| Post Name | ASST. PROFESSOR IN MECHANICAL ENGG. - TECH.EDN. (EGG. COLLEGES) |
|---|---|
| Question Paper Code | 099/2023 |
| Category Code | 727/2021 |
| Date of Test | 30 June 2023 |
| Medium of Question | ENGLISH |
| Exam Type | OMR Examination |
| Total Questions | 100 |
1
If 2 and 3 are the eigen values of a square matrix of order 2, express A^2 in terms of A and I.
Answer
A. 5A - 6I
2
If Ξ± and Ξ² are the eigen values of \begin{pmatrix} 3 & -1 \\ -1 & 5 \end{pmatrix}, form the matrix whose eigen values are \(\alpha^3\) and \(\beta^3\).
Answer
C. \begin{pmatrix} 38 & -50 \\ -50 & 138 \end{pmatrix}
3
The value of the integral \int_{1+i}^{2+4i} z^2 dz along the straight line joining 1 + i and 2 + 4i is
Answer
A. \frac{86}{3} - 6i
4
Find the value of \frac{\partial^2 z}{\partial x \partial y}, if z^3 - xz - y = 0.
Answer
A. \frac{(3z^2+x)}{(3z^2-x)^3}
5
The general solution of xdy - ydx = 0 is
Answer
A. y = cx
6
A unit normal to xy^3z^2 = 4 at the point (-1, -1, 2) is
Answer
B. \frac{1}{\sqrt{11}}(\vec{i} + 3\vec{j} - \vec{k})
7
Find the constants a, b, c, if \overrightarrow{F} = (x + 2y + az) \overrightarrow{i} + (bx - 3y - z) \overrightarrow{j} + (4x + cy + 2z) \overrightarrow{k} is irrotational.
Answer
D. 4.2 - 1
8
If u = \frac{y^2}{v} and v = \frac{x^2}{v}, find \frac{\partial(u, v)}{\partial(x, v)}.
Answer
B. 3
9
The value of \int_{C} \frac{dz}{z-2}, where C is a circle given by |z-2|=1 is
Answer
C. 2\pi i
10
How should f(x) be defined at x = -5, x = 0 and x = 5 in order that the Fourier series will converge to f(x) for \(-5 \le x \le 5\) ? Where \(f(x) = \begin{cases} 0, -5 < x < 0 \\ 3, 0 < x < 5 \end{cases}\)
Answer
D. f(x) = \begin{cases} \frac{3}{2}, x = -5 \\ 0, -5 < x < 0 \\ \frac{3}{2}, x = 0 \\ 3, 0 < x < 5 \\ \frac{3}{2}, x = 5 \end{cases}
11
Air at 300 K flows over a 4 m long and 1.8 m wide surface of a plate with velocity of 5 m/s. The length of the surface beyond which the flow remains turbulent is [For air, K = 0.02 W/mK, Pr = 0.717, \(\gamma\) = 1.7 Γ 10-5 m2/s]
Answer
B. 1.7 m
12
Choose the correct option from the following statements for compressible flow of fluid.
Answer
A. The higher the particle Mach number, the more slender the Mach cone
13
In fully turbulent flow through a rough pipe, the friction factor 'f' is a function of [Where Re is Reynolds number and \(\epsilon_{\text{D}}\) is relative roughness]
Answer
A. 'Re' and '\leq'
14
Match the dimensionless number given in List I to the type of force which is one of its constituents in List II: a. Weber number; b. Froude number; c. Euler number; d. Mach number. List II: 1. Pressure force; 2. Surface tension force; 3. Elastic force; 4. Gravity force.
Answer
B. a-2, b-4, c-1, d-3
15
The typical operating characteristic curves for a fan with backward-curved blades are shown in the figure. Match List I with List II: a. Curve A; b. Curve B; c. Curve C; d. Curve D. List II: i. Total pressure; ii. Shaft power; iii. Total efficiency; iv. Fan static pressure.
Answer
A. a-ii, b-iii, c-iv, d-i
16
Total pressure on the top of a closed cylindrical vessel of diameter 'd' completely filled with water when rotated about its vertical axis is directly proportional to
Answer
B. d2
17
The maximum hydraulic efficiency of an impulse turbine having angle of blade tip at outlet, '\(\phi\)' is given as
Answer
B. \frac{1+\cos\phi}{2}
18
Choose the true statement from the following options.
