NUST Engineering Past Paper-5

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

1. 1

   NUST Engineering Past Paper-5

   What is the dimensional formula for energy?

   A

   B

   C

   D

   Reveal answer
2. 2

   NUST Engineering Past Paper-5

   Which type of electromagnetic radiation is most commonly used in the technique of crystallography to study atomic-scale crystal structures?

   A

   Gamma rays

   B

   X-rays

   C

   Infrared rays

   D

   UV rays

   Reveal answer
3. 3

   NUST Engineering Past Paper-5

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

   A

   Scalar quantity of scalar field

   B

   Vector quantity of scalar field

   C

   Vector quantity of vector field

   D

   Scalar quantity of vector field

   Reveal answer
4. 4

   NUST Engineering Past Paper-5

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

   A

   Capacitance

   B

   Charge

   C

   Resistance

   D

   Inductance

   Reveal answer
5. 5

   NUST Engineering Past Paper-5

   A hanging mass of kg produces a deflection of cm in a vertical spring. Determine the spring constant. (Take m/s.)

   A

   N/m

   B

   N/m

   C

   N/m

   D

   N/m

   Reveal answer
6. 6

   NUST Engineering Past Paper-5

   Determine the dimensional formula for the universal gravitational constant .

   A

   B

   C

   D

   Reveal answer
7. 7

   NUST Engineering Past Paper-5

   Identify which pair(s) of physical quantities share the SAME dimensional formula. (A) Angular velocity and frequency; (B) Torque and work.

   A

   Both A and B

   B

   Angular velocity and Frequency

   C

   Neither A nor B

   D

   Torque and Work

   Reveal answer
8. 8

   NUST Engineering Past Paper-5

   Determine the unit vector in the direction of .

   A

   B

   C

   D

   Reveal answer
9. 9

   NUST Engineering Past Paper-5

   A vector of magnitude makes an angle of with the positive -axis. Determine its -component.

   A

   B

   C

   D

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10. 10

    NUST Engineering Past Paper-5

    A car travels km in the first hour and km in the next hour. Determine its average speed for the entire journey.

    A

    52 km/h

    B

    45 km/h

    C

    48 km/h

    D

    50 km/h

    Reveal answer
11. 11

    NUST Engineering Past Paper-5

    A stone is thrown HORIZONTALLY with speed m/s from the top of a m cliff. Taking m/s, determine the time to reach the ground.

    A

    s

    B

    1 s

    C

    2 s

    D

    4 s

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12. 12

    NUST Engineering Past Paper-5

    A kg body on a FRICTIONLESS surface is pushed with a horizontal force of N. Starting from rest, determine the distance travelled in s.

    A

    27 m

    B

    13.5 m

    C

    9 m

    D

    40.5 m

    Reveal answer
13. 13

    NUST Engineering Past Paper-5

    Determine the coefficient of restitution for a PERFECTLY ELASTIC collision.

    A

    Greater than 1

    B

    Between 0 and 1

    C

    1

    D

    0

    Reveal answer
14. 14

    NUST Engineering Past Paper-5

    Identify the formula for the instantaneous power delivered by a constant force to a body moving with velocity .

    A

    B

    C

    D

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15. 15

    NUST Engineering Past Paper-5

    A body of mass kg falls from rest through a height of m. Taking m/s, determine the work done by gravity.

    A

    50 J

    B

    200 J

    C

    400 J

    D

    100 J

    Reveal answer
16. 16

    NUST Engineering Past Paper-5

    Determine the moment of inertia of a uniform DISC of mass and radius about its central axis (perpendicular to the disc plane).

    A

    B

    C

    D

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17. 17

    NUST Engineering Past Paper-5

    A net external torque of N·m acts on a rigid body of moment of inertia kg·m. Determine the angular acceleration.

    A

    80 rad/s²

    B

    10 rad/s²

    C

    5 rad/s²

    D

    0.2 rad/s²

    Reveal answer
18. 18

    NUST Engineering Past Paper-5

    At approximately what HEIGHT above the Earth's surface do geostationary satellites orbit?

    A

    1,000 km

    B

    6,400 km

    C

    36,000 km

    D

    400 km

    Reveal answer
19. 19

    NUST Engineering Past Paper-5

    Identify the fundamental conservation principle that Bernoulli's equation expresses for steady, incompressible, non-viscous fluid flow along a streamline.

    A

    Angular momentum

    B

    Energy

    C

    Mass

    D

    Momentum

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20. 20

    NUST Engineering Past Paper-5

    An incompressible fluid flows through a pipe whose cross-sectional area changes from cm to cm. If the speed in the wider section is m/s, determine the speed in the narrower section.

    A

    12 m/s

    B

    0.75 m/s

    C

    6 m/s

    D

    3 m/s

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21. 21

    NUST Engineering Past Paper-5

    A simple pendulum has period on Earth. On a planet where the surface gravity is TIMES Earth's, determine the new period.

    A

    B

    C

    D

    Reveal answer
22. 22

    NUST Engineering Past Paper-5

    In SHM, at which position is the velocity of the oscillator MAXIMUM?

