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Posted Date: 14 Nov 2011 Posted By:: vinod Member Level: Bronze Points: 5 (Rs. 1)
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2009 K L University B.Tech Civil Engineering University board,engineering mathematics-3,engineering maths Question paper
KONERU LAKSHMAIAH COLLEGE OF ENGINEERING
(AUTONOMOUS)
II/IV B. Tech I SEMESTER / DECEMBER
(REGULAR)
MATHEMATICS-IV CE-211
Time: 3 Hrs Max. Marks: 60
Answer One Question from each unit
Answer All Units
UNIT – I
I. (a) Obtain a Fourier Series for f (x) = x sin x, 0 < x < 2p
(b) If f (x) = p x, 0 = x = 1
= p (2-x), 1 = x = 2, show that in the interval (0,2),
(OR)
(c) Obtain Fourier Series for the function f (x) given by ,
,
Hence deduce that
(d) Obtain a half range sine series for f (x) = x- x2 in (0,1).
UNIT – II
II. (a) Find the Fourier Transform of f(x)= 1-x2, 1x1= 1
0, 1x1 > 1
Hence evaluate
(b) Express the function f (x) = 1, for 1x1 = 1
0, for 1x1 > 1, as a Fourier ritegral
Hence evaluate
(OR)
(c) Obtain the constant term and the coefficients of the first sine & cosine terms in Fourier Expansion of "y" as given in the following table
x: 0 1 2 3 4 5
y: 9 18 24 28 26 20
(d) Find the Fourier Cosine transform of f (x)= e-ax, (a>0)
UNIT – III
III. (a) Find the first and second derivatives of f(x) at x = 1.5 of
x: 1.5 2.0 2.5 3.0 3.5 4.0
y: 3.375 7.000 13.625 24.000 38.875 59.000
(b) Find an approximate value of log e 5 by calculating to 4 decimal places, by Simpson's Rule dividing the range into 10 equal parts.
(OR)
(c) Using Range Kutta Method of 4th order compute y (2) and y (4) from , taking h = 0.1
(d) Apply Euler's method to solve y1 = x + y, y (0) = 0, choosing the step length h = 0.2 (carry out 6 steps)
UNIT – IV
IV. (a) Find by Taylor's series method, the value of y at x = 0.1 & x = 0.2 to five places of decimals from
(b) Find the value of y for x = 0.1, by picard's method, given that
(OR)
(c) Solve the equation y11=x+y, with the boundary conditions y (0) = y (1) = 0.
(d) Determine the value of y at the pivotal points of the interval (0,1) of y satisfies the
boundary value problem
UNIT – V
V. (a) Find K so that the following can serve as the probability density of a random variable
f(x) = 0, x = 0
(b) If the amount of cosmic radiation to which a person is exposed while flying by jet across the united states is a random variable having the normal distributions with Mean = 4.35 mrem and s = 0.59 mrem, find the probabilities that the amount of cosmic radiation to which a person will be exposed on such a flight is (i) between 4.00 & 5.00 mrem (ii) at least 5.50 mrem
(OR)
(c) If 20 % of the memory chips made in a certain plant are defective, what are the probabilities that in a lot of 100 randomly chosen for inspection
(i) at most 15 will be defective
(ii) Exactly 15 will be defective
(d) In a certain country, the proportion of highway sections requiring repairs in any given year is a random variable having the beta distribution with a = 3, ß = 2
(i) On the average what percentage of the highway sections require repairs in any given year
(ii) Find the probability that at most half of the highway sections will require repairs in any given year.
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