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Let $\sum_{r = 0}^{20} a_{r} x^{r} = {(1 + x + x^{2})}^{10} then$ $a_{5} -^{10} C_{1} \times a_{4} +^{10} C_{2} \times a_{3} -^{10} C_{3} \times a_{2} +^{10} C_{4} \times a_{1} -^{10} C_{5} \times a_{0} =$

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10 C 4

10 C 5

10 C 2

answer is A.

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Detailed Solution

$1 + x + x 2 10 = a 0 + a 1 x + a 2 x 2 + … . (1 − x) 10 = 1 − 10 C 1 ⋅ x + 10 C 2 ⋅ x 2 − 10 C 3 ⋅ x 3 + … … ..$
multiply those two Equation , we get the given series and is the coefficient $x 5 i n 1 + x 3 10$ which is zero

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