Rajiv Gandhi Proudyogiki Vishwavidyalaya 2008-3rd Sem B.E Chemical Engineering - Question Paper

june 2008
mathematics III max marks 100

1)solve any 5 ques.
2)each ques. carry equal marks
1.show that function eX(cosy=isiny)is an anaylitc function and obtain its derivative

2.use bessal formula to obtain value of y if x=3.75,given
x 2.5,3.0,3.5,4.0,4.5,5.0

y 24.125,22.043,20.223,18.645,17.234,16.544

3. obtain the nature of quadratic eqn form
x2+5y2+z2+2xy+2yz+6zx
and decrease it to cannonical form

4.by using newton raphson method obtain the roots of x4-x-10=0,
nearer to x=2 accurate to three decimel places

5. solve equations yb gauss siedal method
27x+6y-z=85
6x+15y+2z=42
x+y-2z=101

6.define vector space
show that vectors (2,1,4),(1,1,2),(3,1,2) forms a basis R3

7.using regula fals imethod obtain a real root of the formula xlogx-1.2=0 accurate up to three places
of decimals

Earning:   Approval pending.