Answer
B. Parameters of the turbulent boundary layer vary as Rev-/5
19
When the boundary layer on the cylinder becomes turbulent, the drag coefficient is reduced by a factor of about
Answer
C. 4
20
The universal velocity distribution for turbulent flow in a channel is well represented by [Where u* is frictional velocity = \(\sqrt{C\omega/\rho}\)]
Answer
A. \frac{u}{u^*} = 2.5ln \frac{yu^*}{v} + 5.0
21
Specific speed of a turbine and pump are (symbols have the usual meaning)
Answer
D. \frac{N\sqrt{P}}{D^{5/4}} and \frac{N\sqrt{Q}}{D^{3/4}} respectively
22
A laminar boundary layer occurs over a flat plate at zero incidence to the flow. The thickness of boundary layer at a section 1.5 m from leading edge is 2 mm. The thickness of boundary layer at a section 3 m from the leading edge will be
Answer
C. 2.828 mm
23
The general form of expression for continuity equation in a Cartesian co-ordinate system for unsteady incompressible flow is given by
Answer
A. \frac{\partial u}{\partial x} + \frac{\partial v}{\partial y} + \frac{\partial w}{\partial z} = 0
24
If a cylindrical boiler drum kept in the horizontal position is full of water, then the time taken to empty it completely depends upon
Answer
C. R^{3/2}
25
Power transmitted through a nozzle is maximum when the head loss due to friction in pipe is
Answer
A. \frac{1}{2} the total head supplied at inlet of pipe
26
In winter, a house need 198 MJ/hr heat requirement. For this purpose, how much amount of heat to be abstracted from outside by the heat pump if it is having 8.0 COP ?
Answer
C. 173250 kJ/hr
27
The effectiveness of a parallel-flow heat exchanger is calculated by using the relation
Answer
D. [1 - exp(-NTU(1 + C))] / (1 + C)
28
Identify the wrong statement. 1. Reversed Carnot cycle is nothing but Carnot Refrigeration cycle. 2. The efficiencies of all reversible heat engines operating the same two reservoirs are the same. 3. The Carnot efficiency approaches unity when the low temperature reservoir goes more than the high temperature reservoir. 4. Work is more valuable form of energy than heat.
Answer
C. 3
29
Heat transfer coefficient for free convection in gases, forced convection in gases and vapours, and for boiling water lie, respectively in the ranges of
Answer
A. 5 - 15, 20 β 200 and 3,000 β 50,000 W/m2K
30
A thin plate 2 m long and 1 m width is placed in an air stream (density = 1.0 \text{ kg/m}^3 and viscosity = \(0.85 \times 10^{-5}\) Pa.s) moving with a velocity of 1 m/s. What will be the type of flow over the plate?
Answer
B. Laminar flow over the entire plate
31
A pipe carrying steam runs in a large room and is exposed to surrounding air at a temperature of 27Β°C. The pipe surface is subjected to 327Β°C. Find the loss of heat to surroundings due to thermal radiation. Assume pipe surface emissivity \(= 0.5\).
Answer
B. 3.44 kW/m2
32
The Nusselt number for fully developed laminar flow in a tube under constant heat flux is equal to
Answer
C. 48/11
33
The Clausius-Clapeyron equation is
Answer
A. \ln\left(\frac{P_1}{P_2}\right) = \frac{\Delta H_{vap}}{R} \left(\frac{1}{T_2} - \frac{1}{T_1}\right)
34
Identify the correct statements with regard to Otto cycle. 1. Its efficiency can be improved by using a working fluid of higher value of ratio of specific heats. 2. It is not a reversible cycle. 3. The practical way of increasing its efficiency is to increase the compression ratio. 4. Carburetted gasoline engines working on Otto cycle can work with compression ratios more than 12.
Answer
B. 1, 2 and 3 are correct
35
In steam turbines, the ratio of the enthalpy drop in the moving blades to the sum of the enthalpy drop in the moving and fixed blades is called
Answer
D. Degree of reaction
36
In a regenerative feed heating cycle, the greatest economy is affected
Answer
C. When steam is extracted from several places in different stages of steam turbine
37
Identify the wrong statement. 1. The knocking tendency in CI engines increase with increasing the temperature of inlet air. 2. To avoid knock in SI engine, the combustion chamber must have large bore. 3. Detonation in SI engine occurs due to pre-ignition of change before spark is struck. 4. Advancing the spark timing in spark ignition engines leads to reduce the knocking tendency.
