Download JNTUK (Jawaharlal Nehru Technological University Kakinada (JNTU kakinada)) B-Tech 2020 R19 ECE 1102 Mathematics II Model Previous Question Paper
[B19 BS 1102]
I B. Tech I Semester (R19) Regular Examinations
MATHEMATICS ? II
(Common to CSE, ECE & 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 M
1.a) Using Newton?s forward difference interpolation formula find Y (3),
from the following table
X 0 5 10 15 20 25
Y 7 11 14 18 24 32
CO3 K2 8
b)
Find the interpolating polynomial f(x) for the data of the following table
x 0 1 4 5
f(x) 4 3 24 39
CO3
K1
7
(OR)
2. a)
Using Gauss backward formula, find f(42), from the following table
X 20 25 30 35 40 45
f(x) 354 332 291 260 231 204
CO4 K2 8
b) Using Lagrange?s interpolation formula find Y (10) from the following
table
x 5 6 9 11
Y 12 13 14 16
CO4 K3 7
UNIT-II
3.a) Find the cube root of 41 using Newton-Raphson method. CO5 K2 8
b)
Evaluate
?? ?? ?? 3
+?? +1
2
0
by using Simpsons 1/3
rd
rule with ? = 0.25
CO5 K2
7
(OR)
4. a) Find a real root of the equation x log
10
x=1.2 by Regula-false method
correct tothree decimal places
CO5 K2 8
b) Evaluate ?? (0.8) using Runge Kutta method given
?? ?
= (?? +?? )
1
2
,?? 0.4 = 0.41
CO5 K3 7
UNIT-III
5.a)
If U = tan
?1
?? 3
+ ?? 3
?? ??? and x U
X
+ y U
y
= sin 2U, prove that
x
2
?? ?? ?? + 2xy ?? ?? ?? + y
2
?? ?? ?? = 2cos 3?? sin?? .
CO1
K2
8
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3
[B19 BS 1102]
I B. Tech I Semester (R19) Regular Examinations
MATHEMATICS ? II
(Common to CSE, ECE & 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 M
1.a) Using Newton?s forward difference interpolation formula find Y (3),
from the following table
X 0 5 10 15 20 25
Y 7 11 14 18 24 32
CO3 K2 8
b)
Find the interpolating polynomial f(x) for the data of the following table
x 0 1 4 5
f(x) 4 3 24 39
CO3
K1
7
(OR)
2. a)
Using Gauss backward formula, find f(42), from the following table
X 20 25 30 35 40 45
f(x) 354 332 291 260 231 204
CO4 K2 8
b) Using Lagrange?s interpolation formula find Y (10) from the following
table
x 5 6 9 11
Y 12 13 14 16
CO4 K3 7
UNIT-II
3.a) Find the cube root of 41 using Newton-Raphson method. CO5 K2 8
b)
Evaluate
?? ?? ?? 3
+?? +1
2
0
by using Simpsons 1/3
rd
rule with ? = 0.25
CO5 K2
7
(OR)
4. a) Find a real root of the equation x log
10
x=1.2 by Regula-false method
correct tothree decimal places
CO5 K2 8
b) Evaluate ?? (0.8) using Runge Kutta method given
?? ?
= (?? +?? )
1
2
,?? 0.4 = 0.41
CO5 K3 7
UNIT-III
5.a)
If U = tan
?1
?? 3
+ ?? 3
?? ??? and x U
X
+ y U
y
= sin 2U, prove that
x
2
?? ?? ?? + 2xy ?? ?? ?? + y
2
?? ?? ?? = 2cos 3?? sin?? .
CO1
K2
8
4
b)
If u = ?? 2
? 2?? 2
, v = 2?? 2
??? 2
where x = rcos?? , y = r sin??
then show that
?? (?? ,?? )
?? (?? ,?? )
= 6 ?? 3
sin 2?? .
CO1
K2
7
(OR)
6. a) Expand ?? 2
?? + 3?? ? 2 in powers of ?? ? 1 and (?? + 2) using
Taylor's theorem. CO1 K2
8
b) By using the method of differentiation under the integral sign prove
that
tan
?1
(?? ?? )
?? (1+ ?? 2
)
?
0
dx =
?? 2
log(1 +?? ), a 0.
CO1 K3 7
UNIT-IV
7. a) Solve x
2
( y - z )p + y
2
( z - x )q = z
2
( x - y ). CO2 K2 8
b)
solve (?? 2
- D?? ?
- 2?? ?
2
) z = ( y - 1 )?? ?? .
CO2 K2 7
(OR)
8. a) Solve x( y - z )p + y( z - x )q = z( x - y ). CO2 K2 8
b) solve ( D + ?? ?
- 1 )( D + 2?? ?
- 3 )z = 3x + 6y + 4.
CO2 K2
7
UNIT-V
9.a)
Obtain the solution of
?? ?? ?? ?? +
?? ?? ?? ?? = 0 by the method of separation of
variables.
CO6 K2 8
b) A tightly stretched elastic string of length L, fixed at its end points is
initially in a position given by?? ?? , 0 =?? 0
?? ?? ?? 3
?? ?? ?? . If it is released from
rest, find the displacement at any subsequent time.
CO6 K3
7
(OR)
10.a)
Obtain the solution of ?? ?? ?? ?? ?? +?? ?? ?? ?? ?? = 0 by the method of separation of
variables.
CO6 K2 8
b) A bar of conducting material of length ?? units is initially kept at a
temperature sin x. Find the temperature at any subsequent time if the
ends of the bar are held at zero temperature.
CO6 K3 7
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This post was last modified on 28 April 2020