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Question
Mathematics
The coefficient of x301 in (1+x)500+x(1+x)499+x2(1+x)498+ ldots ldots .+x500 is :
Q. The coefficient of
x
301
in
(
1
+
x
)
500
+
x
(
1
+
x
)
499
+
x
2
(
1
+
x
)
498
+
……
.
+
x
500
is :
569
121
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JEE Main 2023
Binomial Theorem
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A
500
C
301
0%
B
501
C
200
100%
C
3
500
C
300
0%
D
501
C
302
0%
Solution:
(
1
+
x
)
500
+
x
(
1
+
x
)
499
+
x
2
(
1
+
x
)
498
+
…
+
x
500
=
(
1
+
x
)
500
⋅
{
1
−
1
+
x
x
1
−
(
1
+
x
x
)
501
}
=
(
1
+
x
)
500
(
1
+
x
)
501
(
(
1
+
x
)
501
−
x
501
)
⋅
(
1
+
x
)
=
(
1
+
x
)
501
−
x
501
Coefficient of
x
301
in
(
1
+
x
)
501
−
x
501
is given by
501
C
301
=
501
C
200