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Code No: 53007 Set No. 1 JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD II B.Tech. I Sem., I Mid-Term Examinations, Aug/Sept – 2012 MATHEMATICS – III Objective Exam Name: ______________________________ Hall Ticket No. A
Answer All Questions. All Questions Carry Equal Marks.Time: 20 Min. Marks: 10.
I
Choose the correct alternative: 1
1.
∫x
2
(1 − x)5 / 2 dx =
[
]
[
]
[
]
[
]
[
]
[
]
0
7 a) β (3, ) 2
7 b) β (2, ) 2
5 c) β (3, ) 2
5 d) β (2, ) 2
1
2.
∫ xJ ( x) J (2 x)dx 3
3
=
0
a) 1 ∞
3.
b)
∫x
1/ 2 − x / 5
e
1 2 J 3 (1) 2
c)
1 2 J 2 (1) 2
dx =
R O
0
a)
5 5π 2
5π 2
b)
c) 5 5π
1
4.
∫ P ( x)dx =
W U
0
−1
a) 3
b) 2
1
5.
∫ xT ( x)dx
T N
2
0
a) π 6.
b)
8.
π
2 If f(z) =cos z and g(z) = cos z , then g ( z ) is
J
a) Analytic at o only 7.
c) 1
The harmonic conjugate of e x cos y − y is a) e x sin y + x + C b) e x cos y + x + C
∫ zdz
c) 1
b) Analytic every where
D L
d) 0
c) Not analytic
c) e x cos y + y + C
d)
5 3π 2
d) 0
d) 0
d) Analytic at z = g ( z ) [
]
[
]
[
]
[
]
d) e x sin y − x + C
=
C
9.
a) π i ze z dz
b) 2 π i
c) 4 π i
∫⎛
d) 0
where C is z = 2 is 2 iπ ⎞ ⎜z− ⎟ 2⎠ ⎝ a) −2π − π 2i b) −2π + π 2i c) −π − π 2i d) 0 2 f(z) = (z - z) is a) Continuous at all points b) Not continuous any where c) Not continuous at z=0 only d) Continuous at z=0 only C
10.
Cont……2
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Code No: 53007
:2:
II
Fill in the blanks:
11.
1⎞ ⎛ ∫0 ⎜⎝ log x ⎟⎠ dx = …………………….
Set No. 1
3
1
1
12.
∫ ( P ( x)) dx = …………………. 2
3
−1
13.
J 0 (0) = …………………..
14.
Tn (cos θ ) =…………………………….
15.
U1 ( x) =……………….
16.
If f(z) = x+ ay + i( x+by) differentiable at every point, then the values a and b are …………………..
17.
If f(z) is analytic within and on a simple closed curve C and a is any point inside C then 2π if '( a) =……………
18.
The principal value of log(1+ i
19.
∫ z dz 2
R O
W U
3 ) is ………………
T N
, along the straight line y=x from (0,0) to (1,1) is …………………
C
20.
D L
If f(z) =
a r Cos θ + i( r sin θ + 2) is analytic, then a =………………………….. 2
J
-o0o-
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Code No: 53007 Set No. 2 JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD II B.Tech. I Sem., I Mid-Term Examinations, Aug/Sept – 2012 MATHEMATICS – III Objective Exam Name: ______________________________ Hall Ticket No. A
Answer All Questions. All Questions Carry Equal Marks.Time: 20 Min. Marks: 10.
I
Choose the correct alternative: 1
1.
∫ P ( x)dx = 0
[
]
[
]
[
]
−1
a) 3
b) 2
c) 1
d) 0
1
2.
∫ xT ( x)dx 2
0
a) π 3.
b)
2 If f(z) =cos z and g(z) = cos z , then g ( z ) is
a) Analytic at o only 4. 5.
π
c) 1
d) 0
b) Analytic every where
The harmonic conjugate of e cos y − y is a) e x sin y + x + C b) e x cos y + x + C
c) e cos y + y + C x
=
C
6.
a) π i ze z dz
b) 2 π i
W U
∫⎛
where C is z = 2 is 2 iπ ⎞ ⎜z− ⎟ 2⎠ ⎝ a) −2π − π 2i b) −2π + π 2i 2 f(z) = (z - z) is a) Continuous at all points c) Not continuous at z=0 only C
7.
