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Roll No. | | Total No. of Pages : 02
Total No. of Questions : 18
B.Tech. (CE) (2018 Batch) (Sem.-3)
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MATHEMATICS-IIl (TRANSFORM & DISCRETE MATHEMATICS)
Subject Code : BTAM-301-18
M.Code : 76373
Time : 3 Hrs. Max. Marks : 60
INSTRUCTIONS TO CANDIDATES :
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- SECTION-A is COMPULSORY consisting of TEN questions carrying TWO marks each.
- SECTION-B contains FIVE questions carrying FIVE marks each and students have to attempt any FOUR questions.
- SECTION-C contains THREE questions carrying TEN marks each and students have to attempt any TWO questions.
SECTION-A
Write briefly :
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1. Prove that ? r .dr=0, where r has its usual meaning.
2. If A=2zi+yj —x²k, B=x²yzi —2xz²j —xz²k then find ? (A x B)at(1,1,1).
3. Show that curl curl v = grad div.v-?² v where v is any vector.
4. If F is solenoid vector then show that curl curl curl curl F =?²F.
5. Define Gradient and state its physical significance.
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6. State and prove Second shifting property of Laplace transform.
7. Evaluate L (cos² at sin ßt).
8. Find finite Fourier sine transform of f(x) = 1.
9. Define Euler formulae.
10. State and prove change of scale property of laplace transform.
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SECTION-B
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11. Find directional derivative of f = 3xy² + yz² at a point (2, -1, 1) in the direction normal to the surface x log z—y² + 4 =0 at a point (-1, 2, 1).
12. If F=(2x²+y²)i + (3y—4x)j, evaluate ?c F dr around the triangle ABC whose vertices are A (0,0), B (2,0)and C (2, 1).
13. Using Laplace evaluate ?0^8 t³e^(-t) sint dt .
14. Find inverse laplace of 2/(s²+a²)².
15. Use convolution theorem to find L?¹(1/(s²-5s+7)).
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SECTION-C
16. Verify Green’s theorem in the XY-plane for ?c(xy²z—2xy) dx +(x²y+3)dy around boundary C of the region enclosed y² = 8x and x = 2.
17. The string is stretched between the points (0, 0) and (/, 0). If it is displaced along the curve y = K sin(px/l) and released from rest in that position at time t = 0. Find the displacement y (x, t) at any time t > 0 and at any point, x, 0 18. If f(x)= { x, when 0 < x < p/2; p/2, when p/2 < x < p } show that f(x)=p/4 + 2/p [sinx - sin3x/3² + sin5x/5² - ... ]. --- Content provided by FirstRanker.com --- NOTE : Disclosure of Identity by writing Mobile No. or Making of passing request on any page of Answer Sheet will lead to UMC against the Student.
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