A solid disc of radius r rolls without slipping on a horizontal floor with angular velocity É and angular acceleration α. The magnitude of the acceleration of the point of contact on the disc is
1.zero
2.rα
3.√(rα)2 + (rw2)2
4. rw2
A thin walled spherical shell is subjected to an internal pressure. If the radius of the shell is increased by 1% and the thickness is reduced by 1%, with the internal pressure remaining the same, the percentage change in the circumferential (hoop) stress is
1.0
2.1
3.1.08
4.2.02
Air enters an adiabatic nozzle at 300 kPa, 500 K with a velocity of 10 m/s. It leaves the nozzle at 100 kPa with a velocity of 180 m/s. The inlet area is 80 cm2. The specific heat of air Cp is 1008 J/kg.K. The exit area of the nozzle in cm2 is
1.90.1
2.56.3
3.4.4
4.12.9
Air enters an adiabatic nozzle at 300 kPa, 500 K with a velocity of 10 m/s. It leaves the nozzle at 100 kPa with a velocity of 180 m/s. The inlet area is 80 cm2. The specific heat of air Cp is 1008 J/kg.K. The exit temperature of the air is
1.516 K
2.532 K
3.484 K
4.468 K
An ideal gas of mass m and temperature T1 undergoes a reversible isothermal process from an initial pressure P1 to final pressure P2. The heat loss during the process is Q. The entropy change ∆S of the gas is
1.mR ln(P2/P1)
2.mR ln(P1/P2)
3.mR ln(P2/P1) - Q/T1
4. zero
For a long slender column of uniform cross section, the ratio of critical buckling load for the case with both ends clamped to the case with both ends hinged is
1.1
2.2
3.4
4.8
For an opaque surface, the absorptivity (α) , transmissivity (t) and reflectivity (ÃÂ) are related by the equation:
1. α + à= t
2.α + à+ t = 0
3.α + à= 1
4. α + à= 0
In a single pass drilling operation, a through hole of 15 mm diameter is to be drilled in a steel plate of 50 mm thickness. Drill spindle speed is 500 rpm, feed is 0.2 mm/rev and drill point angle is 118°. Assuming 2 mm clearance at approach and exit, the total drill time (in seconds) is
1.35.1
2.32.4
3.31.2
4.30.1
Which one of the following is NOT a decision taken during the aggregate production planning stage?
1.Scheduling of machines
2.Amount of labour to be committed
3. Rate at which production should happen
4.Inventory to be carried forward
47. x + 2y + z = 4 2x + y + 2z = 5 x - y + z = 1 The system of algebraic equations given above has
1.a unique solution of x = 1, y = 1 and z = 1
2. only the two solutions of (x = 1, y = 1, z = 1) and (x = 2, y = 1, z = 0).
3.infinite number of solutions.
4.no feasible solution.
A box contains 4 red balls and 6 black balls. Three balls are selected randomly from the box one after another, without replacement. The probability that the selected set contains one red ball and two black balls is
1.1/20
2.1/12
3.3/10
4.1/2
A cantilever beam of length L is subjected to a moment M at the free end. The moment of inertia of the beam cross section about the neutral axis is I and the Young's modulus is E. The magnitude of the maximum deflection is
1.ML2/2EI
2. ML2/EI
3.2ML2/EI
4.4ML2/EI
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
1.395
2. 790
3.1580
4.3160
A CNC vertical milling machine has to cut a straight slot of 10 mm width and 2 mm depth by a cutter of 10 mm diameter between points (0, 0) and (100, 100) on the XY plane (dimensions in mm). The feed rate used for milling is 50 mm/min. Milling time for the slot (in seconds) is
1.120
2.170
3.180
4.240
A political party orders an arch for the entrance to the ground in which the annual convention is being held. The profile of the arch follows the equation y = 2x “ 0.1x2 where y is the height of the arch in meters. The maximum possible height of the arch is
1. 8 meters
2.10 meters
3.12 meters
4.14 meters
A room contains 35 kg of dry air and 0.5 kg of water vapor. The total pressure and temperature of air in the room are 100 kPa and 25°C respectively. Given that the saturation pressure for water at 25°C is 3.17 kPa, the relative humidity of the air in the room is
