Download JNTUK (Jawaharlal Nehru Technological University Kakinada (JNTU kakinada)) B-Tech 2020 R19 ECE 1101 Mathematics I Model Previous Question Paper
[B19 BS 1101]
I B. Tech I Semester (R19) Regular Examinations
MATHEMATICS ? I
(Common to All Branches)
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) Solve the system of equations 20?? +?? ? 2?? = 17, 3?? + 20?? ??? =?18,
2?? ? 3?? + 20?? = 25 by Gauss ?Siedel method.
CO1 K2 8
b)
Investigate the values of ?? and ?? so that the equations
2?? + 3?? + 5?? = 9; 7?? + 3?? ? 2?? = 8; 2?? + 3?? +?? ?? =?? ;
has (i)no solution (ii) unique solution (iii) infinite number of solutions
CO1
K3
7
(OR)
2. a)
Solve the system of equations 10x + y+z =12, 2x+10y+z =13, 2x+2y+10z
=14 by Gauss- elimination method.
CO1
K2
8
b) Define rank and find the rank of the matrix A by reducing it in to its normal
form where
A is: A =
2 3
1 ?1
?1 ?1
?2 ?4
3 1
6 3
3 ?2
0 ?7
.
CO1 K1 7
UNIT-II
3.a) Verify Cayley-Hamilton theorem and find the inverse of the matrix
?? =
1 0 3
2 1 ?1
1 ?1 1
.
CO2
K3
8
b)
Reduce the quadratic form 2?? 2
+ 2?? 2
+ 2?? 2
? 2?? ?? ? 2?? ?? ? 2?? ?? to
canonical form by orthogonal transformation
CO2 K3 7
(OR)
4. a) Find the eigenvalues and the corresponding eigen vectors of the matrix
?? =
8 ?6 2
?6 7 ?4
2 ?4 3
.
CO2
K3
8
b)
If A =
3 1
?1 2
, use Cayley-Hamilton theorem to find the value of
2A
5
- 3A
4
+ A
2
- 4 I . Also find the inverse of A.
CO2 K3 7
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1
[B19 BS 1101]
I B. Tech I Semester (R19) Regular Examinations
MATHEMATICS ? I
(Common to All Branches)
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) Solve the system of equations 20?? +?? ? 2?? = 17, 3?? + 20?? ??? =?18,
2?? ? 3?? + 20?? = 25 by Gauss ?Siedel method.
CO1 K2 8
b)
Investigate the values of ?? and ?? so that the equations
2?? + 3?? + 5?? = 9; 7?? + 3?? ? 2?? = 8; 2?? + 3?? +?? ?? =?? ;
has (i)no solution (ii) unique solution (iii) infinite number of solutions
CO1
K3
7
(OR)
2. a)
Solve the system of equations 10x + y+z =12, 2x+10y+z =13, 2x+2y+10z
=14 by Gauss- elimination method.
CO1
K2
8
b) Define rank and find the rank of the matrix A by reducing it in to its normal
form where
A is: A =
2 3
1 ?1
?1 ?1
?2 ?4
3 1
6 3
3 ?2
0 ?7
.
CO1 K1 7
UNIT-II
3.a) Verify Cayley-Hamilton theorem and find the inverse of the matrix
?? =
1 0 3
2 1 ?1
1 ?1 1
.
CO2
K3
8
b)
Reduce the quadratic form 2?? 2
+ 2?? 2
+ 2?? 2
? 2?? ?? ? 2?? ?? ? 2?? ?? to
canonical form by orthogonal transformation
CO2 K3 7
(OR)
4. a) Find the eigenvalues and the corresponding eigen vectors of the matrix
?? =
8 ?6 2
?6 7 ?4
2 ?4 3
.
CO2
K3
8
b)
If A =
3 1
?1 2
, use Cayley-Hamilton theorem to find the value of
2A
5
- 3A
4
+ A
2
- 4 I . Also find the inverse of A.
CO2 K3 7
2
UNIT-III
5.a)
Solve
?? ?? ?? ?? + (tan?? )?? = (sec?? )?? 3
. CO3 K2 8
b) Find the orthogonal trajectories of the family of parabolas ?? ?? 2
= ?? 3
. CO3 K3 7
(OR)
6. a) Solve ?? 4
+ 2?? ?? ?? + ?? ?? 3
+ 2?? 4
? 4?? ?? ?? = 0. CO4 K2 8
b) A body originally at 80
0
?? cools down to 60
0
?? in 20 minutes, the
temperature of air being40
0
?? . What will be the temperature of the body
after 40 minutes from the original?
CO4 K3 7
UNIT-IV
7.a) Solve ?? 3
??? ?? = 2?? + 1 + 4 cos?? . CO5 K2 8
b)
Solve
?? 2
?? ?? ?? 2
? 2
?? ?? ?? ?? +?? =?? ?? log?? by the method of variation of parameters.
CO5 K2 7
(OR)
8. a)
Solve ?? 2
+ 3?? + 2 ?? =?? ?? ?? . CO5 K2 8
b)
Solve the differential equation ?? 2
?? 2
?? ?? ?? 2
??? ?? ?? ?? ?? +?? = log??
CO5 K2 7
UNIT-V
9.a)
Find ?? {?? ?? ?? ?? ?? ?? } and ?? ?? ??? ?? 0
cos?? ?? ?? . CO6 K2 8
b)
Using convolution theorem evaluate ?? ?1
{
1
?? +?? (?? +?? )
}. CO6 K3 7
(OR)
10.a)
Find ?? ?1
{
5?? +3
?? ?1 (?? 2
+2?? +5)
}. CO6 K2 8
b)
Solve
?? 2
?? ?? ?? 2
+ 4
?? ?? ?? ?? + 3?? =?? ??? , ?? 0 =?? ?
0 = 1 by using Laplace
transforms
CO6 K3 7
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This post was last modified on 28 April 2020