The coefficient of x10 in the expansion of (1+x)21+x231+x34 is equal to-

The coefficient of ${x}^{10}$ in the expansion of $\left(1+x{\right)}^{2}$${\left(1+{x}^{2}\right)}^{3}{\left(1+{x}^{3}\right)}^{4}$ is equal to-

1. A

50

2. B

52

3. C

44

4. D

56

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Solution:

=$\left(1+x{\right)}^{2}{\left(1+{x}^{2}\right)}^{3}{\left(1+{x}^{3}\right)}^{4}$

$=\left(1+{x}^{2}+2x\right)×\left(1+{x}^{6}+3{x}^{2}+3{x}^{4}\right)×\left(1+4{x}^{3}+6{x}^{6}+4{x}^{9}+{x}^{12}\right)$

So, coefficient of ${x}^{10}=36+8+8=52$

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