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JEE Advanced 2016 Paper 1
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© examsnet.com
Question : 52
Total: 54
Let
z
=
−
1
+
√
3
i
2
,where
i
=
√
−
1
and
r
,
s
∊
{
1
,
2
,
3
}
.Let P
=
[
(
−
z
)
r
z
2
s
z
2
s
z
r
]
and I be the identitymatrix of order 2. Then the total number of ordered pairs (r, s) for which
P
2
=
−
I
is
Your Answer:
Validate
Solution:
z
=
ω
P
=
[
(
−
ω
)
r
ω
2
s
ω
2
s
ω
r
]
,
P
2
=
−
I
⇒
P
2
[
ω
2
r
+
ω
4
s
ω
r
+
2
s
(
(
−
1
)
r
+
1
)
ω
r
+
2
s
(
(
−
1
)
r
+
1
)
ω
4
s
+
ω
2
r
]
=
−
I
⇒
(
−
1
)
r
+
1
=
0
⇒
r is odd ⇒r=1,3
also
ω
2
r
+
ω
4
s
=
−
1
⇒
s
=
1
(r,s) = (1,1)
only 1 pair
© examsnet.com
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