2011 KL Deemed to be University B.Tech Civil Engineering B.Tech Civil Engineering University board,engineering mathematics Question paper
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KONERU LAKSHMAIAH COLLEGE OF ENGINEERING (AUTONOMOUS)
II/IV B. Tech I SEMESTER / DECEMBER (REGULAR)
MATHEMATICSIV CE211
Time: three Hrs Max. Marks: 60 ans 1 ques. from every unit ans All Units
UNIT – I
I. (a) find a Fourier Series for f (x) = x sin x, 0 < x < 2p (b) If f (x) = p x, 0 = x = 1
= p (2x), one = x = 2, show that in the interval (0,2),
(OR) (c) find Fourier Series for the function f (x) provided by , , Hence deduce that (d) find a half range sine series for f (x) = x x2 in (0,1).
UNIT – II
II. (a) obtain the Fourier Transform of f(x)= 1x2, 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) find the constant term and the coefficients of the 1st sine & cosine terms in Fourier Expansion of "y" as provided in the subsequent table x: 0 1 2 3 4 5 y: 9 18 24 28 26 20
(d) obtain the Fourier Cosine transform of f (x)= eax, (a>0)
UNIT – III
III. (a) obtain the 1st and 2nd 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) obtain an approximate value of log e five by calculating to four decimal places, by Simpsons Rule dividing the range into 10 equal parts. (OR)
(c) Using Range Kutta Method of fourth order calculate y (2) and y (4) from , taking h = 0.1 (d) Apply Eulers method to solve y1 = x + y, y (0) = 0, choosing the step length h = 0.2 (carry out six steps)
UNIT – IV
IV. (a) obtain by Taylors series method, the value of y at x = 0.1 & x = 0.2 to 5 places of decimals from (b) obtain the value of y for x = 0.1, by picards method, provided that
(OR)
(c) Solve the formula 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 issue
UNIT – V
V. (a) obtain K so that the subsequent 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, obtain the probabilities that the amount of cosmic radiation to which a person will be exposed on such a flight is (i) ranging from 4.00 & 5.00 mrem (ii) at lowest 5.50 mrem (OR)
(c) If 20 % of the memory chips made in a certain plant are defective, elaborate 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 parts requiring repairs in any provided year is a random variable having the beta distribution with a = 3, ß = 2 (i) On the avg. what percentage of the highway parts require repairs in any provided year (ii) Find the probability that at most half of the highway parts will require repairs in any provided year.
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