NUST Engineering Past Paper-7

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

1. 1

   NUST Engineering Past Paper-7

   What is the dimensional formula for work?

   A

   B

   C

   D

   Reveal answer
2. 2

   NUST Engineering Past Paper-7

   On which of the following does the speed of sound in an ideal gas depend?

   A

   Density of the gas only

   B

   Pressure of the gas only

   C

   Temperature and nature (molecular mass) of the gas

   D

   Frequency and amplitude of the wave

   Reveal answer
3. 3

   NUST Engineering Past Paper-7

   A particle moves in a circle of radius m at a uniform speed of m/s. Find its centripetal acceleration.

   A

   12 m/s

   B

   18 m/s

   C

   6 m/s

   D

   9 m/s

   Reveal answer
4. 4

   NUST Engineering Past Paper-7

   Which optical phenomenon explains the formation of bright and dark fringes in a Young's double-slit pattern?

   A

   Diffraction

   B

   Refraction

   C

   Polarization

   D

   Interference

   Reveal answer
5. 5

   NUST Engineering Past Paper-7

   Two long parallel wires carry equal currents in *opposite* directions. What is the magnetic field at the midpoint between them?

   A

   Counter clockwise

   B

   Clockwise

   C

   Cannot be determined

   D

   Zero

   Reveal answer
6. 6

   NUST Engineering Past Paper-7

   Among the following media, in which does sound travel the fastest?

   A

   Glass

   B

   Water

   C

   Methanol

   D

   Copper

   Reveal answer
7. 7

   NUST Engineering Past Paper-7

   Identify the SI unit of linear momentum.

   A

   N s

   B

   kg m²/s²

   C

   kg m/s²

   D

   J/s

   Reveal answer
8. 8

   NUST Engineering Past Paper-7

   On a transverse travelling wave, determine the distance between a crest and the next adjacent trough.

   A

   λ

   B

   λ/2

   C

   λ/4

   D

   2λ

   Reveal answer
9. 9

   NUST Engineering Past Paper-7

   Among the following, which is a valid SI unit for momentum?

   A

   N s

   B

   J s

   C

   N m

   D

   Kg m/s²

   Reveal answer
10. 10

    NUST Engineering Past Paper-7

    If the time period of a simple pendulum is increased by a factor of (i.e. ), determine the corresponding change in its frequency.

    A

    Frequency becomes 9 times

    B

    Frequency becomes 3 times

    C

    Frequency becomes of original

    D

    Frequency becomes of original

    Reveal answer
11. 11

    NUST Engineering Past Paper-7

    A body executing SHM with period starts from the equilibrium position moving toward . Determine the time at which it first reaches .

    A

    B

    C

    D

    Reveal answer
12. 12

    NUST Engineering Past Paper-7

    If and are real numbers, , and the vector is perpendicular to , state the resulting algebraic condition on and .

    A

    B

    C

    D

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13. 13

    NUST Engineering Past Paper-7

    Identify the actual external force that propels a non-skidding car forward when the driver presses the accelerator.

    A

    Air pressure pushing the car

    B

    The weight of the car

    C

    The engine directly pushes the car forward

    D

    Static friction from the road acting on the tires

    Reveal answer
14. 14

    NUST Engineering Past Paper-7

    Identify the class of materials from which electrons are most readily liberated when illuminated by light of sufficient frequency (the photoelectric effect).

    A

    Insulators

    B

    Semiconductors

    C

    Metals

    D

    Dielectrics

    Reveal answer
15. 15

    NUST Engineering Past Paper-7

    Identify the type of electromagnetic radiation primarily responsible for the phenomenon of pair production.

    A

    Gamma radiation

    B

    Alpha radiation

    C

    Infrared radiation

    D

    Beta radiation

    Reveal answer
16. 16

    NUST Engineering Past Paper-7

    Identify the principal physical quantity that a torsion balance is designed to measure.

    A

    Angular momentum

    B

    Electric potential

    C

    Magnetic flux

    D

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

    Reveal answer
17. 17

    NUST Engineering Past Paper-7

    Identify the region of the electromagnetic spectrum in which the human body does NOT typically emit radiation under normal conditions.

    A

    Radio waves

    B

    Microwave

    C

    X-rays

    D

    Infrared

    Reveal answer
18. 18

    NUST Engineering Past Paper-7

    A spring-mass oscillator has total mechanical energy and amplitude . Determine the spring constant .

    A

    B

    C

    D

    Reveal answer
19. 19

    NUST Engineering Past Paper-7

    A body in SHM with period starts at the equilibrium position moving toward . Determine the time at which it first reaches .

    A

    B

    C

    D

    Reveal answer
20. 20

    NUST Engineering Past Paper-7

    A point charge moves with velocity relative to an observer. Identify what type(s) of field it generates in the surrounding space.

    A

    Only a magnetic field

    B

    Both an electric and a magnetic field

    C

    Neither an electric nor a magnetic field

    D

    Only an electric field

    Reveal answer
21. 21

    NUST Engineering Past Paper-7

    Identify the energy band in which the free electrons of an N-type extrinsic semiconductor predominantly reside at room temperature.

