CSVTU Exams Questions Papers – Ist Year – Applied Mathematics-I – May-June- 2007

BE (1st Semester)

Examination May-June, 2007

Applied Mathematics-II

UNIT-I

1. (a) If x + = 2 cos and y + 1= 2cos ?

x                                x

Show that one of the value of

xmyn +        1        is 2cos(m ? + n?) 

                         xm + yn 

(b) If (i?) ea show that

? = (n + 1/2)?/2                    and

          ?=log tan (?  + a)

2               4     2

(c) Sum the series by C+ is method:

xsin ? –  x2 sin2 ? +1x3 sin 3? ………?

2                     3

 UNIT- II

2. (a) Solve the equation:

d2y – 2dy + y= xex sin x.

dx2      dx

(b) Solve by the method of variation of parameter:

d2y + y= x sin x

dx2

(c) Solve the equation

x2d2y – 3xdy + 4y= (1+x)2

dx2        dx

 UNIT- III

3. (a) Change the order of the integration in

2-x

l?0 ? xy dx dy

and hence evaluate same.

(b) Find the volume bounded by the cylinder x2 + y2 = 4 and the planes

y + z = 4 and z = 0

(c) Solve  ? ?xy(x2 + y2)n/2 dxxy over the positive quadrant of

x2 + y2 = 4 sup posin g n + 3> 0

 UNIT- IV

4. (a) find the work done in moving a particle in the force field:

F= 3x3I + (2xz – y)+ zk along:

(i) the straight line form (0,0,0) to (2,1,3)

(ii) the curve defined by x2 =4y, 3x2 =8z from x = 0 x = 2

(b) Evaluate divergence & curl of

F = 3x2 I + 5xy2 j +xyz3 K

At the point (1, 2, 3)

(c) Use divergence theorem to evaluate ?F ds where

F = 4xl – 2y2 j + z2 K and S is the surface bounding the region

x2 + y2 = 4, z = 0, z = 3

UNIT-V

5. (a) Solve the equation by Ferrari’s method:

x4  – 12x2 + 41x2 – 18x- 72 = 0

(b) Solve the equation by Cardin’s method:

x3 – 15x – 126 = 0

(c) Solve x3 – 4x2 – 20x + 48 = 0 given that the roots a and ? are connected by the relation a + 2? = 0

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