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Q.

A1,A2…An are points on the line y=x lying in the positive quadrant such that OAn=nOAn−1,O being the origin. If OA1=1 and the coordinates of An are  (25202,25202), then n =

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a

5

b

6

c

7

d

8

answer is C.

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Detailed Solution

We have OAn=n.OAn−1=n(n−1)OAn−2⋯=n(n−1)…2OA1=n!OA1=n!⇒ 2(25202)=n!⇒ 2520×2=n!⇒ 7×6×5×4×3×2=n!⇒ n=7
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