Kurukshetra University 2009 B.Tech Electronics and Communications Engineering Mathematics-1 - Question Paper
MATHEMATICS-1
PAPER :MATH 101E
8026
BTI/D09
MATHEMATICS-1 (2004-05 Onwards) Paper : MATH-101E Opt (ii)
8026
[Maximum Marks : ICO
Time : Three Hours!
Note : Attemptfive questions in ail, selecting at least one question from each unit. All questions carry equal marks.
UNIT-I
1. (a) Find the radius and centre of curvature for ihe curve x* + y2, - 3j> at the point {3/2, 3/2) on it,
(b) Using Madaurinji series, prove that :
e | |
2, (a) Trace the curve ; v = {x2 +1VC*2- 1). |
(b) Find Lhe asymptotes of the curve ;
/Lsin0 = 2cos 20.
UNfT-II
3* State Eulers Theorem for a homogeneous function of
two variables. Given :
4, (a) The ranne R of a projectile which .starts with a velocity
sin fi1
v al an elevation a is given by R = ' Find ihe
K
percentage error in R due to an error of 1% in v and an error of 0.5 in a,
<b) Using the method of differentiation under the sign of integration, evaluate
j[
UN1T-H1
5, (a) Evaluate : *
jj(.r + yfdxdy over the area bounded by the ellipse
J i
JT v*
(b) Using Double integration, prove thui tlie volume generated by the revolution of the cardioid
r = ff(]+cas0) about its axis js
6. (a) Evaluaic :
a v + y
P(m. ft) -k ~
Tw + n)
* IJNJTVIV
7. (a) If A 's a con sum 1 vector anil R = .r 1 + \'j + zk. prove that :
(ii) Curl [(A R)ii] JaxR,
(b) Define gradient of a settlor point function and give its geometrical interpretation,
K. (a) Usifi Stofces Theorem evaluate
|[(.i + ;y)iir + (2x - s)(/v + (y + fijrfz], c
where C is the boundary of the triangle with vertices (2. 0, 0), (0. 3, ()> and <0. 0 6),
(b) Use Divergence Theorem to evaluate :
j J (*t dyrfz + v tfz dx + z dxdy)
' (tver the surfaoc ol' :i sphere rudius tt. .
N026/1900/KD;2
Attachment: |
Earning: Approval pending. |