T N
J
1
8.
c) 4 π i
d) Analytic at z = g ( z )
R O
x
∫ zdz
D L
c) Not analytic
c) −π − π 2i
[
]
[
]
[
]
[
]
[
]
[
]
[
]
d) e sin y − x + C x
d) 0
d) 0
b) Not continuous any where d) Continuous at z=0 only
2 5/ 2 ∫ x (1 − x) dx = 0
7 a) β (3, ) 2
7 b) β (2, ) 2
5 c) β (3, ) 2
5 d) β (2, ) 2
1
9.
∫ xJ ( x) J (2 x)dx 3
3
=
0
a) 1 ∞
10.
∫x
b)
1/ 2 − x / 5
e
1 2 J 3 (1) 2
c)
1 2 J 2 (1) 2
d) 0
dx =
0
a)
5 5π 2
b)
5π 2
c) 5 5π
d)
5 3π 2
Cont……2
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Code No: 53007
:2:
Set No. 2
II
Fill in the blanks:
11.
Tn (cos θ ) =…………………………….
12.
U1 ( x) =……………….
13.
If f(z) = x+ ay + i( x+by) differentiable at every point, then the values a and b are …………………..
14.
If f(z) is analytic within and on a simple closed curve C and a is any point inside C then 2π if '( a) =……………
15.
The principal value of log(1+ i
16.
∫ z dz 2
, along the straight line y=x from (0,0) to (1,1) is …………………
R O
C
a r Cos θ + i( r sin θ + 2) is analytic, then a =………………………….. 2
17.
If f(z) =
18.
1⎞ ⎛ ∫0 ⎜⎝ log x ⎟⎠ dx = …………………….
T N
1
19.
∫ ( P ( x)) dx = …………………. 2
3
−1
20.
W U
3
1
D L
3 ) is ………………
J
J 0 (0) = …………………..
-o0o-
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Code No: 53007 Set No. 3 JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD II B.Tech. I Sem., I Mid-Term Examinations, Aug/Sept – 2012 MATHEMATICS – III Objective Exam Name: ______________________________ Hall Ticket No. A
Answer All Questions. All Questions Carry Equal Marks.Time: 20 Min. Marks: 10.
I
Choose the correct alternative:
1.
If f(z) =cos z and g(z) = cos z , then g ( z ) is a) Analytic at o only
2. 3.
b) Analytic every where
The harmonic conjugate of e x cos y − y is a) e x sin y + x + C b) e x cos y + x + C
∫ zdz
[ c) Not analytic
c) e cos y + y + C x
d) Analytic at z = g ( z )
4.
c) 4 π i
∫⎛
D L
d) 0
where C is z = 2 is 2 iπ ⎞ ⎜z− ⎟ 2⎠ ⎝ a) −2π − π 2i b) −2π + π 2i c) −π − π 2i d) 0 2 f(z) = (z - z) is a) Continuous at all points b) Not continuous any where c) Not continuous at z=0 only d) Continuous at z=0 only
R O
C
5.
W U
1
6.
∫x
2
(1 − x)5 / 2 dx =
T N
0
7 a) β (3, ) 2 1
7.
3
3
0
a) 1 ∞
8.
J
∫ xJ ( x) J (2 x)dx
∫x
1/ 2 − x / 5
e
=
7 b) β (2, ) 2
b)
1 2 J 3 (1) 2
5 c) β (3, ) 2
c)
1 2 J 2 (1) 2
]
[
]
[
]
[
]
[
]
[
]
[
]
[
]
[
]
d) e sin y − x + C
= b) 2 π i
[ x
C
a) π i ze z dz
]
5 d) β (2, ) 2
d) 0
dx =
0
a)
5 5π 2
5π 2
b)
c) 5 5π
d)
5 3π 2
1
9.
∫ P ( x)dx = 0
−1
a) 3
b) 2
c) 1
d) 0
1
10.
