(C) The coefficient of $x^9$ is equal to the number of ways to write $9$ as a sum of distinct positive integers.We list the partitions of $9$ into dis

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(C) The coefficient of $x^9$ is equal to the number of ways to write $9$ as a sum of distinct positive integers.We list the partitions of $9$ into distinct parts:$1) \{9\}$$2) \{1, 8\}$$3) \{2, 7\}$$4) \{3, 6\}$$5) \{4, 5\}$$6) \{1, 2, 6\}$$7) \{1, 3, 5\}$$8) \{2, 3, 4\}$Since there are $8$ such partitions,the coefficient of $x^9$ is $8$.

Class 11 Mathematics Binomial Theorem Expansion of binomial theorem

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The coefficient of $x^9$ in the expansion of $(1+x)(1+x^2)(1+x^3) \ldots (1+x^{100})$ is

IIT 2015 All IIT

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$6$
B
$7$
C
$8$
D
$9$

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Binomial Theorem

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The coefficient of $x^9$ in the expansion of $(1+x)(1+x^2)(1+x^3) \ldots (1+x^{100})$ is

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The first $3$ terms in the expansion of $(1 + ax)^n$ $(n \ne 0)$ are $1, 6x$ and $16x^2$. Then the value of $a$ and $n$ are respectively

For $|x| < \frac{1}{5}$,the coefficient of $x^3$ in the expansion of $\frac{1}{(1-5 x)(1-4 x)}$ is

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