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Byju's Answer
Standard XII
Mathematics
Infinite GP
The value of ...
Question
The value of
r
for which
S
=
20
C
r
10
C
0
+
20
C
r
−
1
10
C
1
.
.
.
.
.
+
20
C
0
10
C
r
is maximum is
A
7
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B
8
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C
10
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D
15
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Solution
The correct option is
D
15
S
=
20
C
r
10
C
0
+
20
C
r
−
1
10
C
1
+
…
+
20
C
0
10
C
r
This is the sum of coefficients of
x
r
in
(
1
+
x
)
20
(
1
+
x
)
10
⇒
(
1
+
x
)
30
So coefficient of
x
r
=
30
C
r
For
r
=
maximum
,
r
=
30
2
=
15
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0
Similar questions
Q.
The value of
r
for which
S
=
20
C
r
10
C
0
+
20
C
r
−
1
10
C
1
+
.
.
.
.
+
20
C
0
10
C
r
is maximum is
Q.
The value of
r
(
0
≤
r
≤
30
)
is
20
C
r
10
C
0
+
20
C
r
−
1
10
C
1
+
.
.
.
.
+
20
C
0
10
C
r
is least, is
Q.
Assertion :The expression
40
C
r
.
60
C
0
+
40
C
r
−
1
.
60
C
1
+
.
.
.
attains maximum value when
r
=
50
. Reason:
2
n
C
r
is maximum when
r
=
n
.
Q.
Let
C
r
stand for
n
C
r
and
S
(
n
,
r
)
=
C
0
−
C
1
+
C
2
−
C
3
+
.
.
.
.
+
(
−
1
)
r
C
r
Q.
If
c
0
,
c
1
,
c
2
,
.
.
.
.
.
.
.
c
n
denote the coefficients in the expansion of
(
1
+
x
)
n
, prove that
c
0
c
r
+
c
1
c
r
+
1
+
c
2
c
r
+
2
+
.
.
.
.
+
c
n
−
r
c
n
=
|
2
n
–
–
–
|
n
−
r
–
––––
–
|
n
+
r
–
––––
–
.
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