∫ xT ( x)dx 2
0
a) π
b)
π 2
c) 1
d) 0 Cont……2
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Code No: 53007
:2:
Set No. 3
II
Fill in the blanks:
11.
If f(z) = x+ ay + i( x+by) differentiable at every point, then the values a and b are …………………..
12.
If f(z) is analytic within and on a simple closed curve C and a is any point inside C then 2π if '( a) =……………
13.
The principal value of log(1+ i
14.
∫ z dz 2
3 ) is ………………
, along the straight line y=x from (0,0) to (1,1) is …………………
D L
C
a r Cos θ + i( r sin θ + 2) is analytic, then a =………………………….. 2
15.
If f(z) =
16.
1⎞ ⎛ ∫0 ⎜⎝ log x ⎟⎠ dx = …………………….
W U
1
17.
R O
3
1
∫ ( P ( x)) dx = …………………. 2
3
−1
T N
18.
J 0 (0) = …………………..
19.
Tn (cos θ ) =…………………………….
20.
U1 ( x) =……………….
J
-o0o-
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Code No: 53007 Set No. 4 JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD II B.Tech. I Sem., I Mid-Term Examinations, Aug/Sept – 2012 MATHEMATICS – III Objective Exam Name: ______________________________ Hall Ticket No. A
Answer All Questions. All Questions Carry Equal Marks.Time: 20 Min. Marks: 10.
I 1.
Choose the correct alternative:
∫ zdz
=
[
]
[
]
[
]
[
]
[
]
[
]
[
]
[
]
[
]
C
2.
a) π i ze z dz
b) 2 π i
c) 4 π i
d) 0
∫⎛
where C is z = 2 is 2 iπ ⎞ ⎜z− ⎟ 2⎠ ⎝ a) −2π − π 2i b) −2π + π 2i c) −π − π 2i d) 0 2 f(z) = (z - z) is a) Continuous at all points b) Not continuous any where c) Not continuous at z=0 only d) Continuous at z=0 only C
3.
D L
R O
1
4.
∫x
2
(1 − x)5 / 2 dx =
0
7 a) β (3, ) 2
7 b) β (2, ) 2
W U
1
5.
∫ xJ ( x) J (2 x)dx 3
3
=
0
T N
a) 1 ∞
6.
b)
∫x
1/ 2 − x / 5
e
dx =
0
a)
5 5π 2
1
7.
∫ P ( x)dx =
5 c) β (3, ) 2
J
1 2 J 3 (1) 2
c)
5π 2
b)
1 2 J 2 (1) 2
c) 5 5π
5 d) β (2, ) 2
d) 0
d)
5 3π 2
0
−1
a) 3
b) 2
c) 1
d) 0
1
8.
∫ xT ( x)dx 2
0
a) π 9.
π
2 If f(z) =cos z and g(z) = cos z , then g ( z ) is
a) Analytic at o only 10.
b)
c) 1
d) 0
b) Analytic every where
The harmonic conjugate of e x cos y − y is a) e x sin y + x + C b) e x cos y + x + C
c) Not analytic
d) Analytic at z = g ( z ) [
c) e cos y + y + C x
]
d) e sin y − x + C x
Cont……2 www.jntuworld.com
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Code No: 53007
:2:
II
Fill in the blanks:
11.
The principal value of log(1+ i
12.
∫ z dz 2
Set No. 4
3 ) is ………………
, along the straight line y=x from (0,0) to (1,1) is …………………
C
a r Cos θ + i( r sin θ + 2) is analytic, then a =………………………….. 2
13.
If f(z) =
14.
1⎞ ⎛ ∫0 ⎜⎝ log x ⎟⎠ dx = …………………….
3
1
D L
R O
1
15.
∫ ( P ( x)) dx = …………………. 2
3
−1
16.
J 0 (0) = …………………..
17.
Tn (cos θ ) =…………………………….
18.
U1 ( x) =……………….
19.
If f(z) = x+ ay + i( x+by) differentiable at every point, then the values a and b are …………………..
20.
If f(z) is analytic within and on a simple closed curve C and a is any point inside C then 2π if '( a) =……………
W U
T N
J
-o0o-
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