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JEE Advanced 2018 Paper 2
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© examsnet.com
Question : 50
Total: 54
Let
X
=
(
10
C
1
)
2
+
2
(
10
C
2
)
2
+
3
(
10
C
3
)
2
+
.
.
.
.
+
10
(
10
C
10
)
2
, where
10
C
r
,
r
∊
{
1
,
2
,
.
.
.10
}
denote binomial coefficients. Then, the value of
1
1430
X is______.
Your Answer:
Validate
Solution:
X
=
n
∑
r
=
0
r
.
(
n
C
r
)
2
;
n
=
10
X
=
n
.
n
∑
r
=
0
n
C
r
.
n
−
1
C
r
−
1
X
=
n
.
n
∑
r
=
0
n
C
n
−
r
.
n
−
1
C
r
−
1
X
=
n
.
2
n
−
1
C
n
−
1
;
n
=
10
X
=
10.
19
C
9
X
1430
=
1
143
.
19
C
9
=
646
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