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Download GTU BE/B.Tech 2019 Summer 4th Sem New 2141703 Numerical Techniques And Statistical Methods Question Paper

Download GTU (Gujarat Technological University) BE/BTech (Bachelor of Engineering / Bachelor of Technology) 2019 Summer 4th Sem New 2141703 Numerical Techniques And Statistical Methods Previous Question Paper

This post was last modified on 20 February 2020

This download link is referred from the post: GTU BE 2019 Summer Question Papers || Gujarat Technological University


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GUJARAT TECHNOLOGICAL UNIVERSITY

SEMESTER-IV(NEW) — EXAMINATION - SUMMER 2019

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Subject Code:2141703

Subject Name: Numerical Techniques & Statistical Methods

Date:09/05/2019

Time:02:30 PM TO 05:30 PM

Total Marks: 70

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Instructions:

  1. Attempt all questions.
  2. Make suitable assumptions wherever necessary.
  3. Figures to the right indicate full marks.

Q1

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(a) If X =3.4327, find the absolute and relative errors if :
(a) X is truncated to three decimal places.
(b) X is rounded off to three decimal places. [03]

(b) Calculate mean and mode for the following data: [04]

Class 0-10 10-20 20-30 30-40 40-50
Frequency 10 14 19 17 13

(c) Use Fourth order Runge-Kutta method to find y(0.2) with h=0.1, given that

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dy/dx = 2x+y, y(0)=1 [07]

Q2

(a) Using the power method, find the largest Eigen value for A:{1 2; 3 4} [03]

(b) Apply Gauss — Seidel iteration method to solve :
20x+y-2z=17, 3x+20y—z=-18, 2x-3y+20z=25 [04]

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(c) Construct an Interpolating polynomial which takes the following values :
x 0 1 2 3 4 5 6 7
y 1 2 4 7 11 16 22 29 [07]

OR

(c) Obtain Cubic spline for subinterval 0 < x <1 & 1< x <2 from the following data:

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x 0 1 2 3
S(x) 1 2 33 244 [07]

Q3

(a) Considering following tabular values, Determine the area bounded by the given curve and X-axis between x =10 to x =16 by Trapezoidal rule. [03]

x 10 11 12 13 14 15 16
y 1.02 0.94 0.89 0.79 0.71 0.62 0.55

(b) Using Newton’s forward formula, find the value of f(1.6) [04]

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x 1 1.4 1.8 2.2
S(x) 3.49 4.82 5.96 6.5

(c) Use Euler’s method to find y(2) from the differential equation dy/dx = x+2y, y(1) =1 with h=0.1 [03]

OR

(c) Using Simpson’s 1/3 rule, evaluate ∫ 1/(1+x2) dx by taking 4 sub intervals. [04]

(c) Evaluate ∫01 exp(-x2) dx using the Gaussian Integration formula with n = 3. [04]

Q.4

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(a) Solve dy/dx = x2 + y2, y(0) = 1.1 to find y(0.2) and y(0.4) by Milne’s Predictor — Corrector method. [03]

(b) There are two boxes A and B containing 4 white, 3 red and 3 white, 7 red balls respectively. A box is chosen at random and a ball is drawn from it, If the ball is white, find the probability that it is from box A. [04]

(c) An unbiased coin is tossed 6 times. Find the probability of getting (1) exactly 4 heads (2) at least 4 heads. [07]

(d) Eleven school boys were given a test in a Subject. They were given a month’s further coaching and a second test of equal category was held at the end of it. Do the marks give evidence that the students have benefited by extra coaching?

Boys 1 2 3 4 5 6 7 8 9 10 11
Marks 1st test 23 20 19 21 18 20 18 17 23 16 19
Marks 2nd test 24 19 22 18 20 22 20 20 23 20 17

(At 5% level of significance for n=10 d. f. t0.05 =2.228) [07]

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OR

(a) Two people are selected at random from a group of seven men and five women. Find the Probability that both are men or both are women. [03]

(b) 100 Electric bulbs are found to be defective in a lot of 5000 bulbs. Find the probability that at the most 3 bulbs are defective in a box of 100 bulbs. [04]

(c) A dice is thrown 150 times and the following results are obtained. [07]

Number turned up 1 2 3 4 5 6
Frequency 19 23 28 17 32 31

Test the Hypothesis that the dice is unbiased at 5% level of significance.

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(At 5% level of significance for n=5 d.f. χ20.05 =11.07)

Q.5

(a) Find the standard deviation of a group of data points: 101.8, 103.2, 104.0, 102.5, 103.5 [03]

(b) Define Chi-square Test. State (a) conditions to apply test (b) application of test [04]

(c) Represent the following information in form of a network. Find average duration time or expected time of each activity and obtain the critical path. [07]

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Activity 1-2 1-3 2-4 3-4 3-5 4-5 4-6 5-7 5-8 9-6 9-10 6-10
Optimistic time 4 1 8 3 2 3 3 4 4 2 4 4
Most Likely time 9 5 10 6 4 7 7 8 7 7 8 7
Pessimistic time 14 8 17 8 5 10 10 9 14 10 18 9

OR

(a) Compute the Median from the data: [03]

Class 0-30 30-60 60-90 90-120 120-150 150-180
Frequency 8 13 22 27 18 7

(b) A bag Contains 5 white and 7 black balls. Find the expectation of a man who is allowed to draw two balls from the bag and who is to receive one rupee for each black ball and two rupees for each white ball. [04]

(c) Draw PERT — diagram after finding out expected time & find critical path. [07]

Activity Sequence Optimistic Time Most Likely Time Pessimistic Time
A 1-2 7 12 13
B 1-3 7 10 12
C 2-5 8 13 15
D 3-5 10 12 22
E 5-6 10 14 18

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This download link is referred from the post: GTU BE 2019 Summer Question Papers || Gujarat Technological University

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