Question 31. The probability that a student knows the correct answer to a multiple choice question is 2/3. If the student does not know the answer, then the student guesses the answer. The probability of the guessed answer being correct is 1/4. Given that the student has answered the question correctly, the conditional probability that the student knows the correct answer is

Question 32. The solution to the differential equation d2u/dx2 - k du/dx = 0 where k is a constant, subjected to the boundary conditions u(0) = 0 and u(L) = U, is

Question 33. Consider the function f(x) = |x| in the interval -1 ≤ x ≤ 1. At the point x = 0, f(x) is

Question 34. For the spherical surface x2 + y2 + z2 = 1, the unit outward normal vector at the point (1/√2, 1/√2, 0) is given by

Question 35. At x = 0, the function f (x) = x3 + 1 has

Question 36. The area enclosed between the straight line y = x and the parabola y = x2 in the x-y plane is

Question 37. Data for a plain milling operation are given below.Length of workpiece   200 mmCutter diameter          100 mmNo. of teeth                   4Cutter speed               100 rpmFeed                             200 mm/minDepth of cut               2 mmTotal clearance (entry     5 mmand exit)Mean undeformed chip thickness (in microns) is

Question 38. Data for four jobs that need to be processed on a single machine are given below.Job                                     P  Q   R    SProcessing time (days)  12 9   21 10Due date (days)              20 40 30 19All the four jobs are available at time zero. If the jobs are scheduled using the Earliest Due Date (EDD) algorithm, then the job with maximum tardiness is

Question 39. Data for a plain milling operation are given below.Length of workpiece   200 mmCutter diameter          100 mmNo. of teeth                   4Cutter speed               100 rpmFeed                             200 mm/minDepth of cut               2 mmTotal clearance (entry     5 mmand exit)Machining time for a single pass (in seconds) is

Question 40. In an EDM process using RC relaxation circuit, a 12 mm diameter through hole is made in a steel plate of
50 mm thickness using a graphite tool and kerosene as dielectric. Assume discharge time to be negligible.
Machining is carried out under the following conditions:Resistance                 40 ΩCapacitance              20 μFSupply voltage          220 VDischarge voltage    110 VThe time for one cycle, in milliseconds, is