PTU B.Tech Robotics ECE Engineering 4th Semester May 2019 62021 NUMERICAL METHODS Question Papers

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Total No. of Pages : 02

Total No. of Questions : 09

B.Tech.(Electronics & Computer Engg.) (2011 Onwards) (Sem.-4)

NUMERICAL METHODS

Subject Code : BTEL-401

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M.Code: 62021

Time: 3 Hrs.

Max. Marks : 60

INSTRUCTIONS TO CANDIDATES :

1. SECTION-A is COMPULSORY consisting of TEN questions carrying TWO marks each.

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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

1. Answer briefly :
   1. Is the sequence x_n+1 = 0.5x_n, n ≥ 0, x₀ = 1 a convergent sequence?
   2. Write the forward finite difference formula for dy/dx.

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   3. Define the row rank of a matrix.
   4. Define a singular matrix and also give one example.
   5. Write the formula for Simpson's 1/3 rule.
   6. Can we use composite Simpson's rule with even number of node points?
   7. Compute ∫e² dx using Trapezoidal rule. X₀ =

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   8. Use the forward-difference formula to approximate the derivative of f(x) = ln x at 1.8 using h = 0.1.
   9. What is the order of convergence when Newton Raphson's method is applied to the equation x² - 4x + 4 = 0 to find its multiple root.
   10. Explain complete pivoting.

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SECTION-B

2. Use Newton's method to find a sequence converging to the root 0 of the equation ln(x+1) – x = 0 starting with an initial guess x₀ = 1.
3. Apply Taylor's method of order 2 with N = 10 to initial value problem : y' = y − t + 1, 0 ≤ t ≤ 2, y(0) = 0.5.
4. Find the order of convergence of Newton's method.
5. Solve the following system of equations
   

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   X₁ + 2x₂-X₃ = 3
   2x₁ + x₂ + x₃ = 3
   -3x₁+x₂+2x₃ = 4
6. Approximate the integral ∫₀^π/4 x sin xdx using composite Simpsons rule with 5 nodes.

SECTION-C

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7. Use R-K method of order 2 to find out y(0.2) with h = 0.1 for the following initial value problem
   y' = te³-2y, 0≤ t = 1, y(0) = 0.
8. Derive Secant's formula for solving the equation f(x) = 0 (specifying the assumptions made). Use the secant method to solve the equation x = cos t starting with an initial guesses 0.5 and π/4
9. Approximate ∫ e^2x sin 3xdx employing:
   1. Gaussian 2 point formula.
   2. Gaussian 3 point formula.

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   Also compute the errors in both the cases.

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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