PTU B.Tech CIVIL 6th Semester May 2019 71085 NUMERICAL METHODS IN CIVIL ENGINEERING Question Papers

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Roll No.

Total No. of Questions : 09

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B.Tech.(CE) (2011 Onwards)

Total No. of Pages : 02

(Sem.-6)

NUMERICAL METHODS IN CIVIL ENGINEERING

Subject Code : BTCE-604

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M.Code: 71085

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

Q1. Answer the following :

1. Define least square interpolation.

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2. Find an interval containing a root of the equation x - cos(x) = 0.
3. Explain Implicit solutions.
4. Determine the Lagrange interpolating polynomial passing through the points (2, 4) and (5, 3).
5. Explain Explicit solutions.
6. Explain briefly the Newmarks procedure.

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7. What is the order of convergence when Newton Raphson's method is applied to the equation x² - 6x + 9 = 0 to find its multiple root.
8. Use the forward-difference formula to approximate the derivative of f(x) = ln x at x₀ = 1.8 using h = 0.01.
9. Write a short note on bisection method.
10. Define initial value problem with a suitable example.

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SECTION-B

Q2. Use the Runge-Kutta method of order 4 to approximate the solution of the following initial value problem

y'= y - t² + 1, 0 = t = 2, y(0) = 0.5.

Q3. Apply Gauss Jordan method to find the inverse of the matrix

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Q4. The following data is given :

Use Lagrange interpolation to approximate f(1.5) with x₀ = 1.6.

Q5. Find a real root, correct to three decimal places of the equation 2x – 3 = cos(x) lying in the interval 3/2, p/2

Q6. Use Newton's iterative method to find the root of the equation 3x – cos(x) + 1=0 starting with an initial guess 0.6.

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SECTION-C

Q7. Determine the values of h that will ensure an approximation error of less than 0.00002 when approximating for ?sin x dx and

1. Composite trapezoidal rule.
2. Composite Simpson's rule.

Q8. The function f(x) = tan px - πarctan6 has a zero at parctan6 ˜ 0.447431543. Let p₀ = 0 and p₁ = 0.48. Use ten iterations of the secant method to approximate this root.

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Q9. A certain stimulus administered to each of the 12 patients resulted in the following increase in blood pressure :

5, 2, 8, -1, 3, 0, -2, 1, 5, 0, 4, 6.

Can it be concluded that the stimulus will, in general, be accompanied by an increase in blood pressure.

NOTE : Disclosure of identity by writing mobile number or making passing request on any page of Answer sheet will lead to UMC case against the Student.

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