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Question 1 of 65
1. Question
Divergence of the curl of a twice differentiable continuous vector function is
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Question 2 of 65
2. Question
For two nonzero vectors is perpendicular to then
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Question 3 of 65
3. Question
For an orthogonal matrix Q, the valid equality is
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Question 4 of 65
4. Question
The product of a complex number z = x + iy and its complex conjugate is
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Question 5 of 65
5. Question
Using Simpson’s 1/3 rule for numerical integration, the consecutive points are joined by a
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Question 6 of 65
6. Question
For a two dimensional stateofstress defined as σ_{xx} = σ_{yy} = τ_{xy} = S, the Mohr’s circle of stress has
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Question 7 of 65
7. Question
A specimen of steel has yield strength of 700 MPa. The specimen is subjected to a state of planestress with σ_{1} = σ_{2} = 500 MPa. The factor of safety according to the vonMises theory of failure is _______
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NAT Type Question

Question 8 of 65
8. Question
The inside and outside radii of a thickwalled cylindrical pressure vessel are denoted by a and b, respectively. If the vessel is subjected to an internal pressure P, then the magnitude of the radial stress σ_{rr} is
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Question 9 of 65
9. Question
A metallic cylindrical casing of an exhaust pipe has inner radius 50 mm and wall thickness 7 mm. If the thermal conductivity of the material of the casing is 50 W/mK, then the thermal resistance of the casing in K/kW is _____(up to three decimal places).
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NAT Type Question

Question 10 of 65
10. Question
In Value Engineering approach, the value of the product is
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Question 11 of 65
11. Question
Match the ASME process charge symbols with their correct description
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Question 12 of 65
12. Question
In Glass fiber Reinforce Plastic (GFRP) composites with long fibers, the role matrix is to
(P) support and transfer the stresses to the fibers
(Q) reduce propagation of cracks
(R) carry the entire load
(S) protect the fibers against damage
The correct statements are
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Question 13 of 65
13. Question
Turning, drilling, boring and milling are commonly used machining operations. Among these, the operation(s) performed by a single point cutting tool is (are)
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Question 14 of 65
14. Question
In chemical machining, the etch factor is expressed as
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Question 15 of 65
15. Question
A Shewhart was developed for an incontrol process. Considering the probability of a point falling outside the 3σ control limits as 0.0026, the value of average run length for this chart is ______
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NAT Type Question

Question 16 of 65
16. Question
Accuracy of measuring instrument is expressed as
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Question 17 of 65
17. Question
The operating characteristic curves of three single sampling plans X, Y and Z with same lot size and acceptance number are shown in the Figure.
Considering the above operating characteristic curves, the correct relationship of the plans with respect to sample size is
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Question 18 of 65
18. Question
In carbon dioxide molding process, the binder used is
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Question 19 of 65
19. Question
A steel wire of 2 mm diameter is to be drawn from a wire of 5 mm diameter. The value of true s train developed is _____(up to three decimal places).
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NAT Type Question

Question 20 of 65
20. Question
In gas tungsten arc welding process, the material coated on pure tungsten electrode to enhance its current carrying capacity is
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Question 21 of 65
21. Question
In powder metallurgy, the process ‘atomization refers to a method of
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Question 22 of 65
22. Question
The ideal stressstrain behavior for a completely brittle material during tensile testing up to failure is described by
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Question 23 of 65
23. Question
With reference to IronCarbon equilibrium phase diagram, the crystal structure of 0.3% plain carbon steel at 1, 100℃ is
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Question 24 of 65
24. Question
If E is the modulus of elasticity in GPa, G is the shear modulus in GPa and v is the Poisson’s ratio of a linear elastic and isotropic material, the three terms are related as
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Question 25 of 65
25. Question
A machined surface with standard symbols indicating the surface texture is shown in the Figure. (All dimensions in the Figure are in micrometer).
The waviness height (in micrometer) of the surface is
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Question 26 of 65
26. Question
The improper integral converges to
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Question 27 of 65
27. Question
The local minima of the function f(x) = x^{2} – x^{4} in the range −0.8 ≤ x ≤ 0.8 is located at
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Question 28 of 65
28. Question
RungeKutta fourth order method is used to solve the differential equation If the initial value y(0) = 2 and stepsize is 0.1, then the value of y(0.1) is _______(up to three decimal places)
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NAT Type Question

Question 29 of 65
29. Question
Two machines are defective in a lot of 10. A combination of four machines is to be picked at a time from the lot. The maximum number of combinations that can be obtained without any defective machine is ______
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NAT Type Question

Question 30 of 65
30. Question
The simplysupported beam shown in the Figure is loaded symmetrically using two equal point loads P. The radius of curvature of deflectioncurve is 15m for the portion of the beam that is subjected to pure bending. The vertical deflection (in mm) at point M, equidistant from both the supports, is _____(up to two decimal places).
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NAT Type Question

