Q.

The number of odd proper divisors of3p.6m.21n is

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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.3p+m+n.7n ∴ The required number of proper divisors = Number of selection of any number of 3’s and 7’s [∴ for odd divisors 2 must not be selected]=(p+m+n+1)(n+1)−1 .
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