The number of divisors of the form $$4n + 2\left( {n \geqslant 0} \right)$$ of the integer 240 is
A.
4
B.
8
C.
10
D.
3
Answer :
4
Solution :
$$\eqalign{
& 240 = {2^4} \times 3 \times 5 \cr
& 4n + 2 = 2\left( {2n + 1} \right) = 2 \times \,{\text{odd}} \cr} $$
∴ the required number of divisors
= the number of selections of one 2 from four $$2’s,$$ any number of $$3’s$$ from one 3 and any number of $$5’s$$ from one 5.
$$ = 1 \times 2 \times 2 = 4.$$
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
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