-8

    Calculate the area of the triangle whose vertices are , , and .

    A

    0 sq. units

    B

    sq. units

    C

    7 sq. units

    D

    sq. units

    Reveal answer
74. 74

    NUST Engineering Past Paper-8

    Compute .

    A

    B

    2

    C

    D

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75. 75

    NUST Engineering Past Paper-8

    Identify the formula for the number of distinct diagonals in a convex -sided polygon.

    A

    B

    C

    D

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76. 76

    NUST Engineering Past Paper-8

    Given that , evaluate .

    A

    B

    C

    D

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77. 77

    NUST Engineering Past Paper-8

    Determine the coefficient of in the binomial expansion of .

    A

    B

    C

    D

    Does not exist

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78. 78

    NUST Engineering Past Paper-8

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

    A

    B

    None of these

    C

    D

    Reveal answer
79. 79

    NUST Engineering Past Paper-8

    Evaluate .

    A

    B

    C

    D

    Reveal answer
80. 80

    NUST Engineering Past Paper-8

    Determine the equation of the directrix of the parabola .

    A

    B

    C

    D

    Reveal answer
81. 81

    NUST Engineering Past Paper-8

    Identify the Maclaurin series expansion of (valid for ).

    A

    B

    C

    D

    Reveal answer
82. 82

    NUST Engineering Past Paper-8

    Differentiate with respect to .

    A

    B

    C

    D

    Reveal answer
83. 83

    NUST Engineering Past Paper-8

    Compute .

    A

    B

    C

    D

    Reveal answer
84. 84

    NUST Engineering Past Paper-8

    Given , compute .

    A

    None

    B

    C

    D

    Reveal answer
85. 85

    NUST Engineering Past Paper-8

    Compute the sum of the first terms of the arithmetic progression .

    A

    B

    C

    D

    Reveal answer
86. 86

    NUST Engineering Past Paper-8

    Two series are given: I: and II: . Identify which of them is convergent.

    A

    II only

    B

    Both

    C

    None

    D

    I only

    Reveal answer
87. 87

    NUST Engineering Past Paper-8

    Identify the Maclaurin series expansion of up to the cubic term.

    A

    B

    C

    D

    Reveal answer
88. 88

    NUST Engineering Past Paper-8

    Rewrite the equation in the standard ellipse form .

    A

    B

    C

    D

    Reveal answer
89. 89

    NUST Engineering Past Paper-8

    Determine the equation of the directrix of the parabola .

    A

    B

    C

    D

    Reveal answer
90. 90

    NUST Engineering Past Paper-8

    Pick the value that lies within the range of .

    A

    B

    C

    D

    Reveal answer
91. 91

    NUST Engineering Past Paper-8

    Determine the MAGNITUDE of the cross product when two non-zero vectors and are PERPENDICULAR to each other.

    A

    Maximum, equal to

    B

    The zero vector

    C

    Equal to their dot product

    D

    Always equal to

    Reveal answer
92. 92

    NUST Engineering Past Paper-8

    For the matrix , determine the determinant .

    A

    B

    C

    D

    Reveal answer
93. 93

    NUST Engineering Past Paper-8

    Given , determine the entry of .

    A

    B

    C

    D

    Reveal answer
94. 94

    NUST Engineering Past Paper-8

    Solve the upper-triangular linear system by back-substitution.

    A

    B

    C

    D

    Reveal answer
95. 95

    NUST Engineering Past Paper-8

    For the matrix , determine the cofactor .

    A

    B

    C

    D

    Reveal answer
96. 96

    NUST Engineering Past Paper-8

    Let be the roots of the quadratic . Determine .

    A

    B

    C

    D

    Reveal answer
97. 97

    NUST Engineering Past Paper-8

    Let be the roots of the quadratic (here and are constants). Express entirely in terms of .

    A

    B

    C

    D

    Reveal answer
98. 98

    NUST Engineering Past Paper-8

    The two roots of the quadratic DIFFER BY . Determine the relationship between and .

    A

    B

    C

    D

    Reveal answer
99. 99

    NUST Engineering Past Paper-8

    The polynomial leaves a remainder of when divided by . Determine the value of .

