Let $$A = \left\{ {x|x{\text{ is a prime number and }}x < 30} \right\}.$$ The number of different rational numbers whose numerator and denominator belong to $$A$$ is
A.
90
B.
180
C.
91
D.
100
Answer :
91
Solution :
We have, $$A = \left\{ {2,3,5,7,11,13,17,19,23,29} \right\}.$$ A contains 10 elements. So numerator and denominator each can be chosen in 10 ways.
So no. of rational numbers
$$= 10 \times 10 - 10 + 1 = 91$$
(Out of these selections, 10 numbers are simply 1)
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