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JEE Advanced 2016 Paper 1 Mathematics Q15
Mathematics
Problem
Let
m
m
m
be the smallest positive integer such that the coefficient of
x
2
x^2
x
2
in the expansion of
(
1
+
x
)
2
+
(
1
+
x
)
3
+
⋯
+
(
1
+
x
)
49
+
(
1
+
m
x
)
50
(1+x)^2+(1+x)^3+\cdots+(1+x)^{49}+(1+mx)^{50}
(
1
+
x
)
2
+
(
1
+
x
)
3
+
⋯
+
(
1
+
x
)
49
+
(
1
+
m
x
)
50
is
(
3
n
+
1
)
51
C
3
(3n+1)\,{}^{51}C_3
(
3
n
+
1
)
51
C
3
for some positive integer
n
n
n
. Then the value of
n
n
n
is
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