Download JNTUK B-Tech 2020 R19 EEE 1202 Mathematics III Model Question Paper

Download JNTUK (Jawaharlal Nehru Technological University Kakinada (JNTU kakinada)) B-Tech 2020 R19 EEE 1202 Mathematics III Model Previous Question Paper

13


[B19 BS 1202]
SAGI RAMA KRISHNAM
I B. Tech II Semester (R19) Regular Examinations
MATHEMATICS ? III
(Common to CE,CSE,ECE,EEE & IT)
MODEL QUESTION PAPER
TIME : 3 Hrs. Max. Marks : 75 M
Answer ONE Question from EACH UNIT
All questions carry equal marks
*****


UNIT-I CO KL Marks
1.a)
Find the Frier series for the function CO1

K2

7
b) Obtain Frier series of the function f(x) = 2x ? x
2
in (0, 3) and hence
deduce that
1
1
2
?
1
2
2
+
1
3
2
?
1
4
2
+? =
?? 12

CO1 K2 8
(OR)
2. a)

Obtain a Frier series for the function f(x) given by
?? (?? ) =
1 +
2x
?? , if -?? ? x ? 0
1?
2x
?? , if 0 ? x ? ??
and deduce that
1
1
2
+
1
3
2
+
1
5
2
+? =
?? 2
8

CO1 K2
8

b) Find the Half ? Range cosine series for the function f(x) = x
2
in the range
0 ? x ??
CO1 K3 7
UNIT-II
3.a)
Using the Frier Sine Transform of ( a > 0), evaluate

CO2 K3 7
b)

Using Frier integral representation, show that

CO2 K3 8
(OR)
4. a)
Find the inverse Frier sine transform f(x) of F
s
(p) =
?? 1+?? 2

CO2 K2 8
b)
Using Parseval?s Identity, prove that
CO2 K3 7




? ?
?
?
?
?
?
? ?
? ? ?
? ? ? ? ?
?
? ?
? ?
? ?
t
t
t
t f
2 / , 1
2 / 2 / , 0
2 / , 1
x a
e
?
?
?
?
0
2 2
sin
dx
x a
kx x
2
0
sin
,0
12
x
x
d e x
? ? ?
?
?
?
?
??
?
?
? ?
?
?
?
?
0
2
2
2
4
1
?
dx
x
x
FirstRanker.com - FirstRanker's Choice
13


[B19 BS 1202]
SAGI RAMA KRISHNAM
I B. Tech II Semester (R19) Regular Examinations
MATHEMATICS ? III
(Common to CE,CSE,ECE,EEE & IT)
MODEL QUESTION PAPER
TIME : 3 Hrs. Max. Marks : 75 M
Answer ONE Question from EACH UNIT
All questions carry equal marks
*****


UNIT-I CO KL Marks
1.a)
Find the Frier series for the function CO1

K2

7
b) Obtain Frier series of the function f(x) = 2x ? x
2
in (0, 3) and hence
deduce that
1
1
2
?
1
2
2
+
1
3
2
?
1
4
2
+? =
?? 12

CO1 K2 8
(OR)
2. a)

Obtain a Frier series for the function f(x) given by
?? (?? ) =
1 +
2x
?? , if -?? ? x ? 0
1?
2x
?? , if 0 ? x ? ??
and deduce that
1
1
2
+
1
3
2
+
1
5
2
+? =
?? 2
8

CO1 K2
8

b) Find the Half ? Range cosine series for the function f(x) = x
2
in the range
0 ? x ??
CO1 K3 7
UNIT-II
3.a)
Using the Frier Sine Transform of ( a > 0), evaluate

CO2 K3 7
b)

Using Frier integral representation, show that

CO2 K3 8
(OR)
4. a)
Find the inverse Frier sine transform f(x) of F
s
(p) =
?? 1+?? 2

CO2 K2 8
b)
Using Parseval?s Identity, prove that
CO2 K3 7




? ?
?
?
?
?
?
? ?
? ? ?
? ? ? ? ?
?
? ?
? ?
? ?
t
t
t
t f
2 / , 1
2 / 2 / , 0
2 / , 1
x a
e
?
?
?
?
0
2 2
sin
dx
x a
kx x
2
0
sin
,0
12
x
x
d e x
? ? ?
?
?
?
?
??
?
?
? ?
?
?
?
?
0
2
2
2
4
1
?
dx
x
x
14

UNIT-III
5.a)
Express in terms of gamma function. CO3 K2 7
b)
Express ?? ?? (1??? ?? )
?? ?? ?? 1
0
in terms of Gamma functions and hence
evaluate ?? 7
(1??? 5
)
8
?? ?? 1
0

CO3 K2 8
(OR)
6. a)
Apply change the order of integration and evaluate
CO3 K3 8
b) Obtain the volume of the tetrahedron bnded by x = 0, y = 0, z = 0,
x+y+z = 1.
CO3 K3 7
UNIT-IV
7.a) Obtain the directional derivative of ?? =?? ?? +?? ?? +?? ?? at A in the
direction of AB where A= (1,2,-1) , B=(5,6,8) .
CO4 K2 8
b) Determine curl (curl F) where ??
= x
2
y ??
? 2 xz ??
+ 2 yz ??

CO4 K2 7
(OR)
8. a) Show that the vector ?? 2
??? ?? ?? + ?? 2
??? ?? ?? + ?? 2
??? ?? ??

Is irrotational and find its scalar potential.
CO4 K2 8
b) Determine the values of a and b such that the surface
a x
2
?b y z = (a+2)x and 4 x
2
y + z
3
=4 cut orthogonally at (1,-1, 2).

CO4 K2 7
UNIT-V
9.a) Obtain Determine the work done in moving a particle once rnd the circle
x
2
+y
2
=9 in the xy- plane by the force
??
= 2?? ??? ??? ?? + ?? +?? ??? 2
?? + 3?? ? 2?? + 4?? ??
.
CO5 K2 7
b) Evaluate the line integral by Stokes?s theorem for the vector function
??
=?? 2
?? +?? 2
?? + (?? +?? )??
and C is the triangle with vertices
(0,0,0),(1,0,0) and (1,1,0).
CO6 K3 8
(OR)
10 Verify Green?s theorem in the plane

3?? 2
? 8?? 2
?? ?? + 4?? ? 6?? ?? ?? ??
?? ,
where C is bndary of the region defined by y = ?? , y = x
2
CO6 K3 15







?
?
?
0
3
dx e x
x
0
.
y
x
e
dy dx
y
?? ?
??
FirstRanker.com - FirstRanker's Choice