Download PTU B.Tech 2020 March Aero 4th Sem ANE 204 Numerical Analysis Question Paper

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

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B.Tech.(Aerospace Engg.) (2012 Onwards)/B.Tech.(ANE) (Sem.-4)
NUMERICAL ANALYSIS
Subject Code : ANE-204
M.Code : 60512
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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1. Answer briefly :
   1. Evaluate the sum S=v3+5+7 to four significant digits and find its absolute and relative errors.
   2. Write the Newton-Cote’s quadrature formula.
   3. Using Euler’s method, find y'(1), given that y' = x+y and y (0) = 1.
   4. Write the normal equations for fitting a straight line to the data using a method of least squares.
   5. Find a root of x² — x — 1 =0 using a bisection method correct to two decimal places.

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   6. Evaluate ? (12/(5+x)) dx by Gauss quadrature formula.
   7. Using Taylor’s series method find y (0.2) for y’ =2y + 3e^x, y (0) = 0.
   8. What is the condition of convergence of fixed point iteration method?
   9. Write a short note on finite difference method.
   10. Classify the partial differential equation :
       

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       V²u — 2xyUxy + x²Uyy + 2u—3u=0

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SECTION-B

1. Find a root of xe^x = cos x using Regula-falsi method correct to four decimal places.

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2. Solve the following system of equation using the Gauss-Seidel iteration method :
   6x+3y+z=9
   2x—5y+2z=-5
   3x+2y+8z=-4
3. Estimate the values of f(22) and f'(42) from the following available data :
   

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   x:	20	25	30	35	40	45
   F(x):	354	332	291	260	231	204

4. Use Runge-Kutta method to approximate y when x = 1.2. given that y = 1.2 when x = 1 and dy/dx =3x+y².
5. Evaluate ?₀^p/2 sinxdx, using Simpson’s 1/3 rule.

SECTION-C

1. Use the power method to find the largest eigen value and the associated eigen vectors of the matrix A=

   1	3	-1
   3	2	4
   1	4	10

   starting with [0, 0, 1]^T as initial eigen vector.

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2. For IVP y' = x—3y², y (0) =1, estimate y (0.8) using the Milne’s predictor-corrector method with h=0.2.
3. Solve the equation V²u=-10 (x² + y² + 10) over the square with sides x=0=y, x=3=y with u = 0 on the boundary and mesh length equal to one.

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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