    A

    B

    C

    D

    Reveal answer
100. 100

     NUST Engineering Past Paper-8

     Given that is a root of the bi-quadratic , determine its COMPLETE solution set.

     A

     B

     C

     D

     Reveal answer
101. 101

     NUST Engineering Past Paper-8

     Determine the condition on the constants and so that the equation has two roots that are EQUAL IN MAGNITUDE but OPPOSITE IN SIGN.

     A

     B

     C

     D

     Reveal answer
102. 102

     NUST Engineering Past Paper-8

     In the partial-fraction decomposition , determine the value of by the COVER-UP method at .

     A

     B

     C

     D

     Reveal answer
103. 103

     NUST Engineering Past Paper-8

     Continuing the decomposition , with , determine the constant by comparing coefficients of .

     A

     B

     C

     D

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104. 104

     NUST Engineering Past Paper-8

     Carrying out the complete coefficient comparison in , identify the FINAL closed form of the decomposition.

     A

     B

     C

     D

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105. 105

     NUST Engineering Past Paper-8

     Determine the th term of the arithmetic progression .

     A

     B

     C

     D

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106. 106

     NUST Engineering Past Paper-8

     If form a geometric progression and also form a geometric progression (so the four numbers are in continued GP), describe the progression formed by .

     A

     in G.P.

     B

     in A.P.

     C

     in H.P.

     D

     have no special relationship

     Reveal answer
107. 107

     NUST Engineering Past Paper-8

     Determine the GEOMETRIC MEAN between the two numbers and .

     A

     B

     C

     D

     Reveal answer
108. 108

     NUST Engineering Past Paper-8

     The arithmetic mean of two positive numbers is and their geometric mean is . Determine the two numbers.

     A

     and

     B

     and

     C

     and

     D

     and

     Reveal answer
109. 109

     NUST Engineering Past Paper-8

     Determine the value of for which equals the GEOMETRIC MEAN of and (with , ).

     A

     B

     C

     D

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110. 110

     NUST Engineering Past Paper-8

     Determine the positive integer for which .

     A

     B

     C

     D

     Reveal answer
111. 111

     NUST Engineering Past Paper-8

     State a closed-form expression for the number of DIAGONALS of a convex polygon with sides, and use it to determine the number of diagonals in a -gon.

     A

     ; for

     B

     ; for

     C

     ; for

     D

     ; for

     Reveal answer
112. 112

     NUST Engineering Past Paper-8

     Determine the TERM INDEPENDENT OF in the binomial expansion of .

     A

     B

     C

     D

     Reveal answer
113. 113

     NUST Engineering Past Paper-8

     Determine the middle term in the binomial expansion of .

     A

     B

     C

     D

     Reveal answer
114. 114

     NUST Engineering Past Paper-8

     Determine the SMALLEST integer such that the identity is valid (by extended induction).

     A

     B

     C

     D

     Reveal answer
115. 115

     NUST Engineering Past Paper-8

     Determine the SMALLEST positive integer for which the inequality first becomes TRUE (and remains true for all larger ).

     A

     B

     C

     D

     Reveal answer
116. 116

     NUST Engineering Past Paper-8

     Identify the trigonometric identity that DIRECTLY proves .

     A

     formula

     B

     formula

     C

     formula

     D

     formula

     Reveal answer
117. 117

     NUST Engineering Past Paper-8

     Given (with in the third quadrant) and (with in the second quadrant), determine .

     A

     B

     C

     D

     Reveal answer
118. 118

     NUST Engineering Past Paper-8

     Determine the EXACT (simplified surd) value of .

     A

     B

     C

     D

     Reveal answer
119. 119

     NUST Engineering Past Paper-8

     Determine the fundamental period of .

     A

     B

     C

     D

     Reveal answer
120. 120

     NUST Engineering Past Paper-8

     Determine the fundamental period of .

     A

     B

     C

     D

     Reveal answer
121. 121

     NUST Engineering Past Paper-8

     State the (open) interval on which the derivative is DEFINED.

     A

     B

     C

     D

     Reveal answer
122. 122

     NUST Engineering Past Paper-8

     State the derivative formula for .

     A

     B

     C

     D

     Reveal answer
123. 123

     NUST Engineering Past Paper-8

     State the derivative formula for .

