03 – 301 ENGINEERING MATHEMATICS – II (CMNPHETARUFB)_june 2009_2003 scheme_11

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Reg. No. : .................................... Name : .........................................

III Semester B.Tech. Degree Examination, June 2009 (2003 Scheme) 03 – 301 : ENGINEERING MATHEMATICS – II (CMNPHETARUFB) Time : 3 Hours

Max. Marks : 100 PART – A

Answer all questions.

(10×4=40 Marks)

1. Solve P(p + y) = x(x + y) 2. Find the orthogonal trajectory of the family of parabolas y = ax2. 3. State the Dirichlet’s condition for the convergence of a Fourier series. −π≤ x ≤0 ⎧0, 4. Obtain the Fourier series of f ( x ) = ⎨ ⎩sin x , 0 ≤ x ≤ π π 2 aec θ 2 5. Evaluate ∫ ∫ r cos 2θ dr dθ 0 0

6. Find the angle between the tangents to the curve x = t, y = t2, z = t3 at t = ± 1. 7. Find the directional derivative of u = xy + yz + zx at the point (1, 2, 3) along the X-axis. B

(

)

8. Show that ∫ 2xy + z 3 dx + x 2dy + 3xz 2dz is independent of path joining the A

points A and B.

(

)

9. Evaluate ∫∫ F.nds where F = x + y2 i − 2 xj + 2 yz k and S is the surface of the plane S

2x + y + 2z = 6 in the first octant. 10. Solve (D2 – 4D + 4)y = e2x. P.T.O.


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