**RGPV Previous Exam Papers BE 3rd Semester **

**Engineering Mathematics **

Note : Attempt any five questions. All questions carry equal marks.

Q.1.show that function eX(cosy=isiny)is an analytic function and find its derivative ?Q.2.find the nature of quadratic eqn form x2+5y2+z2+2xy+2yz+6zx and reduce it to canonical form ?Q.3.by using newton raphson method find the roots of x4-x-10=0, nearer to x=2 correct to 3 decimal places ?

Q.4.solve equations yb gauss siedal method ?

27x+6y-z=85

6x+15y+2z=42

x+y-2z=101

Q.5.define vector space show that vectors (2,1,4),(1,1,2),(3,1,2) forms a basis R3 ?

Q.6.using regula fals imethod find a real root of the equation xlogx-1.2=0 correct up to 3 places

of decimals ?

Q.7.use bessal formula to find 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 | 20.22. | 18.645 | 17.234 | 16.544 |