Assam JLEE 2025 Question Paper Mechanical Engineering

Section – Mathematics
1 2 3 𝑛
1. logn →∞ (1−𝑛2 + 1−𝑛2 + 1−𝑛2 ….. + 1−𝑛2) is equal to
1
A) 1 B) 2
1
C) − 2 D) 2

2. Find the area of the region bounded by the parabola y2 = 16x and the line x = 4x.
A) 12 sq. unit B) 256/5 sq. unit
C) 128/3 sq. unit D) 125 sq. unit
1−𝑖𝑥
3. If 1+𝑖𝑥 = a – ib, then a2 + b2 equals to
1
A) 𝑥 B) 1
C) x D) x2
1 1 1
4. If 8! + 9! = 10! , then x equals to
A) 100 B) 64
C) 80 D) 121

5. The number of diagonals that can be drawn by joining the vertices of an octagon is
A) 28 B) 16
C) 20 D) 24

6. Find the coefficient of a6b3 in the expansion of (a + 2b)9.
A) 144 B) 256
C) 444 D) 672
⨅ 2⨅ 4⨅ 8⨅
7. tan 3 + 2tan 3 + 4tan 3 + 8tan 3 is
A) √3 B) 2√3
C) √5 D) -5√3

8. Find the value of k for which the line (k−3) x− (4 − k2) y−6 = 0 is parallel to the x-axis.
A) 2 B) 3
C) 4 D) 6

9. The curve represented by x = 2(cost + sint), y = 5(cost − sint) is
A) a circle B) a parabola
C) a hyperbola D) an ellipse

10. If the 5th term of an AP is 11 and the 9th term is 7, then the 14th term is
A) -1 B) 2
C) 1 D) 0

11. The polar form of the complex number −1 + i is
3⨅ 3⨅ 1 3⨅ 3⨅
A) √2 (cos 4 + isin 4 ) B) √2 (cos 4 + isin 4 )
⨅ ⨅ 1 ⨅ ⨅
C) √2 (cos4 + isin4 ) D) √2 (cos4 + isin4 )

1 −2 3
12. If the matrix 1 2 1 is singular, then the value of x is
𝑥 2 −3
A) -1 B) 0
C) 1 D) 2

13. Two cylindrical jars have their radii in the ratio 1: 3 and heights in the ratio 2: 3. Then the ratio of their
volume is
A) 2:27 B) 4:9
C) 3:16 D) 2:9

14. If 2n – 2n-1 = 64, then the value of n is
A) 4 B) 8
C) 7 D) 9

15. The sum up to n terms of the series 1 + 3 + 9 + 27 + ⋯ is 364. Then the value of n is
A) 5 B) 6
C) 7 D) 9
1
16. If x = 3 + √8 then the value of x2 + 𝑥 2 .
A) 32 B) 34
C) 38 D) 42

17. A right-angled triangle is formed by the line 4x + 3y = 124 and the coordinate axes. The area of the
triangle in square units is
A) 2 B) 3
C) 4 D) 6

18. The range of f(x)=1 + 3cos 2x is
A) [-2,4] B) [2,3]
C) [2,4] D) [-1,1]

19. ∑10 3
𝑛=1 𝑛 =
A) 972 B) 2025
C) 3025 D) 4650

20. The 3rd term of a geometric progression is 4. The product of the first five terms is
A) 43 B) 44
C) 45 D) None of the above

21. Find the value of a for which the line (4 − a2) x − (a − 3) y + 6 = 0 is parallel to the y - axis.
A) 3 B) 4
C) 7 D) 1

22. If the point P(x, y) is equidistant from the points A (a + b, b − a) and B (a − b, a + b), then
A) ax = by B) bx = ay
2 2
C) x – y = 2 (ax + by) D) ax2 = by2
2
23. The coefficient of x15 in the expansion of (x2 + 𝑥 )15 is
A) 15C728 B) 15C827

C) 15C525 D) 15C10210

24. If (n + 1)! = 12(n − 1)! then n is equal to
A) 3 B) 4
C) 5 D) 8
1−𝑖𝑥
25. If 1+𝑖𝑥 = A + iB, then A2 + B2 equals to
A) -1 B) x2
C) -x2 D) 1

26. Find the area of the region bounded by the line 2y + x = 8, the x - axis and the lines x = 2 and x = 4.
A) 4 sq. unit B) 5 sq. unit
C) 6 sq. unit D) 9 sq. unit

