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Byju's Answer
Standard VI
Mathematics
Cardinality
If X = 1, 1...
Question
If
X
=
{
{
1
}
,
{
1
,
2
}
,
3
,
2
,
1
}
P
=
{
x
|
x
∈
X
,
x
∈
Y
for some
y
∈
X
}
. Find
n
(
P
)
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Solution
If
X
=
{
{
1
}
,
{
1
,
2
}
,
3
,
2
,
1
}
To find cardinal number of a set.
P
=
{
x
|
x
ϵ
X
,
x
ϵ
Y
for some
y
ϵ
X
}
n
(
P
)
=
2
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0
Similar questions
Q.
If
(
1
+
x
+
x
2
+
.
.
.
.
.
+
x
p
)
n
=
a
0
+
a
1
x
+
a
2
x
2
+
.
.
.
.
.
a
n
p
x
n
p
Prove that
(
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)
a
0
+
a
1
+
a
2
+
.
.
.
.
.
+
a
n
p
=
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p
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1
)
n
.
(
2
)
a
1
+
2
a
2
+
3
a
3
+
.
.
.
.
+
n
p
.
a
n
p
=
1
2
n
p
(
p
+
1
)
n
.
Q.
If
P
=
{
x
∈
N
:
14
x
x
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1
−
(
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x
−
30
x
−
4
)
≤
0
}
,
Q
=
{
x
∈
Z
:
|
x
−
1
|
≤
5
and
|
x
−
1
|
≥
2
}
and
R
=
{
x
∈
R
:
log
6
x
+
2
log
6
x
}
=
3
,
then which of the following options is (are) CORRECT?
Q.
Let
n
>
2
be an integer and define a polynomial
p
(
x
)
=
x
n
+
a
n
−
1
x
n
−
1
+
.
.
.
.
.
+
a
1
x
+
a
0
where
a
0
,
a
1
,
.
.
.
.
.
a
n
−
1
are integers. Suppose we know that
n
p
(
x
)
=
(
1
+
x
)
p
′
(
x
)
. If
b
=
p
(
1
)
, then.
Q.
If
p
(
x
)
=
x
+
3
, then find the value of
p
(
x
)
+
p
(
−
x
)
Q.
If
x
=
p
−
2
and
x
p
−
x
+
1
p
=
1
, find
p
.
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