    A

    Valence band

    B

    Conduction band

    C

    Donor energy level only

    D

    Forbidden energy gap

    Reveal answer
22. 22

    NUST Engineering Past Paper-7

    If the absolute temperature of an ideal gas is increased times its original value, determine the corresponding effect on the rms speed of its molecules.

    A

    Quadruples

    B

    Doubles

    C

    Multiplies by

    D

    Remains the same

    Reveal answer
23. 23

    NUST Engineering Past Paper-7

    Determine the physical quantity that has the same dimensions as the product , where is mass, is radius, and is angular acceleration.

    A

    Angular momentum

    B

    Power

    C

    Linear momentum

    D

    Torque

    Reveal answer
24. 24

    NUST Engineering Past Paper-7

    Two coherent waves of equal amplitude travel in the same direction and are exactly in phase. Determine the resultant amplitude after their superposition.

    A

    B

    C

    D

    Reveal answer
25. 25

    NUST Engineering Past Paper-7

    Identify the scientist who coined the term PHOTON for a quantum of light in 1926.

    A

    Max Planck

    B

    Arthur Compton

    C

    Gilbert N. Lewis

    D

    Albert Einstein

    Reveal answer
26. 26

    NUST Engineering Past Paper-7

    An electron initially in the orbit of a hydrogen atom de-excites to lower levels. Identify the spectral series in which the highest-energy emitted photon falls.

    A

    Brackett series

    B

    Balmer series

    C

    Paschen series

    D

    Lyman series

    Reveal answer
27. 27

    NUST Engineering Past Paper-7

    Identify which of the listed electromagnetic radiations X-rays have HIGHER frequencies than (compared one at a time).

    A

    Visible light only

    B

    Cosmic rays

    C

    Ultraviolet (UV) radiation

    D

    Gamma rays

    Reveal answer
28. 28

    NUST Engineering Past Paper-7

    In SHM of a spring-mass oscillator (spring constant , amplitude ), describe the potential energy at the turning points relative to the total mechanical energy .

    A

    Equal to zero

    B

    Equal to half the total energy

    C

    Equal to the kinetic energy

    D

    Equal to the total mechanical energy

    Reveal answer
29. 29

    NUST Engineering Past Paper-7

    If both the mass and radius of a planet are reduced to of their original values, determine the corresponding effect on the escape velocity from its surface.

    A

    Decreases to of original

    B

    Decreases to of original

    C

    Increases 3 times

    D

    Remains the same

    Reveal answer
30. 30

    NUST Engineering Past Paper-7

    A long solenoid produces magnetic field inside it. If the current is tripled AND the number of turns per unit length is doubled, determine the new field.

    A

    B

    C

    D

    Reveal answer
31. 31

    NUST Engineering Past Paper-7

    A long straight wire has its conventional current flowing OUT of the page. Identify the direction in which the magnetic field circulates around the wire as viewed from the observer's side.

    A

    Away from the wire

    B

    Toward the wire

    C

    Counterclockwise

    D

    Clockwise

    Reveal answer
32. 32

    NUST Engineering Past Paper-7

    State the formula for the total relativistic energy of a moving object with rest mass moving at speed .

    A

    B

    C

    D

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33. 33

    NUST Engineering Past Paper-7

    Among the following claims, identify the one that is CORRECTLY established by Einstein's special theory of relativity.

    A

    Momentum is not conserved

    B

    Time is not absolute (time dilation occurs)

    C

    The speed of light is not absolute

    D

    None of the above

    Reveal answer
34. 34

    NUST Engineering Past Paper-7

    In SHM with spring constant , mass , and maximum speed , determine the maximum acceleration.

    A

    B

    C

    D

    Reveal answer
35. 35

    NUST Engineering Past Paper-7

    For a spring-mass oscillator, if the mass is reduced to and the spring constant is increased to , determine the effect on its time period .

    A

    Becomes

    B

    Remains the same

    C

    Becomes (i.e. )

    D

    Becomes

    Reveal answer
36. 36

    NUST Engineering Past Paper-7

    For a rigid body rotating about a fixed axis, determine the magnitude of (angular velocity crossed with angular acceleration).

    A

    B

    C

    D

    Reveal answer
37. 37

    NUST Engineering Past Paper-7

    In the proton-proton fusion chain that powers Sun-like stars, determine the approximate energy released per proton consumed.

    A

    B

    C

    D

    Reveal answer
38. 38

    NUST Engineering Past Paper-7

    Identify the region of the electromagnetic spectrum in which the human body emits radiation most intensely (under normal conditions).

    A

    X-ray

    B

    Visible light

    C

    Infrared

    D

    Ultraviolet

    Reveal answer
39. 39

    NUST Engineering Past Paper-7

    If the frequency of a simple pendulum changes from to , determine the new length expressed in terms of the original length .

    A

    becomes times

    B

    becomes times

    C

    becomes times

    D

    remains unchanged

    Reveal answer
40. 40

    NUST Engineering Past Paper-7

    In a radioactive decay, the parent nucleus's mass number decreases by and its atomic number decreases by . Identify the emitted particle.

