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Roll No. Total No. of Pages : 02
Total No. of Questions : 18
B.Tech. (Automation & Robotics) (2012 & Onward) (Sem.-3)
MATHEMATICS-III
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Subject Code : BTAR-301
M.Code : 63001
Time : 3 Hrs. Max. Marks : 60
INSTRUCTIONS TO CANDIDATES :
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1. SECTION-A is COMPULSORY consisting of TEN questions carrying TWO marks each.
2. SECTION-B contains FIVE questions carrying FIVE marks each and students have to attempt any FOUR questions.
3. SECTION-C contains THREE questions carrying TEN marks each and students have to attempt any TWO questions.
SECTION-A
1. If Laplace transform of f(t) is F(s) then find Laplace Transform L(tf(t)dt), if it exists.
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2. Find Inverse Laplace Transform of (2s+6) / (s2+4)
3. Write down the Bessel’s differential equation of order ‘n’.
4. Define error function.
5. Express the following in terms of Lagendre polynomials 1 —x + x2
6. Show that cosz is an analytic function.
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7. Define a conformal mapping.
8. Evaluate ? (1+2z) dz, C:|z| =3
9. Evaluate the integral ? e3ui along the line y =x/3
10. Expand log(1 + z) about z=0.
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SECTION-B
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11. Solve the differential equation using Method of Laplace transform
y'' + 2y' +5y = sin 2t, given that y (0)=2, y'(0)=-4
12. Prove that (2n + 1) xPn (x) = (n + 1) Pn+1 (x) + nPn-1 (x)
13. Show that the function defined by f(z)= (x3 y3 (x+iy))/(x2+y2) , z?0 is analytic at origin, even though f”(0) does not exist.
0, z=0
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14. If the potential function is log (x2 + y2), find the flux function and complex potential function.
15. Show that the transformation w=(z-1)/(z+i) maps the real axis in the z-plane onto the circle |w|=1.
SECTION-C
16. (a) Define unit step function and find its Laplace transform.
(b) Prove that d/dx [x-nJn(x)] = -x-nJn+1(X)
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17. Solve by applying Frobenius method : 9x (1 - x) y'' - 12y' +4y = 0
18. Using Contour integration, evaluate the integral ? dx/(x2 +1) from 0 to 8.
NOTE : Disclosure of Identity by writing Mobile No. or Marking of passing request on any paper of Answer Sheet will lead to UMC against the Student.
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This download link is referred from the post: PTU B.Tech Question Papers 2020 December (All Branches)
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