Download VTU BE 2020 Jan ECE Question Paper 17 Scheme 3rd Sem 17MAT31 Engineering Mathematics III

Download Visvesvaraya Technological University (VTU) BE ( Bachelor of Engineering) ECE (Electronic engineering) 2017 Scheme 2020 January Previous Question Paper 3rd Sem 17MAT31 Engineering Mathematics III

This post was last modified on 02 March 2020

Download Document

--- Content provided by FirstRanker.com ---

Time: 3 hrs. Max. Marks: 100
Note: Answer any FIVE full questions, choosing ONE full question from each module.
Module-1
1 a. Find the Fourier series expansion of f(x) = x in (-7T, 7). hence deduce that
-

--- Content provided by‌ FirstRanker.com ---

(08 Marks)
b. Find the half range cosine series for the function f(x) = ( x - 1)
2
in 0 < x < 1. (06 Marks)
c. Express y as a Fourier series upto first harmonics given :

--- Content provided by‌ FirstRanker.com ---

x 0 60? 120? 180? 240? 300?
y 7.9 7.2 3.6 0.5 0.9 6.8
(06 Marks)
OR
2 a. Obtain the Fourier series for the function :

--- Content provided by⁠ FirstRanker.com ---

f(x) =
. -3
1+
4x

--- Content provided by⁠ FirstRanker.com ---

? m ? < x 0
3 2
4x
3
1 in 0 x <

--- Content provided by‍ FirstRanker.com ---

3 2

n
2

--- Content provided by⁠ FirstRanker.com ---

12
1
1
2

--- Content provided by‌ FirstRanker.com ---

1
-
7"
2
-

--- Content provided by‍ FirstRanker.com ---

1
3
2

--- Content provided by‌ FirstRanker.com ---

1
4
-

it' 1 1

--- Content provided by FirstRanker.com ---

Hence deduce that ?=--,+?, + ?
1
, +---.
8 1
_

--- Content provided by‌ FirstRanker.com ---

3
,
5
.
x in 071

--- Content provided by‌ FirstRanker.com ---

/
2
IT ? x in r 2
Show that the half range sine series as
[

--- Content provided by FirstRanker.com ---

f(x)
. _4
sin x
sin 3x sin 5x -
n

--- Content provided by FirstRanker.com ---

c.
Obtain the Fourier series upto first harmonics given :
x 0 1 2 3 4 5 6
y 9 18 24 28 26 20 9
Module-2

--- Content provided by FirstRanker.com ---

3 a. Find the complex Fourier transform of the function :
1 for i sn x
f(x) = and hence evaluate f

dx .

--- Content provided by FirstRanker.com ---

0 for lxj>a
? 0
x
Find the Fourier cosine transform of e
x

--- Content provided by FirstRanker.com ---

.
Solve by using z - transforms u
n
+2 - 4un = 0 given that u0 = 0 and ul = 2.
b. If f(x)

--- Content provided by FirstRanker.com ---

3
2
5 2
b.
c.

--- Content provided by FirstRanker.com ---

(08 Marks)
(06 Marks)
(06 Marks)
(08 Marks)
(06 Marks)

--- Content provided by FirstRanker.com ---

(06 Marks)
1 of 3
FirstRanker.com - FirstRanker's Choice
? MEE
17MAT31

--- Content provided by‍ FirstRanker.com ---

USN
Third Semester B.E. Degree Examination, Dec.2019/Jan.2020
Engineering Mathematics - III
Time: 3 hrs. Max. Marks: 100
Note: Answer any FIVE full questions, choosing ONE full question from each module.

--- Content provided by⁠ FirstRanker.com ---

Module-1
1 a. Find the Fourier series expansion of f(x) = x in (-7T, 7). hence deduce that
-
(08 Marks)
b. Find the half range cosine series for the function f(x) = ( x - 1)

--- Content provided by FirstRanker.com ---

2
in 0 < x < 1. (06 Marks)
c. Express y as a Fourier series upto first harmonics given :
x 0 60? 120? 180? 240? 300?
y 7.9 7.2 3.6 0.5 0.9 6.8