    A

    Neutron

    B

    Beta particle

    C

    Gamma ray

    D

    Alpha particle

    Reveal answer
41. 41

    NUST Engineering Past Paper-7

    Identify the physicist credited with first proposing the matter-wave hypothesis (that material particles can exhibit wave-like behaviour).

    A

    Bohr

    B

    de Broglie

    C

    Einstein

    D

    Compton

    Reveal answer
42. 42

    NUST Engineering Past Paper-7

    Identify the physical quantity whose SI unit is equivalent to .

    A

    Electric field

    B

    Magnetic field (Tesla)

    C

    Viscosity

    D

    Electric resistivity

    Reveal answer
43. 43

    NUST Engineering Past Paper-7

    Identify the spatial distribution along which light from an isolated point source propagates in a homogeneous isotropic medium.

    A

    A single plane

    B

    All directions

    C

    A straight line only

    D

    Parallel rays

    Reveal answer
44. 44

    NUST Engineering Past Paper-7

    State the principal charge carrier responsible for current flow in an N-type extrinsic semiconductor.

    A

    Protons

    B

    Electrons

    C

    Positrons

    D

    Holes

    Reveal answer
45. 45

    NUST Engineering Past Paper-7

    A moving electric charge produces which type(s) of field in the surrounding space?

    A

    Both electric and magnetic fields

    B

    Only an electric field

    C

    Only a magnetic field

    D

    Neither electric nor magnetic field

    Reveal answer
46. 46

    NUST Engineering Past Paper-7

    State the numerical factor represented by the SI prefix 'femto-' (symbol f).

    A

    B

    C

    D

    Reveal answer
47. 47

    NUST Engineering Past Paper-7

    If the universal gravitational constant were quadrupled (with and unchanged), determine the corresponding effect on the surface gravitational acceleration .

    A

    Quadruple

    B

    Remain unchanged

    C

    Double

    D

    Halve

    Reveal answer
48. 48

    NUST Engineering Past Paper-7

    If the time period of a simple pendulum is increased by a factor of (i.e. ), determine the new frequency in terms of the original frequency .

    A

    Frequency becomes of original

    B

    Frequency becomes times

    C

    Frequency becomes times

    D

    Frequency becomes of original

    Reveal answer
49. 49

    NUST Engineering Past Paper-7

    In simple harmonic motion, if the total mechanical energy is reduced to one-third of its original value, determine the corresponding change in amplitude .

    A

    becomes

    B

    becomes

    C

    becomes

    D

    remains unchanged

    Reveal answer
50. 50

    NUST Engineering Past Paper-7

    Among the listed types of electromagnetic radiation, identify which has the LONGER wavelength.

    A

    Ultraviolet

    B

    Infrared

    C

    X-rays

    D

    Visible light

    Reveal answer
51. 51

    NUST Engineering Past Paper-7

    A passenger in a lift notices that their apparent weight has DECREASED below their normal weight. Identify the motion of the lift consistent with this observation.

    A

    Downward at constant speed

    B

    Upward at constant speed

    C

    Upward with increasing speed

    D

    Downward with increasing speed

    Reveal answer
52. 52

    NUST Engineering Past Paper-7

    Vector runs from to . A second vector — parallel and equal to — has its terminal point at . Determine the initial point of this second vector, expressed as a position vector.

    A

    B

    C

    D

    Reveal answer
53. 53

    NUST Engineering Past Paper-7

    A charged particle moves on a circular path inside a uniform magnetic field. Given , , , , determine the radius of its circular motion.

    A

    B

    C

    D

    Reveal answer
54. 54

    NUST Engineering Past Paper-7

    Two simple pendulums hang side-by-side with the same length . State the conclusion that follows about their oscillation periods.

    A

    Cannot be determined without mass

    B

    They have different time periods

    C

    They have the same time period

    D

    The heavier one oscillates faster

    Reveal answer
55. 55

    NUST Engineering Past Paper-7

    In a PN junction, identify the majority charge carriers on the P-side and the N-side respectively.

    A

    Electrons and holes

    B

    Electrons and protons

    C

    Holes and electrons

    D

    Protons and neutrons

    Reveal answer
56. 56

    NUST Engineering Past Paper-7

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

    A

    B

    C

    D

    Reveal answer
57. 57

    NUST Engineering Past Paper-7

    An electron moves in the direction with velocity through a uniform magnetic field . Determine the direction of the magnetic force on the electron.

    A

    In the direction (out of the page)

    B

    In the direction (into the page)

    C

    In the direction (right)

    D

    In the direction (left)

    Reveal answer
58. 58

    NUST Engineering Past Paper-7

    When the measurements and are added together, determine how many significant figures the result should be reported with.

    A

    B

    C

    D

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59. 59

    NUST Engineering Past Paper-7

    Sketching Planck's energy-frequency relation with on the -axis and on the -axis, identify the type of graph obtained.

    A

    Hyperbola

    B

    Exponential curve

    C

    Parabola

    D

    Straight line through the origin

    Reveal answer
60. 60

    NUST Engineering Past Paper-7

    Determine the number of significant figures in the measurement .

    A

    B

    C

    D

    Reveal answer
61. 61

    NUST Engineering Past Paper-7

    The length of a simple pendulum is increased to NINE TIMES its original value. Determine the factor by which its time period of oscillation changes.

