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Vector Calculus and Linear Algebra
(2110015)
Winter 2015 Sem-1
MCQ(s) of
Vector Calculus and Linear Algebra
(2110015)
- Winter 2015 Sem-1
Q.
1
E
i
g
e
n
v
a
l
u
e
s
o
f
A
-
1
&
A
T
a
r
e
s
a
m
e
i
f
m
a
t
r
i
x
A
i
s
(A) Symmetric
(B) Orthogonal
(C) Skew symmetric
(D) None of these
Answer
(B)
Orthogonal
Q.
2
Rank of 4×4 invertible matrix is
(A) 1
(B) 2
(C) 3
(D) 4
Answer
(D)
4
Q.
3
F
i
s
s
o
l
e
n
o
i
d
a
l
v
e
c
t
o
r
,
I
f
d
i
v
(
F
)
i
s
(A)
F
(B) 1
(C) 0
(D) -1
Answer
(C)
0
Q.
4
Let A be a Hermition matrix, then A is
(A)
A
*
(B)
A
(C)
A
T
(D)
-
A
*
Answer
(A)
A
*
Q.
5
I
f
A
=
1
0
2
-
1
t
h
e
n
e
i
g
e
n
v
a
l
u
e
s
o
f
A
3
a
r
e
(A) 1,-1
(B) 0,2
(C) 1,1
(D) 0,8
Answer
(A)
1,-1
Q.
6
W
h
i
c
h
s
e
t
f
r
o
m
S
1
=
{
a
0
+
a
1
x
+
a
2
x
2
/
a
0
=
0
}
a
n
d
S
2
=
{
a
0
+
a
1
x
+
a
2
x
2
/
a
0
≠
0
}
i
s
s
u
b
s
p
a
c
e
o
f
P
2
?
(A)
s
2
(B)
s
1
(C)
s
1
&
s
2
(D) None of these
Answer
(B)
s
1
Q.
7
For which value of k vectors u=(2, 1, 3) and v=(1, 7, k) are orthogonal?
(A) -3
(B) -1
(C) 0
(D) 2
Answer
(A)
-3
Q.
8
L
e
t
T
:
R
3
→
R
3
b
e
o
n
e
t
o
o
n
e
l
i
n
e
a
r
t
r
a
n
s
f
o
r
m
a
t
i
o
n
t
h
e
n
t
h
e
d
i
m
e
n
s
i
o
n
o
f
k
e
r
(
T
)
i
s
(A) 0
(B) 1
(C) 2
(D) 3
Answer
(A)
0
Q.
9
The column vector of an orthogonal matrix are
(A) orthogonal
(B) orthonormal
(C) dependent
(D) none of these
Answer
(B)
orthonormal
Q.
10
I
f
r
=
x
i
+
y
j
+
z
k
t
h
e
n
d
i
v
(
r
)
i
s
(A) r
(B) 0
(C) 1
(D) 3
Answer
(D)
3
Q.
11
The number of solution of the system of equation AX=0 (where A is a singular matrix) is
(A) 0
(B) 1
(C) 2
(D) infinite
Answer
(D)
infinite
Q.
12
If the value of line integral does not depend on path C then F is
(A) solenoidal
(B) imcompressible
(C) irrotational
(D) none of these
Answer
(C)
irrotational
Q.
13
A
C
a
y
l
e
y
-
H
a
m
i
l
t
o
n
t
h
e
o
r
e
m
h
o
l
d
f
o
r
_
_
_
_
_
_
m
a
t
r
i
c
e
s
o
n
l
y
(A) singular
(B) all square
(C) null
(D) a few rectangular
Answer
(B)
all square
Q.
14
I
f
A
=
1
2
2
4
t
h
e
n
r
a
n
k
o
f
m
a
t
r
i
x
A
i
s
(A) 1
(B) 0
(C) 2
(D) 4
Answer
(A)
1