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$A_{1}, A_{2} \dots A_{n}$ are points on the line $y = x$ lying in the positive quadrant such that $O A_{n} = n O A_{n - 1}, O$ being the origin. If $O A_{1} = 1$ and the coordinates of $A_{n}$ are $(2520 \sqrt{2}, 2520 \sqrt{2})$ , then $n =$

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Correct option is C

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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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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Ready to Test Your Skills?

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$A_{1}, A_{2} \dots A_{n}$ are points on the line $y = x$ lying in the positive quadrant such that $O A_{n} = n O A_{n - 1}, O$ being the origin. If $O A_{1} = 1$ and the coordinates of $A_{n}$ are $(2520 \sqrt{2}, 2520 \sqrt{2})$ , then $n =$