Answer
D. All are wrong
38
A Carnot refrigerator having the capacity of 15 tonnes. The higher temperature of the refrigerant in the system is \(27^{\circ}\)C and the lower temperature is \(-23^{\circ}\)C. What is the work input value in MJ/hr?
Answer
Question Cancelled
39
Helmholtz free energy (F) relation is
Answer
B. F = U - TS
40
In hydrodynamic boundary layer, the energy, momentum and displacement thickness are observed to be 1/18, 1/15 and 1/3 respectively. The shape factor value will be
Answer
C. 5
41
When trying to turn a key into a lock ____________ is applied.
Answer
Question Cancelled
42
A stone of mass m at the end of a string length l is whirled in a vertical circle at a constant speed. The tension in the string will be maximum when the stone is
Answer
D. At the bottom of the circle
43
A 1 kg block is resting on a surface with coefficient of friction \mu = 0.1. A force of 0.8 N is applied to the block as shown in the figure. The friction force is \(0.8 \text{ N}\) 1 kg
Answer
A. 0.8 N
44
The time variation of the position of a particle in rectilinear motion is given by \(x = 2t^3 + t^2 + 2t\). If y is the velocity and a is the acceleration of the particle in consistent units, the motion started with
Answer
D. v = 2, a = 2
45
A circular solid disc of uniform thickness 20 mm, radius 200 mm and mass 20 kg, is used as a flywheel. If it rotates at 600 rpm, the kinetic energy of the flywheel, in Joules is
Answer
B. 790
46
The most suitable follower motion for high-speed engine is
Answer
B. Cycloidal
47
In a clock mechanism, the hours and minute hands are connected by _________ gear train.
Answer
C. Reverted
48
If the ratio of length of connecting rod to the crank increases
Answer
A. Secondary unbalanced force decrease
49
If the air screw of an aeroplane rotates clockwise when viewed from the rear and the aeroplane takes a right turn, the gyroscopic effect will be
Answer
A. Tend to raise the tail and depress the nose
50
The locus of instantaneous centre of a moving body relative to a fixed body is known as the
Answer
D. Space centrode
51
In the mechanism given below, if the angular velocity of the eccentric circular disc is 1 rad/s, the angular velocity (rad/s) of the follower link for the instant shown in the figure. 19 5 \(\overline{45}\)
Answer
B. 0.1
52
A mass m attached to a spring is subjected to a harmonic force as shown in figure. The amplitude of the forced motion is observed to be 50 mm. The value of m (in kg) is =3000 Nm m \(\blacktriangleright\) F(t)=100cos(100t)
Answer
A. 0.1
53
A rotating disc of 1 m diameter has two eccentric masses of 0.5 kg each at radii of 50 mm and 60 mm at angular positions of \(0^{\circ}\) and 150Β°, respectively. A balancing mass of 0.1 kg is to be used to balance the rotor. What is the radial position of the balancing mass?
Answer
C. 150 mm
54
The mechanism used in a shaping machine is
Answer
D. An inversion of the single slider-crank chain
55
A vibrating machine is isolated from the floor using springs. If the ratio of excitation frequency of vibration of machine to the natural frequency of the isolation system is equal to 0.5, then transmissibility ratio of isolation is
Answer
C. \frac{4}{3}
56
Consider the following statements regarding state of stress at a point: 1. Number of components required to define the state of stress at a point are nine. 2. Number of components required to define the state of stress at a point are twelve. 3. Number of components required to define the state of stress at a point in equilibrium condition are six. 4. Number of components required to define the state of stress at a point in equilibrium condition are sixteen. Which of the following statements is/are correct?
Answer
A. 1 and 3 only
57
State of plane stress at a point is given as : \sigma_x = \sigma_y = 100 MPa and Txy = 0. The radius of Mohr's circle will be
Answer
B. 0
58
A cantilever beam of diameter D, length L, cross-section A is subjected to a uniformly distributed load W and a concentrated load \(W_1\) at a distance \(L_1\) from free end will have maximum bending moment of
Answer
Question Cancelled
59
Consider the following statements regarding point of contraflexure: 1. Shear force is zero at the point of contraflexure. 2. Bending moment is zero at the point of contraflexure. 3. Bending moment changes its sign at the point of contraflexure. 4. Shear force changes its sign at the point of contraflexure. Which of the following statements is/are correct?
