Download PTU B.Tech 2020 March Aero 3rd Sem AM 201 Mathematics Iii Question Paper

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Roll No. HEEEEEEEEEEE Total No. of Pages : 02
Total No. of Questions : 09

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INSTRUCTIONS TO CANDIDATES :

1. SECTION-A is COMPULSORY consisting of TEN questions carrying TWO marks each.
2. SECTION-B contains FIVE questions carrying FIVE marks each and students have to attempt any FOUR questions.
3. SECTION-C contains THREE questions carrying TEN marks each and students have to attempt any TWO questions.

SECTION-A

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1. Attempt the following :
   1. Find L{e^t sin2t}.
   2. Find L^-1 {e^-2s / (s-2)}
   3. What is the value of J_-1(x)+J₊₁(x) in terms of J₀(x)?
   4. Write the complete solution of a differential equation when the roots of the indicial equation are distinct and differ by an integer.
   5. Form the partial differential equation from, z = xf₁ (x + t) + f₂ (x + t).

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   6. Solve pg=p+q.
   7. Write any one property of analytic functions.
   8. Give an example of a harmonic function.
   9. What are Dirichlets conditions?
   10. Find the sine series of x in (0, 2).

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SECTION-B

1. Find the Fourier series of e ^-x in the interval (0, 2p).
2. Using the concept of Laplace equations, solve
   x"+2x' + 5x = e ^-t sin t, where x(0) = 0, x' (0) = 1.

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3. Show that J₀(x) = (1/p) ? 0 to p cos(nt-xsin?)d?
4. Solve, (x² - y² - z²)p + 2xypq = 2xz.
5. Determine the analytic function whose imaginary part is cosx cosh y.

SECTION-C

1. Solve in series, x y" +3y' =y = 0.

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2. A string is stretched and fastened to two points l-apart. Motion is started by displacing the string in the form y = a sin (px/l) from which it is released at time t = 0. Show that the displacement of any point at a distance x from one end at time t is given by,
   y(x,t)=a sin(px/l) cos(pt/l)
3. Evaluate by contour integration ? 0 to 2p d? / (5+4cos?)

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.

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