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3090
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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
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8. Show that ∫ 2xy + z 3 dx + x 2dy + 3xz 2dz is independent of path joining the A
points A and B.
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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.