CS/B.TECH/(EE/ECE/EIE/EEE/PWE/BME/ICE)-New/SEM-3/M-302/2013-14
2013
MATHEMATICS-III
Time Allotted : 3 Hours Full Marks : 70
The figures in the margin indicate full marks.
Candidates are required to give their answers in their own words
as far as practicable.
GROUP – A
1. Answer any ten from the following: 10 x 2 = 20
i) If fx=xsinx, -π≤x≤π be presented in Fourier series as a02+n=1∞(ancosnx+bnsinnx), then find the value of a0.
ii) Show that every function can be expressed as a sum of even and odd functions.
iii) If fx is an odd function, then find the Fourier transform of fx.
iv) If Ffx=F(s), then show that Feiaxfx=F(s+a) , when Fstands for Fourier transform.
v) Find the value of m such that 3y-5x2+my2 is a harmonic function.
vi) Determine the poles of the function fz=z2z-12(z+2)
vii) Find the residue of z2z2-32 at z=3i .
viii) Evaluate C zz2-1 dz where C: |z|=2.
ix) A box contains 6 white and 4 black balls. One ball is drawn at random. What is the probability that the ball drawn is white?
(#N.B.: For correct version, kindly please download the pdf file.)
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