Printed Franker's choice
--- Content provided by FirstRanker.com ---
Roll www.FirstRanker.com
B.TECH.
THEORY EXAMINATION (SEM–II) 2016-17
--- Content provided by FirstRanker.com ---
ENGINEERING MATHEMATICS - II
Time: 3 Hours
--- Content provided by FirstRanker.com ---
Max. Marks : 100
Note: Be precise in your answer. In case of numerical problem assume data wherever not provided.
SECTION - A
--- Content provided by FirstRanker.com ---
- Explain the following: 10 x 2 = 20
- Show that the differential equation y dx – 2x dy = 0 represents a family of parabolas.
- Classify the partial differential equation
(1 - x²) ?2z/?x2 - 2xy ?2z/?y ?x + (1 - y2) ?2z/?y2 = 2z - Find the particular integral of (D - a)²y = eax f"(x).
- Write the Dirichlet's conditions for Fourier series.
- Prove that J'(x) = -J1(x).
- Prove that L [eatf(t)] = F(s – a)
- Find the Laplace transform of f(t) = sin at / t
- Write one and two dimensional wave equations.
- Find the constant term when f(x) = |x| is expanded in Fourier series in the interval (-2, 2).
- Write the generating function for Legendre polynomial P(x).
--- Content provided by FirstRanker.com ---
--- Content provided by FirstRanker.com ---
--- Content provided by FirstRanker.com ---
--- Content provided by FirstRanker.com ---
--- Content provided by FirstRanker.com ---
SECTION - B
Attempt any five of the following questions: 5 x 10 = 50
--- Content provided by FirstRanker.com ---
- Solve the differential equation (D² + 2D + 2)y = e-xsec³x, where D = d/dx
- Prove that (n + 1)Pn+1(x) = (2n+1)xPn(x) - nPn-1(x), where Pn (x) is the Legendre's function.
- Find the series solution of the differential equation 2x² d²y/dx² + x dy/dx + x(x + 1)y = 0.
- Using Laplace transform, solve the differential equation d²y/dt² + 9y = cos 2t ; y(0) = 1, y'(0) = -1.
- Obtain the Fourier series of the function, f(t) = t, -p < t < 0 = -t, 0 < t < p. Hence, deduce that 1/1² + 1/3² + 1/5² + ... = p²/8
- Solve ?²u/?x² + ?²u/?y² = 0 under the conditions u(0, y) = 0, u(l, y) = 0, u(x, 0) = 0 and u(x, a) = sin(npx/l)
- Solve the partial differential equation: (D³ – 4D²D' + 5DD'² – 2D'³)z = ey+2x + v(y + x)
- Using convolution theorem find L-1[1/((s+1)(s²+1))]
--- Content provided by FirstRanker.com ---
--- Content provided by FirstRanker.com ---
--- Content provided by FirstRanker.com ---
--- Content provided by FirstRanker.com ---
--- Content provided by FirstRanker.com ---
Attempt any two of the following questions: 2 x 15 = 30
- Solve the differential equation (D²-2D+1)y = ex sin x
- Solve the equation by Laplace transform method: dy/dt + 2y + ?y dt = sint, y(0) = 1.
- Solve the partial differential equation (y² + z²) p – xyq + zx = 0, where p = ?z/?x & q = ?z/?y
--- Content provided by FirstRanker.com ---
- Find the Laplace transform of (cos at - cos bt) / t
- Express f(x) = 4x³ – 2x² – 3x + 8 in terms of Legendre's polynomial.
- Expand f(x) = 2x – 1 as a cosine series in 0 < x < 2.
--- Content provided by FirstRanker.com ---
--- Content provided by FirstRanker.com ---
- Show that J3/2(x) = (-1/x)J1/2(x) - J-1/2(x).
- Solve ?z/?x + 3 ?z/?y + 5z = 0; z(0,y) = 2e-y by the method of separation of variables.
- A tightly stretched string with fixed end x = 0 and x = l is initially in a position given by y = a sin(px/l). If it is released from rest from this position, find the displacement y(x, t).
--- Content provided by FirstRanker.com ---
--- Content provided by FirstRanker.com ---
--- Content provided by FirstRanker.com ---
--- Content provided by FirstRanker.com ---
--- Content provided by FirstRanker.com ---
This download link is referred from the post: AKTU B-Tech Last 10 Years 2010-2020 Previous Question Papers || Dr. A.P.J. Abdul Kalam Technical University