Categories: First Year First Semester (1-1)

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

1 of 2

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

1 of 2

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

R16

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