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| Roll No. | Total No. of Pages : 02 |
| Total No. of Questions : 09 |
B.Tech. (Aerospace Engg.) (2012 Onwards)/(ANE) (Sem.-3)
MATHEMATICS – III
Subject Code : AM-201
M.Code: 60537
| Time : 3 Hrs. | Max. Marks : 60 |
INSTRUCTIONS TO CANDIDATES :
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- SECTION-A is COMPULSORY consisting of TEN questions carrying TWO marks each.
- SECTION-B contains FIVE questions carrying FIVE marks each and students have to attempt any FOUR questions.
- SECTION-C contains THREE questions carrying TEN marks each and students have to attempt any TWO questions.
SECTION-A
Q1. Answer briefly :
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- Find L{te²? sin 5t} .
- Find L?¹ {e?4? / (S-4)}.
- What is the value of J?1 + J?1(x) in terms of J?(x)?
- Write the complete solution of a differential equation when the roots of the indicial equation are distinct and differ by an integer.
- Form the partial differential equation from, z = f (x² - y²).
- Solve vp+vq=1.
- Write any one important property of analytic functions.
- Give an example of a harmonic function.
- Discuss Dirichlet's conditions?
- Find the sine series of x² in (0,1).
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1| M-60537 (S2)-416
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SECTION-B
Q2. Find the Fourier series of x cos x in the interval (–p, p).
Q3. Using the concept of Laplace equations, solve x" + 9x = 6cos 3t where x (0) = 2, x'(0) = 0.
Q4. Show that J0(x) = (1/p) ?0^p cos(x sin?) d?
Q5. Solve, x(y² – z²) p + y (z² - x²) q = z (x² - y²)
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Q6. Determine the analytic function whose real part is log v(x² + y²) .
SECTION-C
Q7. Solve in series, y" + xy = 0.
Q8. A tightly stretched string with fixed end points x = 0 and x = l is initially at rest in its equilibrium position. If it is set vibrating by giving to each of its points a velocity µx (1 – x), find the displacement of the string at any distance x from one end at any time t.
Q9. Evaluate by contour integration ?0^2p cos3? / (5-4 cos?) d?.
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NOTE : Disclosure of Identity by writing Mobile No. or Making of passing request on any page of Answer Sheet will lead to UMC against the Student.
2| M-60537 (S2)-416
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