Download PTU B.Tech 2020 March EEE 5th Sem 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.(EE/EEE) (Sem.=5)
NUMERICAL ANALYSIS
Subject Code : EE-311/AM-351
M.Code : 57027
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. Write briefly :
   1. State intermediate value property.
   2. State the condition where Newton’s method fails.
   3. Using Euler’s method, find y (1), given that y’ =x+y and y (0) =1 with h = 1.
   4. Write the normal equations for fitting a straight line to the data using a method of least squares.
   5. Show that Newton’s method has quadratic rate of convergence.

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   6. Use Picard’s method to solve dy/dx = 2x + y² upto third approximation where y(0) = 0.
   7. Write the iterative formula for method of false position.
   8. What is the condition of convergence of fixed point iteration method ?
   9. Write a short note on finite difference method.
   10. Use Taylor’s series method to solve dy/dx = 2x²+3y at x =0.1, given that y (0) = 1.

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SECTION-B

2. Use iteration method to obtain the root of equation x³ — 15x + 8 = 0 correct to four decimal places.
3. Solve the following system of equation using the Gauss-elimination method :
   3x—y+2z=12
   

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   x+2y+3z=11
   2x—-2y—z=2.
4. Fit a curve of the form y = ab^x to the given data :
   x: 2, 3, 4, 5, 6
   y: 144, 172.8, 207.4, 248.8, 298.5.

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5. Using modified Euler’s method, find an approximate value of y (0.3), given that y(0) = 0 and dy/dx =1-y+e^x with h=0.1
6. Find the value of dy/dx at x =40 from the following data :
   X: 0, 10, 20, 30, 40
   y: 1, 0.984, 0.939, 0.866, 0.766

SECTION-C

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7. Use the method of triangularization to solve the system of equations
   x+3y+z=3
   x+4y+2z=3
   x+2y-3z=6
8. For the given initial value problem (IVP), dy/dx = x— y², y(0) =1, estimate the value of y (0.2) using Runge-Kutta method of fourth order with step size h =0.1.

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9. The velocities of a car running on a straight road from rest position at intervals of 2 minutes are given below :
   Times (in minutes) : 2, 4, 6, 8, 10, 12
   Velocity (in km/hr) : 22, 30, 27, 18, 7, 0
   Find the total distance covered by the car in 12 minutes.

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