Download JNTUK (Jawaharlal Nehru Technological University Kakinada) B.Tech Regular 2014 Feb-March I Semester (1st Year 1st Sem) MATHEMATICS I Question Paper.
I B. Tech I Semester Regular Examinations Feb./Mar. - 2014
MATHEMATICS-I
(Common to All Branches)
Time: 3 hours Max. Marks: 70
Question Paper Consists of Part-A and Part-B
Answering the question in Part-A is Compulsory,
Three Questions should be answered from Part-B
*****
PART-A
1.(i) Find the orthogonal trajectories of the curve 1 cos
.
(ii) If
,
,
, find
,,
, ,
, given that
, ,
,,
.
(iii) Find the Laplace transform of ! "
!, 0 $ ! $ 1
0, ! % 1
& using Heaviside function.
(iv) Let the heat conduction in a thin metallic bar of length L is governed by the equation
'
(
)
'
)
, t > 0. If both ends of the bar are held at constant temperature zero and the bar
is initially has temperature f(x), find the temperature u(x,t).
(v) Solve p
2
+pq = z
2
.
(vi) Find
*
+
)
,-+.-
. [4+4+4+4+3+3]
PART- B
2.(a) Solve 2
0 1 1 0 1 0
(b) Find the complete solution of
??
2
2
3
2
cos 2 [8+8]
3.(a) Solve
4
4
2
3
(b) Find the solution of
4
)
4
)
4 6 3 cos 2 . [8+8]
4.(a) Find the Laplace transform of !
89: ;(,89: <(
(
.
(b) If ?>?, ?@? , ?@> and
@
, >
1 ?
, find
, ,
,,
. [8+8]
5.(a) Expand , 2
ln1 in powers of x and y using MacLaurin?s Series
(b) Solve
??
0 8
?
15 9!2
(
, 0 5 1
?
0 10 using Laplace transforms
[8+8]
6.(a) Solve F 0 G
0
.
(b) Solve the partial differential equation px+qy =1. [8+8]
7.(a) Find the partial differential equation of all spheres whose centers lie on z- axis.
(b) Find the solution of the wave equation
)
'
(
)
)
'
)
, if the initial deflection is
H
I
J
0 $ $ K/2
I
J
K 0
J
$ $ K
& and initial velocity equal to 0. [8+8]
Page 1 of 1
Set No - 1
FirstRanker.com - FirstRanker's Choice
Subject Code: R13102/R13
I B. Tech I Semester Regular Examinations Feb./Mar. - 2014
MATHEMATICS-I
(Common to All Branches)
Time: 3 hours Max. Marks: 70
Question Paper Consists of Part-A and Part-B
Answering the question in Part-A is Compulsory,
Three Questions should be answered from Part-B
*****
PART-A
1.(i) Find the orthogonal trajectories of the curve 1 cos
.
(ii) If
,
,
, find
,,
, ,
, given that
, ,
,,
.
(iii) Find the Laplace transform of ! "
!, 0 $ ! $ 1
0, ! % 1
& using Heaviside function.
(iv) Let the heat conduction in a thin metallic bar of length L is governed by the equation
'
(
)
'
)
, t > 0. If both ends of the bar are held at constant temperature zero and the bar
is initially has temperature f(x), find the temperature u(x,t).
(v) Solve p
2
+pq = z
2
.
(vi) Find
*
+
)
,-+.-
. [4+4+4+4+3+3]
PART- B
2.(a) Solve 2
0 1 1 0 1 0
(b) Find the complete solution of
??
2
2
3
2
cos 2 [8+8]
3.(a) Solve
4
4
2
3
(b) Find the solution of
4
)
4
)
4 6 3 cos 2 . [8+8]
4.(a) Find the Laplace transform of !
89: ;(,89: <(
(
.
(b) If ?>?, ?@? , ?@> and
@
, >
1 ?
, find
, ,
,,
. [8+8]
5.(a) Expand , 2
ln1 in powers of x and y using MacLaurin?s Series
(b) Solve
??
0 8
?
15 9!2
(
, 0 5 1
?
0 10 using Laplace transforms
[8+8]
6.(a) Solve F 0 G
0
.
(b) Solve the partial differential equation px+qy =1. [8+8]
7.(a) Find the partial differential equation of all spheres whose centers lie on z- axis.
