Sathyabama University 2008 B.Tech : B.E / ,Engineering Mathematics - II - Question Paper

SATHYABAMA UNIVERSITY
(Established under part three of UGC Act, 1956)

Course & Branch: B.E /B.Tech – Common to ALL Branches
(Except to Bio Groups)
Title of the paper: Engineering Mathematics - II
Semester: II Max. Marks: 80
Sub.Code: ET202A/3ET202A/4ET202A/5ET202A Time: three Hours
Date: 24-05-2008 Session: FN

PART – A (10 x two = 20)
ans All the ques.
1. Solve the formula x3 + 6x + 20 = 0, are root being one + 3i.

2. Diminish the roots of x4 – 5x3 + 7x2 – 4x + five = 0 by two and obtain the transformed formula

3. Find the radius of curvature y2 = 2x(3 – x2) at the points where the tangents are parallel to x axis.

4. Find the maximum and minimum values of f(x,y) = x3 + 3xy2 – 15x2 – 15y2 + 72x.

5. Solve the equation:
(x + 2y) dx + (2x + y) dy = 0.

6. Solve the method of variation of parameters:
(D2 – 2D)y = ex sin x.

7. Compute the time needed for a particle, in simple flarmonic motion with amplitude 20cm and periodic time four seconds, in passing ranging from 2 points which are at distances 15 cm and 5cm from the origin 0.

8. Determine the change and current at time t > 0 in a RC-circuit with R = 10, c = two x 10-4, E = 100 V provided that Q(t = 0) = 0.
9. Prove that grade

10. If u = x2 – y2, prove that ?2u = 0.

PART – B (5 x 12 = 60)
ans All the ques.
11. (a) obtain the condition that the roots of the formula
x3 + px2 + qx + r = 0 may be in A-P.

(b)Solve 4x4 – 20x3 + 33x2 – 20x + four = 0.
(or)
12. (a) obtain the condition that the roots of the education
x3 – px2 + qx – r = 0 may be in G-P.
(b) Solve the equation:
6x6 – 35x5 + 56x4 – 56x2 + 35x – six = 0.

13. (a) obtain the radius of curvature at the indicated point:

(b) obtain the evolute of the hyperbola Deduce the evolute of a rectangular hyperbola?
(or)
14. (a) Determine the envelope of the 2 parameter family of parabola where the 2 parameters a and b are connected by the relation a + b = c where c is a provided constant.
(b) obtain the minimum value of x2 + y2 + z2 subject to the condition

15. (a) Solve the formula
(D3 – 2D2 – 5D + 6) y = 2ex + 4e3x + 7e-2x + 8e2x + 15.

(b) Solve the differential formula by the method of variation of parameters (D2 – 3D + 2) y =
(or)
16. Solve (D2 + D + 1) x + (D2 + 1) y = et (D2 + D) x + D2y = e-t.

17. A circuit consists of an inductance of 0.05 henrys, a resistance of five ohms and a condenser of capacitance four x 10-4 farad. If Q = I = o when t = 0, obtain Q (t) and I(t) when
(a) there is a constant emf of 110 volts,
(b) there is an alternating emf 200 cos 100r.
(c) obtain the steady state solution in is (b)
(or)
18. Find the angular motion Q(t) of a forced undamped pendulum whose formula is provided by Q + w2ot = Fo sinkt where wo and Fo are constants. If x = x = 0 at t = 0.

19. Verify the Gauss divergince theorem for over the cube bounded by x = 0, x = 1, y = 0, y = 1, z = 0 and z = 1.
(or)
20. (a) obtain the directional derivative of f = xyz at (1, 1, 1) in the directions of i + j + k, i, -i.

(b) Evaluate and S is the surface of the cylinder x2 + y2 = 1, included in the 1st octant ranging from the planes z = 0 and z = 2.

Earning:   Approval pending.