Answer
C. 2 and 3 only
60
In terms of theoretical stress concentration factor (kt) and the notch sensitivity 'q', the fatigue stress concentration factor \((ki)\), is expressed as
Answer
B. k_1 = 1 + q (k_1 - 1)
61
The state of stress at a point is given as : \(\sigma_{x}\) = 100 N/mm2, \(\sigma_{y}\) = 40 N/mm2 and Txy = 40 N/mm2 If the yield strength \(Sv\) of the material is 300 MPa, the factor of safety using maximum shear stress theory will be
Answer
A. 3
62
The S-N curve for steel becomes asym
Answer
A. 10^6 cycles
63
For the bracket bolted as shown with 4 bolts P, Q, R and S. Which of the bolts are heavily loaded? \(\begin{array}{c}\n\text{PO} & \text{OQ} \\ + \end{array}\)
Answer
D. Q and R
64
The dynamic load factor or velocity factor c_{v} as proposed by AGMA for gears whose teeth are finished by hobbing or shaping, is given by
Answer
B. c_v = 50/(50 + \sqrt{2000})
65
Consider the following statements regarding use of splined shaft: 1. Transmitting power. 2. Holding a fly wheel rigidly in position. 3. Moving axially the gears mounted on it. 4. Mounting V-belt pulley on it. Which of the following statements is/are correct?
Answer
A. 1 and 3 only
66
A helical coil spring with wire diameter 'd' and mean coil diameter 'D' is subjected to axial load. A constant ratio of 'D' and 'd' has to be maintained, such that the extension of the spring is independent of 'D' and 'd'. What is the ratio?
Answer
A. D^3/d^4
67
Match the List -1 with List -1 and select the correct answer using the codes given below in the lists: \(List - I\) \(List - II\) 1. Scooters P. Single-plate clutch Q. Multi-plate clutch 2. Rolling mills 3. Trucks R. Centrifugal clutch S. Jaw clutch 4. Moped Codes: P Q R S
Answer
C. 3 1 4 2
68
Which one of the following is the criterion in the design of hydrodynamic bearings?
Answer
C. Sommerfeld number
69
The value of bearing characteristic number corresponding to minimum coefficient of friction in hydrodynamic bearings is called
Answer
B. Bearing modulus
70
In case of thin cylindrical shell, the volumetric strain is given by
Answer
D. \varepsilon_v = (pd/2tE) (2.5 - 2/m)
71
Which of the following statements are true in the case of Gray Cast Iron? i. It has high compressive strength. ii. It has self-damping property. iii. It forms continuous chips while machining.
Answer
B. Only i and ii
72
Cooling rate faster than critical cooling rate in iron carbon system (TTT diagram) will form
Answer
C. Martensite
73
Which of the following welding is best suited for aluminium?
Answer
A. TIG
74
Which of the following is a single point cutting tool operation carried out in milling machine?
Answer
D. Fly cutting
75
Match the correct pairs: Process Characteristics P. Extrusion 1. Squeezing out of material through hole Q. Forging 2. Application of sudden blows R. Spinning 3. High speed rotation for shaping
Answer
A. P-1, Q-2, R-3
76
N001 G21 G90 G92 X0 Y-50.0 Z0; N002 G00 X20 Y30; A portion of CNC part programme is given above. Which of the following function is possible using these codes?
Answer
C. rapid movement to the point (20, 30) in absolute coordinates
77
De-energized state of a normal relay is represented in PLC ladder logic diagram using
Answer
B. normally closed contact
78
Match the correct pairs : Function of fluid used Processes P. EDM 1. Abrasive action Q. USM 2. Prevents electric cond. R. ECM 3. Electrolyte
Answer
D. P-2, Q-1, R-3
79
A spherical drop of molten metal of radius 5 mm was found to solidify in 20 seconds. A similar drop of radius 10 mm will solidify in
Answer
D. 80 sec
80
Compound rest is a part in lathe used to
Answer
C. turn the tool for angular cuts
81
In a shaping machine, a work piece with 600 mm \times 600 mm surface is to be machined. Return to cutting time ratio is \(2:3\), cutting speed is 6 m/min and feed is 2mm/double stroke. What is the minimum possible machining time required for complete one pass over surface?
