Bangalore University 2005 B.E Engineering Mathematics II-/ch - Question Paper
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MAT21
Second Semester B.E Degree Examination, February/March 2005
Common to All Branches
Engineering Mathematics II
Time: 3 hrs.] [Max.Marks : 100
Note: 1. Answer any FIVE full questions choosing at least one question from each port.
2. All questions carry equal marks.
Part A
2
1. (a) Show that for the curve r2 sec2 9 = a2, p = ' (7 Marks)
" (b) State and prove Lagranges mean value theorem and find its geometrical interpretation. (7 Marks)
: - *
(c) Obtain Taylor's series expansion of log (cos x) about the point i = y upto the fourth degree term. : (6 Marks)
2. (a) Evaluate :
> lirri log(cos x)
J '>2' -
(b) Explain eax+V in the neighborhood of the origin upto the third degree term.
(7 Marks)
|c) if x. v. z are the angles of a triangle show that the maximum value of
- (6 Marks)
Page,No... 1
COS X COS V COS Z IS
(7 Marks)
USN
NEW SCHEME
PART B
3. (a) Change the order of integration and hence evaluate
4a ly/ax-
J J *y dy dx.
l l-x i-x y AAA (b) Evaluate f f f d~ dVd*
0 0 0 (l+*+J/+2,J
'IO Show that / (1 + x)P 1 (1 dx = 2P+<i~i fi(p,q).
-l
lf ,4V (a) A particle moves along the curve z = 1 - f3, y 1 + t2 and z = 2t -5. Determine its velocity and acceleration. Find the components of velocity and acceleration at t = 1 in the direction 2i + j + 2k. (7 Marks)
Contd.... 2
MES14
(4 Marks)
i refrigeration
(8 Harks) (8 Marks)
radial drilling
(8 Marks)
(6 Marks)
(6 Marks)
(6 Marts)
(6 Marks)
(4 Marks)
(4 Marks)
ive. (6 Marks)
im diameter ation of the drive. How
(6 Marks) 1. (4 Marks)
-k diagram.
(4 Marks)
ng-
ii)
(7 Marks)
(7 Marks)
(6 Marks)
.7
..2 MAT21
V . : 'I'*-.
Page No.. (b)
(c)
5. (a) (b) (c)
6. (a)
. (b)
(c)
7. (a)
(b)
(0
, 8. (a) (b)
(c)
Find the constants a* and b' so that the vector F = (axy + r3)i + (3x2 z) j (bxz2 - y)k is irrotational and find <f> such that F grad. <f>. (7 Marks)
Evaluate J xy dx -f xy2 dy bv stokes theorem where C is the square in the xy
C.
plane with vertices (1,0), 1,0), (0,l)i:(0, 1). (6 Marks)
PART - C
Solve : + 4y e2x + cos 2x 4 (7 Marks)
dx/- dx
Solve : -4 + - 4 -f 4y = x2 4z 6 (7 Marks)
dx3 dx- x
Solve : 24 -f 2 = ex tan x using method of variation of parameters.
(6 Marks)
Solve - 4+ 5y = 0 subject to the conditions = 2,y 1 at x = 0.
dx2 dX (7 Marks)
Using method of undetermined coefficients solve
<LlL 2 + 3y X2 + COS X. (7 Marks)
dx- dx.
Solve (3z 2)2 - 3(3z 2) = 9 (3r - 2) sin (log(3x 2)) (6 Marks)
Find the Laplace transforms of
i) te2t 2srn31
i
ii) J e * sin 21 sin3t dt (7 Marks) i)
A periodic (unction of period is definded by fits J E sin ut, 0 <i<%
where Ehw are constants. Show that
L\ f(t)) = -- (7 Marks)
Express the following function in terms of Heaviside unit step function & hence find its Laplace transform where
'> = {, l>li2 16
Find inverse Laplace transform ol ---(7 Marks)
(.s
Using convolution theorem obtain the inverse Laplacc transform of
< (7 Marks)
{.s-4-2l(.2-h9l
Using Laplace transform solve the equation y" + '6y' + 9y = 12t2e 3t subject to the conditions y(0) = 0, y'(0) 0. (6Marks)
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| Earning: Approval pending. |
