Cochin University of Science and Techology (CUST) 2008-2nd Sem B.Tech Electrical and Electronics Engineering University ; I &(Combined) ,; IT/CS/EC/CE/ME/SE/EB/EI/EE/FT 101 ENGINEERING M
B.Tech. Degree I & II Semester (Combined) Examination, June 2008.
IT/CS/EC/CE/ME/SE/EB/EI/EE/FT 101 ENGINEERING MATHEMATICS I
(2006 Scheme)
Summary: ques. paper comprises of 2006 scheme syllabus, which is still in use. Until today they
haven't changed the scheme.
ques. paper has the subsequent topics:
first module has Ordinary Differential Equations.
second module has Infinite series and power series.
third module has Partial Differentiation and Co-ordinate systems.
fourth module has Integral Calculus and Multiple Integrals.
BTS(C)- I & II - 08 - 029(B)
B. Tech. Degree I & II Semester (Combined) Examination, June 2008
IT/CS/EC/CE/ME/SE/EB/EI/ EE/FT 101 ENGINEERING MATHEMATICS I
(2006 Scheme )
Time: 3 Hours
I a) b)
c)
d)
e)
f)
g)
h)
II
n '
2 2loge
d2z
and its asymptote.
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Solve the following differential equations : | ||||||
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Verify whether the functions u =
1 -xy
dependent and if so find the relation between them.
2 4
Show that 102(1 + 6*) = log2+-+----
2 8 19
Solve 7" - v = e Cos x. dx4
v- flO
Test the convergence of the series If xxyyzz =C find
Prove that \n = J(log) ldx(n > 0).
o x
PART B
x + y i i
V ~ tan x + tan- y are functionally
Solve (x - 3xy + 2y )dx + x(3x - 2y)dy = 0.
PART A
(Answer all questions)
Find the area bounded by y ~
Maximum Marks: 100
(15x4 = 60)
(8x5 = 40)
dAy
dxdy
2 4a2 (2 a-x)
OR
An RL circuit has an emf of 5 V, a resistance of 50 Q, an inductance of 1H and no initial cuiTent. Find the current in the circuit at any time t. dx
III
a)
b)
a)
b) c)
(7)
(8)
(6)
(5)
(4)
Solve + 4x + 3 y = t dt
J..
+2x + 5y-el, given that x = y = 0 when f = 0. dt
Expand Sinx in powers of (x . Hence find the value of Sin 91 correct to four decimal places.
x2 x3 x4
Find the interval of convergence of the series X--t=? + j=-------
Define conditional convergence and absolute convergence of series with examples.
OR
(Turn Over)
a {*Y&
V a) Discuss the convergence of the power series x2n. (7)
b) If y = (Sin~xx)2 show that (1 - x2 )yn+2 ~ (2 +l)*Vn+i ~ n2yn = Hence
find the value of yn at x = 0 . (8)
1 1 2
VI a) The focal length of a mirror is given by the formula---= . If equal errors S
v u f
are made in the determination of u and v, show that the relative error in the focal
S. (5)
1 1
U V
length is given by
b) If x - u + v + w, y = uv + vw + wu, z = uvw and f is a function of x,y,z
df _ df _ df df df df
provethat x--v2y--h3z u- + v--hw. (5)
dx dy dz du dv dw
c) Find the expansion of the function ex log(l + y) in a Taylor series in the neighbourhood
of (0,0). (5)
OR
VII a) If = */(%) + (%) provethat x~ + 2xy-~ + y = . (6)
b) In a plane triangle ABC, find the maximum value of Cos CasBOwC . (6)
2
c) Find the total differential coefficient of x y with respect to x when x and y
2 2
are connected by the relation x +xy + y = 1. (3)
VIII a) Find the area of the surface of revolution formed by revolving the loop of the curve
9ay =x(3a x) about x - axis. (5)
Vir xdxdy
b) Change the order of integration in J J-j and hence evaluate the same. (5)
x +y
0 y
c) Evaluate f f f # dxdydz_ over octant of the unit sphere by
J J JVl-x2-y2-z2 transforming into spherical polar co-ordinates. (5)
OR
IX a) Find the area included between the cardioids r a( 1 + CosO) and r a{\ CosO). (5)
2 2 2 x y z 1
b) Find the volume of the ellipsoid r- H l - (7)
a b c
%
c) Express J -JCotOdO in terms of gamma function. (3)
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Attachment: |
| Earning: Approval pending. |
