This download link is referred from the post: SGBAU B.Tech Last 10 Years 2010-2020 Question Papers || Sant Gadge Baba Amravati university
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Pages: 3
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Time : Three Hours
B.Tech. Fourth Semester (Chem. / Poly / Food / Pulp / Oil / Petro) (Old)
Applied Mathematics — 111 : 4 SCE 1
Notes:
- Answer three questions from Section A and three questions from Section B.
- Due credit will be given to neatness and adequate dimensions.
- Assume suitable data wherever necessary.
- Illustrate your answer necessary with the help of neat sketches.
- Use of calculator is permitted.
- Use of pen Blue/Black ink/refill only for writing the answer book.
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SECTION -A
- a) Solve d2y/dx2 +2dy/dx+y =x2cosx
b) Solve (D2 +3D+2)y=e-x by using variation of parameter.
OR - a) Solve (D3 +1)y =sin3x —cos2 x
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b) Solve x2 d2y/dx2 - xdy/dx +4y = cos(log x) + x sin (logx) - a) Evaluate Laplace transform of ∫0t et/t dt
b) Prove that L-1 {log(1 +1/s2)} = ∫0∞ (1-cosu)/u du
c) Express f(t) in terms unit step function and hence find its Laplace transform
f(t)=t, 0<t<1--- Content provided by FirstRanker.com ---
=4t, t>1
OR - a) Find the Laplace transform of
f(t)=asin(pt) , 0<t<π/p
=0 , π/p<t<2π/p--- Content provided by FirstRanker.com ---
where f(t+2π/p)=f(t)
- a) Use convolution theorem to find L-1{1/((s+1)(s2+1))}
b) Solve the differential equation using Laplace transform
d2y/dt2 =2t if y(0)=1, y'(0)=1/2 - a) Find the Fourier sine transform of e-ax/x
OR
b) Using Fourier integral show that
∫0∞ (sin(tx)/t) dt = π/2, 0<x<π
=0, x>π - Use Laplace transform to solve the differential equation dy/dt +2y + ∫0t ydt =sint when y (0) = 1.
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SECTION - B
- Solve the following difference equation -
i) yx+2 +4yx+1+yx = x2
ii) yp+2 -4yp =n2+n-1 - Find the inverse z-transform of (4z2-2z)/(z3+5z2+4z)
- Solve the difference equation yp+2 -2cosαyp+1 +yp =0 with y(0) =1, y(1) = cosα using method of z-transform.
- Find the z-transform of
i) 1/(n+1)
ii) (cosθ+isinθ)n - Find the tangential & normal component of acceleration at any time t of a particle whose position (x, y) at any time t is given by x = log (t2 +1), y=t -2tan-1t.
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- a) Find the directional derivative of φ = e2x cosyz at the origin in the direction of the tangent to the curve X =asint, y=acost, z=at at t=π/2
OR
b) If pF = ∇P, where p, P and F are point functions, prove that F. curlF =0. - a) Prove that a x ∇(B.∇(1/r)) = 3(a.r)(B x r)/r5 - (B.r)(a x r)/r5
b) A vector field is given by F=siny i+ x(1+cos y)j . Evaluate the line integral over the circular path given by x2+ y2 = a2, z=0. - a) Apply Stokes theorem to evaluate ∫C (x+y)dx +(2x—2z)dy + (y+z)dz where C is the boundary of the triangle with vertices (2, 0, 0), (0, 3, 0), (0, 0, 6).
OR
b) Use Divergence theorem to evaluate ∫∫S(y2z3i + z2x3j + x2y3k).dS where s is the upper part of the sphere x2 +y2 +z2 =1. - Prove that F = (x2 —yz)i+(y2 —zx) j+ (z2 —xy)k is irrotational and find φ if F=∇φ.
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This download link is referred from the post: SGBAU B.Tech Last 10 Years 2010-2020 Question Papers || Sant Gadge Baba Amravati university
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