SET1
RAVINDRA COLLEGE OF ENGINEERING FOR WOMEN
Nandikotkur Road, Kurnool – 518 004
Sign of the Invigilator
MID – I OBJECTIVE PAPER
II B.Tech –I Sem
Branch: COMMON TO ALL
Year & Semester:
MATHEMATICS- III (15A54301)
Name of the Subject:
DATE: 29-08-2016
TIME: 20 MIN
Max. Marks: 10M
Regd.No.
Name of the Student:
1) If x3-x-4=0,by bisection method first two approximations x 0 and x 1 are 1 and 2 then x 2 is
a) 1
b) 2
c) 1.5
2) The rank of the matrix
a) three
b) four
d) none
A=
1 0 0
0 1 0
0 0 1
c) one d) none
If λ is the Eigen value of A then Eigen value of A-1 is___________
a) K λ
b) / λ
c λ
d) none
[
]
[
]
4) Example for an algebraic equation is _____________
5) If x3-x-4=0,by Regular Falsi method first two approximations x 0 and x 1 are 1 and 2 then
x 2 is__________
6) A function which is sum or difference or product of two polynomials is called an_____
7) The system of equations AX=B is inconsistent if ____________
a ρ A = ρ AB
b ρ A ≠ρ AB
c ρ A = ρ AB =no. of varia les
8) The rank of a null matrix __________
a) one
b) zero
c) two
b) ��
]
d) none
[
]
[
]
d) none
9) The normal form of a matrix ____________
a) [ �� 0]
[
c) a and b
d) none
SET1
RAVINDRA COLLEGE OF ENGINEERING FOR WOMEN
Nandikotkur Road, Kurnool – 518 004
Sign of the Invigilator
MID – I OBJECTIVE PAPER
II B.Tech –I Sem
Branch: COMMON TO ALL
Year & Semester:
MATHEMATICS- III (15A54301)
Name of the Subject:
DATE: 29-08-2016
TIME: 20 MIN
Max. Marks: 10M
Regd.No.
Name of the Student:
1) If x3-x-4=0,by bisection method first two approximations x 0 and x 1 are 1 and 2 then x 2 is
a) 1
b) 2
c) 1.5
2) The rank of the matrix
d) none
A=
1 0 0
0 1 0
0 0 1
a) three b) four c) one d) none
If λ is the Eigen value of A then Eigen value of A-1 is___________
a) K λ
b) / λ
c λ
d) none
[
]
[
]
4) Example for an algebraic equation is _____________
5) If x3-x-4=0,by Regular Falsi method first two approximations x 0 and x 1 are 1 and 2 then
x 2 is__________
6) A function which is sum or difference or product of two polynomials is called an_____
7) The system of equations AX=B is inconsistent if ____________
a ρ A = ρ AB
b ρ A ≠ρ AB
c ρ A = ρ AB =no. of varia les
8) The rank of a null matrix __________
a) one
b) zero
c) two
b) ��
]
d) none
[
]
[
]
d) none
9) The normal form of a matrix ____________
a) [ �� 0]
[
c) a and b
d) none
SET1
λ is a Eigen value of A ,then there exists Eigen ve tor X su h that___________
11)Which of the following matrix is scalar matrix:
[
a)
d) none
b)
c)
−
12) What type of matrix
a)scalar matrix
this
b) diagonal matrix
[
c) unit matrix
b) A2= I
a) AT =A
b) AT = -A
c) A2= 0
]
d) none
13) A square matrix A is said to be Hermitian matrix if_______________
a) �� = A
]
[
]
[
]
d ) none
14) A square matrix A is said to be skew symmetric if _________________
c) AT A=I
d)
none
15) Index of the Quardratic form =_______________________
16) Canonical form of the Quardratic form is represented by =______________
17) What is the rank of the matrix A =
a) 1
b) 2
c) 3
[
]
d) no
18) Example for an transcendental equation is ________________
19) A square matrix A is said to be unitary if ________________________ [
(a) �� = �
�� = −�
�� � = �
�� � = �
(a) �� = �
�� = −�
�� � = �
�� � = �
20) A square matric A is said to be orthogonal if ______________________ [
]
]
SET1
λ is a Eigen value of A ,then there exists Eigen ve tor X su h that___________
11)Which of the following matrix is scalar matrix:
[
a)
d) none
b)
c)
−
12) What type of matrix
a) scalar matrix
this
b) diagonal matrix
[
c) unit matrix
b) A2= I
a) AT =A
b) AT = -A
c) A2= 0
]
d) none
13) A square matrix A is said to be Hermitian matrix if_______________
a) �� = A
]
[
]
[
]
d ) none
14) A square matrix A is said to be skew symmetric if _________________
c) AT A=I
d)
none
15) Index of the Quardratic form =_______________________
16) Canonical form of the Quardratic form is represented by =______________
17) What is the rank of the matrix A =
a) 1
b) 2
c) 3
[
]
d) no
18) Example for an transcendental equation is ________________
19) A square matrix A is said to be unitary if ________________________ [
(a) �� = �
�� = −�
�� � = �
�� � = �
(a) �� = �
�� = −�
�� � = �
�� � = �
20) A square matric A is said to be orthogonal if ______________________ [
]
]
SET1
RAVINDRA COLLEGE OF ENGINEERING FOR WOMEN
Nandikotkur Road, Kurnool – 518 002, A.P.
I MID EXAMINATIONS
Branch: Common to all
II B.Tech- I Sem
Year :
DATE:29-08-2016
TIME: 90 MIN
MATHEMTICS-III (15A54101)
Max.Marks: 20
Name of the Subject:
1 .
SET-1
[ 2 � × � =10]
(a) Define the rank of the matrix
(b) Define Unitary matrix
(c ) Express the matrix A as a sum of symmetric and skew-symmetric matrix where A= [
]
1 2 5
[2 0 3]
(d) Obtain the quadratic form corresponding matrix
5 3 4
0
2b
(e) Determine the values of a,b,c When [ a
b
c
c]
a b
is orthogonal
c
1 2 3 0
2.
2 4 3 2
Reduce the matrix A =
3 2 1 3
to Echelon form hence find the rank A
[6 8 7 5]
Prove that the eigen values of a Hermitian matrix are real
[6+4=10 m]
( or )
1 2 3
3. (a) Verify Cayley-Hamilton theorem for the matrix A= 2 4 5
[3
In above matrix A , find A
-1
[6+4=10 m]
5 6]
by using Cayley-Hamilton theorem
……….
4.
Find a real root of the equation � 5x  3  0 by bisection method
3
[10 m]
( or )
5. Find a real root of the equation
� x sin x  3
using false position method
[10 m]
M