Download GTU (Gujarat Technological University) BE/BTech (Bachelor of Engineering / Bachelor of Technology) 2019 Winter 3rd Sem New 3130908 Applied Mathematics For Electrical Engineering Previous Question Paper
Seat No.: ________ Enrolment No.___________
GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER ? III (New) EXAMINATION ? WINTER 2019
Subject Code: 3130908 Date: 26/11/2019
Subject Name: Applied Mathematics for Electrical Engineering
Time: 02:30 PM TO 05:00 PM Total Marks: 70
Instructions:
1. Attempt all questions.
2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.
Marks
Q.1 (a)
Find a real root of the equation 0 1
3
? ? ? x x by using Regula-falsi
method correct to two decimal places.
03
(b)
State the formula for finding the
th
q -root and find the square root of 8
using Newton Raphson method correct to two decimal places.
04
(c) Attempt the following.
(i)
Find the positive solution of x e x f
x
? ?
?
) ( by the secant method
starting from 0 . 1 , 0
1 0
? ? x x .
03
(ii) Using method of least squares, find the best fitting straight line to
the given following data.
x : 1 2 3 4 5
y : 1 3 5 6 5
04
Q.2 (a)
If ? ?
x
x f
1
? , prepare the table for finite differences and hence find
? ? b a, and ? ? c b a , , .
03
(b) State Newton?s forward formula and use it to find the approximate
value of ? ? 6 . 1 f , if
x 1 1.4 1.8 2.2
? ? x f
3.49 4.82 5.96 6.5
04
(c) Attempt the following.
(i) Using quadratic Lagrange interpolation, compute 2 . 9 ln from
1972 . 2 0 . 9 ln ? , 2513 . 2 5 . 9 ln ? , 3979 . 2 11 ln ?
03
(ii) State Newton?s Backward formula and use it to find the
approximate value of ? ? 5 . 7 f , if
x 3 4 5 6 7 8
? ? x f
28 65 126 217 344 513
04
OR
(c) Attempt the following.
(i) Using the relation between the operators prove that,
? ? ? ? 1 1 1 ? ? ? ? ? .
03
(ii)
State Simpson?s
8
3
rule and hence evaluate
?
?
3
0
1
1
dx
x
with 6 ? n .
04
Q.3 (a)
Use trapezoidal rule to estimate
?
3 . 1
5 . 0
2
dx e
x
using a strip of width 2 . 0 .
03
(b) The velocity v of a particle at a distance s from a point on its linear path is
given by the following data.
04
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1
Seat No.: ________ Enrolment No.___________
GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER ? III (New) EXAMINATION ? WINTER 2019
Subject Code: 3130908 Date: 26/11/2019
Subject Name: Applied Mathematics for Electrical Engineering
Time: 02:30 PM TO 05:00 PM Total Marks: 70
Instructions:
1. Attempt all questions.
2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.
Marks
Q.1 (a)
Find a real root of the equation 0 1
3
? ? ? x x by using Regula-falsi
method correct to two decimal places.
03
(b)
State the formula for finding the
th
q -root and find the square root of 8
using Newton Raphson method correct to two decimal places.
04
(c) Attempt the following.
(i)
Find the positive solution of x e x f
x
? ?
?
) ( by the secant method
starting from 0 . 1 , 0
1 0
? ? x x .
03
(ii) Using method of least squares, find the best fitting straight line to
the given following data.
x : 1 2 3 4 5
y : 1 3 5 6 5
04
Q.2 (a)
If ? ?
x
x f
1
? , prepare the table for finite differences and hence find
? ? b a, and ? ? c b a , , .
03
(b) State Newton?s forward formula and use it to find the approximate
value of ? ? 6 . 1 f , if
x 1 1.4 1.8 2.2
? ? x f
3.49 4.82 5.96 6.5
04
(c) Attempt the following.
(i) Using quadratic Lagrange interpolation, compute 2 . 9 ln from
1972 . 2 0 . 9 ln ? , 2513 . 2 5 . 9 ln ? , 3979 . 2 11 ln ?
03
(ii) State Newton?s Backward formula and use it to find the
approximate value of ? ? 5 . 7 f , if
x 3 4 5 6 7 8
? ? x f
28 65 126 217 344 513
04
OR
(c) Attempt the following.
(i) Using the relation between the operators prove that,
? ? ? ? 1 1 1 ? ? ? ? ? .
03
(ii)
State Simpson?s
8
3
rule and hence evaluate
?
?
3
0
1
1
dx
x
with 6 ? n .
04
Q.3 (a)
Use trapezoidal rule to estimate
?
3 . 1
5 . 0
2
dx e
x
using a strip of width 2 . 0 .
03
(b) The velocity v of a particle at a distance s from a point on its linear path is
given by the following data.
