Download PTU B.Tech 2020 March ME 6th Sem Statistical And Numerical Methods In Engineering Question Paper

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Roll No. Total No. of Pages : 02

Total No. of Questions : 09

B.Tech.(ME) (2012 Onwards) (Sem.-6)

STATISTICAL AND NUMERICAL METHODS IN ENGINEERING

Subject Code : BTME-604

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M.Code : 71188

Time : 3 Hrs. Max. Marks : 60

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.

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3. SECTION-C contains THREE questions carrying TEN marks each and students have to attempt any TWO questions.

SECTION-A

1. Write briefly :
   1. An incomplete frequency distribution is given below :

      Variable	10-20	20-30	30-40	40-50	50-60	60-70	70-80
      Frequency	12	30	S	65	f	25	18

      Given that the total frequency is 229 and median is 46. Find the missing frequencies S.

   2. The probability that a pen manufactured by a company will be defective is 0.1. If 12 such pens are manufactured, find the probability that at least two will be defective.

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   3. Explain different types of errors.
   4. Discuss intermediate value property.
   5. Prove that if A is an eigen value of an orthogonal matrix A, then 1/A is also its eigen value.
   6. Write Newton’s-backward interpolation formula.
   7. Explain sampling distributions of the means.

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   8. Discuss predictor-corrector method.
   9. Write Euler-Maclaurin’s formula.
   10. Discuss ill-conditioned equations.

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SECTION-B

1. One thousand articles from a factory are examined and found to be three percent defective. Fifteen hundred similar articles from a second factory are found to be only two percent defective. Can it reasonably be concluded that the product of the first factory is inferior to the second.

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2. Use the Newton-Raphson procedure for finding vN where N is a real number. Use it to find v18 correct to two decimal places, assuming 2.5 as the initial approximation.
3. Find an approximate value of ?₁² dx/(1+x) by using :
   1. Trapezoidal rule,
   2. Simpson’s 1/3 rule
   3. Simpson’s 3/8 rule.

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4. Determine the number of terms required in the series for log (1 + x) to evaluate log (1.2) correct to six decimal places.
5. Find the first and second order derivatives of the function f(x) at the point x =1.5, if

   X	1.5	2.0	2.5	3.0	3.5	4.0
   f(x)	3.375	7.000	13.625	24.000	38.875	59.000

SECTION-C

1. Determine the largest eigen value and the corresponding eigen-vector of the matrix
   A = 2 & -1 & 0 \\ -1 & 2 & -1 \\ 0 & -1 & 2

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2. Using modified Euler’s method and Runge-Kutta method of order 4, find y(0.2) for dy/dx = x+y² with y (0) = 1. (Take h=0.1)
3. In an intelligence test administered to 1,000 students, the average score was 42 and the standard deviation was 24. Find :
   1. The number of students exceeding a score of 50.
   2. The number of students lying between 30 and 54.
   3. The value of the score exceeded by the top 100 students.

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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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