# Bharati Vidyapeeth 2007 B.E Biotechnology maths - Question Paper

Friday, 18 January 2013 08:20Web

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Visvesvaraya Technological University

Model ques. Paper – I

B.

**E.**exam

ENGINEERING MATHEMATICS-IV (06MAT41)

(Common to all Branches other than BT)

**Time:**03 hours Ma

**x.**

**Marks:**100

Note: ans any 5 ques. choosing atleast 2 from every part

**PART-A**

**1.**

**(**Employ Taylor’s series method to obtain an approximate solution accurate to 4th decimal

**a)**place for the subsequent initial value issue at x = 0.1 and 0.2

2 three ; (0) 0 x dy

y e y

dx

= + =.

**(**Apply Runge-Kutta method to obtain an approximate value of y for x = 0.2 in steps of

**b)**x = 0.1, provided that two ; with (0) 1

dy

x y y

dx

=+ =.

**(**Using Milne’s predictor-corrector method obtain y when x = 0.8, provided two ;

**c)**dy

x y

dx

= -

(0) 0, (0.

**2)**0.02, (0.

**4)**0.0795, (0.

**6)**0.1762 y y y y = = = = . Apply corrector formula

twic

**e.**(7+7+6)marks

**2.**

**(**describe analytic function. Derive Cauchy-Riemann equations in polar form.

**a)****(**obtain an analytic function two 2 () , where =( )( four ). f z u iv u v x y x xy y =+ - - + +

**b)****(**obtain the Bilinear transformation which maps the points 0, 1, z= ¥into the points

**c)**5, 1,3 w =- - respectively. elaborate the invariant points under this transformation?

(7+7+

**6)**marks

**3.**

**(**State and prove Cauchy’s integral formula.

**a)****(**Expand

**b)**1

( )

( 1)(2 )

f z

z z

=

- -

as a Laurent’s series valid for () one ( )1 two i z ii z < < < .

(c)Using Cauchy’s residue theorem evaluate

( )3

cos

,

2 C

z z

dz

z p - ò where C : one 1 z- = .

(7+7+

**6)**marks

**4.**

**(**find the series solution of the equation:

**a)**2

2 nine (1 ) 12 four 0

dy dy

xx y

dx dx

- - + = .

**(**find the series solution of Bessel’s differential formula in the form

**b)**() ( ) n n y AJ x BJ x - = + .

**(**Prove that two 1

**c)**() {(

**1)**}

2 !

n

n

n n n

d

Px x

n dx

= - , where n is a positive integer.

(7 + seven + 6)marks

**PART-B**

**5.**

**(**obtain a 2nd degree polynomial in the lowest square sense that fits to the subsequent data

**a)**x 0 one two three 4

y one 1.8 1.3 2.5 6.3

**(**obtain the correlation coefficient and regression lines of y on x and x on y for subsequent

**b)**data :

x one two three four 5

y two five three eight 7

**(**In a factory, machines A, B, C produce respectively 25%, 35%, and 40% of the total

**c)**production. Of which 5%, 4% and 2% are defectiv

**e.**An item is drawn at random was obtained

to be defectiv

**e.**obtain the probability that it was manufactured by

**A.**(7 + seven + 6)marks

6.

**(**describe random variable .A random variable(X=

**a)****x)**has the subsequent probability

Earning: Approval pending. |