     A

     ,

     B

     C

     D

     Reveal answer
124. 124

     NUST Engineering Past Paper-8

     State the derivative formula for .

     A

     B

     C

     D

     Reveal answer
125. 125

     NUST Engineering Past Paper-8

     Determine, from first principles, the derivative for a positive integer and constants .

     A

     B

     C

     D

     Reveal answer
126. 126

     NUST Engineering Past Paper-8

     State the Maclaurin (power-series) expansion of , valid for .

     A

     B

     C

     D

     Reveal answer
127. 127

     NUST Engineering Past Paper-8

     State the Maclaurin (power-series) expansion of , valid for .

     A

     B

     C

     D

     Reveal answer
128. 128

     NUST Engineering Past Paper-8

     Determine the general solution of the ordinary differential equation .

     A

     B

     C

     D

     Reveal answer
129. 129

     NUST Engineering Past Paper-8

     Determine the general solution of the ordinary differential equation for and .

     A

     B

     C

     D

     Reveal answer
130. 130

     NUST Engineering Past Paper-8

     Evaluate the indefinite integral , using the factorisation .

     A

     B

     C

     D

     Reveal answer
131. 131

     NUST Engineering Past Paper-8

     Evaluate the indefinite integral (assuming the radicand is non-negative and on the interval of interest).

     A

     B

     C

     D

     Reveal answer
132. 132

     NUST Engineering Past Paper-8

     Evaluate the indefinite integral for .

     A

     B

     C

     D

     Reveal answer
133. 133

     NUST Engineering Past Paper-8

     Evaluate the indefinite integral on an interval where (so the denominator is non-zero).

     A

     B

     C

     D

     Reveal answer
134. 134

     NUST Engineering Past Paper-8

     Evaluate the indefinite integral .

     A

     B

     C

     D

     Reveal answer
135. 135

     NUST Engineering Past Paper-8

     Evaluate the indefinite integral .

     A

     B

     C

     D

     Reveal answer
136. 136

     NUST Engineering Past Paper-8

     Evaluate the indefinite integral .

     A

     B

     C

     D

     Reveal answer
137. 137

     NUST Engineering Past Paper-8

     Evaluate the indefinite integral for and .

     A

     B

     C

     D

     Reveal answer
138. 138

     NUST Engineering Past Paper-8

     Determine whether the three lines , , are CONCURRENT (i.e., pass through a single common point).

     A

     Concurrent

     B

     Not concurrent

     C

     Parallel to each other

     D

     Two of them coincide

     Reveal answer
139. 139

     NUST Engineering Past Paper-8

     Determine the JOINT equation of the pair of tangent lines drawn from the external point to the circle .

     A

     B

     C

     D

     Reveal answer
140. 140

     NUST Engineering Past Paper-8

     For the general second-degree curve (written as ), determine the value of and identify the conic.

     A

     (ellipse)

     B

     (hyperbola)

     C

     (parabola)

     D

     (ellipse)

     Reveal answer
141. 141

     NUST Engineering Past Paper-8

     Determine the angle (with ) of axes-rotation that ELIMINATES the -term in the conic . Provide .

     A

     B

     C

     D

     Reveal answer
142. 142

     NUST Engineering Past Paper-8

     Determine the AREA of the triangle whose vertices are , and .

     A

     B

     C

     D

     Reveal answer
143. 143

     NUST Engineering Past Paper-8

     If , determine the UNIT vector perpendicular to the plane of triangle (in the same direction as the cross product).

     A

     B

     C

     D

     Reveal answer
144. 144

     NUST Engineering Past Paper-8

     If the roots of are , evaluate in the SPECIAL CASE .

     A

     B

     C

     D

     Reveal answer
145. 145

     NUST Engineering Past Paper-8

     State the standard formula for the LENGTH of the tangent drawn from an external point to the circle .

     A

     B

     C

     D

     Reveal answer
146. 146

     NUST Engineering Past Paper-8

     Evaluate the sum of the infinite geometric series .

     A

     B

     C

     D

     Reveal answer
147. 147

     NUST Engineering Past Paper-8

     Let be the roots of . Determine the QUADRATIC equation whose roots are and .