    A

    Between mean and extreme

    B

    Any position

    C

    Extreme position

    D

    Mean position

    Reveal answer
23. 23

    NUST Engineering Past Paper-5

    Two speakers emit sound of the same frequency in phase. At a point EQUIDISTANT from both speakers, identify the type of interference.

    A

    Partial

    B

    Constructive

    C

    Destructive

    D

    No interference

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24. 24

    NUST Engineering Past Paper-5

    Determine the temperature at which the Celsius and Fahrenheit scales give the SAME numerical reading.

    A

    −273°

    B

    100°

    C

    −40°

    D

    0°

    Reveal answer
25. 25

    NUST Engineering Past Paper-5

    An ideal gas undergoes ADIABATIC expansion. Describe the change in its temperature.

    A

    Depends on the gas type

    B

    Increases

    C

    Stays the same

    D

    Decreases

    Reveal answer
26. 26

    NUST Engineering Past Paper-5

    An electric dipole is placed in a UNIFORM electric field. Identify what the dipole experiences.

    A

    Net force only

    B

    Torque only

    C

    Neither force nor torque

    D

    Net force and torque

    Reveal answer
27. 27

    NUST Engineering Past Paper-5

    Determine the total resistance when three resistors of each are connected in PARALLEL.

    A

    3 Ω

    B

    6 Ω

    C

    18 Ω

    D

    2 Ω

    Reveal answer
28. 28

    NUST Engineering Past Paper-5

    A current of A flows through a resistor for seconds. Determine the heat generated.

    A

    160 J

    B

    40 J

    C

    20 J

    D

    80 J

    Reveal answer
29. 29

    NUST Engineering Past Paper-5

    Under what condition is the magnetic force on a moving charged particle in a magnetic field ZERO?

    A

    The charge moves fast

    B

    The field is very strong

    C

    Velocity is parallel to the field

    D

    The charge is large

    Reveal answer
30. 30

    NUST Engineering Past Paper-5

    Lenz's law (the directional content of Faraday's induction law) is fundamentally a consequence of which principle?

    A

    Newton's third law

    B

    Gauss's law

    C

    Ampere's law

    D

    Conservation of energy

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31. 31

    NUST Engineering Past Paper-5

    In a pure capacitive AC circuit (capacitor only), describe the phase relationship between the current and the voltage.

    A

    Lags the voltage by 90°

    B

    Lags the voltage by 45°

    C

    Is in phase with voltage

    D

    Leads the voltage by 90°

    Reveal answer
32. 32

    NUST Engineering Past Paper-5

    In Young's double-slit experiment with fringe width , if the wavelength is INCREASED by (with and unchanged), how does the fringe width change?

    A

    Doubles

    B

    Halves

    C

    Decreases by 10%

    D

    Increases by 10%

    Reveal answer
33. 33

    NUST Engineering Past Paper-5

    Describe the image always formed by a CONVEX mirror of a real object.

    A

    Real and magnified

    B

    Virtual and magnified

    C

    Real and diminished

    D

    Virtual and diminished

    Reveal answer
34. 34

    NUST Engineering Past Paper-5

    The activity of a radioactive sample drops from counts/s to counts/s in days. Determine the half-life.

    A

    4.5 days

    B

    1 day

    C

    9 days

    D

    3 days

    Reveal answer
35. 35

    NUST Engineering Past Paper-5

    In which type of radioactive decay does the atomic number decrease by and the mass number decrease by ?

    A

    Electron capture

    B

    Gamma decay

    C

    Alpha decay

    D

    Beta minus decay

    Reveal answer
36. 36

    NUST Engineering Past Paper-5

    If the kinetic energy of a non-relativistic particle is DOUBLED, how does its de Broglie wavelength change?

    A

    Decreases by a factor of

    B

    Doubles

    C

    Increases by a factor of

    D

    Halves

    Reveal answer
37. 37

    NUST Engineering Past Paper-5

    In an n-type semiconductor, what are the majority charge carriers?

    A

    Electrons

    B

    Holes

    C

    Ions

    D

    Protons

    Reveal answer
38. 38

    NUST Engineering Past Paper-5

    Describe the effective resistance of a p-n junction diode under FORWARD bias.

    A

    Infinite resistance

    B

    Zero resistance

    C

    High resistance

    D

    Low resistance

    Reveal answer
39. 39

    NUST Engineering Past Paper-5

    Identify the physical quantity that is conserved in ALL types of collisions (elastic AND inelastic).

    A

    Velocity

    B

    Linear momentum

    C

    Temperature

    D

    Kinetic energy

    Reveal answer
40. 40

    NUST Engineering Past Paper-5

    A ball of mass moving at speed collides ELASTICALLY (head-on) with a wall. Determine the magnitude of its change in momentum.

    A

    B

    C

    0

    D

    Reveal answer
41. 41

    NUST Engineering Past Paper-5

    Determine the gravitational field strength at a point INSIDE a hollow, uniform spherical SHELL.

    A

    Equal to (surface value)

    B

    Zero

    C

    Maximum at center

    D

    Reveal answer
42. 42

    NUST Engineering Past Paper-5

    Identify the value of for an ideal DIATOMIC gas.

