Download PTU B.Tech 1st Semester [2019] 70970 ENGINEERING MATH III Question Papers

Roll No.

Total No. of Questions : 09

B.Tech. (EE) PT (Sem.-1)

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ENGINEERING MATH-III

Subject Code : BTAM-301

M.Code: 70970

Total No. of Pages : 02

Time: 3 Hrs.

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Max. Marks : 60

INSTRUCTIONS TO CANDIDATES :

1. SECTION-A is COMPULSORY consisting of TEN questions carrying TWO marks each.
2. SECTION - B & C have FOUR questions each.
3. Attempt ANY FIVE questions from SECTION B & C carrying EIGHT marks each.

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4. Select atleast TWO questions from SECTION - B & C.

SECTION-A

1. Solve the following :
   1. Find half range cosine series for x in (0, p).
   2. State Dirichlet's condition for expansion of a function in terms of Fourier Series.
   3. If L (f(t)) = F(s) then prove that L (f(at)) = ?

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   4. Find laplace transform of e^-2t sin²t.
   5. Find the solution of d²y/dx² + (1/x) dy/dx + (1 - 1/4x²)y = 0 in terms of Bessel's function
   6. Define regular singular and irregular point of a second order Linear differential equation.
   7. Form the Partial Differential Equation corresponding to z = y² + 2f(1/x + log y)
   8. Solve the partial differential equation (z – y) p + (x - z) q = y – x, where p = ?z/?x, q= ?z/?y

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   9. Is the function u = 2xy + 3xy² – 2y³ harmonic? Given reason.
   10. Find the poles and residue at the poles of z/COS z

SECTION-B

2. Find Fourier series for f (x) = | sin x |, - p = x = p.

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3. State and prove second shifting theorem and hence find inverse Laplace transform of e^-2ss/(s² + s +1)
4. Solve the homogeneous partial differential equation (?²z/?x²) - (?²z/?x?y) - 2(?²z/?y²) = 4 sin (2x + y).
5. Prove that J_1/2(x) = v(2/px) sinx

SECTION-C

6. If f(z) = u + iv is an analytic function. Find f (z) if u+v=x/(x² + y²), f(1) = 1

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7. Find series solution of the differential equation 9x(1-x) d²y/dx² - 4y=0.
8. A tightly stretched elastic string with fixed end points x = 0 and x = l is initially in a position given by y=ysin(3px/l). If it is released from rest from this position find the displacement y(x, t).
9. a) Using Residue theorem, evaluate the integral ?_C (z+3)/((z+1)(z-2)) dz where C is the circle | z | = 3
   b) Prove that w=(z/(i-z)) maps the upper half of the z-plane into the upper half of w-plane.

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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