    A

    B

    C

    D

    Reveal answer
62. 62

    NUST Engineering Past Paper-7

    The length of a simple pendulum is INCREASED by . Determine the resulting PERCENTAGE INCREASE in its time period.

    A

    B

    C

    D

    Reveal answer
63. 63

    NUST Engineering Past Paper-7

    By what FACTOR must the length of a simple pendulum be changed so that its time period DOUBLES?

    A

    B

    C

    D

    Reveal answer
64. 64

    NUST Engineering Past Paper-7

    A spring-mass oscillator has time period . If the suspended mass is reduced to ONE-QUARTER of its original value (spring constant unchanged), determine the new time period.

    A

    B

    C

    D

    Reveal answer
65. 65

    NUST Engineering Past Paper-7

    A uniform spring of natural time period (with a given attached mass) is cut into THREE equal pieces. One of those pieces is then used to suspend the SAME mass. Determine the new time period.

    A

    B

    C

    D

    Reveal answer
66. 66

    NUST Engineering Past Paper-7

    The amplitude of a simple harmonic oscillator is tripled while its mass and spring constant remain unchanged. Determine the effect on its time period.

    A

    Remains unchanged

    B

    Triples

    C

    Becomes times

    D

    Becomes

    Reveal answer
67. 67

    NUST Engineering Past Paper-7

    The distance between two point charges is HALVED. Determine the factor by which the electrostatic force between them changes (charges held constant).

    A

    (force quadrupled)

    B

    C

    D

    Reveal answer
68. 68

    NUST Engineering Past Paper-7

    Two point charges initially exert force on each other. If BOTH charges are TRIPLED and the distance between them is HALVED, determine the new force in terms of .

    A

    B

    C

    D

    Reveal answer
69. 69

    NUST Engineering Past Paper-7

    The magnetic-field strength on the axial line of a short bar magnet at distance from its centre is . Determine the field strength when the distance is TRIPLED (along the same axial line).

    A

    B

    C

    D

    Reveal answer
70. 70

    NUST Engineering Past Paper-7

    Given and , find .

    A

    B

    C

    D

    Reveal answer
71. 71

    NUST Engineering Past Paper-7

    For any complex number , simplify .

    A

    B

    None of these

    C

    D

    Reveal answer
72. 72

    NUST Engineering Past Paper-7

    For the ellipse with , along which axis does the major axis lie?

    A

    y-axis

    B

    None of these

    C

    Both

    D

    x-axis

    Reveal answer
73. 73

    NUST Engineering Past Paper-7

    Find the only point that satisfies .

    A

    B

    C

    D

    None of these

    Reveal answer
74. 74

    NUST Engineering Past Paper-7

    How many degrees does the radius vector sweep out in one complete revolution?

    A

    B

    C

    D

    Reveal answer
75. 75

    NUST Engineering Past Paper-7

    Determine the value of such that the piecewise function is continuous at .

    A

    B

    None of these

    C

    D

    Reveal answer
76. 76

    NUST Engineering Past Paper-7

    Determine the perpendicular distance between the parallel lines and .

    A

    B

    C

    D

    Reveal answer
77. 77

    NUST Engineering Past Paper-7

    Simplify .

    A

    B

    C

    D

    Reveal answer
78. 78

    NUST Engineering Past Paper-7

    Determine the coefficient of the term in the expansion of .

    A

    B

    C

    D

    Reveal answer
79. 79

    NUST Engineering Past Paper-7

    In an arithmetic progression, and . Determine .

    A

    B

    C

    D

    Reveal answer
80. 80

    NUST Engineering Past Paper-7

    Determine the value(s) of for which the upper-triangular matrix has rank exactly .

    A

    B

    C

    D

    None

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81. 81

    NUST Engineering Past Paper-7

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

    A

    B

    C

    D

    Reveal answer
82. 82

    NUST Engineering Past Paper-7

    Evaluate .

    A

    B

    C

    None of these

    D

    Reveal answer
83. 83

    NUST Engineering Past Paper-7

    Evaluate the infinite series .

    A

    B

    C

    D

    Reveal answer
84. 84

    NUST Engineering Past Paper-7

    For positive reals , determine the sign of the expression .

    A

    None

    B

    C

    D

    Reveal answer
85. 85

    NUST Engineering Past Paper-7

    Evaluate .

    A

    B

    C

    D

    Reveal answer
86. 86

    NUST Engineering Past Paper-7

    Determine the complement and supplement (in that order) of the angle .

    A

    and

    B

    and

    C

    and

    D

    No complement exists; supplement

    Reveal answer
87. 87

    NUST Engineering Past Paper-7

    A vector of magnitude lies in the second quadrant of the -plane (between the NEGATIVE -axis and the POSITIVE -axis), making a angle with the negative -axis. Determine its -component (horizontal component).

    A

    B

    C

    D

    Reveal answer
88. 88

    NUST Engineering Past Paper-7

    Describe the behaviour of the sequence for .

    A

    Stationary

    B

    Always increasing

    C

    Has a critical point

    D

    Always decreasing

    Reveal answer
89. 89

    NUST Engineering Past Paper-7

    Given , determine .

