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Standard XI
Maths
Question
(
n
!
)
2
>
n
n
is true for
n
=
3
∀
n
∈
Z
∀
n
∈
N
∀
n
>
2
,
n
∈
N
A
∀
n
∈
N
B
∀
n
>
2
,
n
∈
N
C
n
=
3
D
∀
n
∈
Z
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Solution
Verified by Toppr
(
n
!
)
2
>
n
n
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2
Similar Questions
Q1
For natural number n,
(
n
!
)
2
>
n
n
, if
View Solution
Q2
For natural number n,
(
n
!
)
2
>
n
n
if
View Solution
Q3
For a fixed
+
i
v
e
integer
n
, let
D
=
∣
∣ ∣ ∣
∣
(
n
−
1
)
!
(
n
+
2
)
!
(
n
+
3
)
!
/
n
(
n
+
1
)
!
(
n
+
1
)
!
(
n
+
3
)
!
(
n
+
5
)
!
/
(
n
+
2
)
!
(
n
+
3
)
!
(
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)
!
(
n
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5
)
!
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)
!
/
(
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+
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)
!
(
n
+
5
)
!
∣
∣ ∣ ∣
∣
then
D
(
n
−
1
)
!
(
n
+
1
)
!
(
n
+
3
)
!
is equal to
View Solution
Q4
If
N
=
n
!
(
n
∈
N
,
n
>
2
)
then
(
(
log
2
N
)
−
1
+
(
log
3
N
)
−
1
+
.
.
.
.
.
+
(
log
n
N
)
−
1
]
is
View Solution
Q5
Among the inequalities, which ones are true for all natural numbers n greater than
1000
?
I.
n
!
≤
n
n
II.
(
n
!
)
2
≤
n
n
III.
10
n
≤
n
!
IV.
n
n
≤
(
2
n
)
!
.
View Solution