(b) Find the solution of the wave equation
)
'
(
)
)
'
)
, if the initial deflection is
H
I
J
0 $ $ K/2
I
J
K 0
J
$ $ K
& and initial velocity equal to 0. [8+8]
Page 1 of 1
Set No - 1
Subject Code: R13102/R13
I B. Tech I Semester Regular Examinations Feb./Mar. - 2014
MATHEMATICS-I
(Common to All Branches)
Time: 3 hours Max. Marks: 70
Question Paper Consists of Part-A and Part-B
Answering the question in Part-A is Compulsory,
Three Questions should be answered from Part-B
*****
PART-A
1.(i) Find the complete solution of M
-
16 0.
(ii) If
,
, , find
,,
, ,
, given that
, ,
,,
.
(iii) Solve
F
G
.
(iv) Find the solution, by Laplace transform method, of the integro-differential equation
?
3 2 O ! 1! !
(
P
(v) Find the differential equation of the orthogonal trajectories for the family of parabola
through the origin and foci on y-axis.
(vi) Find the solution of wave equation in one dimension using the method of separation of
variables.
[3+3+4+4+4+4]
PART-B
2.(a) Solve
0 2
1 2
0
1 0
(b) Find the complete solution of
??
5
?
0 6 4 .
[8+8]
3.(a) Solve cos x dy ysinx 0 y 1 .
(b) Find the solution of
4
)
4
)
0 4
4
4
3 2 2
3
32
cos 2 .
[8+8]
4.(a) Find the Laplace transform of ! O 2
,'
@ 1@
(
P
.
(b) Find the shortest distance from origin to the surface
2.
[8+8]
5.(a) Find
',U
,
if @ 2 1 >
0
,where
1
.
(b) Solve
??
0 8
?
15 9!2
(
, 0 5 1
?
0 10 using Laplace transforms
[8+8]
6.(a) Form the partial differential equation by eliminating the arbitrary function
from .
(b) Find the solution of VM
0 MM
W
0 2M
W
X 0 1 2
, where M
and M
W
.
[8+8]
7.(a) Solve the partial differential equation F G .
(b) Find the temperature in a bar of length l which is perfectly insulated laterally and whose
ends O and A are kept at 0
o
C, given that the initial temperature at any point P of the rod is
given by f(x).
[8+8]
Page 1 of 1
Set No - 2
FirstRanker.com - FirstRanker's Choice
Subject Code: R13102/R13
I B. Tech I Semester Regular Examinations Feb./Mar. - 2014
MATHEMATICS-I
(Common to All Branches)
Time: 3 hours Max. Marks: 70
Question Paper Consists of Part-A and Part-B
Answering the question in Part-A is Compulsory,
Three Questions should be answered from Part-B
*****
PART-A
1.(i) Find the orthogonal trajectories of the curve 1 cos
.
(ii) If
,
,
, find
,,
, ,
, given that
, ,
,,
.
(iii) Find the Laplace transform of ! "
!, 0 $ ! $ 1
0, ! % 1
& using Heaviside function.
(iv) Let the heat conduction in a thin metallic bar of length L is governed by the equation
'
(
)
'
)
, t > 0. If both ends of the bar are held at constant temperature zero and the bar
is initially has temperature f(x), find the temperature u(x,t).
(v) Solve p
2
+pq = z
2
.
(vi) Find
*
+
)
,-+.-
. [4+4+4+4+3+3]
PART- B
2.(a) Solve 2
0 1 1 0 1 0
(b) Find the complete solution of
??
2
2
3
2
cos 2 [8+8]
3.(a) Solve
4
4
2
3
(b) Find the solution of
4
)
4
)
4 6 3 cos 2 . [8+8]
4.(a) Find the Laplace transform of !
89: ;(,89: <(
(
.
(b) If ?>?, ?@? , ?@> and
@
, >
1 ?
, find
, ,
,,
. [8+8]
5.(a) Expand , 2
ln1 in powers of x and y using MacLaurin?s Series
(b) Solve
??
0 8
?
15 9!2
(
, 0 5 1
?
0 10 using Laplace transforms
[8+8]
6.(a) Solve F 0 G
0
.
(b) Solve the partial differential equation px+qy =1. [8+8]
7.(a) Find the partial differential equation of all spheres whose centers lie on z- axis.
