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in Mathematics by (71.2k points)

(1+px)n = 1+ 24x + 252x2 + -----then.......

(a) p = 3, n = 8 

(b) p = 2, n = 6 

(c) p = 3, n = 6 

(d) p = 3, n = 5

1 Answer

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Best answer

Correct option: (a) p = 3, n = 8

Explanation:

(1 +  px)n = 1 + 24x + 252x2 + -------

  nc0 + nc1(px) + nc2(px)2 + nc3(px)3 = 1 + 24x + 252x2 + -----

   24 = nc1 ∙ p ⇒ np = 24

252 = nc2p2 ⇒ [{n(n – 1)} / 2]p2 = 252

   n(n – 1)p2 = 504

   n(n – 1) (24 / n)2 = 504

   [(n – 1) / n2] = [(504) / (576)]

   (n – 1) / n] = [(504) / (576)]

    576 n – 576 = 504 n

72 n = 576

 n = 8 and p = 3

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