Download VTU BE 2020 Jan CSE Question Paper 17 Scheme 4th Sem 17MATDIP41 Additional Mathematics II

17MATDIP41
Fourth Semester B.E. Degree Examination, Dec.2019/Jan.2020
Additional Mathematics - II
Time: 3 hrs. Max. Marks: 100
Note: Answer any FIVE full questions, choosing ONE full question from each module.

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

ti Module-1
0 1 a_ Find the rank of the matrix:
2 3 5 4 -
cr, A = 0 2 3 4 by elementary row transformations. (08 Marks)
CS

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

4 8 13 12
t'.1)
4 .3 kr)
tj)
OC

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

E
C u

C rr
tu

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

2
b.
c.
a.
Solve by Gauss elimination method

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

2x + v + 4z ---- 12
4x+ lly?z= 33
8x ? 3y + 2z = 20
Find all the eigen values for the matrix A
OR

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

Reduce the matrix
8
?6
2
? 6

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

7
-4
2
-- 4
3

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

(06 Marks)
(06 Marks)
1 2 3 2
2 3 5 1 into its echelon form and hence find its rank. (06 Marks)
1 3 4 5

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

b. Applying Gauss elimination method, solve the system of equations
2x + 5y + 7z = 52
2x+y?z= 0
x + y + z = 9
7

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

?2
0
c. Find all the eigen values for the matrix A =
2 6 ? 2
0 ? 2 5

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

Module-2
(06 Marks)
(08 Marks)
a.
b.

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

c.
a.
b.
Solve
Solve

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

Solve
Solve
Solve
d
4

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

y 2d y d
2
y
0
=

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

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

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

dx
4
dx
3
dx

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

2

d2 y 6dy
+ 9y 5e
-2

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

' =
dx
2
dx
2

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

d y+
by the method of variation y = sec x of parameters.
dx
-
OR

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

d'y

0 y=
dx
y" + 3y' + 2y = I 2x

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

2

USN
3
4

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

l oft
FirstRanker.com - FirstRanker's Choice
17MATDIP41
Fourth Semester B.E. Degree Examination, Dec.2019/Jan.2020
Additional Mathematics - II

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

Time: 3 hrs. Max. Marks: 100
Note: Answer any FIVE full questions, choosing ONE full question from each module.
ti Module-1
0 1 a_ Find the rank of the matrix:
2 3 5 4 -

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

cr, A = 0 2 3 4 by elementary row transformations. (08 Marks)
CS
4 8 13 12
t'.1)
4 .3 kr)

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

tj)
OC
E
C u

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

C rr
tu
2
b.
c.

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

a.
Solve by Gauss elimination method
2x + v + 4z ---- 12
4x+ lly?z= 33
8x ? 3y + 2z = 20

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

Find all the eigen values for the matrix A
OR
Reduce the matrix
8
?6

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

2
? 6
7
-4
2

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

-- 4
3
(06 Marks)
(06 Marks)
1 2 3 2

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

2 3 5 1 into its echelon form and hence find its rank. (06 Marks)
1 3 4 5
b. Applying Gauss elimination method, solve the system of equations
2x + 5y + 7z = 52
2x+y?z= 0

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

x + y + z = 9
7
?2
0
c. Find all the eigen values for the matrix A =

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

2 6 ? 2
0 ? 2 5
Module-2
(06 Marks)
(08 Marks)

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

a.
b.
c.
a.
b.

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

Solve
Solve
Solve
Solve
Solve

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

d
4
y 2d y d
2
y

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

0
=
(06 Marks)
(06 Marks)
(08 Marks)

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

(06 Marks)
(06 Marks)
dx
4
dx

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

3
dx
2

d2 y 6dy

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

+ 9y 5e
-2
' =
dx
2

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

dx
2
d y+
by the method of variation y = sec x of parameters.
dx

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

-
OR
d'y

0 y=

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

dx
y" + 3y' + 2y = I 2x
2

USN

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

3
4
l oft
17MATDIP41
c. Solve by the method of undetermined coefficients :

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

y" ? 4y' + 4y = e
X
(08 Marks)
Module-3
5 a. Find the Laplace transforms of sin5t cos2t (06 Marks)

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

b. Find the Laplace transforms of (3t + 4)
3
(06 Marks)
sin 2t 0 < t <
c. Express f(t)

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

0 tin
in terms of unit step function and hence find L[f(t)]. (08 Marks)
OR
. 1
6 a. Find the Laplace transforms of

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

t
(06 Marks)
b. Find the Laplace transform of 2' + t sin t (06 Marks)
c. If f(t) = t
2

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

0 < t < 2 and I(t + 2) = fft) , for t > 2, find L[Rt)j. (08 Marks)
Module-4
7 a_ Find the Laplace Inverse of
(08 Marks)
(06 Marks)

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

(06 Marks)
(06 Marks)
(06 Marks)
(08 Marks)
(s +1)(s ?1)(s + 2)

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

b. Find the inverse Laplace transform of ,
3s + 7
s
-
? 2s ?3

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

c. Solve y" + 2y` ? 3y = sin t, y(0) = 0, y
1
(0)
OR
8 a. Find the inverse Laplace transform of

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

+ a
\
~s+b 1
b. Find the inverse Laplace transform of
4s ?1

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

?
s' + 25
c. Find the inverse Laplace of y" 5y` + 6y = e' with y(0) = yr(0) = 0.
log
Module-5

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

9 a. State and prove Addition theorem on probability_ (05 Marks)
b. A student A can solve 75% of the problems given in the book and a student B can solve
70%. What is the probability that A or B can solve a problem chosen at random. (06 Marks)
c. Three machines A, B, C produce 50%, 30% and 20% of the items in a factory. The

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

percentage of defective outputs of these machines are 3, 4 and 5 respectively. If an item is
selected at random, what is the probability that it is defective? If a selected item is defective,
vvrhat is the probability that it is from machine A? (09 Marks)
OR
10 a. Find the probability that the birth days of 5 persons chosen at random will fall in 12 different

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

calendar months. (05 Marks)
b. A box A contains 2 white balls and 4 black balls. Another box B contains 5 white balls and
7 black balls. A ball is transferred from box A to box B. Then a ball is drawn from box B.
Find the probability that it is white. (06 Marks)
c. State and prove Baye's theorem.

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

(09 Marks)
* * * * *
2
of 2
FirstRanker.com - FirstRanker's Choice

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