Guru Nanak Dev University 2012 B.Tech Computer Science and Engineering Mathematics -II - Question Paper

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B Tech. Computer Science 4 Engineering 2nd Seneter(UC***

(2412)

Paper-MTL-102 : Mtbemetc-ll (Same for B. Tech. Food Tech. ECB b EC (System) 2nd Bern I Time Allowed: 3 hr.    Max. marks SO

Note: \t1cmpl nil questions. Ench quctiun carrier equal markv

1. (a> Find the sum to infinity ol the series

1    1.3    1.3.5

1 - -CO.V0 + COSlO - -COSAO + (-7T < ft < 7T),

2    2,4    2.4.6 lb) Test for convergence Ihe scries

2 6 14    2" - 2

^{1 +} 5* ⁺ 9*^{2 +} 17 ⁺ " ⁺ WTl*'"' ⁺ " ^{<Z > 01}

2. (a) Using Residue Theorem, evaluate

09

dx

x⁴ + 1

0

(b) Find Ihe bilinear transformation which map* the point* z = 1.1, 1 nlotbe Points w 1,0, -I. f lencc find the image of |/l < 1

3. (a) Find the inverse Laplace of

21s-33

(s + l)(s-2)^J

fb) Using Laplace transforms, solve (D¹ - 30* + 3D - t)y * t^J# given that y(0) = l,y'(0) * 0.y"(0) -2.

(a) Show that

sln²&    2n / /-

dO as yjyd     ) where 0 < b <. .

a + bcosO b¹

o

(h) Find tlic Fourier cosine littiislorm ol *~*

( x,    0 < x < J

5 (a) If /(*) = {    _n    show ihul

{ n - X,    - < * < n

it 2 reus 2a ios6j cos 10.x

(h Obtain the first three* coclhcirnLs in the 1 ouricr cosine scno for v. where y is given in the following iahlc * i 0 I 2 i 4 S y 4 # H 7 ft -

1

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Earning:   Approval pending.