    A

    5/3

    B

    4/3

    C

    7/5

    D

    1

    Reveal answer
43. 43

    NUST Engineering Past Paper-5

    In the photoelectric effect, identify the property of the incident light on which the STOPPING POTENTIAL depends.

    A

    Distance from the light source

    B

    Intensity of incident light

    C

    Frequency of incident light

    D

    Area of the metal surface

    Reveal answer
44. 44

    NUST Engineering Past Paper-5

    Identify the energy of a photon in terms of its frequency .

    A

    B

    C

    D

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45. 45

    NUST Engineering Past Paper-5

    The magnetic flux through a flat surface in a uniform magnetic field is MAXIMUM under what orientation condition?

    A

    The field is anti-parallel to the area vector

    B

    The surface is at 45° to the field

    C

    The surface is perpendicular to the field

    D

    The surface is parallel to the field

    Reveal answer
46. 46

    NUST Engineering Past Paper-5

    Among the listed electromagnetic radiations, identify the one with the LONGEST wavelength.

    A

    Radio waves

    B

    Infrared

    C

    Ultraviolet

    D

    X-rays

    Reveal answer
47. 47

    NUST Engineering Past Paper-5

    Identify the capacitance of a parallel-plate capacitor whose plates are separated by a dielectric of relative permittivity , compared to the vacuum capacitance .

    A

    B

    C

    D

    Reveal answer
48. 48

    NUST Engineering Past Paper-5

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

    A

    8 Ω

    B

    2 Ω

    C

    4 Ω

    D

    16 Ω

    Reveal answer
49. 49

    NUST Engineering Past Paper-5

    Determine the energy of an electron in the THIRD Bohr orbit of hydrogen (with eV).

    A

    −0.85 eV

    B

    −13.6 eV

    C

    −1.51 eV

    D

    −3.40 eV

    Reveal answer
50. 50

    NUST Engineering Past Paper-5

    Identify the physical phenomenon responsible for the production of BEATS in sound.

    A

    Diffraction of sound

    B

    Polarization of sound

    C

    Refraction of sound

    D

    Interference of sound

    Reveal answer
51. 51

    NUST Engineering Past Paper-5

    A charged particle accelerated from rest through potential difference has de Broglie wavelength . If is increased to , determine the new wavelength.

    A

    B

    C

    D

    Reveal answer
52. 52

    NUST Engineering Past Paper-5

    Determine the impedance of a series RLC circuit AT RESONANCE.

    A

    B

    Zero

    C

    D

    Reveal answer
53. 53

    NUST Engineering Past Paper-5

    Determine the critical angle for total internal reflection at the interface from a medium of refractive index to air ().

    A

    30°

    B

    60°

    C

    45°

    D

    90°

    Reveal answer
54. 54

    NUST Engineering Past Paper-5

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

    A

    2200 V

    B

    110 V

    C

    1100 V

    D

    44 V

    Reveal answer
55. 55

    NUST Engineering Past Paper-5

    A body performing SHM has amplitude and angular frequency . Determine its maximum speed.

    A

    B

    C

    D

    Reveal answer
56. 56

    NUST Engineering Past Paper-5

    An object is placed cm from a converging (convex) lens of focal length cm. Determine the image distance.

    A

    10 cm

    B

    30 cm

    C

    20 cm

    D

    15 cm

    Reveal answer
57. 57

    NUST Engineering Past Paper-5

    A sound source moves AWAY from a stationary observer. How does the observed frequency compare to the source frequency?

    A

    Increases

    B

    Decreases

    C

    Becomes zero

    D

    Remains the same

    Reveal answer
58. 58

    NUST Engineering Past Paper-5

    Determine the equivalent capacitance of two capacitors of F each connected in SERIES.

    A

    2 μF

    B

    4 μF

    C

    8 μF

    D

    1 μF

    Reveal answer
59. 59

    NUST Engineering Past Paper-5

    The magnetic flux through a -turn coil changes from Wb to Wb in s. Determine the magnitude of the induced EMF.

    A

    60 V

    B

    12 V

    C

    240 V

    D

    120 V

    Reveal answer
60. 60

    NUST Engineering Past Paper-5

    Which type of radioactive emission does NOT change the atomic number or mass number of the nucleus?

    A

    Beta-minus decay

    B

    Positron emission

    C

    Gamma emission

    D

    Alpha decay

    Reveal answer
61. 61

    NUST Engineering Past Paper-5

    Determine the work done by a CONSERVATIVE force when the object traverses any CLOSED path.

    A

    Infinite

    B

    Zero

    C

    Minimum

    D

    Maximum

    Reveal answer
62. 62

    NUST Engineering Past Paper-5

    When a wave travels from one medium to another, which of the following wave properties remains UNCHANGED?

    A

    Wavelength

    B

    Speed

    C

    Amplitude

    D

    Frequency

    Reveal answer
63. 63

    NUST Engineering Past Paper-5

    A concave mirror has focal length cm. An object is placed cm in front of the mirror. Determine the location of the image.

    A

    22.5 cm in front of mirror

    B

    30 cm in front of mirror

    C

    45 cm in front of mirror

    D

    22.5 cm behind mirror

    Reveal answer
64. 64

    NUST Engineering Past Paper-5

    Identify the name of the total number of nucleons (protons plus neutrons) in a nucleus.