     A

     B

     C

     D

     Reveal answer
148. 148

     NUST Engineering Past Paper-8

     State a closed-form expression for the sum of ODD-INDEXED binomial coefficients (for a positive integer ).

     A

     B

     C

     D

     Reveal answer
149. 149

     NUST Engineering Past Paper-8

     Determine the polynomial QUOTIENT (whole-number part) obtained by performing the polynomial division required before decomposing into partial fractions.

     A

     B

     C

     D

     Reveal answer
150. 150

     NUST Engineering Past Paper-8

     Given with in QUADRANT I, evaluate .

     A

     B

     C

     D

     Reveal answer
151. 151

     NUST Engineering Past Paper-8

     Find two positive numbers and whose sum is such that is MAXIMUM, and state the two numbers.

     A

     and

     B

     and

     C

     and

     D

     and

     Reveal answer
152. 152

     NUST Engineering Past Paper-8

     A square-based open box has base side and height , with the constraint . Determine the value of that MAXIMISES the volume .

     A

     B

     C

     D

     Reveal answer
153. 153

     NUST Engineering Past Paper-8

     Evaluate the indefinite integral by first rationalising the denominator (assume ).

     A

     B

     C

     D

     Reveal answer
154. 154

     NUST Engineering Past Paper-8

     Given with (Q2), determine .

     A

     B

     C

     D

     Reveal answer
155. 155

     NUST Engineering Past Paper-8

     Determine the LINES of SYMMETRY of the ellipse .

     A

     and

     B

     and

     C

     Only the -axis

     D

     Origin only

     Reveal answer
156. 156

     NUST Engineering Past Paper-8

     The colour 'Azure' refers to which of the following shades?

     A

     Sky blue

     B

     Deep green

     C

     Dark grey

     D

     Pale yellow

     Reveal answer
157. 157

     NUST Engineering Past Paper-8

     Pick the option that best defines 'Precarious':

     A

     Wealthy and prosperous

     B

     Stable and secure

     C

     Dangerous and uncertain

     D

     Calm and peaceful

     Reveal answer
158. 158

     NUST Engineering Past Paper-8

     Which of the following pairs best matches the relationship 'Rain : Drenched'?

     A

     Snow : Frozen

     B

     Wind : Dusty

     C

     Sun : Cold

     D

     Fire : Warm

     Reveal answer
159. 159

     NUST Engineering Past Paper-8

     Which of the following spells the adverb form of 'fierce' correctly?

     A

     Feircely

     B

     Fiercely

     C

     Fiersely

     D

     Fiercly

     Reveal answer
160. 160

     NUST Engineering Past Paper-8

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

     A

     A formal greeting upon arrival

     B

     A word of gratitude

     C

     A farewell expression

     D

     An expression of surprise

     Reveal answer
161. 161

     NUST Engineering Past Paper-8

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

     A

     Realistic

     B

     Optimistic

     C

     Ambitious

     D

     Visionary

     Reveal answer
162. 162

     NUST Engineering Past Paper-8

     Complete the analogy: Trigger : Pistol :: ____ : ____

     A

     Engine : Car

     B

     None of the above

     C

     Rifle : Revolver

     D

     Fire : Wood

     Reveal answer
163. 163

     NUST Engineering Past Paper-8

     Pick the option that best defines 'Abate':

     A

     To argue persistently

     B

     To celebrate loudly

     C

     To reduce or lessen in intensity

     D

     To increase in intensity

     Reveal answer
164. 164

     NUST Engineering Past Paper-8

     Pick the option that best defines 'Agog':

     A

     Deeply saddened

     B

     Thoroughly exhausted

     C

     Completely indifferent

     D

     Very eager or excited

     Reveal answer
165. 165

     NUST Engineering Past Paper-8

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

     A

     Enmity

     B

     Rivalry

     C

     Conflict

     D

     Harmony

     Reveal answer
166. 166

     NUST Engineering Past Paper-8

     Pick the option that best defines 'Base' (used as an adjective):

     A

     Highly educated and refined

     B

     Without moral principles; ignoble

     C

     Noble and honorable

     D

     Physically strong

     Reveal answer
167. 167

     NUST Engineering Past Paper-8

     Pick the word most nearly OPPOSITE in meaning to 'Base' (ignoble):

