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

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* + y^2, - 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 tT*¹ cosaxiix.

j[

UN1T-H1

5, (a) Evaluate :    *

jj(.r + yfdxdy over the area bounded by the ellipse

J    i

JT v*

7⁺?^=l-

(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

Jl| J i^,x*^yJrt<izdydx

, . y(^|f)

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 :

(i)    Curl (A x kJ = 2*

(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: kurukshetra-university-2009-b-tech-electronics-and-communications-engineering-47912-1.pdf

Earning:   Approval pending.