Download PTU B.Tech 2020 March EE 6th Sem Numerical And Statistical Methods 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) PT (Sem.-6)

NUMERICAL AND STATISTICAL METHODS

Subject Code : BTEE-505

M.Code : 72790

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. Define Relative and percentage error.
   2. Discuss convergence of Bisection method.
   3. Evaluate ?(e^x log 3x).
   4. Evaluate ?₀¹ dx / (1+x²) by trapezoidal method.
   5. Discuss Picard method.

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   6. Define Expectation.
   7. Write Pdf of Geometric distribution.
   8. Define critical region in sampling.
   9. Find the least square fit of y = ax².
   10. Discuss Gauss Seidel method.

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SECTION-B

2. Develop Newton Iterative formula for finding vN, N being the positive integer. Hence evaluate v13.
3. Solve using Gauss elimination method :
   

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   2x+y+z=10
   3x+2y+3z=18
   x+4y+9z=16
4. A curve passes through the points (0, 18), (1, 10), (3, -18) and (6, 90). Using Lagrange formula, find the slope of the curve at x = 4.
5. Using Gauss-Legendre 2-point formula, evaluate :
   

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   I = ?_-1² 2x / (1+x⁴) dx
6. Using method of Least squares fit the curve y = ax + bx² to the following table
   

   X	1	2	3	4	5
   y	1.8	5.1	8.9	14.1	19.8

SECTION-C

7. Given dy/dx = (y+x) / (y+x), y(0)=1. Find y (0.4) using Runge Kutta Method of fourth order with the step size of 0.2.

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8. A set of five coins is tossed 320 times and the customers
   

   No. of Heads :	0	1	2	3	4	5
   Frequency :	6	27	72	112	71	32

   
   Given that ?² for 5 degrees of freedom is 11.07. Test the goodness of fit of Binomial distribution.
9. 1. In a normal distribution, 31% of the item are under 45 and 8% are over 64. Find the mean and S.D. of the distribution.
   2. In 240 sets of 12 tosses of a coin, in how many cases one can expect 7 heads and 5 tails.

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

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