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If $a_{i} (i = 0, 1, 2, \dots, 16)$ be real constants such that for every real value of $x, {(1 + x + x^{2})}^{8} = a_{0} + a_{1} x +$ $a_{2} x^{2} + \dots + a_{16} x^{16},$ then $a_{5}$ is equal to:

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Correct option is B

1+x+x28=∑p,q,r≥0P+q+r=8 8!p!q!r!1pxqx2rFor a5, we require, q+2r=5⇒q=5,r=0,p=3 or q=3,r=1,p=4 or q=1,r=2,p=5Thus, coefficient of x5 is 8!5!3!+8!3!1!4!+8!1!2!5!=504.

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If ai(i=0,1,2,…,16) be real constants such that for every real value of x,1+x+x28=a0+a1x+a2x2+…+a16x16, then a5 is equal to:

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If $a_{i} (i = 0, 1, 2, \dots, 16)$ be real constants such that for every real value of $x, {(1 + x + x^{2})}^{8} = a_{0} + a_{1} x +$ $a_{2} x^{2} + \dots + a_{16} x^{16},$ then $a_{5}$ is equal to: