Download JNTUK (Jawaharlal Nehru Technological University Kakinada) B.Tech Regular 2014 FebMarch I Semester (1st Year 1st Sem) MATHEMATICS I Question Paper.
I B. Tech I Semester Regular Examinations Feb./Mar.  2014
MATHEMATICSI
(Common to All Branches)
Time: 3 hours Max. Marks: 70
Question Paper Consists of PartA and PartB
Answering the question in PartA is Compulsory,
Three Questions should be answered from PartB
*****
PARTA
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
MATHEMATICSI
(Common to All Branches)
Time: 3 hours Max. Marks: 70
Question Paper Consists of PartA and PartB
Answering the question in PartA is Compulsory,
Three Questions should be answered from PartB
*****
PARTA
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
MATHEMATICSI
(Common to All Branches)
Time: 3 hours Max. Marks: 70
Question Paper Consists of PartA and PartB
Answering the question in PartA is Compulsory,
Three Questions should be answered from PartB
*****
PARTA
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 integrodifferential 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 yaxis.
(vi) Find the solution of wave equation in one dimension using the method of separation of
variables.
[3+3+4+4+4+4]
PARTB
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 12
, 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
MATHEMATICSI
(Common to All Branches)
Time: 3 hours Max. Marks: 70
Question Paper Consists of PartA and PartB
Answering the question in PartA is Compulsory,
Three Questions should be answered from PartB
*****
PARTA
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
MATHEMATICSI
(Common to All Branches)
Time: 3 hours Max. Marks: 70
Question Paper Consists of PartA and PartB
Answering the question in PartA is Compulsory,
Three Questions should be answered from PartB
*****
PARTA
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 integrodifferential 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 yaxis.
(vi) Find the solution of wave equation in one dimension using the method of separation of
variables.
[3+3+4+4+4+4]
PARTB
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 12
, 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
MATHEMATICSI
(Common to All Branches)
Time: 3 hours Max. Marks: 70
Question Paper Consists of PartA and PartB
Answering the question in PartA is Compulsory,
Three Questions should be answered from PartB
*****
PARTA
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 (x1) and (y1).
(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
MATHEMATICSI
(Common to All Branches)
Time: 3 hours Max. Marks: 70
Question Paper Consists of PartA and PartB
Answering the question in PartA is Compulsory,
Three Questions should be answered from PartB
*****
PARTA
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
MATHEMATICSI
(Common to All Branches)
Time: 3 hours Max. Marks: 70
Question Paper Consists of PartA and PartB
Answering the question in PartA is Compulsory,
Three Questions should be answered from PartB
*****
PARTA
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 integrodifferential 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 yaxis.
(vi) Find the solution of wave equation in one dimension using the method of separation of
variables.
[3+3+4+4+4+4]
PARTB
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 12
, 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
MATHEMATICSI
(Common to All Branches)
Time: 3 hours Max. Marks: 70
Question Paper Consists of PartA and PartB
Answering the question in PartA is Compulsory,
Three Questions should be answered from PartB
*****
PARTA
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 (x1) and (y1).
(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
MATHEMATICSI
(Common to All Branches)
Time: 3 hours Max. Marks: 70
Question Paper Consists of PartA and PartB
Answering the question in PartA is Compulsory,
Three Questions should be answered from PartB
*****
PARTA
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 integrodifferential
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 21 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