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JEE Advanced 2020 Full Test 4 Paper 2
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© examsnet.com
Question : 41
Total: 54
If the probability of choosing an integer 'k' out of
2
m
integers
1
,
2
,
3
,
.
.
.
.
.
.
.2
m
is inversely proportional to
k
4
(
1
≤
k
≤
m
)
. If
x
1
is the probability that choosen number is odd and
x
2
is the probability that chosen number is even, then
x
1
<
2
3
x
1
>
1
2
x
1
>
2
3
x
2
<
1
2
Validate
Solution:
Let one probability of choosing one integer
k
be
P
(
k
)
=
λ
k
4
.
(
λ
is one constant of proportionality). Then,
2
m
∑
k
=
1
λ
k
4
=
1
⇒
λ
2
m
∑
k
=
1
1
k
4
=
1
Let
x
1
be the probability of choosing the odd number. Then
x
1
=
2
m
∑
k
=
1
P
(
2
k
−
1
)
=
λ
m
∑
k
=
1
1
(
2
k
−
1
)
4
Also,
1
−
x
1
=
x
2
=
∑
k
=
1
m
P
(
2
k
)
=
λ
∑
k
=
1
m
1
(
2
k
)
4
<
λ
∑
k
=
1
m
1
(
2
k
−
1
)
4
⇒
1
−
x
1
<
x
1
⇒
x
1
>
1
2
⇒
x
2
<
1
2
© examsnet.com
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