Question 31 of 65
31. Question
A solid circular shaft is subjected to a bending moment M and torque T simultaneously. Neglecting the effects of stress concentration, the equivalent bending moment is expressed as
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Question 32 of 65
32. Question
A pair of spur gears with 20° fulldepth involute teeth is used to transmit 3.5 kW of power. The pinion rotates at 700 rpm and has pitch circle diameter of 100 mm. Assuming a single pair of teeth in contact, the total force acting on a gear tooth (in kN) is
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Question 33 of 65
33. Question
A manometer is used for the pressure measurement in a closed tank. The three fluids f1, f2 and f3 have specific weights γ, 2γ and 0.5γ, respectively. The schematic arrangement with manometric readings and other dimensions are shown in the Figure. In order to ensure zero gauge pressure in the tank at the midheight level (h/2), the height of the tank h(in m) is _______
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NAT Type Question

Question 34 of 65
34. Question
A pipeline with variable crosssection contains water with specific weight 10^{4}N/m^{3}. The flow conditions at two points 1 and 2 on the axis of the pipe are:
P_{1} = 3 bar, V_{1} = 10 m/s
P_{2} = 1 bar, V_{2} = 20 m/s
Consider frictional losses to be negligible. For noflow condition between points 1 and 2(as shown in Figure), if the height z_{1} from the datum is 1 m, then the height z_{2}(in m) is _______ (g = 9.81 m/s^{2})
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NAT Type Question

Question 35 of 65
35. Question
A reversible heat engine (E) operating in a cycle interacts with three reservoirs 1, 2 and 3 maintained at temperatures T_{1} = 500 K, T_{2} = 400 K and T_{3} = 300 K, respectively. The engine receives 10 kJ of heat from reservoir 1 and rejects 3 kJ to reservoir 3. The net work output, W_{net}(in kJ) from the engine is ______
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NAT Type Question

Question 36 of 65
36. Question
A schematic diagram of peripheral milling is shown in the Figure.
If t is the depth of cut and d is the diameter of the milling cutter, then the length of approach (l_{a}) is expressed as
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Question 37 of 65
37. Question
An electrical appliances showroom sells 2,400 ceiling fans in one year (52 weeks). The holding cost is 10% the cost of the ceiling fan. The cost of one ceiling fan is Rs. 600. The cost incurred for placing an order is Rs. 201. There is a lead time of 5 weeks. The economic order quantity (EOQ) and the reorder level, respectively (rounded to the next higher integer) are
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Question 38 of 65
38. Question
In a calendar year, the demand forecast of motorbikes for the month of June is 200. The actual demand of motorbikes for the month of June and July are 300 and 350, respectively. If single exponential smoothing method with smoothing constant 0.7 is used, then the demand forecast for the month of August is _____
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NAT Type Question

Question 39 of 65
39. Question
In a project, tasks, A, B, C, D, E, F, G, H, I and J are to be performed. The precedence relationships and the time required (in days) to complete the tasks are given in the Table.
The time required (in days) to complete the project along the critical path is ______
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NAT Type Question

Question 40 of 65
40. Question
The potential production alternative for manufacturing a product along with their unit cost and monthly capacity are given in the Table.
The inventory at the end of July is 100 units. If the demand for the month of August is 620, then the minimum total cost (in Rs.) to meet the demand is _______
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NAT Type Question

Question 41 of 65
41. Question
The preparatory and miscellaneous codes used in CNC part programming and the functions are given in the Table.
The correct combinations of code and the respective function is
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Question 42 of 65
42. Question
A surface of 30 mm × 30 mm of an iron block is machined using electrochemical machining process. The atomic weight and valency of iron of 55.85 and 2, respectively. The density o f iron is 7,860 kg/m^{3}. If input current is 1,000 A and Faraday’s constant is 96,540 Coulombs, then the feed rate (in mm/min) is _______(up to two decimal places).
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NAT Type Question

Question 43 of 65
43. Question
Quality control department of a company maintains ‘c’ chart to assess the quality of laptops. In this process, twenty laptops are examined randomly. The number of nonconformities observed per laptop is given in the Table.
Based on the data, the upper control limit for the ‘c’ chart is _______(up to two decimal places).
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NAT Type Question

Question 44 of 65
44. Question
The Merchant circle diagram showing various forces associated with a cutting process using a wedgeshaped tool is given in the Figure.
The coefficient of friction can be estimated from the ratio
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Question 45 of 65
45. Question
An air conditioner unit is expected to run continuously. The mean time between failures (MTBF) for this unit is 2,000 hours and the mean time to repair (MTTR) is 48 hours. The availability of the air conditioning unit is ______(up to three decimal places).
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NAT Type Question

Question 46 of 65
46. Question
A firm manufactures capacitors using a specialized process. The desired specification for the capacitance is 40 ≠ 10 picofarads (pF). The process used is in statistical control. If the process mean is 41 pF and the estimated standard deviation is 3 pF, then the process capability index C_{pk} is _______
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NAT Type Question

Question 47 of 65
47. Question
A metallic strip having thickness of 12 mm is to be rolled using two steel rolls, each of 800 mm diameter. It is assumed that there is no change in width of the strip during rolling. In order to achieve 10% reduction in crosssectional area of the strip after rolling, the angle subtended (in degrees) by the deformation zone at the center of the roll is
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Question 48 of 65
48. Question
An electron beam welding process uses 15 mA beam current at an accelerating voltage of 150 kV. The energy released per second by the beam (in J) is ______(up to one decimal place).
(1 Ampere = 6.28 × 10^{18} electrons per second, 1 eV= 1.6 × 10^{−19} J)
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NAT Type Question