    A

    B

    C

    D

    Reveal answer
90. 90

    NUST Engineering Past Paper-7

    Consider the arithmetic progression of complex numbers Identify which of the listed complex numbers is NOT a term of this sequence.

    A

    B

    C

    D

    Reveal answer
91. 91

    NUST Engineering Past Paper-7

    For an arithmetic series with and common difference , find .

    A

    B

    C

    D

    Reveal answer
92. 92

    NUST Engineering Past Paper-7

    If , determine .

    A

    B

    C

    D

    Reveal answer
93. 93

    NUST Engineering Past Paper-7

    A student claims that . Determine the correct value of the integral.

    A

    B

    C

    D

    Reveal answer
94. 94

    NUST Engineering Past Paper-7

    Evaluate .

    A

    B

    C

    D

    Does not exist

    Reveal answer
95. 95

    NUST Engineering Past Paper-7

    Determine the perpendicular distance between the parallel lines and .

    A

    B

    C

    D

    Reveal answer
96. 96

    NUST Engineering Past Paper-7

    The sum of the first terms of an arithmetic progression is and the sum of the first terms is . Determine the first term .

    A

    B

    C

    D

    Reveal answer
97. 97

    NUST Engineering Past Paper-7

    Given the general-form circle equation , determine the radius of the circle.

    A

    B

    C

    D

    Reveal answer
98. 98

    NUST Engineering Past Paper-7

    State the general (the th) term in the binomial expansion of for non-negative integer .

    A

    B

    C

    D

    Reveal answer
99. 99

    NUST Engineering Past Paper-7

    For the hyperbola , determine the distance between the two foci.

    A

    B

    C

    D

    Reveal answer
100. 100

     NUST Engineering Past Paper-7

     If , determine the TRACE of the matrix .

     A

     B

     C

     D

     Reveal answer
101. 101

     NUST Engineering Past Paper-7

     The FOURTH term of a geometric progression equals . Determine the product of its first SEVEN terms.

     A

     B

     C

     D

     Reveal answer
102. 102

     NUST Engineering Past Paper-7

     Two positive numbers have arithmetic mean and geometric mean . Determine the two numbers.

     A

     and

     B

     and

     C

     and

     D

     and

     Reveal answer
103. 103

     NUST Engineering Past Paper-7

     Determine the derivative .

     A

     B

     C

     D

     Reveal answer
104. 104

     NUST Engineering Past Paper-7

     Determine the derivative of the function .

     A

     B

     C

     D

     Reveal answer
105. 105

     NUST Engineering Past Paper-7

     Given the parametric equations and (for constant ), determine in terms of .

     A

     B

     C

     D

     Reveal answer
106. 106

     NUST Engineering Past Paper-7

     Determine the SECOND derivative of the function for .

     A

     B

     C

     D

     Reveal answer
107. 107

     NUST Engineering Past Paper-7

     Determine the largest interval on which the function is STRICTLY DECREASING.

     A

     B

     C

     D

     None of these

     Reveal answer
108. 108

     NUST Engineering Past Paper-7

     Determine the interval(s) of on which the function is INCREASING.

     A

     B

     C

     D

     Reveal answer
109. 109

     NUST Engineering Past Paper-7

     Evaluate the definite integral .

     A

     B

     C

     D

     Reveal answer
110. 110

     NUST Engineering Past Paper-7

     If , determine the value of (assuming ).

     A

     B

     C

     D

     Reveal answer
111. 111

     NUST Engineering Past Paper-7

     Determine the eccentricity of the ellipse .

     A

     B

     C

     D

     Reveal answer
112. 112

     NUST Engineering Past Paper-7

     Determine the coordinates of the VERTICES of the hyperbola .

     A

     B

     C

     D

     Reveal answer
113. 113

     NUST Engineering Past Paper-7

     A circle has centre at and passes through the point . Determine the equation of the circle.

     A

     B

     C

     D

     Reveal answer
114. 114

     NUST Engineering Past Paper-7

     Determine the length of the latus rectum of the ellipse .

     A

     B

     C

     D

     Reveal answer
115. 115

     NUST Engineering Past Paper-7

     Determine the distance between the two foci of the hyperbola .

     A

     B

     C

     D

     Reveal answer
116. 116

     NUST Engineering Past Paper-7

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

     A

     B

     C

     D

     Reveal answer
117. 117

     NUST Engineering Past Paper-7

     Evaluate the sum of the infinite series .

     A

     B

     C

     D

     Reveal answer
118. 118

     NUST Engineering Past Paper-7

     The sum of the first terms of a series is given by . Determine the th term of the series.

     A

     B

     C

     D

     Reveal answer
119. 119

     NUST Engineering Past Paper-7

     A geometric progression has first term and the sum of its first three terms equals . Determine the common ratio (take the positive root).

     A

     B

     C

     D

     Reveal answer
120. 120

     NUST Engineering Past Paper-7

     The sum of the first terms of an arithmetic progression is . Determine a closed-form expression for the th term .

     A

     B

     C

     D

     Reveal answer
121. 121

     NUST Engineering Past Paper-7

     Determine the derivative of the function (for ).

