RGPV IST SEMESTER EXAMINATION (SEP-2009)
COMMON FOR ALL BRANCH
ENGINEERING MATHEMATICS-II (BE-202)
Time: Three Hours
Maximum Marks: 100 Min Marks: 35
Note : Attempt any five questions taking one question from each unit. All question Carry equal marks.
UNIT-I
Q.1 (a) Find the fourier series of function x sinx for -π < x < π ?10
(b) Find inverse laplace for the function ? 10
F(x) = log(s+1)-- log(s-1) OR
Q.2 (a) Solve laplace differential equation ? 10
y" + 2y' + 5y =e^(-x). sin x where y(0) = 0 and y'(0) = 1
(b) Find half range cosine & sine series if F(x)= x 0< x <2 ?10
UNIT-II
Q.3 (a) solve equation y" + 4y = 4 tan2x by variation of parameter?10
(b) Find the solution of given Bessels equation? 10
x y'' + (1+x) y' +2y =0
OR
Q.4 (a) Solution of equation one known integral ? 10
(x)^2.y'' + xy' -- y =0 given x+ (1/x)
(b) Prove that: 10
J-n (x) = (-1) ^n Jn (x)
UNIT-III
Q.5 (a) Write and Solve the Heat equation? 10
(b) Form a Partial Differential Equation ? 10
Z = Y^2 + 2 f ( 1/x + log y)
OR
Q.6 (a) solve the give differential equation ? 10
(b) Write and solve the Wave equation ? 10
UNIT-IV
Q.7 (a) Show that Div grad r^m = ∇.∇ r^m = m (m+1) r^(m-2) ? 10
(b) Solve using Stoke Theorem for function ? 10
Where c is the circle x^2 + y^2 = 1
OR
Q.8 (a) Show that ∇ f(r) = f'' (r) + 2/r f'(r) ? 10
(b) Verify show the gauss divergence theorem ? 10
∫ ∫s [(x^3-yz)i - 2 x^2 y j +2k].nds =a^5/3
Where s denote the surface of cube bounded by the plane x =0,x=a ,y=0,y=a ,z=0, z=a
UNIT-V
(b)Define the following ? 10
Q.9 (a) 6 Dices are thrown 729 times how many times would we expected to have atleast 3 dices to show 5 or 6 ? 10
(b) Fit a parabola of the following data : 10
x : 0 1 2 3 4
y : 1 5 10 22 38
OR
Q.10 (a) Fit the straight line of following data : 10
x : 0 1 2 3 4
y : 1 1.8 3.3 4.5 6.3
(b)Define the following ? 10
(i) Forecasting Theory (ii) Decision Theory (iii) Relaibilty Theory
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