Question 49 of 65
49. Question
In a machine shop, four jobs need to be assigned to four different machines. Each of the jobs is to be assigned to one machine only at a time. The time taken to complete the job in different machines is given in the Table.
In order ensure that the total time required to complete all the jobs is minimum, the optimal assignment of the job is
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Question 50 of 65
50. Question
A hose coupling manufacturing company has production capacity of 2,500 units per year. The unit selling price of the item is Rs. 150/ The fixed cost of production is Rs. 80,000 and variable cost of production per unit its Rs. 70. If the company wishes to achieve a profit of Rs. 20,000 during the calendar year, then the minimum quantity to be produced is ______
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NAT Type Question

Question 51 of 65
51. Question
Schematic diagram of pouring basin and sprue of a gating system is shown in the Figure. Depth of molten metal in the pouring basin is 100 mm and the height of the sprue is 1,500 mm.
Consider the crosssection of the sprue is circular, the ratio d_{1} : d_{2} to avoid aspiration is
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Question 52 of 65
52. Question
In a numerical control (NC) machine positioning system, the measures of precision are expressed by considering a single axis as shown in the Figure.
If σ is standard deviation of the error distribution, then l, m and n are
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Question 53 of 65
53. Question
In a machining operation with turning tool, the tool life (T) is related to cutting speed v(m/s), feed f(mm) and depth of cut d(mm) as
T=Cv^{−}^{2.5}f^{−}^{0.9}d^{−}^{0.15}
where, C is a constant. The suggested values for the cutting parameters are: v = 1.5 m/s, f = 0.25 mm and d = 3 mm for normal rough turning. If the operation is performed at twice the cutting speed and the other parameters remain unchanged, the corresponding percentage change in tool life is ______
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NAT Type Question

Question 54 of 65
54. Question
The annual demand of wrist produced on an assembly line is 1,03,125 units. The line operates 50 weeks/year, 5 shifts/week and 7.5 hours/shift. The uptime efficiency of the line is 99%. The cycle time (T_{c}) of the assembly line (in minutes/unit) is _____(up to two decimal places).
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NAT Type Question

Question 55 of 65
55. Question
In a gear manufacturing company, three orders P, Q and R are to be processed on a hobbing machine. The orders were received in the sequence P – Q – R. The Table indicates the process time remaining and production calendar due date for each order.
Considering today as the Day 10 in the production calendar of the Hobbing Shop, the sequence of the order scheduled using the ‘Critical Ratio’ rule is
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Question 56 of 65
56. Question
She has a sharp tongue and it occasionally turn _______
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Question 57 of 65
57. Question
I_____ made arrangements had I _______ informed earlier.
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Question 58 of 65
58. Question
In the summer, water consumption is known to decrease overall by 25%. A Water Board official states that in the summer household consumption decreases by 20%, while other consumption increases by 70%.
Which of the following statements is correct?
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Question 59 of 65
59. Question
40% of deaths on city roads may be attributed to drunken driving. The number of degrees needed to represents this as a slice of a pie chart is
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Question 60 of 65
60. Question
Some tables are shelves. Some shelves are chairs. All chairs are benches. Which of the following conclusions can be deduced from the preceding sentences?
i. At least one bench is a table
ii. At least one shelf is a bench
iii. At least one chair is a table
iv. All benches are chairs
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Question 61 of 65
61. Question
‘If you are looking for a history of India, or for an account of the rise and fall of the British Raj, or for the reason of the cleaving of the subcontinent into two mutually antagonistic parts and the effects this mutilation will have in the respective sections, and ultimately on Asia, you will not find it in these page; for though I have spent a lifetime in the country, I lived too near the seat of events, and was too intimately associated with the actors, to get the perspective needed for the impartial recording of these matters”.
Here, the word ‘antagonistic’ is closest in meaning to
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Question 62 of 65
62. Question
S, T, U, V, W, X, Y, and Z are seated around a circular table. T’s neighbours are Y and V, Z is seated third to the left of T and second to the right of S,. U’s neighbours are S and Y; and T and W are not seated opposite each other. Who is third to the left of V?
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Question 63 of 65
63. Question
Trucks (10 m long) and cars (5 m long) go on a single lane bridge.. There must be a gap of at least 20 m after each truck and a gap of at least 15 m after each car. Trucks and cars travel at a speed of 36 km/h. If cars and trucks go alternately, what is the maximum number of vehicles that can use the bridge in one hour?
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Question 64 of 65
64. Question
There are 3 Indians and 3 Chinese in a group of 6 people. How many subgroups of this group can we choose so that every subgroup has at least one Indian?
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Question 65 of 65
65. Question
A contour line joins locations having the same height above the mean sea level. The following is a contour plot of a geographical region. Contour lines are shown at 25 m intervals in this plot.
The path from P to Q is best described by
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