     A

     B

     C

     D

     Reveal answer
122. 122

     NUST Engineering Past Paper-7

     Determine the derivative of the function for .

     A

     B

     C

     D

     Reveal answer
123. 123

     NUST Engineering Past Paper-7

     If , determine .

     A

     B

     C

     D

     Reveal answer
124. 124

     NUST Engineering Past Paper-7

     State the derivative formula for .

     A

     B

     C

     D

     Reveal answer
125. 125

     NUST Engineering Past Paper-7

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

     A

     B

     C

     D

     Reveal answer
126. 126

     NUST Engineering Past Paper-7

     Determine the SECOND derivative of .

     A

     B

     C

     D

     Reveal answer
127. 127

     NUST Engineering Past Paper-7

     Given , determine the SECOND derivative .

     A

     B

     C

     D

     Reveal answer
128. 128

     NUST Engineering Past Paper-7

     Determine the rate of change of the surface area of a sphere with respect to its radius at .

     A

     B

     C

     D

     Reveal answer
129. 129

     NUST Engineering Past Paper-7

     The total revenue function (in rupees) of a firm is , where is the number of units sold. Determine the marginal revenue when .

     A

     B

     C

     D

     Reveal answer
130. 130

     NUST Engineering Past Paper-7

     Determine the largest interval on which the linear function is strictly DECREASING.

     A

     B

     C

     D

     None of these

     Reveal answer
131. 131

     NUST Engineering Past Paper-7

     Determine the largest interval (within ) on which the function is strictly DECREASING.

     A

     B

     C

     D

     None of these

     Reveal answer
132. 132

     NUST Engineering Past Paper-7

     Determine the interval on which the function is strictly INCREASING.

     A

     B

     C

     D

     None of these

     Reveal answer
133. 133

     NUST Engineering Past Paper-7

     Determine the set on which the cubic function is strictly INCREASING.

     A

     B

     C

     D

     Reveal answer
134. 134

     NUST Engineering Past Paper-7

     Given the function (defined for ), determine in simplest factored form.

     A

     B

     C

     D

     Reveal answer
135. 135

     NUST Engineering Past Paper-7

     State the largest interval on which the exponential function is strictly INCREASING.

     A

     B

     C

     D

     None of these

     Reveal answer
136. 136

     NUST Engineering Past Paper-7

     Identify an interval on which the function is NEITHER strictly increasing NOR strictly decreasing.

     A

     B

     C

     D

     None of these

     Reveal answer
137. 137

     NUST Engineering Past Paper-7

     Among the listed functions, identify the one that is STRICTLY DECREASING on the interval .

     A

     B

     C

     D

     Reveal answer
138. 138

     NUST Engineering Past Paper-7

     Determine the interval(s) on which the function is strictly DECREASING.

     A

     No interval (the function is increasing everywhere)

     B

     C

     D

     Reveal answer
139. 139

     NUST Engineering Past Paper-7

     Determine the LEAST value of the real parameter such that is strictly INCREASING on the open interval .

     A

     B

     C

     D

     Reveal answer
140. 140

     NUST Engineering Past Paper-7

     Determine the derivative of the function (for ).

     A

     B

     C

     D

     Reveal answer
141. 141

     NUST Engineering Past Paper-7

     Evaluate the definite integral .

     A

     B

     C

     D

     Reveal answer
142. 142

     NUST Engineering Past Paper-7

     If , determine the (positive) value of .

     A

     B

     C

     D

     Reveal answer
143. 143

     NUST Engineering Past Paper-7

     Evaluate the definite integral .

     A

     B

     C

     D

     Reveal answer
144. 144

     NUST Engineering Past Paper-7

     Evaluate the definite integral .

     A

     B

     C

     D

     Reveal answer
145. 145

     NUST Engineering Past Paper-7

     Determine how many distinct -digit numbers can be formed using the digits if NO DIGIT may be repeated.

     A

     B

     C

     D

     Reveal answer
146. 146

     NUST Engineering Past Paper-7

     Find the positive integer satisfying .

     A

     B

     C

     D

     Reveal answer
147. 147

     NUST Engineering Past Paper-7

     Determine how many distinct signals can be generated by HOISTING FLAGS one above the other, chosen from a stock of differently-coloured flags.

     A

     B

     C

     D

     Reveal answer
148. 148

     NUST Engineering Past Paper-7

     Determine the number of distinct arrangements of the letters of the word 'BANANA'.

     A

     B

     C

     D

     Reveal answer
149. 149

     NUST Engineering Past Paper-7

     Find the positive integer satisfying .

     A

     B

     C

     D

     Reveal answer
150. 150

     NUST Engineering Past Paper-7

     Determine the value of the binomial coefficient .

     A

     B

     C

     D

     Reveal answer
151. 151

     NUST Engineering Past Paper-7

     Determine the number of distinct permutations of the letters of the word 'NUMBERS'.

     A

     B

     C

     D

     Reveal answer
152. 152

     NUST Engineering Past Paper-7

     Given and , determine .

     A

     B

     C

     D

     Reveal answer
153. 153

     NUST Engineering Past Paper-7

     Determine how many distinct -DIGIT numbers can be formed using the digits if NO DIGIT may be repeated.

