North Maharashtra University 2011 B.E Computer Science and Engineering .f.ecommon - exam paper

I* f f., ( o* m t) , -i* <|

Sc* No. [Olfcfeli

ENGINEERING MATHEMA'I ICS -1 (New)

R Pages: 4

Time: 3 Hour*    _

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

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b) Attempt any our ;

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 ;

*²ym.2*<²ⁿ*    2n²y_B0

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

f * 1 1 i¹ [ x - 1 log X j

ii) Evaluate

3. a) Attempt any two,

i-¹ X*'* (1 - x)***    uii,hj

i) Prove that J .-~--r----dx

* * (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) erf_c (-x) + erf_c (x) * 2

I    

q) J erf (ax)dx J erf_c (ax)dx * I,

4 Solve any four

(I xy) ydx (1 - xy) xdy * 0

b)    (y log y> dx + (x - log y) dy 0

^d> 1 . > *

c)    $mxr~ + 2y - tan ~

dx    2

d> 00* x y sin x

c) 4** y* (xdx ydy) (ydx - xdy) a^a -x¹ -y¹ * 0

dx 2x* 6y + 2

iKiiniKiii

14

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 P^res*^urc* *^TOMnd

\ f ; ttUft

Attachment: north-maharashtra-university-2011-b-e-computer-science-and-engineering-5977-1.jpg north-maharashtra-university-2011-b-e-computer-science-and-engineering-5977-2.jpg north-maharashtra-university-2011-b-e-computer-science-and-engineering-5977-3.jpg north-maharashtra-university-2011-b-e-computer-science-and-engineering-5977-4.jpg

Earning:   Approval pending.