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Contests
National and Regional Contests
India Contests
India LIMIT
2019 LIMIT
2019 LIMIT Category C
Problem 6
connectedness
connectedness
Source: LIMIT 2019 CCS1 P6
April 28, 2021
abstract algebra
Problem Statement
Which of the following are true?
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
A
)
<
/
s
p
a
n
>
G
L
(
n
,
R
)
is connected
<span class='latex-bold'>(A)</span>~GL(n,\mathbb R)\text{ is connected}
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
A
)
<
/
s
p
an
>
G
L
(
n
,
R
)
is connected
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
B
)
<
/
s
p
a
n
>
G
L
(
n
,
C
)
is connected
<span class='latex-bold'>(B)</span>~GL(n,\mathbb C)\text{ is connected}
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
B
)
<
/
s
p
an
>
G
L
(
n
,
C
)
is connected
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
C
)
<
/
s
p
a
n
>
O
(
n
,
R
)
is connected
<span class='latex-bold'>(C)</span>~O(n,\mathbb R)\text{ is connected}
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
C
)
<
/
s
p
an
>
O
(
n
,
R
)
is connected
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
D
)
<
/
s
p
a
n
>
O
(
n
,
C
)
is connected
<span class='latex-bold'>(D)</span>~O(n,\mathbb C)\text{ is connected}
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
D
)
<
/
s
p
an
>
O
(
n
,
C
)
is connected
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