(b) Find the solution of the wave equation
)
'
(
)
)
'
)
, if the initial deflection is
H
I
J
0 $ $ K/2
I
J
K 0
J
$ $ K
& and initial velocity equal to 0. [8+8]
Page 1 of 1
Set No - 1
Subject Code: R13102/R13
I B. Tech I Semester Regular Examinations Feb./Mar. - 2014
MATHEMATICS-I
(Common to All Branches)
Time: 3 hours Max. Marks: 70
Question Paper Consists of Part-A and Part-B
Answering the question in Part-A is Compulsory,
Three Questions should be answered from Part-B
*****
PART-A
1.(i) Find the complete solution of M
-
16 0.
(ii) If
,
, , find
,,
, ,
, given that
, ,
,,
.
(iii) Solve
F
G
.
(iv) Find the solution, by Laplace transform method, of the integro-differential equation
?
3 2 O ! 1! !
(
P
(v) Find the differential equation of the orthogonal trajectories for the family of parabola
through the origin and foci on y-axis.
(vi) Find the solution of wave equation in one dimension using the method of separation of
variables.
[3+3+4+4+4+4]
PART-B
2.(a) Solve
0 2
1 2
0
1 0
(b) Find the complete solution of
??
5
?
0 6 4 .
[8+8]
3.(a) Solve cos x dy ysinx 0 y 1 .
(b) Find the solution of
4
)
4
)
0 4
4
4
3 2 2
3
32
cos 2 .
[8+8]
4.(a) Find the Laplace transform of ! O 2
,'
@ 1@
(
P
.
(b) Find the shortest distance from origin to the surface
2.
[8+8]
5.(a) Find
',U
,
if @ 2 1 >
0
,where
1
.
(b) Solve
??
0 8
?
15 9!2
(
, 0 5 1
?
0 10 using Laplace transforms
[8+8]
6.(a) Form the partial differential equation by eliminating the arbitrary function
from .
(b) Find the solution of VM
0 MM
W
0 2M
W
X 0 1 2
, where M
and M
W
.
[8+8]
7.(a) Solve the partial differential equation F G .
(b) Find the temperature in a bar of length l which is perfectly insulated laterally and whose
ends O and A are kept at 0
o
C, given that the initial temperature at any point P of the rod is
given by f(x).
[8+8]
Page 1 of 1
Set No - 2
Subject Code: R13102/R13
I B. Tech I Semester Regular Examinations Feb./Mar. - 2014
MATHEMATICS-I
(Common to All Branches)
Time: 3 hours Max. Marks: 70
Question Paper Consists of Part-A and Part-B
Answering the question in Part-A is Compulsory,
Three Questions should be answered from Part-B
*****
PART-A
1.(i) Find the dimensions of rectangular box of maximum capacity whose surface area is S.
(ii) Find the orthogonal trajectories of the family of curves
/3
/3
/3
.
(iii) A generator having emf 100 volts is connected in series with a 10 ohm resistor and an
inductor of 2 henries. If the switch is closed at a time t =0, find the current at time t>0.
(iv) Find the Laplace transform of ! "
!, 0 $ ! $ 1
0, ! % 1
& using Heaviside function.
(v) Solve pq+qx = y.
(vi) Find the solution of 2
0 3
0 by the method of separation of variables.
[4+4+4+4+3+3]
PART- B
2.(a) Solve 1 1 1 0 1 0
(b) Find the complete solution of
??
4 2
.
[8+8]
3.(a) Solve 2x y
?
y
Y
)
Z
[
, y1 2.
(b) Find the solution of
4
)
4
)
0 4
4
4
0 5 2
3 cos4 3 .
[8+8]
4.(a) Find the Laplace transform of ! !2
, (
!.
(b) Find the maxima and minima of
3
3
0 15
0 15
72 .
[8+8]
5.(a) Expand , 2
in powers of (x-1) and (y-1).
(b) Solve
??
7
?
10 42
,3(
, 0 0 1
?
0 01 using Laplace transforms.
[8+8]
6.(a) Form the partial differential equation by eliminating the arbitrary constants ?a? and ?b?
from 2
)
;
)
)
<
)
.
(b) Find the solution of V4M
12MM
W
9M
W
X 2
3 ,
, where M
and M
W
.
[8+8]
7.(a) Solve the partial differential equation F tan G tan tan .
(b) A tightly stretched string with fixed end points x=0 and x=l is initially in a position given
by
P
3
_
J
. If it is released from rest from this position, find the displacement
, ! .
