Download PTU B.Tech 2020 March ECE 4th Sem BTEL 401 Numerical Methods Question Paper

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Roll No. Total No. of Pages : 03
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. Write briefly :
   1. If U=2V, find the percentage error in u at V =1 if error in V is 0.05.
   2. Show that the following rearrangement of equation x³ + 6x² + 10x — 20 = 0 does not yield a convergent sequence of successive approximations by iteration method near x=1.
   3. Write Geometrical Interpretation of regula Falsi Method.
   4. Construct a backward difference table for y = log x given that :
      x: 10 20 30 40 50
      

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      y: 1 1.3010 1.4771 1.6021 1.6990
      and find V² log40, V² log 50
   5. Write Newton’s general interpolation formula.
   6. Write normal equations for fitting the straight line using Method of least square method.
   7. Write formula of Simpson’s 1/3 rule for numerical integration.

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   8. Define Pivoting and types of pivoting.
   9. Define initial value problem and Boundary value problem.
   10. Write formula of Runga Kutta method of third order.

SECTION-B

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1. Find a real root of 2x-log₁₀ x = 7 correct to four decimal places using Newton Raphson Method.
2. Use Lagrange’s Interpolation formula to fit a polynomial to the data :
   x -1 0 2 3
   u_x -8 3 1 12
   Hence or otherwise find the value of u₁.

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3. Fit the curve pvⁿ = k to the following data :
   p(kg/cm²) 0.5 1 1.5 2 2.5 3
   v(liters) 1620 1000 750 620 520 460
4. The velocity “v” of a particle at distance “s” from a point on its linear path is given in the following table :
   s(m): 0 2.5 5 7.5 10 12.5 15 17.5 20
   

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   v(m/sec): 16 19 21 22 20 17 13 11 9
   Estimate the time taken by the particle to traverse the distance of 20 meters.
5. Solve the system of equations
   x+y+z=6
   3x+(3+ ε)y+4z=20
   

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   2x+y+3z=13
   Using Gauss Elimination method where ε is small such that 1+ ε²=1. What happens if we do not use partial pivoting at second step?

SECTION-C

1. Find the largest Eigen value and the associated Eigen vector of the matrix A
   

   2	3	2
   4	3	5
   3	2	9

   by Power’s method.

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2. Using Milne’s method, solve dy/dx =1+ y² with y(0) =0, y(0.2) = 0.2027, y(0.4) = 0.4228, y(0.6) = 0.6841, obtain y(0.8), y(1) and y(-0.2).
3. Obtain cubic spline for the following given data :
   X: 0 1 2 3
   f: 2 -6 8 2

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