     A

     Noble

     B

     Vile

     C

     Sordid

     D

     Wretched

     Reveal answer
168. 168

     NUST Engineering Past Paper-8

     Pick the option that best defines 'Bashful':

     A

     Cheerful and outgoing

     B

     Reluctant to draw attention to oneself; shy

     C

     Overly aggressive in behavior

     D

     Arrogant and boastful

     Reveal answer
169. 169

     NUST Engineering Past Paper-8

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

     A

     Coy

     B

     Diffident

     C

     Meek

     D

     Audacious

     Reveal answer
170. 170

     NUST Engineering Past Paper-8

     Pick the option that best defines 'Bewildering':

     A

     Extremely simple and straightforward

     B

     Causing one to become confused or puzzled

     C

     Bringing calm and clarity

     D

     Making something more organized

     Reveal answer
171. 171

     NUST Engineering Past Paper-8

     Pick the option that best defines 'Bona fide':

     A

     Legally prohibited

     B

     Genuine and real; in good faith

     C

     Temporarily valid

     D

     Doubtful and suspicious

     Reveal answer
172. 172

     NUST Engineering Past Paper-8

     Pick the option that best defines 'Docile':

     A

     Overly intelligent and opinionated

     B

     Constantly restless and active

     C

     Aggressive and difficult to manage

     D

     Ready to accept control; submissive

     Reveal answer
173. 173

     NUST Engineering Past Paper-8

     Pick the word closest in meaning to 'Gambol':

     A

     Plod

     B

     Frolic

     C

     Trudge

     D

     Stumble

     Reveal answer
174. 174

     NUST Engineering Past Paper-8

     Pick the word closest in meaning to 'Idealistic':

     A

     Cynical

     B

     Visionary

     C

     Pessimistic

     D

     Pragmatic

     Reveal answer
175. 175

     NUST Engineering Past Paper-8

     Pick the word closest in meaning to 'Immature':

     A

     Childish

     B

     Responsible

     C

     Mature

     D

     Sophisticated

     Reveal answer
176. 176

     NUST Engineering Past Paper-8

     Pick the word closest in meaning to 'Kindle':

     A

     Ignite

     B

     Suppress

     C

     Dampen

     D

     Extinguish

     Reveal answer
177. 177

     NUST Engineering Past Paper-8

     Pick the word closest in meaning to 'Temerity':

     A

     Prudence

     B

     Audacity

     C

     Timidity

     D

     Caution

     Reveal answer
178. 178

     NUST Engineering Past Paper-8

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

     A

     Empathetic

     B

     Callous

     C

     Responsive

     D

     Tender

     Reveal answer
179. 179

     NUST Engineering Past Paper-8

     Pick the word closest in meaning to 'Prevailing':

     A

     Marginal

     B

     Rare

     C

     Uncommon

     D

     Dominant

     Reveal answer
180. 180

     NUST Engineering Past Paper-8

     Pick the word closest in meaning to 'Fear':

     A

     Bravery

     B

     Courage

     C

     Confidence

     D

     Dread

     Reveal answer
181. 181

     NUST Engineering Past Paper-8

     Choose the pair of words that completes the analogy: 'Ambiguous : Clear :: ___ : ___'.

     A

     Definite : Indefinite

     B

     Simple : Complex

     C

     None of these

     D

     Singular : Plural

     Reveal answer
182. 182

     NUST Engineering Past Paper-8

     Pick the option that best defines 'hideous':

     A

     Extremely ugly or repulsive

     B

     Frightening but attractive

     C

     Secretive or hidden

     D

     Extremely beautiful

     Reveal answer
183. 183

     NUST Engineering Past Paper-8

     Identify the meaning of the idiom 'A bull in a china shop.'

     A

     A person who is very enthusiastic

     B

     A person who becomes too excited unnecessarily

     C

     A person who is very careful with fragile things

     D

     One who is aggressive and clumsy in a situation requiring delicacy

     Reveal answer
184. 184

     NUST Engineering Past Paper-8

     Identify the meaning of the phrase 'On tenterhooks.'

