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If (1+ax)^n = 1 + 8x + 24x^2 + … and a l...

If `(1+ax)^n = 1 + 8x + 24x^2 + …` and a line through `P(a, n)` cuts the circle `x^2 + y^2 = 4` in `A and B`, then `PA.PB = `

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The correct Answer is:
A
Given , `(1+alphax)^n =1+8x + 24x^2`+…. `rArr 1 + n (alpha x ) + (n(n-1))/1.2 (alpha x)^2 ` +….=1 +8x + `24x^2`+…
Equating the coefficients of x and `x^2` we get : `nalpha =8` and `(n alpha (n alpha -alpha ))/1.2=24`
`rArr (8(8-alpha))/2=24 rArr 8-alpha=6 rArr alpha =2` and n=4
So point P is (2,4) `therefore` PA.PB =16 `[S_1]`
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