27. Evaluate ∫√1 − 𝑠𝑖𝑛2𝑥 dx
A) sinx + cosx + c B) sinx – cosx + c
1 1
C) 2 sin2x + c D) - 2 cos2x + c
𝑑𝑦
28. If y = √𝑠𝑖𝑛𝑥 + 𝑦, then 𝑑𝑥 =
𝑐𝑜𝑠𝑥 𝑠𝑖𝑛𝑥
A) 1−2𝑦 B) 2𝑦−1
𝑠𝑖𝑛𝑥 𝑐𝑜𝑠𝑥
C) 1−2𝑦 D) 2𝑦−1

1
(2𝑥 2 + 3), 𝑥 ≤ 1
5
29. The point(s) of discontinuity of the function g (x) = {6 − 5𝑥, 1 < 𝑥 < 3
𝑥 − 3, 𝑥≥3
A) 1 B) 3
C) 1, 3 D) 0, 1, 3

30. Let f(x) = x + 2, g(x) = x2 + 2, then g(f(x)) =
A) x2 – 4x + 5 B) x2 + 4x + 6
C) (x2 + 2)(x + 2) D) x2 - 4

Section – Basic of Computer Science

31. Which of the following values is the correct value of this hexadecimal code ABCDEF?
A) 11259375 B) 11259379
C) 11259372 D) 11259371

31. The part of the OS that manages the CPU, memory and I/O devices is called
A) Compiler B) Kernel
C) Shell D) Driver

32. What is the function of the "ATTRIB" command in DOS?
A) Change file attributes B) Display file contents
D) Rename files C) Remove hidden files

33. A key difference between LAN and WAN is
A) WAN is faster than LAN
B) LAN operates in a small geographic area, while WAN covers a broader area
C) WAN does not require any cables
D) LAN uses more advanced technology than WAN

34. Which of the following is the default slide layout in PowerPoint?
A) Title Slide B) Title and Content
C) Blank D) Two Content

35. In MS Word, what is the maximum number of columns you can insert in a table?
A) 35 B) 63
C) 100 D) 255

36. Which memory stores the most frequently used instructions to increase processing speed?
A) ROM B) RAM
C) Cache D) Secondary storage

37. How do you find the 2's complement of a binary number?
A) Invert all bits B) Invert all bits and add 1
C) Add 1 D) Change the sign bit

38. Which command in DOS is used to display information about the system's hardware and software
configuration?
A) CONFIG B) SYSTEMINFO
C) INFO D) HARDWARE

39. Which of the following is an example of a device used to connect different LAN to form a WAN?
A) Hub B) Router
C) Switch D) Access Point

40. What does the "Mail Merge" feature in MS Word do?
A) Merges multiple documents into one
B) Allows you to combine a document with a data source to create personalized letters
or labels

C) Merges different text styles into one document
D) Combines multiple email messages into one

Section – Engineering Graphics

41. A scale where the drawing is made smaller than the actual object is called a
A) Full scale B) Enlarged scale
C) Reduced scale D) Diagonal scale

42. Which of the following is a key requirement of dimensioning?
A) To make the drawing look more complex
B) To provide all necessary information for manufacturing or construction
C) To fill empty spaces on the drawing sheet
D) To indicate the color of the object

43. The rectangular method can be used for the construction of which of the following conic sections?
A) Ellipse and Parabola only
B) Parabola and Hyperbola only
C) Ellipse and Hyperbola only
D) Ellipse, Parabola, and Hyperbola

44. If a point is located in the first quadrant, its projection on the Horizontal Plane (HP) will be
A) Above the XY line
B) Below the XY line
C) On the XY line
D) Any of the above depending on the Vertical Plane (VP)

45. When a straight line is perpendicular to one reference plane and parallel to the other, its projection on
the plane to which it is perpendicular will be
A) A line of true length
B) A line shorter than true length
C) A point
D) A line longer than true length

46. Isometric projection is a type of
A) Orthographic projection
B) Axonometric projection (specifically, a type of orthographic axonometric
projection)
C) Perspective projection
D) Oblique projection

47. A diagonal scale is used to measure
A) Only two units or a unit and its sub-unit
B) Only angles
C) Up to three units (e.g., meters, decimetres, and centimetres) or a unit and its two
sub-divisions
D) Curved lines accurately

48. The concentric circle method is specifically used for the construction of which conic section?
A) Parabola

B) Hyperbola
C) Ellipse
D) All conic sections

49. What is a key difference between first angle and third angle projection symbols?
A) The arrangement of the circle and truncated cone views
B) The type of lines used
C) The scale indicated
D) The number of views shown

50. The process of creating isometric views from orthographic projections involves
A) Projecting views at 90 degrees to each other
B) Representing the 3D object on a 2D plane showing three faces
C) Using only one principal view
D) Scaling down all dimensions by half

