Register Number

Register Number

SATHYABAMA UNIVERSITY

(Established under section 3 of UGC Act,1956)Course & Branch :B.E/B.Tech Common to ALL Branches Except to Bio groups

Title of the Paper :Engineering Mathematics IMax. Marks :80

Sub. Code :SMTX1001

Time : 3 Hours

Date :31/05/2011

Session :FN

______________________________________________________________________________________________________________________

PART - A (10 x 2 = 20)

Answer ALL the Questions

1.Given that A =, find the eigen values of AT.

2.Find the sum and product of the eigen values of the matrix

3.If tan(x/2) = tanh(y/2) prove that cosxcoshy = 14.State Demoivres Theorem.5.Define evolutes and envelope of a curve6.Find the envelope of

7.If x = r cos ( and y = r sin ( prove that

8.Expand ex siny in powers of x and y as far as the terms of the second degree.

9.Find the particular integral of (D 1) y = ex.

10.Solve xy// + y/ + = 0.

PART B

(5 x 12 = 60)

Answer All the Questions

11.Reduce the Quadratic form 2x2 + 5y2 + 3z2 + 4xy to canonical form by an orthogonal reduction.

(or)

12.Find the inverse of the matrix by using Cayley-Hamilton theorem.

13.(a) If prove that is 1 58' nearly.

(b) If sin(+i) = cos + i sin prove that cos2 = sin.

(or)

14.(a) Express Cos 7( in power of (.

(b) Show that

15.(a) Find the radius of curvature for

(b) Find the envelope (x - ()2 + y2 = k( where ( is the parameter.

(or)

16.(a) Find the evolute of the parabola x2 = 4ay

(b) Find the envelop of where a and b are connected by the relation a2 + b2 = c2.

17.Show that

Hence deduce that

(or)

18.(a) If u = f(x y, y z, z x) show that

(b) A rectangular box open at the top is to have a given capacity k. Find the dimensions of the box requiring least material for its construction.

19.(a) Solve: (D2 4D + 3) y = sin 3x.

(b) Solve: (x2D2 2xD 4) y = 32 (log x)2(or)

20.(a). Solve: (x2D2 +4 xD + 2)y = xlogx (b) Solve the simultaneous equations

_1352635668.unknown

_1352636968.unknown

_1352638416.unknown

_1352706970.unknown

_1352707497.unknown

_1352637981.unknown

_1352636786.unknown

_1351835197.unknown

_1352635013.unknown

_1352635284.unknown

_1234165409.unknown

_1250506302.unknown

_1243778642.unknown

_1234164683.unknown