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Answer :
(c) 20
Solution :
- Given : (n + 2)! = 462•(n)!
- To find : n = ?
We have ;
=> (n + 2)! = 462•(n)!
=> (n + 2)•(n + 1)•(n)! = 462•(n)!
=> (n + 2)(n + 1) = 462
=> n² + n + 2n + 2 = 462
=> n² + 3n + 2 = 462
=> n² + 3n + 2 - 462 = 0
=> n² + 3n - 460 = 0
=> n² + 23n - 20n - 460 = 0
=> n(n + 23) - 20(n + 23) = 0
=> (n + 23)(n - 20) = 0
=> Either (n + 23) = 0 or (n - 20) = 0
• If (n + 23) = 0 , then n = -23 (rejected value , as n = -23 is not a natural number)
• If (n - 20) = 0 , then n = 20 (appropriate value)
Hence , n = 20 .
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