Section – Mechanical Engineering

51. What is the purpose of a "servo subsystem" in a CNC machine?
A) Controlling the machine's power
B) Moving the machine's axes according to the program
C) Cooling the machine
D) Generating the machine's program

52. For an open belt drive, the velocity ratio is directly proportional to:
A) The square of the diameters of the pulleys
B) The sum of the diameters of the pulleys
C) The inverse of the diameters of the pulleys
D) The diameters of the pulleys

53. In a reciprocating engine, the maximum fluctuation of energy occurs during:
A) The compression stroke B) The power stroke
C) The exhaust stroke D) The intake stroke

54. Dynamic balancing is necessary when:
A) Masses are rotating in a single plane
B) Masses are rotating in different planes
C)The system is only experiencing static unbalance
D) The system is not experiencing any unbalanced forces

55. What type of heat treatment is used to modify the properties of the surface layers of a component?
A) Hardening B) Case hardening
C) Annealing D) Tempering

56. What is the name of the casting process where molten metal is forced into a mold under high pressure?
A) Investment easting B) Die casting
C) Slush casting D) Centrifugal casting

57. In mechanical working processes, what type of deformation is typically employed?
A) Elastic deformation B) Plastic deformation
C) Thermal deformation D) Magnetic deformation

58. What is the primary function of the shielding gas in MIG welding?
A) To cool the weld pool
B) To protect the weld area from atmospheric contamination
C) To provide additional hent to the weld
D) To assist with material removal

59. Which welding equipment is used to deliver the filler metal in gas metal are welding (GMAW)?
A) Welding torch B) Power source
C) Wire feeder D) Electrode holder

60. ln machining, which of the following is the primary mechanism by which cutting tool removes material
from a workpiece?
A) Thermal ablation B) Shear deformation

C) Electrochemical dissolution D) Evaporation

61. What is the purpose of the rake angle on a cutting tool?
A) To create a clearance for the tool to cut without rubbing
B) To assist in chip removal and heat dissipation
C) To determine the depth of cut
D) To control the feed rate

62. What is the name of the process where a gas expands or contracts at constant temperature?
A) Adiabatic B) Isochoric
C) Isothermal D) Isobaric

63. In which air standard cycle does hent addition occur at constant pressure?
A) Otto cycle B) Diesel cycle
C) Stirling cycle D) Brayton cycle

64. What is the term for the ratio of the maximum deflection of a vibrating body to its static deflection?
A) Dynamic Magnification factor
B) Frequency Ratio
C) Damping Ratio
D) Transmissibility

65. In a ship, the gyroscopic effect caused by the propeller rotation will tend to:
A) Cause the ship to roll
B) Cause the ship to pitch
C) Increase the ship's speed
D) Help the ship maintain a straight course

66. Which type of boiler is commonly used for high-pressure steam generation, such as in power plants?
A) Firetube boiler B) Water tube boiler
C) Small boiler D) Package boiler

67. What is the main function of the valve mechanism in a reciprocating steam engine?
A) To ensure proper lubrication
B) To control the flow of steam into and out of the cylinder
C) To maintain the correct cylinder temperature
D) To convert rotary motion into linear motion.

68. "Least count" of a measuring instrument signifies:
A) The maximum value the instrument can measure
B) The smallest value that can be reliably measured by the instrument.
C) The error always presents in the instrument
D) The number of measurements taken

69. What is the typical cross-sectional size of a rectangular slip gauge?
A) 9 mm wide and 30-35 mm long
B) 10 mm wide and 25-30 mm long
C) 12 mm wide and 35--10 mm long
D) 15 mm wide and 40--15 mm long

70. Which type of fit is characterized by a negative allowance?
A) Clearance Fit B) Interference Fit
C) Transition Fit D) Running Fit

71. Which of the following is a key principle of Method Study?
A) Reduce the number of operations
B) Increase the number of workers
C) Ignore the ergonomics of the workplace
D) Increase the complexity of the process

72. Which of the following materials is NOT commonly used as an electrolyte in ECM?
A) Sodium Chloride B) Potassium Nitrate
C) Water D) Sulfuric Acid

73. Which of the following equations represents the relationship between sensible heat (Q), specific heat
capacity (c), mass (m), and temperature change (ΔT)?
A) Q= mcΔP B) Q= mcΔT
C) Q=mc/ΔT D) Q=m/cΔT

74. Heat does not spontaneously flow from a colder body to a hotter one. Which of the following
thermodynamics law states this?
A) Zeroth law of thermodynamics
B) First law of thermodynamics
C) Second law of thermodynamics
D) Third Iaw of thermodynamics