    A

    Binding number

    B

    Neutron number

    C

    Atomic number

    D

    Mass number

    Reveal answer
65. 65

    NUST Engineering Past Paper-5

    By dimensional analysis, the SI unit combination corresponds to which physical quantity?

    A

    Magnetic field

    B

    Electric potential

    C

    Electric field

    D

    Electromagnetic pressure

    Reveal answer
66. 66

    NUST Engineering Past Paper-5

    Identify the principal physical quantity measured by a torsion balance.

    A

    Temperature

    B

    Very small forces (e.g., gravitational or electrostatic)

    C

    Magnetic field intensity

    D

    Electric potential difference

    Reveal answer
67. 67

    NUST Engineering Past Paper-5

    Two waves, each of amplitude , travel in the same direction and are exactly out of phase (destructive interference). Determine the resultant amplitude after superposition.

    A

    B

    C

    D

    Reveal answer
68. 68

    NUST Engineering Past Paper-5

    In simple harmonic motion of a mass on a spring (spring constant , amplitude ), determine the potential energy when the displacement is zero (i.e. at the equilibrium position).

    A

    B

    C

    D

    Reveal answer
69. 69

    NUST Engineering Past Paper-5

    Evaluate .

    A

    B

    C

    D

    None of these

    Reveal answer
70. 70

    NUST Engineering Past Paper-5

    Which of the following structures does NOT satisfy the commutative law under multiplication?

    A

    (2×2 Matrices)

    B

    (Natural numbers)

    C

    (Real numbers)

    D

    (Rational numbers)

    Reveal answer
71. 71

    NUST Engineering Past Paper-5

    If , find the sum of the first terms of the arithmetic progression.

    A

    228

    B

    143

    C

    300

    D

    None of these

    Reveal answer
72. 72

    NUST Engineering Past Paper-5

    Write the derivative formula for .

    A

    B

    C

    None of these

    D

    Reveal answer
73. 73

    NUST Engineering Past Paper-5

    Write the Maclaurin series of (first four non-zero terms).

    A

    B

    C

    None of these

    D

    Reveal answer
74. 74

    NUST Engineering Past Paper-5

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

    A

    29

    B

    C

    15

    D

    None of these

    Reveal answer
75. 75

    NUST Engineering Past Paper-5

    If , evaluate .

    A

    None of these

    B

    C

    D

    Reveal answer
76. 76

    NUST Engineering Past Paper-5

    If the eccentricity of an ellipse approaches , the conic approaches which shape?

    A

    A portion of Parabola

    B

    Circle

    C

    Parabola

    D

    Point

    Reveal answer
77. 77

    NUST Engineering Past Paper-5

    Find the sum of all seventh roots of unity.

    A

    0

    B

    1

    C

    D

    7

    Reveal answer
78. 78

    NUST Engineering Past Paper-5

    Differentiate with respect to .

    A

    B

    C

    D

    Reveal answer
79. 79

    NUST Engineering Past Paper-5

    Given that is a skew-symmetric matrix, determine the nature of the matrix .

    A

    Unit Matrix

    B

    Symmetric Matrix

    C

    Skew Symmetric Matrix

    D

    Null Matrix

    Reveal answer
80. 80

    NUST Engineering Past Paper-5

    Evaluate , with .

    A

    B

    C

    D

    1

    Reveal answer
81. 81

    NUST Engineering Past Paper-5

    Determine the slope of the line passing through the points and .

    A

    B

    C

    Undefined

    D

    Reveal answer
82. 82

    NUST Engineering Past Paper-5

    Compute the sum of the FIRST terms of a geometric progression whose first term is and common ratio is .

    A

    B

    C

    D

    Reveal answer
83. 83

    NUST Engineering Past Paper-5

    Determine the area enclosed between the curve and the -axis on the interval .

    A

    B

    C

    D

    Reveal answer
84. 84

    NUST Engineering Past Paper-5

    Given , compute .

    A

    B

    C

    D

    Reveal answer
85. 85

    NUST Engineering Past Paper-5

    Identify the values of the positive integer for which the inequality holds.

    A

    B

    C

    D

    Reveal answer
86. 86

    NUST Engineering Past Paper-5

    A lock has distinguishable parts that can be arranged in any order. How many distinct orderings (permutations) are possible?

    A

    B

    C

    D

    Reveal answer
87. 87

    NUST Engineering Past Paper-5

    For the function on , determine the location(s) of any relative maxima.

    A

    B

    C

    D

    None

    Reveal answer
88. 88

    NUST Engineering Past Paper-5

    Classify the algebraic property of integer subtraction (i.e., the operation on ).

    A

    None

    B

    Closed

    C

    Commutative

    D

    Associative

    Reveal answer
89. 89

    NUST Engineering Past Paper-5

    Evaluate .

    A

    B

    C

    D

    Reveal answer
90. 90

    NUST Engineering Past Paper-5

    Evaluate the indefinite integral .

    A

    B

    C

    D

    Reveal answer
91. 91

    NUST Engineering Past Paper-5

    Identify the equation of the directrix of the parabola (with ).