[8+8]
Page 1 of 1
Set No - 3
FirstRanker.com - FirstRanker's Choice
Subject Code: R13102/R13
I B. Tech I Semester Regular Examinations Feb./Mar. - 2014
MATHEMATICS-I
(Common to All Branches)
Time: 3 hours Max. Marks: 70
Question Paper Consists of Part-A and Part-B
Answering the question in Part-A is Compulsory,
Three Questions should be answered from Part-B
*****
PART-A
1.(i) Find the orthogonal trajectories of the curve 1 cos
.
(ii) If
,
,
, find
,,
, ,
, given that
, ,
,,
.
(iii) Find the Laplace transform of ! "
!, 0 $ ! $ 1
0, ! % 1
& using Heaviside function.
(iv) Let the heat conduction in a thin metallic bar of length L is governed by the equation
'
(
)
'
)
, t > 0. If both ends of the bar are held at constant temperature zero and the bar
is initially has temperature f(x), find the temperature u(x,t).
(v) Solve p
2
+pq = z
2
.
(vi) Find
*
+
)
,-+.-
. [4+4+4+4+3+3]
PART- B
2.(a) Solve 2
0 1 1 0 1 0
(b) Find the complete solution of
??
2
2
3
2
cos 2 [8+8]
3.(a) Solve
4
4
2
3
(b) Find the solution of
4
)
4
)
4 6 3 cos 2 . [8+8]
4.(a) Find the Laplace transform of !
89: ;(,89: <(
(
.
(b) If ?>?, ?@? , ?@> and
@
, >
1 ?
, find
, ,
,,
. [8+8]
5.(a) Expand , 2
ln1 in powers of x and y using MacLaurin?s Series
(b) Solve
??
0 8
?
15 9!2
(
, 0 5 1
?
0 10 using Laplace transforms
[8+8]
6.(a) Solve F 0 G
0
.
(b) Solve the partial differential equation px+qy =1. [8+8]
7.(a) Find the partial differential equation of all spheres whose centers lie on z- axis.
(b) Find the solution of the wave equation
)
'
(
)
)
'
)
, if the initial deflection is
H
I
J
0 $ $ K/2
I
J
K 0
J
$ $ K
& and initial velocity equal to 0. [8+8]
Page 1 of 1
Set No - 1
Subject Code: R13102/R13
I B. Tech I Semester Regular Examinations Feb./Mar. - 2014
MATHEMATICS-I
(Common to All Branches)
Time: 3 hours Max. Marks: 70
Question Paper Consists of Part-A and Part-B
Answering the question in Part-A is Compulsory,
Three Questions should be answered from Part-B
*****
PART-A
1.(i) Find the complete solution of M
-
16 0.
(ii) If
,
, , find
,,
, ,
, given that
, ,
,,
.
(iii) Solve
F
G
.
(iv) Find the solution, by Laplace transform method, of the integro-differential equation
?
3 2 O ! 1! !
(
P
(v) Find the differential equation of the orthogonal trajectories for the family of parabola
through the origin and foci on y-axis.
(vi) Find the solution of wave equation in one dimension using the method of separation of
variables.
[3+3+4+4+4+4]
PART-B
2.(a) Solve
0 2
1 2
0
1 0
(b) Find the complete solution of
??
5
?
0 6 4 .
[8+8]
3.(a) Solve cos x dy ysinx 0 y 1 .
(b) Find the solution of
4
)
4
)
0 4
4
4
3 2 2
3
32
cos 2 .
[8+8]
4.(a) Find the Laplace transform of ! O 2
,'
@ 1@
(
P
.
(b) Find the shortest distance from origin to the surface
2.
[8+8]
5.(a) Find
',U
,
if @ 2 1 >
0
,where
1
.
(b) Solve
??
0 8
?
15 9!2
(
, 0 5 1
?
0 10 using Laplace transforms
[8+8]
6.(a) Form the partial differential equation by eliminating the arbitrary function
from .
(b) Find the solution of VM
0 MM
W
0 2M
W
X 0 1 2
, where M
and M
W
.
[8+8]
7.(a) Solve the partial differential equation F G .
(b) Find the temperature in a bar of length l which is perfectly insulated laterally and whose
ends O and A are kept at 0
o
C, given that the initial temperature at any point P of the rod is
given by f(x).