1.67%
2.55%
3.83%
4.71%
A solid circular shaft needs to be designed to transmit a torque of 50 N.m. If the allowable shear stress of the material is 140 MPa, assuming a factor of safety of 2, the minimum allowable design diameter in mm is
1.8
2.16
3.24
4.32
A solid cylinder of diameter 100 mm and height 50 mm is forged between two frictionless flat dies to a height of 25 mm. The percentage change in diameter is
1.0
2.2.07
3.20.7
4.41.4
A solid steel cube constrained on all six faces is heated so that the temperature rises uniformly by ∆T. If the thermal coefficient of the material is α, Young's modulus is E and the Poisson's ratio is Ã… , the thermal stress developed in the cube due to heating is
1.-[α(∆T)E]/(1 - 2Ã…)
2.-[2α(∆T)E]/(1 - 2Ã…)
3.-[3α(∆T)E]/(1 - 2Ã…)
4.-[α(∆T)E]/3(1 - 2Ã…)
An automobile plant contracted to buy shock absorbers from two suppliers X and Y. X supplies 60% and Y supplies 40% of the shock absorbers. All shock absorbers are subjected to a quality test. The ones that pass the quality test are considered reliable. Of X's shock absorbers, 96% are reliable. Of Y's shock absorbers, 72% are reliable. The probability that a randomly chosen shock absorber, which is found to be reliable, is made by Y is
1.0.288
2.0.334
3.0.667
4.0.720
An incompressible fluid flows over a flat plate with zero pressure gradient. The boundary layer thickness is 1 mm at a location where the Reynolds number is 1000. If the velocity of the fluid alone is increased by a factor of 4, then the boundary layer thickness at the same location, in mm will be
1.4
2.2
3.0.5
4.0.25
At x = 0, the function f(x) = x3 + 1 has
1.a maximum value
2. a minimum value
3. a singularity
4.a point of inflection
Calculate the punch size in mm, for a circular blanking operation for which details are given below. Size of the blank 25 mm Thickness of the sheet 2 mm Radial clearance between punch and die 0.06 mm Die allowance 0.05 mm
1.24.83
2.24.89
3. 25.01
4.25.17
Choose the grammatically INCORRECT sentence:
1.They gave us the money back less the service charges of Three Hundred rupees.
2.This country's expenditure is not less than that of Bangladesh.
3.The committee initially asked for a funding of Fifty Lakh rupees, but later settled for a lesser sum.
4.This country's expenditure on educational reforms is very less.
Choose the most appropriate alternative from the options given below to complete the following sentence: Despite several “““““““““ the mission succeeded in its attempt to resolve the conflict.
1.attempts
2.setbacks
3.meetings
4.delegations
Consider the differential equation x2 d2y/dx2 + x dy/dx - 4y = 0 with the boundary conditions of y(0) = 0 and y(1) = 1. The complete solution of the differential equation is
1.x2
2.sin(Àx/2)
3.ex sin(Àx/2).
4.e-x sin(Àx/2)
Consider the function f(x) = |x| in the interval -1 ≤ x ≤ 1. At the point x = 0, f(x) is
1.continuous and differentiable
2.non-continuous and differentiable
3.continuous and non-differentiable
4.neither continuous nor differentiable.
During normalizing process of steel, the specimen is heated
1.between the upper and lower critical temperature and cooled in still air.
2.above the upper critical temperature and cooled in furnace
3.above the upper critical temperature and cooled in still air.
4.between the upper and lower critical temperature and cooled in furnace.
Given the sequence of terms, AD CG FK JP, the next term is
1.OV
2.OW
3.PV
4.PW
In a single pass rolling process using 410 mm diameter steel rollers, a strip of width 140 mm and thickness 8 mm undergoes 10 % reduction of thickness. The angle of bite in radians is
1.0.006
2.0.031
3.0.062
4. 0.600
In abrasive jet machining, as the distance between the nozzle tip and the work surface increases, the material removal rate
1. increases continuously.
