The number of proper divisors of 1800 which are also divisible by 10, is
A.
18
B.
34
C.
27
D.
None of these
Answer :
18
Solution :
$$1800 = {2^3} \times {3^2} \times {5^2}$$
∴ the required number of proper divisors
= total number of selections of at least one 2 and one 5 from 2, 2, 2, 3, 3, 5, 5
$$ = 3 \times \left( {2 + 1} \right) \times 2 = 18.$$
Releted MCQ Question on Algebra >> Permutation and Combination
Releted Question 1
$$^n{C_{r - 1}} = 36,{\,^n}{C_r} = 84$$ and $$^n{C_{r + 1}} = 126,$$ then $$r$$ is:
Ten different letters of an alphabet are given. Words with five letters are formed from these given letters. Then the number of words which have at least one letter repeated are
Eight chairs are numbered 1 to 8. Two women and three men wish to occupy one chair each. First the women choose the chairs from amongst the chairs marked 1 to 4 ; and then the men select the chairs from amongst the remaining. The number of possible arrangements is