[8+8]
Page 1 of 1
Set No - 2
Subject Code: R13102/R13
I B. Tech I Semester Regular Examinations Feb./Mar. - 2014
MATHEMATICS-I
(Common to All Branches)
Time: 3 hours Max. Marks: 70
Question Paper Consists of Part-A and Part-B
Answering the question in Part-A is Compulsory,
Three Questions should be answered from Part-B
*****
PART-A
1.(i) Find the dimensions of rectangular box of maximum capacity whose surface area is S.
(ii) Find the orthogonal trajectories of the family of curves
/3
/3
/3
.
(iii) A generator having emf 100 volts is connected in series with a 10 ohm resistor and an
inductor of 2 henries. If the switch is closed at a time t =0, find the current at time t>0.
(iv) Find the Laplace transform of ! "
!, 0 $ ! $ 1
0, ! % 1
& using Heaviside function.
(v) Solve pq+qx = y.
(vi) Find the solution of 2
0 3
0 by the method of separation of variables.
[4+4+4+4+3+3]
PART- B
2.(a) Solve 1 1 1 0 1 0
(b) Find the complete solution of
??
4 2
.
[8+8]
3.(a) Solve 2x y
?
y
Y
)
Z
[
, y1 2.
(b) Find the solution of
4
)
4
)
0 4
4
4
0 5 2
3 cos4 3 .
[8+8]
4.(a) Find the Laplace transform of ! !2
, (
!.
(b) Find the maxima and minima of
3
3
0 15
0 15
72 .
[8+8]
5.(a) Expand , 2
in powers of (x-1) and (y-1).
(b) Solve
??
7
?
10 42
,3(
, 0 0 1
?
0 01 using Laplace transforms.
[8+8]
6.(a) Form the partial differential equation by eliminating the arbitrary constants ?a? and ?b?
from 2
)
;
)
)
<
)
.
(b) Find the solution of V4M
12MM
W
9M
W
X 2
3 ,
, where M
and M
W
.
[8+8]
7.(a) Solve the partial differential equation F tan G tan tan .
(b) A tightly stretched string with fixed end points x=0 and x=l is initially in a position given
by
P
3
_
J
. If it is released from rest from this position, find the displacement
, ! .
[8+8]
Page 1 of 1
Set No - 3
Subject Code: R13102/R13
I B. Tech I Semester Regular Examinations Feb./Mar. - 2014
MATHEMATICS-I
(Common to All Branches)
Time: 3 hours Max. Marks: 70
Question Paper Consists of Part-A and Part-B
Answering the question in Part-A is Compulsory,
Three Questions should be answered from Part-B
*****
PART-A
1.(i) Find the distance from the centre at which the velocity in simple harmonic motion
will be 1/3rd of the maximum.
(ii) Find a point with in a triangle such that the sum of the squares of its distances from the
three vertices is minimum.
(iii) Find the solution, by Laplace transform method, of the integro-differential
equation
?
4 O ! 1!
(
P
, 0 0.
(iv) Uranium disintegrates at a rate proportional to the amount present at that time. If M and N
grams of Uranium that rae present at times T
1
and T
2
respectively, find the half life of
Uranium.
(v) Find the complete solution of
M
3
0 3M
2
M
W
3 MM
W 2
0 M`
3
0.
(vi) Solve
1 F
G
.
[4+4+4+4+3+3]
PART- B
2.(a) Solve 3
4 0 1 2 1 0
(b) Find the solution of
4
)
4
)
5
4
4
0 6 4 .
[8+8]
3.(a) Find the complete solution of " 2
2
3
2
cos 2 .
(b) Solve x z? zlogz zlogz
.
[8+8]
4.(a) Find the Laplace transform of ! !2
(
2!.
(b) If @
,*
[
.
[
? .
?
, prove that @
@
d
tan @.
[8+8]
5.(a) If ? 0 0 0 , find the value of
e
e
e
.
(b) Solve
??
2
?
5 2
,(
sin ! , 0 0 1
?
0 1 using Laplace transforms.
[8+8]
6.(a) Form the partial differential equation by eliminating the arbitrary constants ?a? and ?b?
from f
f
.
(b) Using method of separation of variables, solve @
(
2
,(
with @ , 0 @0, ! 0.
[8+8]
7.(a) Find the temperature in a thin metal rod of length L, with both ends insulated and with
initial temperature in the rod is
_
g
.
(b) Solve the partial differential equation F x
qy
z
.
[8+8]
Page 1 of 1
Set No - 4
FirstRanker.com - FirstRanker's Choice
This post was last modified on 03 December 2019