Let $$A$$ = {$$x|x$$ is a prime number and $$x < 30$$ }. The number of different rational numbers whose numerator and denominator belong to $$A$$ is
A.
90
B.
180
C.
91
D.
None of these
Answer :
91
Solution :
$$A$$ = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29}. A rational number is made by taking
any two in any order.
∴ the required number of rational numbers $$ = {\,^{10}}{P_2} + 1$$ (including 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
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