    A

    B

    C

    D

    Reveal answer
92. 92

    NUST Engineering Past Paper-5

    Let be a non-real complex cube root of unity. Evaluate .

    A

    B

    C

    D

    Reveal answer
93. 93

    NUST Engineering Past Paper-5

    Differentiate with respect to .

    A

    B

    C

    D

    Reveal answer
94. 94

    NUST Engineering Past Paper-5

    Determine the set of real values of for which the geometric series converges.

    A

    B

    C

    D

    Reveal answer
95. 95

    NUST Engineering Past Paper-5

    Determine the coefficient of in the binomial expansion of .

    A

    B

    C

    None of these

    D

    Reveal answer
96. 96

    NUST Engineering Past Paper-5

    In a sequence with and the relation (where is the sum of the first terms), determine .

    A

    B

    C

    D

    None of these

    Reveal answer
97. 97

    NUST Engineering Past Paper-5

    Determine the equation of the line passing through the point and parallel to the -axis.

    A

    B

    C

    D

    Reveal answer
98. 98

    NUST Engineering Past Paper-5

    An arithmetic sequence satisfies . Among the listed candidates for the th-term formula, identify the one consistent with this datum.

    A

    B

    C

    D

    Reveal answer
99. 99

    NUST Engineering Past Paper-5

    Let and be real numbers and . If the vector is perpendicular to , state the condition that and must satisfy.

    A

    and

    B

    and

    C

    and

    D

    or

    Reveal answer
100. 100

     NUST Engineering Past Paper-5

     Evaluate .

     A

     B

     C

     D

     Reveal answer
101. 101

     NUST Engineering Past Paper-5

     Given the complex number , determine the value of its modulus .

     A

     B

     C

     D

     Reveal answer
102. 102

     NUST Engineering Past Paper-5

     Determine the REAL PART of the complex number .

     A

     B

     C

     D

     None of these

     Reveal answer
103. 103

     NUST Engineering Past Paper-5

     Evaluate the complex-number expression .

     A

     B

     C

     D

     Reveal answer
104. 104

     NUST Engineering Past Paper-5

     Let denote a primitive cube root of unity (so and ). Evaluate .

     A

     B

     C

     D

     None of these

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105. 105

     NUST Engineering Past Paper-5

     Given the complex number , evaluate and express it in rectangular () form.

     A

     B

     C

     D

     Reveal answer
106. 106

     NUST Engineering Past Paper-5

     Determine the principal argument of the complex number .

     A

     B

     C

     D

     Reveal answer
107. 107

     NUST Engineering Past Paper-5

     Given a complex number satisfying , determine the possible value(s) of the real number .

     A

     B

     C

     D

     None of these

     Reveal answer
108. 108

     NUST Engineering Past Paper-5

     Determine the multiplicative inverse of the complex number .

     A

     B

     C

     D

     Reveal answer
109. 109

     NUST Engineering Past Paper-5

     Given , evaluate .

     A

     B

     C

     D

     Reveal answer
110. 110

     NUST Engineering Past Paper-5

     Express in the standard rectangular form .

     A

     B

     C

     D

     None of these

     Reveal answer
111. 111

     NUST Engineering Past Paper-5

     An arithmetic progression has first term and common difference . Determine the sum of its first terms.

     A

     B

     C

     D

     None of these

     Reveal answer
112. 112

     NUST Engineering Past Paper-5

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

     A

     B

     C

     D

     None of these

     Reveal answer
113. 113

     NUST Engineering Past Paper-5

     The th term of an arithmetic progression is given by . Determine the sum of its first terms.

     A

     B

     C

     D

     None of these

     Reveal answer
114. 114

     NUST Engineering Past Paper-5

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

     A

     B

     C

     D

     None of these

     Reveal answer
115. 115

     NUST Engineering Past Paper-5

     Determine the harmonic mean (HM) of the two positive numbers and .

     A

     B

     C

     D

     None of these

     Reveal answer
116. 116

     NUST Engineering Past Paper-5

     Determine a closed-form expression for the sum .

     A

     B

     C

     D

     None of these

     Reveal answer
117. 117

     NUST Engineering Past Paper-5

     Given and , determine the matrix product .

     A

     B

     C

     D

     None of these

     Reveal answer
118. 118

     NUST Engineering Past Paper-5

     Evaluate the determinant of the matrix .

     A

     B

     C

     D

     None of these

     Reveal answer
119. 119

     NUST Engineering Past Paper-5

     If is a matrix with , determine the value of .

     A

     B

     C

     D

     None of these

     Reveal answer
120. 120

     NUST Engineering Past Paper-5

     Matrix has order and matrix has order . Determine the order of .

     A

     B

     C

     D

     None of these

     Reveal answer
121. 121

     NUST Engineering Past Paper-5

     For any real square matrix , identify the type of matrix that is ALWAYS.

     A

     None of these

     B

     Skew-symmetric

     C

     Null

     D

     Symmetric

     Reveal answer
122. 122

     NUST Engineering Past Paper-5

     For a matrix , determine the adjugate (classical adjoint) .

     A

     B

     C

     None of these

     D

     Reveal answer
123. 123

     NUST Engineering Past Paper-5

     Let and be the roots of the quadratic . Express entirely in terms of and .

