PTU B.Tech EE Engineering 5th Semester May 2019 70558 NUMERICAL AND STATISTICAL METHODS Question Papers

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

Total No. of Questions : 09

B.Tech. (Electrical Engineering & Industrial Control) (2012 Onwards)

B.Tech.(Electrical & Electronics/Electronics & Electrical/EE) (2011 Onwards)

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(Sem.=-5)

NUMERICAL AND STATISTICAL METHODS

Subject Code : BTEE-505

M.Code : 70558

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.

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SECTION-A

1. a) What is the difference between Rounding Error and Chopping?
2. b) Find order of Convergence of Bisection Method.
3. c) Define Pivoting and types of Pivoting.
4. d) Write Gauss-Legendre quadrature formula.

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5. e) Write General Euler’s formula; What is the disadvantage of this method?
6. f) Differentiate between interpolation and curve fitting.
7. g) Determine the step size that can be used in the tabulation of f'(x) = sin x in the interval [0,1] at equally spaced nodal point so that the truncation error of quadratic interpolation is less than 5 x 10^-5.
8. h) Is there any fallacy in the statement: The mean of binomial Distribution is 20 and its standard deviation is 7?
9. i) Define level of significance.

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10. j) Define probability distribution.

SECTION-B

2. Compute root of equation x² -1 = 0 in the interval [0, 2] using fixed point iteration Method. The root should be correct to three decimal places.

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3. Solve the following system of equations using Gauss-Seidal iterative method.

   27x + 6y - z = 85

   x + y + 54z = 110

   6x + 15y + 2z = 72

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4. The velocity ‘v’ of a particle at distance ‘s’ from a point on its linear path is given in the following table :

   S (m):	0	2.5	5	7.5	10	12.5	15	17.5	20
   V(m/sec):	16	19	21	22	20	17	13	11	9

   Estimate the time taken by the particle to traverse the distance of 20 meters.

5. Derive relation between Divided Differences and Ordinary Differences.
6. Obtain a relation of the form y = ab^x for the following data by the method of least squares:

   X	2	3	4	5	6
   Y	8.3	15.4	33.1	65.2	126.4

SECTION-C

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7. Use the Runga-Kutta fourth order method to find the value of y when x = 1, given that y = 1 when x = 0 (taking n = 2) and dy/dx = (y-x)/(y+x).
8. After correcting the proofs of the first 50 pages of a book, it is found that on an average there are 3 errors per 5 pages. Use Poisson distribution to estimate the number of pages with 0, 1, 2, 3 are more than 3 errors in the whole book of 1000 pages. (Given e^-6 = 0.5488).
9. A sample of 200 persons with a particular disease was selected. Out of them 100 were given drug and others were not. The results were observed as follows :

   	Drug	No Drug	Total
   Cured	55	65	120
   Not Cured	45	35	80
   Total	100	100	200

   Test whether the drug has been effective in curing the disease. (Given χ² =3.84)

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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