Checkout JEE MAINS 2022 Question Paper Analysis : Checkout JEE MAINS 2022 Question Paper Analysis :

Out of 21 tickets marked with numbers from 1 to 21, three are drawn at random. The chance that the numbers on then are in AP is

1) 10/133

2) 9/133

3) 9/1330

4) None of these

Solution: Option (1) 10/133

Total Ways = 21C3

If the common difference is 1, then the possible ways = 1, 2, 3; 4, 5, 6; …19, 20, 21.

If the common difference is 2, then the possible ways = 1, 3, 5; 2, 4, 6; ….17,19, 21.

Similarly, in the same way, if the common difference is 10, then the possible way= 1, 10, 21.

Hence, if the common difference is greater than 10, then there will be no favourable case.

So, the total number of favourable cases = 100

Therefore the required probability = 100/21C3

= 100/1330

= 10/133.

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