Download PTU B.Tech 2021 Jan Automation-And-Robotics 3rd Sem 76502 Mathematics Iii Question Paper

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Total No. of Pages : 02

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Total No. of Questions : 18

B.Tech. (Automation & Robotics) (2018 Batch) (Sem.-3) MATHEMATICS-III

Subject Code : BTAR-303-18

M.Code: 76502

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 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.

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SECTION-A

Write briefly :

1. Define odd function and write Fourier series for an odd function satisfying Dirichlet conditions in the interval (-c,c).
2. Find Laplace inverse transform of 1/(2-3s)
3. Find Laplace Transform of t sin 2t.

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4. Write down the Bessel's equation.
5. Express f (x) = 2x² + x + 1 in terms of Legendre function.
6. Form a partial differential equation by eliminating arbitrary functions from z = f.
7. Solve the partial differential equation p tan x + q tan y = tan z, where p = dz/dx, q = dz/dy.
8. Evaluate ∫ (2-3)/(z²+2z+5) dz, C :| z |= 2.

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9. Write down the necessary and sufficient conditions for a function to be analytic.
10. Write down the mathematical function for Triangular wave form.

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SECTION-B

11. Obtain the Fourier series for f (x) = x cos x in the interval (− π, π).

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12. Solve the differential equation using Method of Laplace transform d²y/dt² + 2 dy/dt + 2y = e^t, y(0) = 0, y'(0) = 1
13. If α and β are the roots of the equation J₀(x) = 0, then prove that ∫ J₀(αx) J₀(βx)dx = 0, if α ≠ β
14. Expand f(z) = (-4z+3)/(z(z-1)(z-3)) in Laurents series for 1 <|z|<3.
15. Solve the Partial differential equation ∂z/∂x ∂z/∂y = 1

SECTION-C

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16. a) Find half-range cosine series for f (x) = x + x²
    b) Find the Bilinear transformation which maps z = 1, i, -1 onto the points w = i, 0 – i.
17. A string is stretched between the fixed points (0, 0) and (l, 0) and released at rest from the initial deflection given by
18. Solve in series using Frobenius method : x² d²y/dx² + (x² + x) y = 0

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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