--- Content provided by FirstRanker.com ---

(06 Marks)
OR
2 a. Obtain the Fourier series for the function :
f(x) =
. -3

--- Content provided by FirstRanker.com ---

1+
4x

? m ? < x 0
3 2

--- Content provided by FirstRanker.com ---

4x
3
1 in 0 x <
3 2

--- Content provided by‌ FirstRanker.com ---

n
2

12
1

--- Content provided by‍ FirstRanker.com ---

1
2

1
-

--- Content provided by FirstRanker.com ---

7"
2
-

1

--- Content provided by FirstRanker.com ---

3
2

1
4

--- Content provided by‍ FirstRanker.com ---

-

it' 1 1
Hence deduce that ?=--,+?, + ?
1

--- Content provided by FirstRanker.com ---

, +---.
8 1
_
3
,

--- Content provided by‍ FirstRanker.com ---

5
.
x in 071
/
2

--- Content provided by⁠ FirstRanker.com ---

IT ? x in r 2
Show that the half range sine series as
[
f(x)
. _4

--- Content provided by‌ FirstRanker.com ---

sin x
sin 3x sin 5x -
n
c.
Obtain the Fourier series upto first harmonics given :

--- Content provided by⁠ FirstRanker.com ---

x 0 1 2 3 4 5 6
y 9 18 24 28 26 20 9
Module-2
3 a. Find the complex Fourier transform of the function :
1 for i sn x

--- Content provided by FirstRanker.com ---

f(x) = and hence evaluate f

dx .
0 for lxj>a
? 0

--- Content provided by FirstRanker.com ---

x
Find the Fourier cosine transform of e
x
.
Solve by using z - transforms u

--- Content provided by‌ FirstRanker.com ---

n
+2 - 4un = 0 given that u0 = 0 and ul = 2.
b. If f(x)
3
2

--- Content provided by FirstRanker.com ---

5 2
b.
c.
(08 Marks)
(06 Marks)

--- Content provided by FirstRanker.com ---

(06 Marks)
(08 Marks)
(06 Marks)
(06 Marks)
1 of 3

--- Content provided by⁠ FirstRanker.com ---

17
OR
4 a. Find the Fourier sine and Cosine transforms of :
f
{x 0 < x < 2

--- Content provided by‍ FirstRanker.com ---

(x) =
0 elsewhere .
(08 Marks)
b. Find the Z ? transform of : i) n
2

--- Content provided by FirstRanker.com ---

ii) ne'. (06 Marks)
c. Obtain the inverse Z ? transform of
2z
2
+3z

--- Content provided by FirstRanker.com ---

(z + 2)(z ? 4)
(06 Marks)
Module-3
5 a. Obtain the lines of regression and hence find the co-efficient of correlation for the data :

--- Content provided by‌ FirstRanker.com ---

x 1 3 4 2 5 8 9 10 13 15
y 8 6 10 8 12 16 16 10 32 32
(08 Marks)
b.
Fit a parabola y = ax

--- Content provided by FirstRanker.com ---

2
+ bx + c in the least square sense for the data :
x 1 2 3 4 5
y 10 12 13 16 19
(06 Marks)

--- Content provided by‍ FirstRanker.com ---

C. Find the root of the equation xe
x
? cosx = 0 by Regula ? Falsi method correct to three
decimal places in (0, 1). (06 Marks)
OR

--- Content provided by FirstRanker.com ---

6 a. If 8x ? lOy + 66 = 0 and 40x ? 18y = 214 are the two regression lines, find the mean of x's,
mean of y's and the co-efficient of correlation. Find a
y
if a
= 3.

--- Content provided by⁠ FirstRanker.com ---

(08 Marks)
b. Fit an exponential curve of the form y = ae
bx
by the method of least squares for the data :
No. of petals 5 6 7 8 9 10

--- Content provided by‌ FirstRanker.com ---

No. of flowers 133 55 23 7 2 2
(06 Marks)
c. Using Newton?Raphson method, find the root that lies near x = 4.5 of the equation tanx = x
correct to four decimal places. (06 Marks)
Module-4

--- Content provided by FirstRanker.com ---

7 a. From the following table find the number of students who have obtained marks :
i) less than 45 ii) between 40 and 45.
Marks 30 ? 40 40 ? 50 50 ? 60 60 ? 70 70 ? 80
No. of students 31 42 51 35 31
(06 Marks)

--- Content provided by FirstRanker.com ---

b. Using Newton's divided difference formula construct an interpolating polynomial for the
following data :
x 4 5 7 10 11 13
f(x) 48 100 294 900 1210 2028
and hence find g8).