2. decreases continuously.
3.decreases, becomes stable and then increases
4.increases, becomes stable and then decreases.
Match the following metal forming processes with their associated stresses in the workpiece. Metal forming process Type of stress 1. Coining P. Tensile 2. Wire Drawing Q. Shear 3. Blanking R. Tensile and compressive 4. Deep Drawing S. Compressive
1.1-S, 2-P, 3-Q, 4-R
2.1-S, 2-P, 3-R, 4-Q
3.1-P, 2-Q, 3-S, 4-R
4.1-P, 2-R, 3-Q, 4-S
Oil flows through a 200 mm diameter horizontal cast iron pipe (friction factor, f = 0.0225) of length 500 m. The volumetric flow rate is 0.2 m3/s. The head loss (in m) due to friction is (assume g = 9.81 m/s2)
1.116.18
2.0.116
3.18.22
4. 232.36
The area enclosed between the straight line y = x and the parabola y = x2 in the x-y plane is
1.1/6
2.1/4
3.1/3
4.1/2
The cost function for a product in a firm is given by 5q2, where q is the amount of production. The firm can sell the product at a market price of Rs. 50 per unit. The number of units to be produced by the firm such that the profit is maximized is
1.5
2.10
3.15
4.25
The following are the data for two crossed helical gears used for speed reduction: Gear I : Pitch circle diameter in the plane of rotation 80 mm and helix angle 30o Gear II : Pitch circle diameter in the plane of rotation 120 mm and helix angle 22.5o If the input speed is 1440 rpm, the output speed in rpm is
1.1200
2.900
3.875
4.720
The inverse Laplace transform of the function F(s) = 1/s(s + 1) is given by
1.f (t) = sint
2.f (t) = e-t sint
3. f (t) = e-t
4.f (t) = 1 - e-t
The state of stress at a point under plane stress condition is ÃÆ’xx = 40 MPa, ÃÆ’yy = 100 MPa and Äxy = 40 MPa. The radius of the Mohr's circle representing the given state of stress in MPa is
1.40
2.50
3.60
4.100
Wanted Temporary, Part-time persons for the post of Field Interviewer to conduct personal interviews to collect and collate economic data. Requirements: High School-pass, must be available for Day, Evening and Saturday work. Transportation paid, expenses reimbursed. Which one of the following is the best inference from the above advertisement?
1.Gender-discriminatory
2.Xenophobic
3.Not designed to make the post attractive
4.Not gender-discriminatory
Water (Cp = 4.18 kJ/kg.K) at 80°C enters a counter flow heat exchanger with a mass flow rate of 0.5 kg/s. Air (Cp = 1 kJ/kg.K) enters at 30°C with a mass flow rate of 2.09 kg/s. If the effectiveness of the heat exchanger is 0.8, the LMTD (in °C) is
1.40
2.20
3.10
4.5
Which of the following assertions are CORRECT? P: Adding 7 to each entry in a list adds 7 to the mean of the list Q: Adding 7 to each entry in a list adds 7 to the standard deviation of the list R: Doubling each entry in a list doubles the mean of the list S: Doubling each entry in a list leaves the standard deviation of the list unchanged
1.P, Q
2.Q, R
3.P, D
4. R, S
Which one of the following configurations has the highest fin effectiveness?
1.Thin, closely spaced fins
2.Thin, widely spaced fins
3. Thick, widely spaced fins
4.Thick, closely spaced fins
Which one of the following options is the closest in meaning to the word given below? Mitigate
1.Diminish
2.Divulge
3.Dedicate
4.Denote
Which one of the following options is the closest in meaning to the word given below? Mitigate
1.Diminish
2.Divulge
3.Dedicate
4.Denote
Which one of the following options is the closest in meaning to the word given below? Mitigate
1.Diminish
2.Divulge
3.Dedicate
4.Denote
Which one of the following options is the closest in meaning to the word given below? Mitigate
1.Diminish
2.Divulge
3.Dedicate
4.Denote