04
2
Time
? ? t
0 5 10 15 20 25 30
Speed ? ? v
30 24 19 16 13 11 10
Estimate the time taken by the particle to travel the distance of 20m using
Simpson?s
3
1
rule.
(c) Attempt the following.
(i)
Using Euler?s method, find ? ? 2 . 0 y given that
? ? 1 0 ;
2
? ? ? y
y
x
y
dx
dy
taking 1 . 0 ? h .
03
(ii) State the formula for Runge-Kutta method of fourth order and use
it to calculate ? ? 2 . 0 y given that ? ? 1 0 ,
'
? ? ? y y x y taking 1 . 0 ? h .
04
OR
Q.3 (a) Define the following.
1) Favorable Events
2) Random Variable
3) Probability Density function
03
(b) An urn contains 10 white and 3 black balls, while another urn contains
3 white and 5 black balls. Two balls are drawn from the first urn and
put into the second urn and then a ball is drawn from the latter. What is
the probability that it is a white ball?
04
(c) Attempt the following.
(i) In producing screws, let A mean ?screw too slim? and B ?screw
too small?. Let ? ? 1 . 0 ? A P and let the conditional probability that
a slim screw is also too small be ? ? 2 . 0 / ? A B P . What is the
probability that the screw that we pick randomly from a lot
produced will be both too slim and too short?
03
(ii) The joint probability density function of two random variables X
and Y is given by
? ?
? ?
?
?
? ? ? ? ? ?
?
elsewhere
y x y x k
y x f
; 0
2 0 , 1 0 ; 2
,
Find the marginal density function of X and Y.
04
Q.4 (a) Define the following.
1) Mutually Exclusive Events
2) Probability
3) Compound Events
03
(b) State Bayes? theorem. In a bolt factory, three machines A,B and C
manufacture 25% , 35% and 40% of the total product respectively. Of
these outputs 5% , 4% and 2% respectively, are defective bolts. A bolt
is picked up at random and found to be defective. What are the
probabilities that it was manufactured by machines A,B and C?
04
(c) Attempt the following.
(i) A person is known to hit the target in 3 out of 4 shots, where as
another person is known to hit the target in 2 out of 3 shots. Find
the probability of the target being hit at all when they both try.
03
(ii) Out of five cars, two have tyre problems and one has brake
problem and tow are in good running condition. Two cars are
required for the journey. If two cars are selected among five at
random and if X denotes the number with tyre problem, Y denotes
with brake problem then find the marginal probability function of
X and Y.
04
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1
Seat No.: ________ Enrolment No.___________
GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER ? III (New) EXAMINATION ? WINTER 2019
Subject Code: 3130908 Date: 26/11/2019
Subject Name: Applied Mathematics for Electrical Engineering
Time: 02:30 PM TO 05:00 PM Total Marks: 70
Instructions:
1. Attempt all questions.
2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.
Marks
Q.1 (a)
Find a real root of the equation 0 1
3
? ? ? x x by using Regula-falsi
method correct to two decimal places.
03
(b)
State the formula for finding the
th
q -root and find the square root of 8
using Newton Raphson method correct to two decimal places.
04
(c) Attempt the following.
(i)
Find the positive solution of x e x f
x
? ?
?
) ( by the secant method
starting from 0 . 1 , 0
1 0
? ? x x .
03
(ii) Using method of least squares, find the best fitting straight line to
the given following data.
x : 1 2 3 4 5
y : 1 3 5 6 5
04
Q.2 (a)
If ? ?
x
x f
1
? , prepare the table for finite differences and hence find
? ? b a, and ? ? c b a , , .
03
(b) State Newton?s forward formula and use it to find the approximate
value of ? ? 6 . 1 f , if
x 1 1.4 1.8 2.2
? ? x f
3.49 4.82 5.96 6.5
04
(c) Attempt the following.
(i) Using quadratic Lagrange interpolation, compute 2 . 9 ln from
1972 . 2 0 . 9 ln ? , 2513 . 2 5 . 9 ln ? , 3979 . 2 11 ln ?
03
(ii) State Newton?s Backward formula and use it to find the
approximate value of ? ? 5 . 7 f , if
x 3 4 5 6 7 8
? ? x f
28 65 126 217 344 513
04
OR
(c) Attempt the following.
(i) Using the relation between the operators prove that,
? ? ? ? 1 1 1 ? ? ? ? ? .
03
(ii)
State Simpson?s
8
3
rule and hence evaluate
?
?
3
0
1
1
dx
x
with 6 ? n .
04
Q.3 (a)
Use trapezoidal rule to estimate
?
3 . 1
5 . 0
2
dx e
x
using a strip of width 2 . 0 .
03
(b) The velocity v of a particle at a distance s from a point on its linear path is
given by the following data.
04
2
Time
? ? t
0 5 10 15 20 25 30
Speed ? ? v
30 24 19 16 13 11 10
Estimate the time taken by the particle to travel the distance of 20m using
Simpson?s
3
1
rule.