--- Content provided by FirstRanker.com ---

Evaluate
i dx
taking seven ordinates by applying Simpson's %
th
rule. (06 Marks)

--- Content provided by‌ FirstRanker.com ---

6
1
1 + x
(08 Marks)
c.

--- Content provided by FirstRanker.com ---

2 of 3
FirstRanker.com - FirstRanker's Choice
? MEE
17MAT31
USN

--- Content provided by‍ FirstRanker.com ---

Third Semester B.E. Degree Examination, Dec.2019/Jan.2020
Engineering Mathematics - III
Time: 3 hrs. Max. Marks: 100
Note: Answer any FIVE full questions, choosing ONE full question from each module.
Module-1

--- Content provided by FirstRanker.com ---

1 a. Find the Fourier series expansion of f(x) = x in (-7T, 7). hence deduce that
-
(08 Marks)
b. Find the half range cosine series for the function f(x) = ( x - 1)
2

--- Content provided by FirstRanker.com ---

in 0 < x < 1. (06 Marks)
c. Express y as a Fourier series upto first harmonics given :
x 0 60? 120? 180? 240? 300?
y 7.9 7.2 3.6 0.5 0.9 6.8
(06 Marks)

--- Content provided by FirstRanker.com ---

OR
2 a. Obtain the Fourier series for the function :
f(x) =
. -3
1+

--- Content provided by FirstRanker.com ---

4x

? m ? < x 0
3 2
4x

--- Content provided by‌ FirstRanker.com ---

3
1 in 0 x <
3 2

n

--- Content provided by‍ FirstRanker.com ---

2

12
1
1

--- Content provided by⁠ FirstRanker.com ---

2

1
-
7"

--- Content provided by⁠ FirstRanker.com ---

2
-

1
3

--- Content provided by FirstRanker.com ---

2

1
4
-

--- Content provided by‍ FirstRanker.com ---

it' 1 1
Hence deduce that ?=--,+?, + ?
1
, +---.

--- Content provided by FirstRanker.com ---

8 1
_
3
,
5

--- Content provided by FirstRanker.com ---

.
x in 071
/
2
IT ? x in r 2

--- Content provided by FirstRanker.com ---

Show that the half range sine series as
[
f(x)
. _4
sin x

--- Content provided by FirstRanker.com ---

sin 3x sin 5x -
n
c.
Obtain the Fourier series upto first harmonics given :
x 0 1 2 3 4 5 6

--- Content provided by FirstRanker.com ---

y 9 18 24 28 26 20 9
Module-2
3 a. Find the complex Fourier transform of the function :
1 for i sn x
f(x) = and hence evaluate f

--- Content provided by‍ FirstRanker.com ---

dx .
0 for lxj>a
? 0
x

--- Content provided by FirstRanker.com ---

Find the Fourier cosine transform of e
x
.
Solve by using z - transforms u
n

--- Content provided by‍ FirstRanker.com ---

+2 - 4un = 0 given that u0 = 0 and ul = 2.
b. If f(x)
3
2
5 2

--- Content provided by FirstRanker.com ---

b.
c.
(08 Marks)
(06 Marks)
(06 Marks)

--- Content provided by‌ FirstRanker.com ---

(08 Marks)
(06 Marks)
(06 Marks)
1 of 3
17

--- Content provided by FirstRanker.com ---

OR
4 a. Find the Fourier sine and Cosine transforms of :
f
{x 0 < x < 2
(x) =

--- Content provided by‍ FirstRanker.com ---

0 elsewhere .
(08 Marks)
b. Find the Z ? transform of : i) n
2
ii) ne'. (06 Marks)

--- Content provided by FirstRanker.com ---

c. Obtain the inverse Z ? transform of
2z
2
+3z

--- Content provided by‍ FirstRanker.com ---

(z + 2)(z ? 4)
(06 Marks)
Module-3
5 a. Obtain the lines of regression and hence find the co-efficient of correlation for the data :
x 1 3 4 2 5 8 9 10 13 15

--- Content provided by⁠ FirstRanker.com ---

y 8 6 10 8 12 16 16 10 32 32
(08 Marks)
b.
Fit a parabola y = ax
2

--- Content provided by FirstRanker.com ---

+ bx + c in the least square sense for the data :
x 1 2 3 4 5
y 10 12 13 16 19
(06 Marks)
C. Find the root of the equation xe

