JNTU Kakinada B-Tech 1-1 R161110 MATHEMATICS-II (NM and CV) R16 May 2018 Question Paper

JNTU Kakinada (JNTUK) B-Tech First Year First Semester (1-1) MATHEMATICS-II NM&CV Com to ECE, EIE, ECom E R16 Regulation May 2018 Question Paper

Code No: R161110
I B. Tech I Semester Supplementary Examinations, May – 2018
MATHEMATICS-II (NM&CV) (Com to ECE, EIE, ECom E)Time: 3 hours Max. Marks: 70
Note: 1. Question Paper consists of two parts (Part-A and Part-B) 2. Answer ALL the questions in Part-A
3. Answer any FOUR Questions from Part-B
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
PART ?A
1. a)Find the v15 using Bisection method. (2M)
b) Construct the difference table for the following data.
x 0 5 10 15
y 2 10 23 29 (2M)

c)Evaluate
1
2
0
x dx
?
using Trapezoidal Rule (taking n = 5). (2M)
d) Show that the function f(z)=z is continuous. (2M)
e)If C is a simple closed curve then evaluate
3 +

+


(2M)
f)Determine the poles of f(z) =





(2M)
g)Find the singularity of f(z) =


at z = 2. (2M)
PART -B
2. a) Find the root of the equation x
3
– x ? 4 = 0 using False position method. (7M)
b) Find the root of the equation e
x
sinx = 1 using Newton Raphson method. (7M)
3. a) Given that Sin45
0
=0.7077, Sin50
0
= 0.766, Sin55
0
=0.8192, Sin60
0
=0.866 find
Sin48
0
using Newton?s forward difference formula. (7M)
b) Using Gauss Forward difference formula find y(8) from the following table.
X 0 5 10 15 20 25
Y 7 11 14 18 24 32 (7M)

4.

a)Evaluate
1
2
2
0
1
dx
x –
?
by (i) simpson?s 1/3
rd
rule (iii) Simpson?s 3/8
th
Rule.
(7M)

b)Solve xy
dx
dy
= using Modified Euler?s method for x=1.1 given y (1)=1

(7M)
SET – 1
R16
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Code No: R161110
I B. Tech I Semester Supplementary Examinations, May – 2018
MATHEMATICS-II (NM&CV) (Com to ECE, EIE, ECom E)Time: 3 hours Max. Marks: 70
Note: 1. Question Paper consists of two parts (Part-A and Part-B) 2. Answer ALL the questions in Part-A
3. Answer any FOUR Questions from Part-B
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
PART ?A
1. a)Find the v15 using Bisection method. (2M)
b) Construct the difference table for the following data.
x 0 5 10 15
y 2 10 23 29 (2M)

c)Evaluate
1
2
0
x dx
?
using Trapezoidal Rule (taking n = 5). (2M)
d) Show that the function f(z)=z is continuous. (2M)
e)If C is a simple closed curve then evaluate
3 +

+


(2M)
f)Determine the poles of f(z) =





(2M)
g)Find the singularity of f(z) =


at z = 2. (2M)
PART -B
2. a) Find the root of the equation x
3
– x ? 4 = 0 using False position method. (7M)
b) Find the root of the equation e
x
sinx = 1 using Newton Raphson method. (7M)
3. a) Given that Sin45
0
=0.7077, Sin50
0
= 0.766, Sin55
0
=0.8192, Sin60
0
=0.866 find
Sin48
0
using Newton?s forward difference formula. (7M)
b) Using Gauss Forward difference formula find y(8) from the following table.
X 0 5 10 15 20 25
Y 7 11 14 18 24 32 (7M)

4.

a)Evaluate
1
2
2
0
1
dx
x –
?
by (i) simpson?s 1/3
rd
rule (iii) Simpson?s 3/8
th
Rule.
(7M)

b)Solve xy
dx
dy
= using Modified Euler?s method for x=1.1 given y (1)=1

(7M)
SET – 1
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Code No: R161110
5. a) Prove that f
1(z) does not exist at z= 0 if

3
6 2( )
0( )
0 0
x y y ix
if z
f z x y
if z
? –
?
?
= +
?
?
=
?(7M)

b)Determine analytic function whose real part is
2
2 2
Sin x
u
Cosh y Cos x
=
–

(7M)
6. a)Evaluate








?
dz where ?: || = 4 using Cauchy?s integral formula. (7M)
b)Expand f(z) =



!
0 | (7M)
7. a) Evaluate ?
%&





Where c : |z| =1.5 by Cauchy?s Residue theorem. (7M)

b) Evaluate
2
2
cos
1 2 cos
0
n
d
a a
p
?
?
?
?
+ +
where n is a positive integer ,0 1 a SET – 1
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