75. What is the primary purpose of the tempering heat treatment process?
A) To increase the hardness of steel
B) To reduce the brittleness of hardened steel
C) To improve the machinability of steel
D) To increase the corrosion resistance of steel

76. Which of the following casting processes uses a pattern made of wax?
A) Sand casting B) Die casting
C) Investment casting D) Plaster mold casting

77. Which type of steam turbine uses steam expansion to directly drive the turbine blades?
A) Reaction turbine B) Impulse turbine
C) Compounded turbine D) Velocity-compounded turbine

78. What is the process of splitting an atom's nucleus into two or more lighter nuclei called?
A) Fission B) Fusion
C) Radioactivity D) Ionization

79. What is the purpose of a "process chart in Method Study?
A) To determine the standard time for a job
B) To analyse the sequence of operations in a process
C) To record the time taken by a worker to perform a task
D) To measure the output of a machine

80. Which of the following materials is NOT typically suitable for EDM?
A) Hardened steel B) Non-ferrous alloys
C) Plastics D) Super alloys

81. Which of the following processes is an example of an abrasive cutting process?
A) CNC milling B) Laser cutting
C) Waterjet cutting D) Grinding

82. In static balancing, what is the primary objective?
A) To ensure that the resultant centrifugal force is zero
B) To make sure the center of gravity lies on the axis of rotation
C) To minimize -vibrations caused by unbalanced forces
D) To maintain a constant speed of rotation

83 Which of the following types of vibrations is characterized by a decrease in amplitude over each cycle?
A) Free Vibration B) Forced Vibration
C) Damped Vibration D) Resonance

84. Which of the following refrigerants is commonly used in modern refrigeration systems due to its low
Ozone Depletion Potential (ODP)?
A) R-22 B) R-134a
C) R-12 D) R-502

85. What is the main purpose of a safety valve in a steam boiler?
A) To regulate the steam pressure
B) To prevent steam leaks
C) To prevent boiler explosions
D) To control the water level

86. What is the purpose of a superheater in a steam power plant?
A) To raise the pressure of the steam
B) To increase the temperature of the steam
C) To reduce the moisture content of the steam
D) To convert water into steam

87. Which joining process involves the application of pressure and heat to fuse metal parts together?
A) Brazing B) Soldering
C) Resistance welding D) Thermit welding

88. In TIG (Tungsten Inert Gas) welding, what is used to generate the arc between the tungsten electrode
and the work piece?
A) A filler wire B) An electric current
C) An electrode holder D) A flux powder

89. Which of the following is a type of quick return mechanism often found in shaper machines?
A) Cam mechanism
B) Crank and slotted lever mechanism
C) Hydraulic quick return
D) Pneumatic quick return

90. What is the term for the process of dividing the periphery of a workpiece into equal parts?
A) Indexing B) Dressing
C) Boring D) Chamfering

91. Galvanization: is a protective coating process where a metal is coated with:
A) Chromium B) Zine
C) Nickel D) Aluminium

92. Which type of milling operation is best suited for creating large, flat surfaces?
A) Slab Milling B) Form Milling
C) Straddle Milling D) Profile Milling

93. What is the primary energy source for ultrasonic machining?
A) Electrical energy
B) Chemical energy
C) Mechanical energy (high frequency vibrations)
D) Thermal energy

94. In a slider-crank mechanism, the connecting rod transmits motion from the to the
A) Slider, Frame B) Crank, Slider
C)Frame, Slider D) Slider. Crank

95. If the driving pulley is rotating at 600 RPM and the driven pulley has me twice that of the driving pulley,
what is the speed of the driven pulley in RPM assuming no slip?
A) 100 RPM B) 300 RPM
C) 600 RPM D) 1200 RPM

96. In thread cutting, what is the term for the distance the tool travels in one complete revolution of the
thread?
A) Pitch B) Lead
C) Depth D) Angle

97. According to Charles's Law, what happens to the volume of a gas if the temperature is increased at
constant pressure?
A) The volume decreases
B) The volume remains constant
C) The volume increases
D) The relationship is not directly proportional

98. Which air standard cycle uses a hent exchanger?
A) Otto cycle B) Diesel cycle
C) Stirling cycle D) Brayton cycle

99. Which of the following is a type of fossil fuel?
A) Coal B) Biomass
C) Ethanol D) Nuclear fuel

100. In a counter-flow heat exchanger, where fluids move in opposite directions, what is the primary
advantage?

A) Higher overall heat transfer coefficient
B) Lower overall heat transfer coefficient
C) Increased fluid mixing
D) Reduced fouling potential