     A

     In seething anger

     B

     In a state of suspense or agitation

     C

     In excited wait

     D

     On constant move

     Reveal answer
185. 185

     NUST Engineering Past Paper-8

     Pick the adverb that best completes: 'The miser gazed ___ at the pile of gold coins.'

     A

     admiringly

     B

     thoughtfully

     C

     earnestly

     D

     avidly

     Reveal answer
186. 186

     NUST Engineering Past Paper-8

     Pick the verb that best completes: 'If you smuggle goods into the country, they may be ___ by customs authority.'

     A

     punished

     B

     confiscated

     C

     retained

     D

     possessed

     Reveal answer
187. 187

     NUST Engineering Past Paper-8

     Pick the adjective phrase that completes: 'Reconstructing the skeletons of extinct species like dinosaurs is ___ process that requires much patience.'

     A

     an easy

     B

     a simple

     C

     a boring

     D

     an exacting

     Reveal answer
188. 188

     NUST Engineering Past Paper-8

     Pick the pair of verbs that best completes: 'The employees ___ Jill because she constantly ___ them.'

     A

     cherished, decided

     B

     disregarded, eulogized

     C

     deified, goaded

     D

     loathed, berated

     Reveal answer
189. 189

     NUST Engineering Past Paper-8

     Pick the adjective that best completes: 'Views on the bonus issue are ___, with some thinking it good and others opposing it.'

     A

     modest

     B

     divergent

     C

     adverse

     D

     independent

     Reveal answer
190. 190

     NUST Engineering Past Paper-8

     Pick the corrected phrase for: 'The man to who I sold my house was a cheat.'

     A

     to who I sell

     B

     to whom I sell

     C

     who was sold to

     D

     to whom I sold

     Reveal answer
191. 191

     NUST Engineering Past Paper-8

     Pick the synonym of the noun HIATUS.

     A

     Gap

     B

     Tight

     C

     Narrow

     D

     Contempt

     Reveal answer
192. 192

     NUST Engineering Past Paper-8

     Pick the participial phrase that completes: '___ found the purse, he returned it to the owner.'

     A

     Founded

     B

     Find

     C

     Found

     D

     Having found

     Reveal answer
193. 193

     NUST Engineering Past Paper-8

     Identify the tense used in: 'She will have been writing the report for two hours by 5 PM.'

     A

     Future Continuous

     B

     Future Perfect Continuous

     C

     Future Perfect

     D

     Present Perfect Continuous

     Reveal answer
194. 194

     NUST Engineering Past Paper-8

     Pick the verb pair that completes: 'People ___ recycle; otherwise they will waste natural resources.'

     A

     aren't recycling / wasted

     B

     don't recycle / are wasting

     C

     haven't been recycling / were wasting

     D

     didn't recycle / waste

     Reveal answer
195. 195

     NUST Engineering Past Paper-8

     Pick the correct articles to fill the blanks: 'On that foggy day, ___ fog was so thick on ___ left side of ___ road.'

     A

     no article, the, a

     B

     a, the, a

     C

     the, no article, no article

     D

     the, the, the

     Reveal answer
196. 196

     NUST Engineering Past Paper-8

     Convert to passive voice: 'He is playing in the field.' Pick the correct passive sentence.

     A

     The field has been played in by him.

     B

     The field is played in by him.

     C

     The field is being played in by him.

     D

     The field was played in by him.

     Reveal answer
197. 197

     NUST Engineering Past Paper-8

     Convert to indirect speech: She said to me, 'Will you help me?'

     A

     She asked me that I would help her.

     B

     She said to me if I will help her.

     C

     She asked me whether I would help her.

     D

     She told me whether I would help her.

     Reveal answer
198. 198

     NUST Engineering Past Paper-8

     Choose the option that best gives the meaning of the verb 'ABRIDGE'.

     A

     To destroy or demolish completely

     B

     To translate into another language

     C

     To expand or elaborate in detail

     D

     To shorten a text by condensing it without losing the core meaning

     Reveal answer
199. 199

     NUST Engineering Past Paper-8

     Identify the CORRECTLY spelt noun meaning 'a practice or trial performance' (typically of a play, concert, etc.).

     A

     Rehersall

     B

     Rehersal

     C

     Rehursal

     D

     Rehearsal

     Reveal answer