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 $(1 + x)^{2}$ ${(1 + x^{2})}^{3} {(1 + x^{3})}^{4}$ is equal to-

A
50
B
52
C
44
D
56

Solution:

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

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

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

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