Download PTU B.Tech 2020 March CSE-IT 4th Sem CS 204 Mathematics Iii Question Paper

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Roll No. Total No. of Pages : 02

Total No. of Questions : 18

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B.Tech(IT/CSE) (Sem.-4)

MATHEMATICS-III/ENGG. MATHEMATICS-III

Subject Code : CS-204

M.Code : 56514

Time : 3 Hrs. Max. Marks : 60

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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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Write briefly :

1. Check the convergence of the sequence
   a_n = (2n+1)/(2n-1)
2. Define Roll’s theorem.
3. Write down the formula for finding centre of gravity of a uniform plane Lamina.

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4. Show that sin z is analytic function.
5. State Cauchy’s integral formula.
6. Define conformal mapping.
7. Evaluate ? z²/(z³-5z²+4) dz, C:|z|=1
8. Write down the Euler’s formula for finding solution of an initial value problem.

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9. Write down the wave equation for transverse vibrations in one dimensional string.
10. Classify the partial differential equation as elliptic, parabolic or hyperbolic :
    ?²u/?x² - 5 ?²u/?x?y + 6 ?²u/?y² = 0

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SECTION-B

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11. Evaluate ? ydxdy , where R is the region bounded by the parabolas y² = 4x and x² = 4y
    R
12. Determine the analytic function whose real part is log v(x² + y²) .
13. Expand f(z) = 1/((z+1)(z+3)) in Laurent’s series, valid for | z | > 3.
14. Show that the transformation w = (z-i)/(z+i) maps the real axis in the z-plane onto the circle |w|=1.

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15. Find the general solution of Laplace equation by variable separable method.

SECTION-C

16. Evaluate ?₀^2p 1/(1-2acos?+a²) d?, 0 < a < 1 using Contour integration.
17. A homogeneous conducting rod of length 100 cm has its ends kept at zero temperature and temperature initially is
    u(x,0) = { x, 0 < x < 50
    

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    100-x, 50 < x < 100 }
    Find the temperature u(x, t) at any time t.
18. Apply Runge-Kutta method of order 4 to find y(0.1) for the initial value problem
    dy/dx = xy + y², y(0) = 1.

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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