Yashwantrao Chavan Maharashtra Open University 2006 Certification TML Aplied mathematics - Question Paper
Aplied mathematics
TML022/EE/20070813
Applied Mathematics Time : 180 minutes Marks : 100
Instructions for the students :
1. All questions are compulsory.
2. "Long Answer type Question (LAQ)" is a supply type question of 20 marks, which require typical answer of about 60-80 lines in about 32-40 minutes.
3. "Short Answer type Question (SAQ)" is a supply type question of 5 marks, which require typical answer of about 15-20 lines in about 08-10 minutes.
4. Use of non-programmable type of scientific calculator is allowed.
5. Draw neat diagrams wherever necessary.
6. Assume suitable data if necessary.
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Q- No. |
Question (Q) |
Question Marks |
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Long Answer type Questions (LAQ's) | ||
|
1. |
12 + 22 +.. + n2 (a) Evaluate Lim -3- n nro (b) Find the equation of tangent to the curve y = x3 - 4x2 + 5 at a point (2, -3) on it. |
10 10 |
|
2. |
f dx (a) Evaluate J- 5 - 4Sinx (b) Find the R.M.S. Value of the alternating current I = 2 Cos 3 t taken over complete cycle. |
10 10 |
|
3. |
(a) Solve the differential equation dy 2xy 1 --1--= --- given y = 0 when x = 1 dx x2 +1 (x2 +1)2 (b) Show that the equation (x2 -4xy-2y2)dx+(y2 -4xy-2x2)dx = 0 is exact and find its solution. |
10 10 |
|
4 |
r-i [ 2S2 - 6S + 5 1 |
10 10 |
|
(a) rind l _ S3 - 6S + 11S - 6 _ (b) Solve the differential equation by Laplace transform method. dy 2 t ty = t e given y = 3 , when t = 0 dt |
|
Short Answer type Questions (SAQ's) | ||
|
5. |
Find the derivative of the function y = Log X + VX2 + a2 |
5 |
|
6. |
n/2 , r Sinx , Evaluate J --ax (1 + Cosx )2 0 |
5 |
|
7. |
Form the differential equation from x = aSin(wt + c), where a and c are arbitrary constants. |
5 |
|
8. |
Find the Laplace transform of e-2t [2Cos5t - 3Sin5t ] |
5 |
N-67 TML022/EE/20070813: 2
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Attachment: |
| Earning: Approval pending. |
