FirstRanker Logo

FirstRanker.com - FirstRanker's Choice is a hub of Question Papers & Study Materials for B-Tech, B.E, M-Tech, MCA, M.Sc, MBBS, BDS, MBA, B.Sc, Degree, B.Sc Nursing, B-Pharmacy, D-Pharmacy, MD, Medical, Dental, Engineering students. All services of FirstRanker.com are FREE

📱

Get the MBBS Question Bank Android App

Access previous years' papers, solved question papers, notes, and more on the go!

Install From Play Store

Download SGBAU B-Tech 4th Sem Applied Mathematics III Question Paper

Download SGBAU (Sant Gadge Baba Amravati university) B-Tech/BE (Bachelor of Technology) 4th Sem Applied Mathematics III Previous Question Paper

This post was last modified on 10 February 2020

This download link is referred from the post: SGBAU B.Tech Last 10 Years 2010-2020 Question Papers || Sant Gadge Baba Amravati university


FirstRanker.com

A Firstranker's choice

Pages: 3

--- Content provided by FirstRanker.com ---

Time : Three Hours

B.Tech. Fourth Semester (Chem. / Poly / Food / Pulp / Oil / Petro) (Old)

Applied Mathematics — 111 : 4 SCE 1

Notes:

  1. Answer three questions from Section A and three questions from Section B.
  2. --- Content provided by FirstRanker.com ---

  3. Due credit will be given to neatness and adequate dimensions.
  4. Assume suitable data wherever necessary.
  5. Illustrate your answer necessary with the help of neat sketches.
  6. Use of calculator is permitted.
  7. Use of pen Blue/Black ink/refill only for writing the answer book.
  8. --- Content provided by FirstRanker.com ---

SECTION -A

  1. a) Solve d2y/dx2 +2dy/dx+y =x2cosx
    b) Solve (D2 +3D+2)y=e-x by using variation of parameter.
    OR
  2. a) Solve (D3 +1)y =sin3x —cos2 x

    --- Content provided by FirstRanker.com ---

    b) Solve x2 d2y/dx2 - xdy/dx +4y = cos(log x) + x sin (logx)
  3. 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
  4. 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)

FirstRanker.com

  1. 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
  2. --- Content provided by FirstRanker.com ---

  3. 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
  4. --- Content provided by FirstRanker.com ---

  5. Use Laplace transform to solve the differential equation dy/dt +2y + ∫0t ydt =sint when y (0) = 1.

SECTION - B

  1. Solve the following difference equation -
    i) yx+2 +4yx+1+yx = x2
    ii) yp+2 -4yp =n2+n-1
  2. --- Content provided by FirstRanker.com ---

  3. Find the inverse z-transform of (4z2-2z)/(z3+5z2+4z)
  4. Solve the difference equation yp+2 -2cosαyp+1 +yp =0 with y(0) =1, y(1) = cosα using method of z-transform.
  5. Find the z-transform of
    i) 1/(n+1)
    ii) (cosθ+isinθ)n
  6. --- Content provided by FirstRanker.com ---

  7. 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.

FirstRanker.com

  1. 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.
  2. --- Content provided by FirstRanker.com ---

  3. 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.
  4. 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.
  5. --- Content provided by FirstRanker.com ---

  6. Prove that F = (x2 —yz)i+(y2 —zx) j+ (z2 —xy)k is irrotational and find φ if F=∇φ.


This download link is referred from the post: SGBAU B.Tech Last 10 Years 2010-2020 Question Papers || Sant Gadge Baba Amravati university

--- Content provided by FirstRanker.com ---