     A

     B

     C

     D

     None of these

     Reveal answer
124. 124

     NUST Engineering Past Paper-5

     If one of the roots of the quadratic equation is three times the other, determine the value of .

     A

     B

     C

     D

     None of these

     Reveal answer
125. 125

     NUST Engineering Past Paper-5

     Determine the quadratic equation whose roots are the NEGATIVES of the roots of .

     A

     B

     C

     D

     None of these

     Reveal answer
126. 126

     NUST Engineering Past Paper-5

     Determine the discriminant of the quadratic equation and identify the nature of its roots.

     A

     B

     C

     D

     None of these

     Reveal answer
127. 127

     NUST Engineering Past Paper-5

     Determine the sum of the roots of the cubic equation .

     A

     B

     C

     D

     None of these

     Reveal answer
128. 128

     NUST Engineering Past Paper-5

     Evaluate exactly.

     A

     B

     C

     D

     None of these

     Reveal answer
129. 129

     NUST Engineering Past Paper-5

     Given , determine the value of .

     A

     B

     C

     D

     None of these

     Reveal answer
130. 130

     NUST Engineering Past Paper-5

     Determine the exact value of (i.e., ).

     A

     B

     C

     D

     None of these

     Reveal answer
131. 131

     NUST Engineering Past Paper-5

     State the sum-to-product trigonometric identity for .

     A

     B

     C

     D

     None of these

     Reveal answer
132. 132

     NUST Engineering Past Paper-5

     Determine the fundamental period of the function .

     A

     B

     C

     D

     None of these

     Reveal answer
133. 133

     NUST Engineering Past Paper-5

     Evaluate , where denotes the principal-value inverse sine.

     A

     B

     C

     D

     None of these

     Reveal answer
134. 134

     NUST Engineering Past Paper-5

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

     A

     B

     C

     D

     None of these

     Reveal answer
135. 135

     NUST Engineering Past Paper-5

     Given and , evaluate .

     A

     B

     C

     D

     None of these

     Reveal answer
136. 136

     NUST Engineering Past Paper-5

     Determine the MAXIMUM possible value of the expression as varies over the reals.

     A

     B

     C

     D

     None of these

     Reveal answer
137. 137

     NUST Engineering Past Paper-5

     Determine for .

     A

     B

     C

     D

     None of these

     Reveal answer
138. 138

     NUST Engineering Past Paper-5

     If , determine for .

     A

     B

     C

     D

     None of these

     Reveal answer
139. 139

     NUST Engineering Past Paper-5

     Determine for .

     A

     B

     C

     D

     None of these

     Reveal answer
140. 140

     NUST Engineering Past Paper-5

     Let for constant . Determine .

     A

     B

     C

     D

     None of these

     Reveal answer
141. 141

     NUST Engineering Past Paper-5

     Determine the derivative of the function .

     A

     B

     C

     D

     None of these

     Reveal answer
142. 142

     NUST Engineering Past Paper-5

     Determine the LOCAL MAXIMUM value of the cubic function .

     A

     B

     C

     D

     None of these

     Reveal answer
143. 143

     NUST Engineering Past Paper-5

     Determine the SECOND derivative of the polynomial .

     A

     B

     C

     D

     None of these

     Reveal answer
144. 144

     NUST Engineering Past Paper-5

     Evaluate the indefinite integral .

     A

     B

     C

     D

     None of these

     Reveal answer
145. 145

     NUST Engineering Past Paper-5

     Evaluate the definite integral .

     A

     B

     C

     D

     None of these

     Reveal answer
146. 146

     NUST Engineering Past Paper-5

     Evaluate the definite integral .

     A

     B

     C

     D

     None of these

     Reveal answer
147. 147

     NUST Engineering Past Paper-5

     Evaluate the limit .

     A

     B

     C

     D

     None of these

     Reveal answer
148. 148

     NUST Engineering Past Paper-5

     Given and , compute the cross product .

     A

     B

     C

     D

     None of these

     Reveal answer
149. 149

     NUST Engineering Past Paper-5

     Determine how many 3-DIGIT numbers can be formed using the digits if NO DIGIT IS REPEATED.

     A

     B

     C

     D

     None of these

     Reveal answer
150. 150

     NUST Engineering Past Paper-5

     Determine the MIDDLE TERM in the binomial expansion of .

     A

     B

     C

     D

     None of these

     Reveal answer
151. 151

     NUST Engineering Past Paper-5

     Simplify (i.e., evaluate to a constant) the expression .

     A

     B

     C

     D

     None of these

     Reveal answer
152. 152

     NUST Engineering Past Paper-5

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

     A

     B

     C

     D

     None of these

     Reveal answer
153. 153

     NUST Engineering Past Paper-5

     Determine the SECOND derivative of .

     A

     B

     C

     D

     None of these

     Reveal answer
154. 154

     NUST Engineering Past Paper-5

     Evaluate the indefinite integral .

     A

     B

     C

     D

     None of these

     Reveal answer
155. 155

     NUST Engineering Past Paper-5

     Determine a closed-form expression for the th term of the sequence .

