Multiple correct answer.
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Answers
(b)
We know that there are 10 digits from 0 to 9.
So, we select 6 digits in C(10,6) ways and we can arrange them in decreasing order in only 1 way.
Therefore, required number of 6-digit numbers = C(10,6).
(c)
Given, 10 objects are arranged in a row. We have to select 3 objects such that no tow of them are next to each other = C(7,3).
(d)
Total number of ways in which all the letters of the word can be arranged = 8!.
There are three vowels in the word.
Total number of ways in which these 3 vowels can be arranged = 3!.
Therefore, required number of ways = 8!/3!
(a)
A = {2,3,5,7,11,13,17,19}.
Numerator ≠ Denominator.
⇒ {2/3, 2/5,2/7,2/11,2/13,2/17,2/19}
⇒ {3/2, 3/5,3/7,3/11,3/13, 3/17, 3/19}
⇒ {5/2,5/3,5/7,5/11,5/13,5/17,5/19}
⇒ ....
⇒ ....
⇒ ....
⇒ ....
⇒ .....
Total number of ways = 56.
Therefore, the correct options are A and D.
Hope this helps!