Download PTU B.Tech 2020 March CHE 5th Sem BTCH 501 Numerical Method Question Paper

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Roll No. Total No. of Pages : 03
Total No. of Questions : 09

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B.Tech (Chemical Engg) (Sem.=5)

NUMERICAL METHOD

Subject Code : BTCH-501
M.Code : 70521

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. Differentiate between ‘Interpolation’ and ‘Extrapolation’.
   2. Define various types of errors in numerical computations.
   3. Write the Simpson’s 3/8 rule.
   4. Define significant digits: How many significant digits are there in 1.001?
   5. Write any disadvantage of Newton-Raphson method.

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   6. Define algebraic equations and transcendental equations with example.
   7. Define forward operator ? and shift operator E. Hence prove that E=1 + ?.
   8. Define eigen values and eigen vectors of a matrix.
   9. Write the Lagrange’s interpolation formula.
   10. Write iterative methods to solve linear algebraic equations.

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SECTION-B

1. Evaluate ? dx / (1+x) from 0 to 1 using Trapezoidal rule and Simpson’s 1/3 rule taking h = 0.1.
2. Solve the following system of equations by using the relaxation method :
   12x+y+z=31
   

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   2x+8y—z=24
   3x+4y+10z=58.
3. Fit a straight line to the given data : y(0) =4, y(1) =6, y(2) = 10, and y(3) = 8 by the method of least squares.
4. Find the cubic curve that passes through the points (-1, -8), (0, 3), (2, 1) and (3, 2) using Newton divided difference formula.
5. From the following table find the values of y’ and y" at x =0 :
   

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   X:	0	1	2	3	4	5
   y:	4	8	15	7	6	2

SECTION-C

1. Determine the largest eigen value and the corresponding eigen vector of the matrix
   A=[ 1 -3 2
   4 4 -1
   

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   6 3 5 ]
   By power method.
2. a) Use the method of triangularization to solve the system of equations
   2x+y+4z=12
   8x—-3y+2z=20
   

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   4x+ 11y —z=33
   b) Find a real root of the equation f (x) = cos x — 2x + 3 = 0 by fixed point iteration method correct upto three decimal places.
3. a) Using Runge-Kutta fourth order method to find y (0.4) given that
   dy/dx = (y² - x²) / (y² + x²)
   y(0)=1
   

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   With h =0.2
   b) Solve the following system
   x² —2xy+9.62=0,
   xy—2y²+14.97=0,
   by Newton-Raphson method with the initial values x0 =2 and y0 = 2.

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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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