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1.
Statement for linked Answer Questions ::
The subset –sum problem is defined as follows. Given a set of n positive integers, S = {a1, a2, a3, ......, an} and a positive integer W, is there a subset of S whose elements sum of W? A dynamic program for solving this problem uses a 2-dimensional Boolean array, X, with W+1 rows and n columns X[i, j], 1 ≤ i ≤ n, 0 ≤ j ≤ W, is TRUE if and only if there is a subset of {a1, a2, …., ai} whose elements sums to j.
[1] Which of the following is valid for 2 ≤ i ≤ n and ai ≤ j ≤ W? [2 marks]
(A) X[i, j] = X[i – 1, j] ∨ X[i, j – a1]
(B) X[i, j] = X[i – 1, j] ∨ X[i – 1, j – a1]
(C) X[i, j] = X[i – 1, j] Λ X[i, j – a1]
(D) X[i, j] = X[i – 1, j] Λ X[i – 1, j – a1][2] Which entry of the array X, if TRUE, implies that there is a subset whose elements sum to W? [2 marks]
(A) X[ 1, W]
(B) X[ n, 0]
(C) X[ n, W]
(D) X[n – 1, n]asked in Mechanical Engineering, 2008
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2.
In the feed drive of a Point – to – point open loop CNC drive, a steeper motor rotating at 200 steps/rev drives a table through a gear box and lead screw – nut mechanism (pitch = 4mm, number of starts =1).
The gear ratio = (Output rotation speed/Input rotational speed) is given by U = 1/4.The stepper motor (driven by voltage pulses from a pulse generator) executes 1 step/ pulse of the pulse generator. The frequency of the pulse train from the pulse generator is f = 10,000 pulses per minute.
[1] The Basic Length Unit (BLU), i.e. , the table movement corresponding to 1 pulse of the pulse generator, is [2 marks]
(A) 0.5 microns
(B) 5 microns
(C) 50 microns
(D) 500 microns
[2] A customer insists on a modification to change the BLU the CNC drive to 10 microns without changing the table speed. The modification can be accomplished by
[2 marks]
(A) changing U to 1/2 and reducing f to f/2
(B) changing U to 1/8 and reducing f to 2f
(C) changing U to 1/2 and keeping f unchanged
(D) keeping U unchanged and increasing f to 2f.asked in Mechanical Engineering, 2008
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3.
Orthogonal turning is performed on a cylindrical workpiece with shear strength of 250 MPa. The following conditions are used: cutting velocity is 180 m/min, feed is 0.20 mm/rev, depth of cut is 3 mm, chip thickness ratio = 0.5. The orthogonal rake angle is 7˚. Apply Merchant’s theory for analysis.
[1] The shear plane angle (in degrees) and the shear force respectively are [2 marks]
(A) 52; 320N
(B) 52; 400N
(C) 28 ; 400 N
(D) 28 ; 320 N[2] The cutting and frictional forces, respectively, are [2 marks]
(A) 568 N ; 387 N
(B) 565 N ; 381 N
(C) 440 N ; 342 N
(D) 480 N ; 356 Nasked in Mechanical Engineering, 2008
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4.
The gap between a moving circular plate and a stationary surface is being continuously reduced, as the circular plate comes down at a uniform speed V towards the stationary bottom surface, as shown in the figure. In the process, the fluid contained between the two plates flows out radially. The fluid is assumed to be incompressible and inviscid.
[1] The radial velocity Vr at any radium r, when the gap width is h, is [2 marks]
(A) Vr = Vr/2h
(B) Vr = 2Vh/r
(C) Vr = Vr/h
(D) Vr =Vh/r[2] The radial component of the fluid acceleration at r = R is [2 marks]
(A) 3V2R/4h2
(B) V2R/2h2
(C) V2R/4h2
(D) None of theseasked in Mechanical Engineering, 2008
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5.
A steel bar of 10 × 50 mm is cantilevered with two M 12 bolts (P and Q) to support a static load of 4 kN as shown in the figure.
[1] The primary and secondary shear loads on bolt P, respectively, are [2 marks]
(A) 2kN, 20kN
(B) 20kN, 2 kN,
(C) 20 kN, 0kN
(D) 0kN, 20 kN[2] The resultant shear stress on bolt P is closest to [2 marks]
(A) 132MPa
(B) 159 MPa
(C) 178 MPa
(D) 195 MPaasked in Mechanical Engineering, 2008
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6.
A cylindrical container of radius R = 1 m, wall thickness 1 mm is filled with water up to a depth of 2 m and suspended along its upper rim. The density of water is 1000kg/m3 and acceleration due to gravity is 10 m/s2. The self-weight of the cylinder is negligible. The formula for hoop stress in a thin – walled cylinder can be used at all points along the height of the cylindrical container.
[1] The axial and circumferential stress (σd, σc) experienced by the cylinder wall at mid-depth (1 m as shown) are [2 marks]
(A) (10, 10) MPa
(B) (5, 10) MPa
(C) (10, 5) MPa
(D) (5, 5) MPa[2] If the Young’s modulus and Poisson’s ratio of the container material are 100GPa and 0.3, respectively, the axial strain in the cylinder wall at mid-depth is [2 marks]
(A) 2 × 10-5
(B) 6 × 10-5
(C) 7 × 10-5
(D) 1.2 × 10-4asked in Mechanical Engineering, 2008
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