North Maharashtra University 2011 B.E Computer Science and Engineering .f.ecommon - exam paper
wax* - 08
ENGINEERING MATHEMA'I ICS -1 (New)
R Pages: 4
Mu Marks. 100
Instructions : 1) Do not write anything on question paper except Sent No
2) Answer sheet should be written with blue Ink only J) Student should not*, no supplement will be provided
4) AU questions are compulsory 5i Use of non-prognmunable electronic calculator it allowed
14
if Examine for consistency and solve if consistent
5x 3y 7z * 4
3x 26y It 9
7k 2y 10* 3 m) Find the Eigen values and torrcspooding ctgen vector* ol the awtm
| -* 6 4
0 4 2 0 ~6 -3
1. a) Attempt any two T
rUrfind non singular matrices P and Q such that PAQ is in the normal Also find the rank of A Hence obtain A'* where
r.TXh
b) Attempt any our ;
flunsmiim
#***r 6 t Tf dependent find the
0 Test whether the vectors are linearly ilcf* relation between them
(2.-1. 3.2). (1. 3,4. 2), and (3,-5.2. 2)
1 |
2 |
-2 ' |
1 \ * >> *4 . | |
A |
-1 |
3 |
0 |
4 ' f |
0 |
-2 |
I |
2. a) Attempt any two ;
12
O'
If cor1
lOf
prove that
Expand 2x3 7x2 x - 6 in powers o
ii) Prove that e* * I tan x + rr tan2 x ~ r: tan3 x - J- tun4 \
.* 7 H it
i) Uw Taylor * theorem to find 25.15
M) Evaluate
i-1 X*'* (1 - x)*** uii,hj
* * (a bx )p-f q a (a+b)
i O J
W) Prove thut (erf (x)]* -7-c'* and uk 11 to show that
dx VR
a,- '- Jn* '
b) Attempt any two :
-x4
i) Evaluate J -7 dx
ii) Evaluate J x* (l ~ Vx )5dx
o
in) Prove that.
p) erfc (-x) + erfc (x) * 2
I
q) J erf (ax)dx J erfc (ax)dx * I,
4 Solve any four
(I xy) ydx (1 - xy) xdy * 0
b) (y log y> dx + (x - log y) dy 0
c) $mxr~ + 2y - tan ~
dx 2
d> 00* x y sin x
c) 4** y* (xdx ydy) (ydx - xdy) aa -x1 -y1 * 0
5. *) Attempt any two .
0 Water at temperature 100 C cook n 10 mwwte* lo 8# Cm a room temperature is 25* C. Find the tempcnmire of wrr alter 20 minute.
i.) Find the current V in the ctnuu having R and cowWr <>f
capacity *C* in series with e m f E n <ot
A body of mu *m' fall from re under gravity resm*
.1 >n si any instant is ink ume* ** vetoctty. where k is comunt to motu n y t mmA .U A- i~ ~~----
one half of its limning speed
b> l} Thc mjier and outer surface* of a spherical shell are maintained ai T0 and T, temperatures respectively If the umer and or wdu of the shell art r0and r, respectively and thermal conductivity of the sheil K, fmd the amount of heat loss from thc shell per unit time Find aho the temperature dttinbuuon
through thc shell.
n). The differential equation of the atmotplienc pressure is * - gp, where ;p; M thc densuy *i .val hth. h~ rniyk*
atmoipltefrc pSBlJtt.'WWIlIx *** **
P PoC * *hcrc *Po Pres*urc* *TOMnd
\ f ; ttUft
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