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Q.

The number of odd proper divisors of 3p.6m.21n is equal to?


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a

(p + 1) (m + 1) (n + 1) – 2

b

(p + m + n + 1) (n + 1) – 1

c

(p + 1) (m + 1) (n + 1) – 1

d

None of these 

answer is B.

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Detailed Solution

3p.6m.21n = 2m×3(p+m+n) × 7n
As we are finding the odd proper divisors, the even powers can be omitted
i.e.  3(p+m+n) × 7n
∴ number of divisors = (p+m+n+1) (n+1)
but this also includes the proper divisor 1,
∴ number of proper divisors = (p+m+n+1) (n+1) −1
Hence, Option (2) is the correct answer.
  
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