     A

     B

     C

     D

     None of these

     Reveal answer
156. 156

     NUST Engineering Past Paper-5

     Evaluate and express the answer in rectangular form.

     A

     B

     C

     D

     None of these

     Reveal answer
157. 157

     NUST Engineering Past Paper-5

     Determine the total number of distinct arrangements of the letters of the word 'STATISTICS'.

     A

     B

     C

     D

     None of these

     Reveal answer
158. 158

     NUST Engineering Past Paper-5

     Pick the word that is the closest opposite of 'Neglect':

     A

     Overlook

     B

     Ignore

     C

     Abandon

     D

     Attend

     Reveal answer
159. 159

     NUST Engineering Past Paper-5

     Choose the word that is closest in meaning to 'Exigency':

     A

     Luxury

     B

     Urgency

     C

     Comfort

     D

     Leisure

     Reveal answer
160. 160

     NUST Engineering Past Paper-5

     Pick the option that best defines 'Abundant':

     A

     Present in large quantities; plentiful

     B

     Barely sufficient

     C

     Extremely scarce

     D

     Unevenly distributed

     Reveal answer
161. 161

     NUST Engineering Past Paper-5

     Pick the option that best defines 'Ambiguity':

     A

     Excessive detail in communication

     B

     A single clear definition

     C

     Absolute certainty in meaning

     D

     The quality of being open to more than one interpretation

     Reveal answer
162. 162

     NUST Engineering Past Paper-5

     Pick the procedure MOST OPPOSITE in concept to 'Autopsy':

     A

     Dissection

     B

     Forensic analysis

     C

     Necropsy

     D

     Antenatal examination

     Reveal answer
163. 163

     NUST Engineering Past Paper-5

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

     A

     Vulgar

     B

     Lewd

     C

     Decent

     D

     Coarse

     Reveal answer
164. 164

     NUST Engineering Past Paper-5

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

     A

     Done consciously and intentionally

     B

     Performed accidentally

     C

     Done without thought or planning

     D

     Carried out in secret

     Reveal answer
165. 165

     NUST Engineering Past Paper-5

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

     A

     Yielding

     B

     Tame

     C

     Obstinate

     D

     Meek

     Reveal answer
166. 166

     NUST Engineering Past Paper-5

     Pick the word closest in meaning to 'Fierce':

     A

     Mild

     B

     Meek

     C

     Gentle

     D

     Ferocious

     Reveal answer
167. 167

     NUST Engineering Past Paper-5

     Pick the word closest in meaning to 'Fugitive':

     A

     Volunteer

     B

     Prisoner

     C

     Runaway

     D

     Captive

     Reveal answer
168. 168

     NUST Engineering Past Paper-5

     Pick the option that best defines 'Immature':

     A

     Highly responsible and reliable

     B

     Excessively wise for one's age

     C

     Not fully developed; childish in behavior

     D

     Having full mental and emotional development

     Reveal answer
169. 169

     NUST Engineering Past Paper-5

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

     A

     Spectacle

     B

     Miracle

     C

     Phenomenon

     D

     Banality

     Reveal answer
170. 170

     NUST Engineering Past Paper-5

     Pick the word closest in meaning to 'Monotonous':

     A

     Dynamic

     B

     Exciting

     C

     Varied

     D

     Tedious

     Reveal answer
171. 171

     NUST Engineering Past Paper-1 NUST Engineering Past Paper-5

     Pick the word closest in meaning to 'perpetual':

     A

     Brief

     B

     Occasional

     C

     Temporary

     D

     Eternal

     Reveal answer
172. 172

     NUST Engineering Past Paper-5

     Pick the word closest in meaning to 'Premeditated':

     A

     Spontaneous

     B

     Calculated

     C

     Impulsive

     D

     Accidental

     Reveal answer
173. 173

     NUST Engineering Past Paper-5

     Pick the option that best defines 'Sanguine':

     A

     Indifferent about outcomes

     B

     Pessimistic about the future

     C

     Fearful and anxious

     D

     Optimistic, especially in difficult situations

     Reveal answer
174. 174

     NUST Engineering Past Paper-5

     Pick the option that best defines 'Prevailing':

     A

     Declining rapidly in influence

     B

     Rare and unusual in occurrence

     C

     Existing most commonly or widely at a given time

     D

     Confined to a small group

     Reveal answer
175. 175

     NUST Engineering Past Paper-5

     Pick the word closest in meaning to 'Comparative':

     A

     Relative

     B

     Unconditional

     C

     Independent

     D

     Absolute

     Reveal answer
176. 176

     NUST Engineering Past Paper-5

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

     A

     Related

     B

     Absolute

     C

     Contextual

     D

     Proportional

     Reveal answer
177. 177

     NUST Engineering Past Paper-5

     Pick the option that best defines 'Fear':

     A

     An unpleasant emotion caused by threat or danger

     B

     Excitement about an upcoming event

     C

     A feeling of complete calm and safety

     D

     A feeling of joy and anticipation

     Reveal answer
178. 178

     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
179. 179

     NUST Engineering Past Paper-5

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

     A

     Noisy and demanding

     B

     Joyful and lively

     C

     Quiet and reserved

     D

     Fearful and timid

     Reveal answer
180. 180

     NUST Engineering Past Paper-5

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

     A

     Extremely poor or miserly

     B

     Extremely wealthy

     C

     Extremely content

     D

     Extremely generous

     Reveal answer
181. 181

     NUST Engineering Past Paper-5

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

     A

     Slow and careless

     B

     Highly skilled or proficient

     C

     Clumsy and awkward

     D

     Inexperienced and naive

     Reveal answer
182. 182

     NUST Engineering Past Paper-5

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

     A

     Making one feel very happy and excited

     B

     Causing extreme sadness

     C

     Producing boredom and fatigue

     D

     Causing confusion and stress

     Reveal answer
183. 183

     NUST Engineering Past Paper-5

     Identify the single-word term used for a very large and grand house.