--- Content provided by‌ FirstRanker.com ---

x
? cosx = 0 by Regula ? Falsi method correct to three
decimal places in (0, 1). (06 Marks)
OR
6 a. If 8x ? lOy + 66 = 0 and 40x ? 18y = 214 are the two regression lines, find the mean of x's,

--- Content provided by⁠ FirstRanker.com ---

mean of y's and the co-efficient of correlation. Find a
y
if a
= 3.
(08 Marks)

--- Content provided by FirstRanker.com ---

b. Fit an exponential curve of the form y = ae
bx
by the method of least squares for the data :
No. of petals 5 6 7 8 9 10
No. of flowers 133 55 23 7 2 2

--- Content provided by FirstRanker.com ---

(06 Marks)
c. Using Newton?Raphson method, find the root that lies near x = 4.5 of the equation tanx = x
correct to four decimal places. (06 Marks)
Module-4
7 a. From the following table find the number of students who have obtained marks :

--- Content provided by‌ FirstRanker.com ---

i) less than 45 ii) between 40 and 45.
Marks 30 ? 40 40 ? 50 50 ? 60 60 ? 70 70 ? 80
No. of students 31 42 51 35 31
(06 Marks)
b. Using Newton's divided difference formula construct an interpolating polynomial for the

--- Content provided by FirstRanker.com ---

following data :
x 4 5 7 10 11 13
f(x) 48 100 294 900 1210 2028
and hence find g8).
Evaluate

--- Content provided by FirstRanker.com ---

i dx
taking seven ordinates by applying Simpson's %
th
rule. (06 Marks)
6

--- Content provided by FirstRanker.com ---

1
1 + x
(08 Marks)
c.
2 of 3

--- Content provided by‌ FirstRanker.com ---

17MAT31
OR
8 a. In a table given below, the values of y are consecutive terms of a series of which 23.6 is the
6
th

--- Content provided by⁠ FirstRanker.com ---

term. Find the first and tenth terms of the series by Newton's formulas.
x 3 4 5 6 7 8 9
y 4.8 8.4 14.5 23.6 36.2 52.8 73.9
(08 Marks)
b. Fit an interpolating polynomial of the form x = f(y) for data and hence find x(5) given :

--- Content provided by‍ FirstRanker.com ---

x 2 10 17
y 1 3 4
0.6
c.
Use Simpson's

--- Content provided by‌ FirstRanker.com ---

3
rd
ruleto find I e
-
x

--- Content provided by‌ FirstRanker.com ---

-
dx by taking 6 sub-intervals.
(06 Marks)
(06 Marks)
Module-5

--- Content provided by‍ FirstRanker.com ---

9 a. Verify Green's theorem in the plane for ili
c
(3x
2
? 8y

--- Content provided by FirstRanker.com ---

2
)dx + (4y ? 6xy)dy where C is the
closed curve bounded by y = -srx and y = x
2
. (08 Marks)

--- Content provided by FirstRanker.com ---

b.
Evaluate
e
i xydx + xy
2

--- Content provided by FirstRanker.com ---

dy by Stoke's theorem where C is the square in the x ? y plane with
vertices (1, 0)(-1, 0)(0, 1)(0, ?1). (06 Marks)
c. Prove that Catenary is the curve which when rotated about a line generates a surface of
minimum area. (06 Marks)
OR

--- Content provided by FirstRanker.com ---

10 a. If F = 2xyl+ yz
2
xz k and S is the rectangular parallelepiped bounded by x = 0, y = 0,
c.
z = 0, x = 2, y = 1, z = 3 evaluate ^ A ?

--- Content provided by⁠ FirstRanker.com ---

F. n us ?
Derive Euler's equation in the standard form viz ?
of
?
[ af

--- Content provided by FirstRanker.com ---

a
y
dx ay'
= 0 .
n.

--- Content provided by‌ FirstRanker.com ---

2

Find the external of the functional I = J(y
2
? y'

--- Content provided by⁠ FirstRanker.com ---

2
? 2y sin x )dx under the end
(08 Marks)
(06 Marks)
conditions

--- Content provided by‌ FirstRanker.com ---

y(0) = y(n/2) = O. (06 Marks)
3 of 3
FirstRanker.com - FirstRanker's Choice

This post was last modified on 02 March 2020

Get the MBBS Question Bank Android App

Download VTU BE 2020 Jan ECE Question Paper 17 Scheme 3rd Sem 17MAT31 Engineering Mathematics III

Share This Post:

Share This Post: