Mathematics-I (A & B) Past Paper - April 2021 - MA100 - PDF
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Uploaded by SucceedingMossAgate8179
National Institute of Technology Goa
2021
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Summary
This past paper from the National Institute of Technology Goa, in April 2021, focuses on mathematics-I. The document contains different questions based on vector analysis, such as finding the work done in moving a particle, determining if a force field is conservative, calculating areas cut by surfaces, and verifying Green's theorem.
Full Transcript
Roll No National Institute of Technology Goa B.Tech. Minor Examination, April-2021 Department of Humanities and Sciences Course Name: MATHEMATICS-I (A & B)...
Roll No National Institute of Technology Goa B.Tech. Minor Examination, April-2021 Department of Humanities and Sciences Course Name: MATHEMATICS-I (A & B) Course Code: MA100 Date: April 2, 2021 Time: 11:00 AM Duration: 40 Min. Max. Marks: 25 ANSWER ALL QUESTIONS 1. Find the work done in moving a particle once around a circle C in the xy plane, if the circle has center at the origin and radius 3 and if the force field is given by F = (2x − y + z)i + (x + y − z 2 )j + (3x − 2y + 4z)k. 2. (a) Show that F = (2xy + z 3 )i + x2 j + 3xz 2 k is a conservative force field. (b) Find the scalar potential. 3. Find the area of the region cut from the plane x + 2y + 2z = 5 by the cylinder whose walls are x = y 2 and x = 2 − y 2. 4. Find the flux of the field F (x, y, z) = 4xi + 4yj + 2k outward (away from the z-axis) through the surface cut from the bottom of the paraboloid z = x2 + y 2 by the plane z = 1. R 5. Verify Green’s theorem in the plane for C (xy + y 2 )dx + x2 dy where C is the closed curve of the region bounded by y = x and y = x2. ∗ ∗ ∗ ALL THE BEST ∗ ∗∗
