RGPV Question Papers
BE Engineering Mathematics 2nd Sem June 2004
Note: Attempt Any five questions.
Answer to the same question should be given at one place.
All question carry equal marks.
1 (a) Find the Fourier series expansion of f (x) when:
F (x) = -π < x < 0
X, 0< x <π
Hence deduce 1/i2 + 1/32 + 1/52 +……… = π2/8
(b) Find the Fourier series of:
πx, 0 ≤ x ≤ 1
π (2-x), 1 ≤ x ≤ 2
2 Obtain a half range cosine series for:
Kx, 0 ≤ x ≤1/2
F (x) = k (l- x), l/2 ≤x ≤
(b) Find the Laplace transform of t2 sing at.S
3 (a) Computed the inverse Laplace transform of log s( s+ 1)/ (s2 + 4).
(b) Using Laplace transform, solve:
D3y/dt3 + 2d2y/ dt2 – dy/dt -2y = 0
y = 1, dy/dt =2, d2y/ dt2 = 2 at t =0
4 (a) Solve:
X d2y/dx2 -2 (x + 1) dy/dx y = (x -2) y = (x – 2) e2x
(b) Solve by the method of variation of parameters:
d2y/ dx2 + 4y = 4 tan 2x
5 (a) Solve by series method, the differential equation:
(2x+x3) d2y/ dx2 – dy/ dx – 6xy = 0
(b) Determaine tha analytic function f (z) = u + iv whose real part is e2x (x cos 2y sin 2y).
6 (a) Find the gernel solution of:
(2x – 2yz – y2) p + (xy + zx) q = (xy – zx)
(b) A tightly stretched string with fixed end points x = 0 and x = l is initially ina position, given by y =y0 sin (πx / l). If it is released from rest from this position, find the displacement y (x,t).
7 (a) find A when div grad rm = Ar m – 2 where r2 =x2 + y2 + z2.
(b) Evaluate F. dr where F = yi + zj +xk and C is the circle x2 + y2 = 1, z = 0
8 (a) Calculate the mean and variance of a binomial distribution.
(b) Fit a second degree parabola to the following data:
X: 0 1 2 3 4
Y: 1 1.8 1.3 2.5 6.3