Jadavpur University 2007 B.E Mechanical Engineering MATHEMATICS-IVM - exam paper
Wednesday, 23 January 2013 10:05Web
Ex/ME/Math/T/122/76/2006
FIRST ENGG. (MECH.) EXAMINATION, 2006
( second Semester )
MATHEMATICS IV M
Time : 3 hours Full Marks : 100
( 50 marks for every group )
Use a separate Answer-Script for every Group
PART I
ans any 6 ques..
( All ques. carry equal marks )
( 2 marks for general proficiency )
1. Solve (y2 +z2 -x2 ) p - two x y q + 2zx = 02
2. Form the partial differential formula by eliminating f, where
f(x + y + z, x2+y2-z2) = 0
3. obtain the integral surface of (x-y)p + (y-x-z)q = z through
the circle z = 1, x2 +y2 =1.
4. Using Chanpits method solve, p2 + q2 - 2px - 2qy + one = 0
5. Solve : (D2 +DD1 –6D12) z = y cos x
6. Solve: (D2 – D12 –3D + 3D1) z = xy + ex+2y
[ Turn over
[2]
7. decrease the formula to canonical form and solve :
8. Solve 2 dimensional Laplaces formula by the method of
separation of variables.
PART II
ans any 5 ques..
( All ques. carry equal marks )
9. Final the Fourier series to represent (x-x2 ) in (–p , p) and
hence deduce that
10. An alternating current after passing through a rectifier has
the form
i = I0 sin x, 0
i as a Fourier series.
11. find a Fourier series to represent x2 in-p
[3]
12. obtain the Fourier series expression for f(x)
where f(x) = —p , – p
13. find the Fourier series for f(x) = x + x2 in (–l, l)
14. obtain the Half-range sine and cosine series for f(x) = x in (0,2).
15. The displacement y of a part of a mechanism is tabulated
with corresponding angular movement x0 of the crank.
Express y as a Fourier series neglecting the harmonics above
the second.
x0 0 30 60 90 120 150 180 210 240 270 300 330
y 1.80 1.10 0.30 0.16 1.50 1.30 2.16 1.25 1.30 1.52 1.76 2.00
| Earning: Approval pending. |