     A

     Bungalow

     B

     Mansion

     C

     Cottage

     D

     Apartment

     Reveal answer
184. 184

     NUST Engineering Past Paper-5

     Identify the single-word term for a person who behaves inconsistently — professing one set of beliefs while acting on another.

     A

     Hypocrite

     B

     Pessimist

     C

     Narcissist

     D

     Introvert

     Reveal answer
185. 185

     NUST Engineering Past Paper-5

     Complete the analogy: Peel is to Banana as ___ is to Turtle.

     A

     Fin

     B

     Shell

     C

     Scale

     D

     Root

     Reveal answer
186. 186

     NUST Engineering Past Paper-5

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

     A

     Irregular

     B

     Difficult

     C

     Appropriate

     D

     Reluctant

     Reveal answer
187. 187

     NUST Engineering Past Paper-5

     Complete the analogy: Judge is to Justice as Teacher is to ___.

     A

     Knowledge

     B

     School

     C

     Teach

     D

     Lessons

     Reveal answer
188. 188

     NUST Engineering Past Paper-5

     Identify the intended meaning of the proverb 'A stitch in time saves nine.'

     A

     Always fix torn clothes immediately for fashion

     B

     Nine stitches are always better than one

     C

     Sewing quickly is a valuable skill

     D

     Dealing with problems early prevents bigger issues later

     Reveal answer
189. 189

     NUST Engineering Past Paper-5

     Pick the correctly spelled noun denoting a printed list of questions used to gather information.

     A

     Questionnaire

     B

     Questionnayre

     C

     Questionare

     D

     Questionaire

     Reveal answer
190. 190

     NUST Engineering Past Paper-5

     Complete the analogy: Fins is to Fish as Wings is to ___.

     A

     Sky

     B

     Bird

     C

     Fly

     D

     Eagle

     Reveal answer
191. 191

     NUST Engineering Past Paper-5

     Place the following four sentences in the most LOGICAL order to form a coherent story: P: She mailed both her resume and a tailored cover letter. Q: She came across a suitable job posting on a recruitment website. R: The hiring manager called her in for a face-to-face interview. S: She was eventually offered the position.

     A

     P-Q-R-S

     B

     Q-R-P-S

     C

     P-R-Q-S

     D

     Q-P-R-S

     Reveal answer
192. 192

     NUST Engineering Past Paper-5

     Arrange the following four sentences in the most logical sequence to form a coherent narrative: P: The patient was rushed to the hospital. Q: A physician thoroughly examined him. R: He was prescribed appropriate medication. S: He eventually made a complete recovery.

     A

     Q-P-R-S

     B

     P-R-Q-S

     C

     Q-R-P-S

     D

     P-Q-R-S

     Reveal answer
193. 193

     NUST Engineering Past Paper-5

     Choose the word that best completes the following analogy by preserving the same relational pattern: DOCTOR is to HOSPITAL as TEACHER is to ____.

     A

     Student

     B

     School

     C

     Library

     D

     Classroom

     Reveal answer
194. 194

     NUST Engineering Past Paper-5

     Identify the term that completes the analogy in keeping with the same relationship: BIRD is to NEST as BEE is to ____.

     A

     Honey

     B

     Wax

     C

     Flower

     D

     Hive

     Reveal answer
195. 195

     NUST Engineering Past Paper-5

     Select the word that maintains the same relational analogy: CHAPTER is to BOOK as SCENE is to ____.

     A

     Stage

     B

     Actor

     C

     Theatre

     D

     Play

     Reveal answer
196. 196

     NUST Engineering Past Paper-5

     Pick the option that completes the analogy by maintaining the relationship: HEAT is to SUN as LIGHT is to ____.

     A

     Candle

     B

     Fire

     C

     Bulb

     D

     Electricity

     Reveal answer
197. 197

     NUST Engineering Past Paper-5

     Choose the word that completes the analogy of opposites: COWARD is to BRAVE as MISER is to ____.

     A

     Stingy

     B

     Generous

     C

     Rich

     D

     Wealthy

     Reveal answer
198. 198

     NUST Engineering Past Paper-5

     Arrange the following four sentences in the most logical chronological order: P: Firefighters reached the scene promptly. Q: After about an hour, the blaze was fully extinguished. R: A fire suddenly broke out inside the building. S: The residents were safely evacuated.

     A

     R-P-S-Q

     B

     R-S-P-Q

     C

     R-P-Q-S

     D

     P-R-S-Q

     Reveal answer