Question

41.
If P=2^a 3^b 5^C, a,b,c eN is the no. of words which can be formed using all the letters of the word
"NAMAKEEN' so that no two alike vowels are together then
(A) no. of odd divisors of P is 6
(B) no. of even divisors of P is 42
(C) no. of zeroes at the end of Pis 2

Answer 1

Answer:

Correct option is B)

3

p

×6

m

×21

n

= 2

m

×3

(p+m+n)

×7

n

as we are finding the odd proper divisors, the even powers can be omitted

i.e. 3

(p+m+n)

×7

n

∴ 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