     A

     B

     C

     D

     Reveal answer
154. 154

     NUST Engineering Past Paper-7

     Determine the eccentricity of the hyperbola .

     A

     B

     C

     D

     Reveal answer
155. 155

     NUST Engineering Past Paper-7

     State the condition on the line (slope , -intercept ) so that it is TANGENT to the hyperbola .

     A

     B

     C

     D

     Reveal answer
156. 156

     NUST Engineering Past Paper-7

     State the equation of the NORMAL to the hyperbola at the point lying on it.

     A

     B

     C

     D

     Reveal answer
157. 157

     NUST Engineering Past Paper-7

     In a harmonic progression, the nd term is and the th term is . Determine the th term.

     A

     B

     C

     D

     Reveal answer
158. 158

     NUST Engineering Past Paper-7

     Determine how many distinct five-digit numbers GREATER THAN can be formed using the digits (each digit used exactly once).

     A

     B

     C

     D

     Reveal answer
159. 159

     NUST Engineering Past Paper-7

     Pick the option that best defines 'Arduous':

     A

     Happening very quickly

     B

     Extremely easy and effortless

     C

     Involving or requiring strenuous effort

     D

     Relating to music and arts

     Reveal answer
160. 160

     NUST Engineering Past Paper-7

     Pick the option that best defines the verb 'Obviate':

     A

     To make something worse

     B

     To observe carefully

     C

     To clearly explain something

     D

     To remove a difficulty or obstacle before it arises

     Reveal answer
161. 161

     NUST Engineering Past Paper-7

     Which option spells the name of the common city bird correctly?

     A

     Piegon

     B

     Pidgeon

     C

     Pigeon

     D

     Pegion

     Reveal answer
162. 162

     NUST Engineering Past Paper-7

     Pick the phrase closest in meaning to 'Abide by':

     A

     Comply with

     B

     Reject

     C

     Oppose

     D

     Defy

     Reveal answer
163. 163

     NUST Engineering Past Paper-7

     Pick the option that best defines 'Acrimonious':

     A

     Overly enthusiastic

     B

     Gentle and pleasant in manner

     C

     Filled with bitterness or ill feeling

     D

     Indifferent or neutral

     Reveal answer
164. 164

     NUST Engineering Past Paper-7

     Pick the word closest in meaning to 'Azure':

     A

     Scarlet

     B

     Cerulean

     C

     Amber

     D

     Crimson

     Reveal answer
165. 165

     NUST Engineering Past Paper-7

     Pick the word closest in meaning to 'Base' (in the sense of 'ignoble'):

     A

     Virtuous

     B

     Honorable

     C

     Noble

     D

     Despicable

     Reveal answer
166. 166

     NUST Engineering Past Paper-7

     Pick the option that best defines 'Exonerate':

     A

     To officially declare someone guilty

     B

     To punish someone for wrongdoing

     C

     To investigate a case thoroughly

     D

     To officially absolve someone from blame or criminal charges

     Reveal answer
167. 167

     NUST Engineering Past Paper-7

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

     A

     Rash

     B

     Hasty

     C

     Prudent

     D

     Foolhardy

     Reveal answer
168. 168

     NUST Engineering Past Paper-7

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

     A

     Prankish

     B

     Roguish

     C

     Obedient

     D

     Naughty

     Reveal answer
169. 169

     NUST Engineering Past Paper-7

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

     A

     Varied

     B

     Uniform

     C

     Repetitive

     D

     Humdrum

     Reveal answer
170. 170

     NUST Engineering Past Paper-7

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

     A

     Corrupt

     B

     Malicious

     C

     Sinister

     D

     Virtuous

     Reveal answer
171. 171

     NUST Engineering Past Paper-7

     Pick the word closest in meaning to 'Periphery':

     A

     Center

     B

     Interior

     C

     Core

     D

     Boundary

     Reveal answer
172. 172

     NUST Engineering Past Paper-7

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

     A

     Core

     B

     Margin

     C

     Border

     D

     Outskirts

     Reveal answer
173. 173

     NUST Engineering Past Paper-7

     Pick the option that best defines 'Precarious':

     A

     Not securely held; dependent on chance; uncertain

     B

     Stable and well-established

     C

     Perfectly balanced and safe

     D

     Carefully planned and executed

     Reveal answer
174. 174

     NUST Engineering Past Paper-7

     Pick the word closest in meaning to 'Upbraid':

     A

     Praise

     B

     Rebuke

     C

     Flatter

     D

     Commend

     Reveal answer
175. 175

     NUST Engineering Past Paper-7

     Pick the option that best defines 'Valetudinarian':

     A

     A person who ignores health warnings

     B

     A person who is excessively concerned with their health

     C

     A medical professional

     D

     A person who is robust and in excellent health

     Reveal answer
176. 176

     NUST Engineering Past Paper-7

     Pick the term most nearly OPPOSITE in meaning to 'Venial':

     A

     Excusable

     B

     Minor

     C

     Trivial

     D

     Mortal (sin)

     Reveal answer
177. 177

     NUST Engineering Past Paper-7

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

     A

     Rescind

     B

     Abolish

     C

     Annul

     D

     Enact

     Reveal answer
178. 178

     NUST Engineering Past Paper-7

     Pick the word closest in meaning to 'Impressive':

     A

     Forgettable

     B

     Mediocre

     C

     Ordinary

     D

     Remarkable

     Reveal answer
179. 179

     NUST Engineering Past Paper-7

     Pick the word closest in meaning to 'Clear':

     A

     Murky

     B

     Obscure

     C

     Lucid

     D

     Vague

     Reveal answer
180. 180

     NUST Engineering Past Paper-7

     Pick the option that best captures the meaning of the noun ALTRUISM.

