Karnataka State Open University (KSOU) 201-3rd Sem B.Tech Civil Engineering Matematics 1 - Question Paper
CE 3001 (CH 3001/CS 3001/TT 3001/ME 3001/ET 3001/EE 3001)
III Semester B.Tech. in (Chemical/Civil/Computer/Textile/Mechanical/ Electrical/Electronics and Tele Communication) Engineering
Examination, August 2011 MATHEMATICS-III
Time : 3 Hours Max. Marks : 75
Instruction : Answer any five questions from Part - A and Part - B.
PART - A
Answer any five questions : (5x5=25)
1) Solve : p2y(l + x2) = qx2.
2) Find the singular integral of z = px + qy + p2 - q2.
3) Obtain the half range cosine series for f(x) = x in (0, n ).
4) Write the differences between the solution of one dimensional wave equation and one dimensional heat equation.
5) In steady state conditions derive the solution of one dimensional heat flow equation.
6) State the Fourier transforms of the derivatives of a function.
7) Find z[an/n!] in z transform.
8) Find the z transform of {1/n}.
PART - B
Answer any five questions : (5x10=50)
9) Form a partial differential equation by elimination arbitrary functions from z = xf (2x + y) + g (2x + y).
10) Solve (x2 t- y2 + yz) p + (x2 + y2 - xz) q = z(x + y).
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CE 30U1 (CH 3001/CS 3001/TT 3001/ME 30Q1/ET 3001/EE 3001) |
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11) Solve Z = p2 + q2.
12) Find the Fourier series for f(x) = |cosx| in the interval (-%, n ).
13) A metal bar 10 cm long with insulated sides has its ends A and B kept at 20C and 40C respectively until steady state condition prevail. The temperature at A is then suddenly raised to 50C and at the same instant that at B is lowered to 10C. Find the subsequent temperature at any point at the bar at any time.
14) Evaluate integral 0 to infinity dx/(x square + a square) (x square + b square) using transforms.
15) State and prove the second shifting theorem in 7 transform.
16) Find the Z-transform of {an} and {nan}.
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| Earning: Approval pending. |