(c) Attempt the following.
(i)
Using Euler?s method, find ? ? 2 . 0 y given that
? ? 1 0 ;
2
? ? ? y
y
x
y
dx
dy
taking 1 . 0 ? h .
03
(ii) State the formula for Runge-Kutta method of fourth order and use
it to calculate ? ? 2 . 0 y given that ? ? 1 0 ,
'
? ? ? y y x y taking 1 . 0 ? h .
04
OR
Q.3 (a) Define the following.
1) Favorable Events
2) Random Variable
3) Probability Density function
03
(b) An urn contains 10 white and 3 black balls, while another urn contains
3 white and 5 black balls. Two balls are drawn from the first urn and
put into the second urn and then a ball is drawn from the latter. What is
the probability that it is a white ball?
04
(c) Attempt the following.
(i) In producing screws, let A mean ?screw too slim? and B ?screw
too small?. Let ? ? 1 . 0 ? A P and let the conditional probability that
a slim screw is also too small be ? ? 2 . 0 / ? A B P . What is the
probability that the screw that we pick randomly from a lot
produced will be both too slim and too short?
03
(ii) The joint probability density function of two random variables X
and Y is given by
? ?
? ?
?
?
? ? ? ? ? ?
?
elsewhere
y x y x k
y x f
; 0
2 0 , 1 0 ; 2
,
Find the marginal density function of X and Y.
04
Q.4 (a) Define the following.
1) Mutually Exclusive Events
2) Probability
3) Compound Events
03
(b) State Bayes? theorem. In a bolt factory, three machines A,B and C
manufacture 25% , 35% and 40% of the total product respectively. Of
these outputs 5% , 4% and 2% respectively, are defective bolts. A bolt
is picked up at random and found to be defective. What are the
probabilities that it was manufactured by machines A,B and C?
04
(c) Attempt the following.
(i) A person is known to hit the target in 3 out of 4 shots, where as
another person is known to hit the target in 2 out of 3 shots. Find
the probability of the target being hit at all when they both try.
03
(ii) Out of five cars, two have tyre problems and one has brake
problem and tow are in good running condition. Two cars are
required for the journey. If two cars are selected among five at
random and if X denotes the number with tyre problem, Y denotes
with brake problem then find the marginal probability function of
X and Y.
04
3
*************
OR
Q.4 (a)
Evaluate ? ?
?
?
1
0
2
exp dx x by using the Gaussian integration formula for 3 ? n
03
(b) Using method of least squares, find the best fitting second degree curve
to the following data.
x : 1 2 3 4
y : 6 11 18 27
04
(c) Attempt the following.
(i)
Solve the Ricatti equation
2 2 '
y x y ? ? using Taylor series
method for the initial condition ? ? , 0 0 ? y where 2 . 0 0 ? ? x and
2 . 0 ? h .
03
(ii) Find a positive root of the equation 0 cos ? ? x x using bisection
method correct to two places of decimals.
04
Q.5 (a) Define Mean, Median and Mode for the ungrouped data. 03
(b) Find the first four moments about mean 4 , 13 , 8 , 10 , 5 ? x 04
(c) Attempt the following.
(i) In a distribution of two different groups the variances are 15 and
27, whereas the third central moments are 32.4 and 67.56
respectively. Compare the skewness of two groups.
03
(ii) Two automatic filling machines A and B are used to fill mixture
of cement concrete in beam. A random sample of beam on each
machine showed following results.
A 32 28 47 63 71 39 10 60 96 14
B 19 31 48 53 67 90 10 62 40 80
Find standard deviation of each machine and also comment on the
performance of the tow machines.
04
OR
Q.5 (a) The pH solution is measured eight times using the same instrument and
the data obtained are as follows.
7.15 , 7.20 , 7.18 , 7.19 , 7.21 , 7.20 , 7.16 , 7.18
Calculate the mean, variance and standard deviation.
03
(b) In environmental geology computer simulation was employed to
estimate how far a block from a collapsing rock wall bounce down a
soil slope.Based on the depth, location and angle of block soil impact
marks left on the slope of the actual rock fall, the following 10 rebound
lengths (meters) were estimated. Compute mean and standard deviation
of the rebounds.
10.2 , 9.5 , 8.3 , 9.7 , 9.5 , 11.1 , 7.8 , 8.8 , 9.5 , 10
04
(c) Attempt the following.
(i) Find the Co-efficient of Quartile Deviation for the following data:
6,8,10,4,20,18,16,14,12,10
03
(ii) State the formula for coefficient of Skewness based on central
moments and finds it for the following frequency distribution.
Class 50-55 55-60 60-65 65-70 70-75
Frequency 8 10 15 17 8
04
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This post was last modified on 20 February 2020