     A

     Selfishness and greed

     B

     Excessive pride in oneself

     C

     Selfless concern for the well-being of others

     D

     Desire for wealth

     Reveal answer
181. 181

     NUST Engineering Past Paper-7

     Pick the synonym of the adjective PIOUS.

     A

     Pretentious

     B

     Devout

     C

     Clean

     D

     Pure

     Reveal answer
182. 182

     NUST Engineering Past Paper-7

     Pick the synonym of the noun RESTRAINT.

     A

     Repression

     B

     Hindrance

     C

     Obstacle

     D

     Restriction

     Reveal answer
183. 183

     NUST Engineering Past Paper-7

     Pick the synonym of the noun AUGURY.

     A

     Prophecy

     B

     Intention

     C

     Future

     D

     Astronomy

     Reveal answer
184. 184

     NUST Engineering Past Paper-7

     Pick the synonym of the adjective DELECTABLE.

     A

     Sumptuous

     B

     Enjoyable

     C

     Delicious

     D

     Noble

     Reveal answer
185. 185

     NUST Engineering Past Paper-7

     Pick the synonym of the verb DEFER.

     A

     Differ

     B

     Postpone

     C

     Defy

     D

     Indifferent

     Reveal answer
186. 186

     NUST Engineering Past Paper-7

     Pick the synonym of the verb ENTANGLE.

     A

     Confuse

     B

     Perplex

     C

     Trap

     D

     Submerge

     Reveal answer
187. 187

     NUST Engineering Past Paper-7

     Pick the synonym of the adjective BENEVOLENT.

     A

     Beneficial

     B

     Charitable

     C

     Sympathetic

     D

     Liberal

     Reveal answer
188. 188

     NUST Engineering Past Paper-7

     Pick the synonym of the adjective ERUDITE.

     A

     Courteous

     B

     Learned

     C

     Precious

     D

     Strong

     Reveal answer
189. 189

     NUST Engineering Past Paper-7

     Pick the antonym of the noun SPLENDOUR.

     A

     Fame

     B

     Debasement

     C

     Reputation

     D

     Notoriety

     Reveal answer
190. 190

     NUST Engineering Past Paper-7

     Pick the antonym of the noun ACCELERATION (used in its general sense of 'speeding up').

     A

     Retrogression

     B

     Transgression

     C

     Progress

     D

     Retardation

     Reveal answer
191. 191

     NUST Engineering Past Paper-7

     Pick the antonym of the adjective MAGNANIMOUS.

     A

     Mean

     B

     Loyal

     C

     Generous

     D

     Loving

     Reveal answer
192. 192

     NUST Engineering Past Paper-7

     Pick the antonym of the noun REPUGNANCE.

     A

     Affection

     B

     Approval

     C

     Disinclination

     D

     Like

     Reveal answer
193. 193

     NUST Engineering Past Paper-7

     Identify the single-word term for a person characterised by severe self-discipline and abstention from indulgence.

     A

     Devotee

     B

     Ascetic

     C

     Antiquarian

     D

     Sceptic

     Reveal answer
194. 194

     NUST Engineering Past Paper-7

     Identify the single-word term for a person who renounces a religious or political belief they previously held.

     A

     Agnostic

     B

     Prostate

     C

     Apostate

     D

     Profane

     Reveal answer
195. 195

     NUST Engineering Past Paper-7

     Identify the single-word term for a song or lament sung at a burial or funeral.

     A

     Knell

     B

     Ditty

     C

     Lyric

     D

     Dirge

     Reveal answer
196. 196

     NUST Engineering Past Paper-7

     Identify the meaning of the idiom 'To make a clean breast of.'

     A

     To destroy before it blooms

     B

     To gain prominence

     C

     To confess without reserve

     D

     To praise oneself

     Reveal answer
197. 197

     NUST Engineering Past Paper-7

     Identify the meaning of the idiom 'To have an axe to grind.'

     A

     To have no result

     B

     To work for both sides

     C

     To work on a task

     D

     To have a personal interest in something

     Reveal answer
198. 198

     NUST Engineering Past Paper-7

     Identify the meaning of the idiom 'To speak daggers.'

     A

     To indulge in voracious talks

     B

     To speak harshly or maliciously

     C

     To speak to a person with hostility

     D

     To speak with a loud voice

     Reveal answer
199. 199

     NUST Engineering Past Paper-7

     Identify the meaning of the idiom 'To haul (someone) over the coals.'

     A

     To say the wrong words

     B

     To scold or reprimand severely

     C

     To put hand in a wrong task

     D

     To throw into the fire

     Reveal answer