Download PTU B.Tech 2020 March ME 5th Sem Numerical Method Analysis Numerical Methods In Engg Question Paper

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Roll No. [ TTTTTT] [ ] Total No. of Pages : 02

Total No. of Questions : 09

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B.Tech (ME) (Sem.=5)

NUMERICAL METHOD ANALYSIS/
NUMERICAL METHODS IN ENGG.

Subject Code : ME-309

M.Code : 59028

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Time : 3 Hrs. 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

1. Write briefly :
   1. Define relative and absolute errors.
   2. State Newton-Raphson method for nonlinear equation f'(x) = 0.
   3. Define Eigen value and Eigen vector of a matrix.
   4. Write the Euler’s method for solving the ordinary differential equation.

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   5. Write Newton-cote’s quadrature formula.
   6. What is the difference between Simpson 1/3 and Simpson 3/8 rule.
   7. Write the governing equation of cubic splines.
   8. State Lagrange’s formula for equally spaced data points.
   9. Write the difference between Euler’s and modified Euler’s method.

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   10. State the Laplace equation for the partial differential equation.

SECTION-B

2. Using Newton’s iterative method, find the real root of x log₁₀x = 1.2 correct to five decision places.
3. Determine f (x) as a polynomial in x for the following data, using Newton’s divided difference formulae.
   

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   X: —4 -1 0 2
   f(x): 1245 33 5 9 1335
4. Use the method of least squares to fit the curve f(x) = ae^-x+ be^x for the following data :
   X: 0.1 0.2 0.3 0.4
   f(x): 0.76 0.58 0.44 0.35

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5. Solve the following equation by Gauss elimination method :
   2x+y+z=10; 3x+2y+3z=18; x+4y+9z=16
6. Find all the eigen values and the eigen vector corresponding to the largest eigen value (only) of the matrix
   

   2	2
   1	1
   3	-1

SECTION-C

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7. a) Use Simpson’s 1/3 rule to find
   ∫₀¹ e^x dx
   By taking seven ordinates.
   b) From the table below, for what value of x, y is minimum? Also find this value of y.
   X: 3 4 5 6 7 8
   

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   y: 0.205 0.240 0.259 0.262 0.250 0.224
8. Using Runge-Kutta method of fourth order, solve
   dy/dx = (y²-x²)/(y²+x²)
   with y(0)=1 at x=0.2, 0.4.
9. Solve the equation ∂²u/∂x² = ∂u/∂t subjected to the condition u (x, 0) =sinπx, 0 < x < 1 ; u (0, t) =u (1, t) = 0. Carry out computations for two levels taking h = 1/3 and k = 1/36.

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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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