Answer
A. 50 min
82
For checking the flatness of a surface which of the following instruments can be used? i. Dial gauge ii. Autocollimator iii. Plug gauge
Answer
B. only i and ii
83
The main objective of honing operation is
Answer
D. to remove the marks on machined surface
84
Which of the following are the different types of CMM? i. Bridge type ii. Grantry type iii. Cantilever type
Answer
C. All i, ii and iii
85
Carbonyl process in powder metallurgy is used as
Answer
Question Cancelled
86
Under the assumption that the quality characteristic follows a normal distribution, the standard deviation of the relative range W = \(R/\sigma\) is estimated as \(d_3\) for a specified sample size 'n'. The upper control limit of R chart is given as \(D_4\) where its value is
Answer
A. 1+3\frac{d_3}{d_2}
87
A multiple sampling plan has the parameters as follows: \(N\) β Lot size \(n_1\) β First sample \(n_2\) β Second sample \(n_3\) β Third sample Using the notation \(P_{a_1}\), \(P_{a_2}\) and \(P_{a_3}\) as the probabilities of accepting the lot on 1st, 2nd and 3rd samples respectively if rectifying inspection is employed, the ATI is given as
Answer
D. n_1 P_{a_1} + (n_1 + n_2) P_{a_2} + (n_1 + n_2 + n_3) P_{a_3} + N(1 - P_{a_1} - P_{a_2} - P_{a_3})
88
If the reliability R(t + T) = R(t), the reliability can be modelled by the following distribution
Answer
C. Exponential distribution
89
The expected time to complete a project is estimated to be 42 weeks with a standard deviation of 2 weeks. What is the probability of completing the project by the scheduled time, if the scheduled time is given as 48 weeks?
Answer
C. 0.9987
90
An \overline{X} β control chart has shown a point above the control limit (UCL) during the monitoring period. The quality engineer suspected the process and finally could not find any assignable cause for the above situation. Finally, he concluded that this is a false alarm. The false alarm probability depends on
Answer
C. Control limit coefficient only
91
The primal LP is given as follows : Min \(Z = x_1 + 2x_2\) S.T. \(2x_1 + 4x_2 \le 160\) \(X_1 - X_2 = 30\) \(x_1 \ge 10\) and \(x_1, x_2 \ge 0\) The dual of the problem is:
Answer
D. Max W = -160y_1 + 30y_1 + 10y_4 S.T. \(-2y_1 + y + y_2 \le 1\) \(-4y_1 - y \le 2\) \(y_1, y_2 \ge 0\) y unrestricted in sign
92
Two machines are located at the coordinates (-d, 0) and (d, 0). A new machine is located at the coordinate \((x, y)\) and the level curves are found to be confocal ellipses with foci located at the two existing machines. The measure of distance between the new and existing facilities is
Answer
A. Euclidean
93
Which of the following ASME symbols used in recording techniques has a different representation in two-handed process charts?
Answer
D. [inverted triangle symbol]
94
A sample plotted above UCL or below LCL of a control chart is considered bad since it may represent the out-of-control situation for a process. But, a quality engineer was happy to see a point below the LCL and spent a lot of time to find the reason for the same. The quality engineer is using
Answer
D. p-chart
95
Find the option which contains a fake selective inventory technique.
Answer
D. ABC, SDE, VED, HMT
96
After a pilot study, the number of observations (n) to be taken in a work sampling technique is given by the formula \(n = \frac{X^2}{\sqrt{2}} \frac{(1-\overline{p})}{\overline{n}}\) For a confidence level of 95% and accuracy of \(\pm\) 3% the values of X and Y are respectively
Answer
C. 1.96 and 0.03
97
A firm uses simple exponential smoothing with \alpha = 0.2 to forecast demand. The forecast for the month of January was 400 units, whereas actual demand turned out to be 450 units. The forecast for the month of February is
Answer
B. 410
98
The first cost of a road laying machine is Rs. 80,00,000. Its salvage value after five years is Rs. 5,00,000. The length of the road that can be laid by the machine during its life time is 75,000 km. In its third year of operation, the length of road laid is 10,000 km. Find the depreciation of the equipment for that year from the below options :
Answer
A. 10 lakhs
99
A firm has a fixed cost of Rs. 50,000/-, selling price per unit Rs. 50/- and variable cost per unit Rs. 25. Present level of production is 3500 units. If the fixed cost is changed from Rs. 50,000/- to Rs. 60,000, the change in break even point is by ______ units.
Answer
D. 400
100
In six sigma concept, the defectives number of 3.4 ppm is achieved by allowing a shift in the mean by
Answer
D. 6.0\sigma
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